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72ac97cd TM |
1 | /* Decimal number arithmetic module for the decNumber C Library. |
2 | Copyright (C) 2005, 2007 Free Software Foundation, Inc. | |
3 | Contributed by IBM Corporation. Author Mike Cowlishaw. | |
4 | ||
5 | This file is part of GCC. | |
6 | ||
7 | GCC is free software; you can redistribute it and/or modify it under | |
8 | the terms of the GNU General Public License as published by the Free | |
9 | Software Foundation; either version 2, or (at your option) any later | |
10 | version. | |
11 | ||
12 | In addition to the permissions in the GNU General Public License, | |
13 | the Free Software Foundation gives you unlimited permission to link | |
14 | the compiled version of this file into combinations with other | |
15 | programs, and to distribute those combinations without any | |
16 | restriction coming from the use of this file. (The General Public | |
17 | License restrictions do apply in other respects; for example, they | |
18 | cover modification of the file, and distribution when not linked | |
19 | into a combine executable.) | |
20 | ||
21 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY | |
22 | WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
23 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
24 | for more details. | |
25 | ||
26 | You should have received a copy of the GNU General Public License | |
27 | along with GCC; see the file COPYING. If not, write to the Free | |
28 | Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA | |
29 | 02110-1301, USA. */ | |
30 | ||
31 | /* ------------------------------------------------------------------ */ | |
32 | /* Decimal Number arithmetic module */ | |
33 | /* ------------------------------------------------------------------ */ | |
34 | /* This module comprises the routines for General Decimal Arithmetic */ | |
35 | /* as defined in the specification which may be found on the */ | |
36 | /* http://www2.hursley.ibm.com/decimal web pages. It implements both */ | |
37 | /* the full ('extended') arithmetic and the simpler ('subset') */ | |
38 | /* arithmetic. */ | |
39 | /* */ | |
40 | /* Usage notes: */ | |
41 | /* */ | |
42 | /* 1. This code is ANSI C89 except: */ | |
43 | /* */ | |
44 | /* If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ | |
45 | /* uint64_t types may be used. To avoid these, set DECUSE64=0 */ | |
46 | /* and DECDPUN<=4 (see documentation). */ | |
47 | /* */ | |
48 | /* 2. The decNumber format which this library uses is optimized for */ | |
49 | /* efficient processing of relatively short numbers; in particular */ | |
50 | /* it allows the use of fixed sized structures and minimizes copy */ | |
51 | /* and move operations. It does, however, support arbitrary */ | |
52 | /* precision (up to 999,999,999 digits) and arbitrary exponent */ | |
53 | /* range (Emax in the range 0 through 999,999,999 and Emin in the */ | |
54 | /* range -999,999,999 through 0). Mathematical functions (for */ | |
55 | /* example decNumberExp) as identified below are restricted more */ | |
56 | /* tightly: digits, emax, and -emin in the context must be <= */ | |
57 | /* DEC_MAX_MATH (999999), and their operand(s) must be within */ | |
58 | /* these bounds. */ | |
59 | /* */ | |
60 | /* 3. Logical functions are further restricted; their operands must */ | |
61 | /* be finite, positive, have an exponent of zero, and all digits */ | |
62 | /* must be either 0 or 1. The result will only contain digits */ | |
63 | /* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ | |
64 | /* */ | |
65 | /* 4. Operands to operator functions are never modified unless they */ | |
66 | /* are also specified to be the result number (which is always */ | |
67 | /* permitted). Other than that case, operands must not overlap. */ | |
68 | /* */ | |
69 | /* 5. Error handling: the type of the error is ORed into the status */ | |
70 | /* flags in the current context (decContext structure). The */ | |
71 | /* SIGFPE signal is then raised if the corresponding trap-enabler */ | |
72 | /* flag in the decContext is set (is 1). */ | |
73 | /* */ | |
74 | /* It is the responsibility of the caller to clear the status */ | |
75 | /* flags as required. */ | |
76 | /* */ | |
77 | /* The result of any routine which returns a number will always */ | |
78 | /* be a valid number (which may be a special value, such as an */ | |
79 | /* Infinity or NaN). */ | |
80 | /* */ | |
81 | /* 6. The decNumber format is not an exchangeable concrete */ | |
82 | /* representation as it comprises fields which may be machine- */ | |
83 | /* dependent (packed or unpacked, or special length, for example). */ | |
84 | /* Canonical conversions to and from strings are provided; other */ | |
85 | /* conversions are available in separate modules. */ | |
86 | /* */ | |
87 | /* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ | |
88 | /* to 1 for extended operand checking (including NULL operands). */ | |
89 | /* Results are undefined if a badly-formed structure (or a NULL */ | |
90 | /* pointer to a structure) is provided, though with DECCHECK */ | |
91 | /* enabled the operator routines are protected against exceptions. */ | |
92 | /* (Except if the result pointer is NULL, which is unrecoverable.) */ | |
93 | /* */ | |
94 | /* However, the routines will never cause exceptions if they are */ | |
95 | /* given well-formed operands, even if the value of the operands */ | |
96 | /* is inappropriate for the operation and DECCHECK is not set. */ | |
97 | /* (Except for SIGFPE, as and where documented.) */ | |
98 | /* */ | |
99 | /* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ | |
100 | /* ------------------------------------------------------------------ */ | |
101 | /* Implementation notes for maintenance of this module: */ | |
102 | /* */ | |
103 | /* 1. Storage leak protection: Routines which use malloc are not */ | |
104 | /* permitted to use return for fastpath or error exits (i.e., */ | |
105 | /* they follow strict structured programming conventions). */ | |
106 | /* Instead they have a do{}while(0); construct surrounding the */ | |
107 | /* code which is protected -- break may be used to exit this. */ | |
108 | /* Other routines can safely use the return statement inline. */ | |
109 | /* */ | |
110 | /* Storage leak accounting can be enabled using DECALLOC. */ | |
111 | /* */ | |
112 | /* 2. All loops use the for(;;) construct. Any do construct does */ | |
113 | /* not loop; it is for allocation protection as just described. */ | |
114 | /* */ | |
115 | /* 3. Setting status in the context must always be the very last */ | |
116 | /* action in a routine, as non-0 status may raise a trap and hence */ | |
117 | /* the call to set status may not return (if the handler uses long */ | |
118 | /* jump). Therefore all cleanup must be done first. In general, */ | |
119 | /* to achieve this status is accumulated and is only applied just */ | |
120 | /* before return by calling decContextSetStatus (via decStatus). */ | |
121 | /* */ | |
122 | /* Routines which allocate storage cannot, in general, use the */ | |
123 | /* 'top level' routines which could cause a non-returning */ | |
124 | /* transfer of control. The decXxxxOp routines are safe (do not */ | |
125 | /* call decStatus even if traps are set in the context) and should */ | |
126 | /* be used instead (they are also a little faster). */ | |
127 | /* */ | |
128 | /* 4. Exponent checking is minimized by allowing the exponent to */ | |
129 | /* grow outside its limits during calculations, provided that */ | |
130 | /* the decFinalize function is called later. Multiplication and */ | |
131 | /* division, and intermediate calculations in exponentiation, */ | |
132 | /* require more careful checks because of the risk of 31-bit */ | |
133 | /* overflow (the most negative valid exponent is -1999999997, for */ | |
134 | /* a 999999999-digit number with adjusted exponent of -999999999). */ | |
135 | /* */ | |
136 | /* 5. Rounding is deferred until finalization of results, with any */ | |
137 | /* 'off to the right' data being represented as a single digit */ | |
138 | /* residue (in the range -1 through 9). This avoids any double- */ | |
139 | /* rounding when more than one shortening takes place (for */ | |
140 | /* example, when a result is subnormal). */ | |
141 | /* */ | |
142 | /* 6. The digits count is allowed to rise to a multiple of DECDPUN */ | |
143 | /* during many operations, so whole Units are handled and exact */ | |
144 | /* accounting of digits is not needed. The correct digits value */ | |
145 | /* is found by decGetDigits, which accounts for leading zeros. */ | |
146 | /* This must be called before any rounding if the number of digits */ | |
147 | /* is not known exactly. */ | |
148 | /* */ | |
149 | /* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ | |
150 | /* numbers up to four digits, using appropriate constants. This */ | |
151 | /* is not useful for longer numbers because overflow of 32 bits */ | |
152 | /* would lead to 4 multiplies, which is almost as expensive as */ | |
153 | /* a divide (unless a floating-point or 64-bit multiply is */ | |
154 | /* assumed to be available). */ | |
155 | /* */ | |
156 | /* 8. Unusual abbreviations that may be used in the commentary: */ | |
157 | /* lhs -- left hand side (operand, of an operation) */ | |
158 | /* lsd -- least significant digit (of coefficient) */ | |
159 | /* lsu -- least significant Unit (of coefficient) */ | |
160 | /* msd -- most significant digit (of coefficient) */ | |
161 | /* msi -- most significant item (in an array) */ | |
162 | /* msu -- most significant Unit (of coefficient) */ | |
163 | /* rhs -- right hand side (operand, of an operation) */ | |
164 | /* +ve -- positive */ | |
165 | /* -ve -- negative */ | |
166 | /* ** -- raise to the power */ | |
167 | /* ------------------------------------------------------------------ */ | |
168 | ||
7a4e543d | 169 | #include "qemu/osdep.h" |
727385c4 | 170 | #include "qemu/host-utils.h" |
0f2d3732 TM |
171 | #include "libdecnumber/dconfig.h" |
172 | #include "libdecnumber/decNumber.h" | |
173 | #include "libdecnumber/decNumberLocal.h" | |
72ac97cd TM |
174 | |
175 | /* Constants */ | |
176 | /* Public lookup table used by the D2U macro */ | |
177 | const uByte d2utable[DECMAXD2U+1]=D2UTABLE; | |
178 | ||
179 | #define DECVERB 1 /* set to 1 for verbose DECCHECK */ | |
180 | #define powers DECPOWERS /* old internal name */ | |
181 | ||
182 | /* Local constants */ | |
183 | #define DIVIDE 0x80 /* Divide operators */ | |
184 | #define REMAINDER 0x40 /* .. */ | |
185 | #define DIVIDEINT 0x20 /* .. */ | |
186 | #define REMNEAR 0x10 /* .. */ | |
187 | #define COMPARE 0x01 /* Compare operators */ | |
188 | #define COMPMAX 0x02 /* .. */ | |
189 | #define COMPMIN 0x03 /* .. */ | |
190 | #define COMPTOTAL 0x04 /* .. */ | |
191 | #define COMPNAN 0x05 /* .. [NaN processing] */ | |
192 | #define COMPSIG 0x06 /* .. [signaling COMPARE] */ | |
193 | #define COMPMAXMAG 0x07 /* .. */ | |
194 | #define COMPMINMAG 0x08 /* .. */ | |
195 | ||
196 | #define DEC_sNaN 0x40000000 /* local status: sNaN signal */ | |
197 | #define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ | |
198 | /* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ | |
199 | #define BIGEVEN (Int)0x80000002 | |
200 | #define BIGODD (Int)0x80000003 | |
201 | ||
202 | static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ | |
203 | ||
204 | /* Granularity-dependent code */ | |
205 | #if DECDPUN<=4 | |
206 | #define eInt Int /* extended integer */ | |
207 | #define ueInt uInt /* unsigned extended integer */ | |
208 | /* Constant multipliers for divide-by-power-of five using reciprocal */ | |
209 | /* multiply, after removing powers of 2 by shifting, and final shift */ | |
210 | /* of 17 [we only need up to **4] */ | |
211 | static const uInt multies[]={131073, 26215, 5243, 1049, 210}; | |
212 | /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ | |
213 | #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) | |
214 | #else | |
215 | /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ | |
216 | #if !DECUSE64 | |
217 | #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 | |
218 | #endif | |
219 | #define eInt Long /* extended integer */ | |
220 | #define ueInt uLong /* unsigned extended integer */ | |
221 | #endif | |
222 | ||
223 | /* Local routines */ | |
224 | static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, | |
225 | decContext *, uByte, uInt *); | |
226 | static Flag decBiStr(const char *, const char *, const char *); | |
227 | static uInt decCheckMath(const decNumber *, decContext *, uInt *); | |
228 | static void decApplyRound(decNumber *, decContext *, Int, uInt *); | |
229 | static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); | |
230 | static decNumber * decCompareOp(decNumber *, const decNumber *, | |
231 | const decNumber *, decContext *, | |
232 | Flag, uInt *); | |
233 | static void decCopyFit(decNumber *, const decNumber *, decContext *, | |
234 | Int *, uInt *); | |
235 | static decNumber * decDecap(decNumber *, Int); | |
236 | static decNumber * decDivideOp(decNumber *, const decNumber *, | |
237 | const decNumber *, decContext *, Flag, uInt *); | |
238 | static decNumber * decExpOp(decNumber *, const decNumber *, | |
239 | decContext *, uInt *); | |
240 | static void decFinalize(decNumber *, decContext *, Int *, uInt *); | |
241 | static Int decGetDigits(Unit *, Int); | |
242 | static Int decGetInt(const decNumber *); | |
243 | static decNumber * decLnOp(decNumber *, const decNumber *, | |
244 | decContext *, uInt *); | |
245 | static decNumber * decMultiplyOp(decNumber *, const decNumber *, | |
246 | const decNumber *, decContext *, | |
247 | uInt *); | |
248 | static decNumber * decNaNs(decNumber *, const decNumber *, | |
249 | const decNumber *, decContext *, uInt *); | |
250 | static decNumber * decQuantizeOp(decNumber *, const decNumber *, | |
251 | const decNumber *, decContext *, Flag, | |
252 | uInt *); | |
253 | static void decReverse(Unit *, Unit *); | |
254 | static void decSetCoeff(decNumber *, decContext *, const Unit *, | |
255 | Int, Int *, uInt *); | |
256 | static void decSetMaxValue(decNumber *, decContext *); | |
257 | static void decSetOverflow(decNumber *, decContext *, uInt *); | |
258 | static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); | |
259 | static Int decShiftToLeast(Unit *, Int, Int); | |
260 | static Int decShiftToMost(Unit *, Int, Int); | |
261 | static void decStatus(decNumber *, uInt, decContext *); | |
262 | static void decToString(const decNumber *, char[], Flag); | |
263 | static decNumber * decTrim(decNumber *, decContext *, Flag, Int *); | |
264 | static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, | |
265 | Unit *, Int); | |
266 | static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); | |
21d7826f | 267 | static bool mulUInt128ByPowOf10(uLong *, uLong *, uInt); |
72ac97cd TM |
268 | |
269 | #if !DECSUBSET | |
270 | /* decFinish == decFinalize when no subset arithmetic needed */ | |
271 | #define decFinish(a,b,c,d) decFinalize(a,b,c,d) | |
272 | #else | |
273 | static void decFinish(decNumber *, decContext *, Int *, uInt *); | |
274 | static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); | |
275 | #endif | |
276 | ||
277 | /* Local macros */ | |
278 | /* masked special-values bits */ | |
279 | #define SPECIALARG (rhs->bits & DECSPECIAL) | |
280 | #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) | |
281 | ||
282 | /* Diagnostic macros, etc. */ | |
283 | #if DECALLOC | |
284 | /* Handle malloc/free accounting. If enabled, our accountable routines */ | |
285 | /* are used; otherwise the code just goes straight to the system malloc */ | |
286 | /* and free routines. */ | |
287 | #define malloc(a) decMalloc(a) | |
288 | #define free(a) decFree(a) | |
289 | #define DECFENCE 0x5a /* corruption detector */ | |
290 | /* 'Our' malloc and free: */ | |
291 | static void *decMalloc(size_t); | |
292 | static void decFree(void *); | |
293 | uInt decAllocBytes=0; /* count of bytes allocated */ | |
294 | /* Note that DECALLOC code only checks for storage buffer overflow. */ | |
295 | /* To check for memory leaks, the decAllocBytes variable must be */ | |
296 | /* checked to be 0 at appropriate times (e.g., after the test */ | |
297 | /* harness completes a set of tests). This checking may be unreliable */ | |
298 | /* if the testing is done in a multi-thread environment. */ | |
299 | #endif | |
300 | ||
301 | #if DECCHECK | |
302 | /* Optional checking routines. Enabling these means that decNumber */ | |
303 | /* and decContext operands to operator routines are checked for */ | |
304 | /* correctness. This roughly doubles the execution time of the */ | |
305 | /* fastest routines (and adds 600+ bytes), so should not normally be */ | |
306 | /* used in 'production'. */ | |
307 | /* decCheckInexact is used to check that inexact results have a full */ | |
308 | /* complement of digits (where appropriate -- this is not the case */ | |
309 | /* for Quantize, for example) */ | |
310 | #define DECUNRESU ((decNumber *)(void *)0xffffffff) | |
311 | #define DECUNUSED ((const decNumber *)(void *)0xffffffff) | |
312 | #define DECUNCONT ((decContext *)(void *)(0xffffffff)) | |
313 | static Flag decCheckOperands(decNumber *, const decNumber *, | |
314 | const decNumber *, decContext *); | |
315 | static Flag decCheckNumber(const decNumber *); | |
316 | static void decCheckInexact(const decNumber *, decContext *); | |
317 | #endif | |
318 | ||
319 | #if DECTRACE || DECCHECK | |
320 | /* Optional trace/debugging routines (may or may not be used) */ | |
321 | void decNumberShow(const decNumber *); /* displays the components of a number */ | |
322 | static void decDumpAr(char, const Unit *, Int); | |
323 | #endif | |
324 | ||
325 | /* ================================================================== */ | |
326 | /* Conversions */ | |
327 | /* ================================================================== */ | |
328 | ||
329 | /* ------------------------------------------------------------------ */ | |
330 | /* from-int32 -- conversion from Int or uInt */ | |
331 | /* */ | |
332 | /* dn is the decNumber to receive the integer */ | |
333 | /* in or uin is the integer to be converted */ | |
334 | /* returns dn */ | |
335 | /* */ | |
336 | /* No error is possible. */ | |
337 | /* ------------------------------------------------------------------ */ | |
338 | decNumber * decNumberFromInt32(decNumber *dn, Int in) { | |
339 | uInt unsig; | |
340 | if (in>=0) unsig=in; | |
341 | else { /* negative (possibly BADINT) */ | |
342 | if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ | |
343 | else unsig=-in; /* invert */ | |
344 | } | |
345 | /* in is now positive */ | |
346 | decNumberFromUInt32(dn, unsig); | |
347 | if (in<0) dn->bits=DECNEG; /* sign needed */ | |
348 | return dn; | |
349 | } /* decNumberFromInt32 */ | |
350 | ||
351 | decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { | |
352 | Unit *up; /* work pointer */ | |
353 | decNumberZero(dn); /* clean */ | |
354 | if (uin==0) return dn; /* [or decGetDigits bad call] */ | |
355 | for (up=dn->lsu; uin>0; up++) { | |
356 | *up=(Unit)(uin%(DECDPUNMAX+1)); | |
357 | uin=uin/(DECDPUNMAX+1); | |
358 | } | |
359 | dn->digits=decGetDigits(dn->lsu, up-dn->lsu); | |
360 | return dn; | |
361 | } /* decNumberFromUInt32 */ | |
362 | ||
363 | /* ------------------------------------------------------------------ */ | |
364 | /* to-int32 -- conversion to Int or uInt */ | |
365 | /* */ | |
366 | /* dn is the decNumber to convert */ | |
367 | /* set is the context for reporting errors */ | |
368 | /* returns the converted decNumber, or 0 if Invalid is set */ | |
369 | /* */ | |
370 | /* Invalid is set if the decNumber does not have exponent==0 or if */ | |
371 | /* it is a NaN, Infinite, or out-of-range. */ | |
372 | /* ------------------------------------------------------------------ */ | |
373 | Int decNumberToInt32(const decNumber *dn, decContext *set) { | |
374 | #if DECCHECK | |
375 | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; | |
376 | #endif | |
377 | ||
378 | /* special or too many digits, or bad exponent */ | |
379 | if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ | |
380 | else { /* is a finite integer with 10 or fewer digits */ | |
381 | Int d; /* work */ | |
382 | const Unit *up; /* .. */ | |
383 | uInt hi=0, lo; /* .. */ | |
384 | up=dn->lsu; /* -> lsu */ | |
385 | lo=*up; /* get 1 to 9 digits */ | |
386 | #if DECDPUN>1 /* split to higher */ | |
387 | hi=lo/10; | |
388 | lo=lo%10; | |
389 | #endif | |
390 | up++; | |
391 | /* collect remaining Units, if any, into hi */ | |
392 | for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; | |
393 | /* now low has the lsd, hi the remainder */ | |
394 | if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ | |
395 | /* most-negative is a reprieve */ | |
396 | if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; | |
397 | /* bad -- drop through */ | |
398 | } | |
399 | else { /* in-range always */ | |
400 | Int i=X10(hi)+lo; | |
401 | if (dn->bits&DECNEG) return -i; | |
402 | return i; | |
403 | } | |
404 | } /* integer */ | |
405 | decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ | |
406 | return 0; | |
407 | } /* decNumberToInt32 */ | |
408 | ||
409 | uInt decNumberToUInt32(const decNumber *dn, decContext *set) { | |
410 | #if DECCHECK | |
411 | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; | |
412 | #endif | |
413 | /* special or too many digits, or bad exponent, or negative (<0) */ | |
414 | if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 | |
415 | || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ | |
416 | else { /* is a finite integer with 10 or fewer digits */ | |
417 | Int d; /* work */ | |
418 | const Unit *up; /* .. */ | |
419 | uInt hi=0, lo; /* .. */ | |
420 | up=dn->lsu; /* -> lsu */ | |
421 | lo=*up; /* get 1 to 9 digits */ | |
422 | #if DECDPUN>1 /* split to higher */ | |
423 | hi=lo/10; | |
424 | lo=lo%10; | |
425 | #endif | |
426 | up++; | |
427 | /* collect remaining Units, if any, into hi */ | |
428 | for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; | |
429 | ||
430 | /* now low has the lsd, hi the remainder */ | |
431 | if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ | |
432 | else return X10(hi)+lo; | |
433 | } /* integer */ | |
434 | decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ | |
435 | return 0; | |
436 | } /* decNumberToUInt32 */ | |
437 | ||
8e706db2 TM |
438 | decNumber *decNumberFromInt64(decNumber *dn, int64_t in) |
439 | { | |
440 | uint64_t unsig = in; | |
441 | if (in < 0) { | |
442 | unsig = -unsig; | |
443 | } | |
444 | ||
445 | decNumberFromUInt64(dn, unsig); | |
446 | if (in < 0) { | |
447 | dn->bits = DECNEG; /* sign needed */ | |
448 | } | |
449 | return dn; | |
450 | } /* decNumberFromInt64 */ | |
451 | ||
452 | decNumber *decNumberFromUInt64(decNumber *dn, uint64_t uin) | |
453 | { | |
454 | Unit *up; /* work pointer */ | |
455 | decNumberZero(dn); /* clean */ | |
456 | if (uin == 0) { | |
457 | return dn; /* [or decGetDigits bad call] */ | |
458 | } | |
459 | for (up = dn->lsu; uin > 0; up++) { | |
460 | *up = (Unit)(uin % (DECDPUNMAX + 1)); | |
461 | uin = uin / (DECDPUNMAX + 1); | |
462 | } | |
463 | dn->digits = decGetDigits(dn->lsu, up-dn->lsu); | |
464 | return dn; | |
465 | } /* decNumberFromUInt64 */ | |
466 | ||
727385c4 LP |
467 | decNumber *decNumberFromInt128(decNumber *dn, uint64_t lo, int64_t hi) |
468 | { | |
469 | uint64_t unsig_hi = hi; | |
470 | if (hi < 0) { | |
471 | if (lo == 0) { | |
472 | unsig_hi = -unsig_hi; | |
473 | } else { | |
474 | unsig_hi = ~unsig_hi; | |
475 | lo = -lo; | |
476 | } | |
477 | } | |
478 | ||
479 | decNumberFromUInt128(dn, lo, unsig_hi); | |
480 | if (hi < 0) { | |
481 | dn->bits = DECNEG; /* sign needed */ | |
482 | } | |
483 | return dn; | |
484 | } /* decNumberFromInt128 */ | |
485 | ||
486 | decNumber *decNumberFromUInt128(decNumber *dn, uint64_t lo, uint64_t hi) | |
487 | { | |
488 | uint64_t rem; | |
489 | Unit *up; /* work pointer */ | |
490 | decNumberZero(dn); /* clean */ | |
491 | if (lo == 0 && hi == 0) { | |
492 | return dn; /* [or decGetDigits bad call] */ | |
493 | } | |
494 | for (up = dn->lsu; hi > 0 || lo > 0; up++) { | |
495 | rem = divu128(&lo, &hi, DECDPUNMAX + 1); | |
496 | *up = (Unit)rem; | |
497 | } | |
498 | dn->digits = decGetDigits(dn->lsu, up - dn->lsu); | |
499 | return dn; | |
500 | } /* decNumberFromUInt128 */ | |
501 | ||
79af3572 TM |
502 | /* ------------------------------------------------------------------ */ |
503 | /* to-int64 -- conversion to int64 */ | |
504 | /* */ | |
505 | /* dn is the decNumber to convert. dn is assumed to have been */ | |
506 | /* rounded to a floating point integer value. */ | |
507 | /* set is the context for reporting errors */ | |
508 | /* returns the converted decNumber, or 0 if Invalid is set */ | |
509 | /* */ | |
510 | /* Invalid is set if the decNumber is a NaN, Infinite or is out of */ | |
511 | /* range for a signed 64 bit integer. */ | |
512 | /* ------------------------------------------------------------------ */ | |
513 | ||
514 | int64_t decNumberIntegralToInt64(const decNumber *dn, decContext *set) | |
515 | { | |
516 | if (decNumberIsSpecial(dn) || (dn->exponent < 0) || | |
517 | (dn->digits + dn->exponent > 19)) { | |
518 | goto Invalid; | |
519 | } else { | |
520 | int64_t d; /* work */ | |
521 | const Unit *up; /* .. */ | |
522 | uint64_t hi = 0; | |
523 | up = dn->lsu; /* -> lsu */ | |
524 | ||
525 | for (d = 1; d <= dn->digits; up++, d += DECDPUN) { | |
526 | uint64_t prev = hi; | |
527 | hi += *up * powers[d-1]; | |
528 | if ((hi < prev) || (hi > INT64_MAX)) { | |
529 | goto Invalid; | |
530 | } | |
531 | } | |
532 | ||
533 | uint64_t prev = hi; | |
534 | hi *= (uint64_t)powers[dn->exponent]; | |
535 | if ((hi < prev) || (hi > INT64_MAX)) { | |
536 | goto Invalid; | |
537 | } | |
538 | return (decNumberIsNegative(dn)) ? -((int64_t)hi) : (int64_t)hi; | |
539 | } | |
540 | ||
541 | Invalid: | |
542 | decContextSetStatus(set, DEC_Invalid_operation); | |
543 | return 0; | |
544 | } /* decNumberIntegralToInt64 */ | |
545 | ||
21d7826f LP |
546 | /* ------------------------------------------------------------------ */ |
547 | /* decNumberIntegralToInt128 -- conversion to int128 */ | |
548 | /* */ | |
549 | /* dn is the decNumber to convert. dn is assumed to have been */ | |
550 | /* rounded to a floating point integer value. */ | |
551 | /* set is the context for reporting errors */ | |
552 | /* returns the converted decNumber via plow and phigh */ | |
553 | /* */ | |
554 | /* Invalid is set if the decNumber is a NaN, Infinite or is out of */ | |
555 | /* range for a signed 128 bit integer. */ | |
556 | /* ------------------------------------------------------------------ */ | |
557 | ||
558 | void decNumberIntegralToInt128(const decNumber *dn, decContext *set, | |
559 | uint64_t *plow, uint64_t *phigh) | |
560 | { | |
561 | int d; /* work */ | |
562 | const Unit *up; /* .. */ | |
563 | uint64_t lo = 0, hi = 0; | |
564 | ||
565 | if (decNumberIsSpecial(dn) || (dn->exponent < 0) || | |
566 | (dn->digits + dn->exponent > 39)) { | |
567 | goto Invalid; | |
568 | } | |
569 | ||
570 | up = dn->lsu; /* -> lsu */ | |
571 | ||
572 | for (d = (dn->digits - 1) / DECDPUN; d >= 0; d--) { | |
573 | if (mulu128(&lo, &hi, DECDPUNMAX + 1)) { | |
574 | /* overflow */ | |
575 | goto Invalid; | |
576 | } | |
577 | if (uadd64_overflow(lo, up[d], &lo)) { | |
578 | if (uadd64_overflow(hi, 1, &hi)) { | |
579 | /* overflow */ | |
580 | goto Invalid; | |
581 | } | |
582 | } | |
583 | } | |
584 | ||
585 | if (mulUInt128ByPowOf10(&lo, &hi, dn->exponent)) { | |
586 | /* overflow */ | |
587 | goto Invalid; | |
588 | } | |
589 | ||
590 | if (decNumberIsNegative(dn)) { | |
591 | if (lo == 0) { | |
592 | *phigh = -hi; | |
593 | *plow = 0; | |
594 | } else { | |
595 | *phigh = ~hi; | |
596 | *plow = -lo; | |
597 | } | |
598 | } else { | |
599 | *plow = lo; | |
600 | *phigh = hi; | |
601 | } | |
602 | ||
603 | return; | |
604 | ||
605 | Invalid: | |
606 | decContextSetStatus(set, DEC_Invalid_operation); | |
607 | } /* decNumberIntegralToInt128 */ | |
8e706db2 | 608 | |
72ac97cd TM |
609 | /* ------------------------------------------------------------------ */ |
610 | /* to-scientific-string -- conversion to numeric string */ | |
611 | /* to-engineering-string -- conversion to numeric string */ | |
612 | /* */ | |
613 | /* decNumberToString(dn, string); */ | |
614 | /* decNumberToEngString(dn, string); */ | |
615 | /* */ | |
616 | /* dn is the decNumber to convert */ | |
617 | /* string is the string where the result will be laid out */ | |
618 | /* */ | |
619 | /* string must be at least dn->digits+14 characters long */ | |
620 | /* */ | |
621 | /* No error is possible, and no status can be set. */ | |
622 | /* ------------------------------------------------------------------ */ | |
623 | char * decNumberToString(const decNumber *dn, char *string){ | |
624 | decToString(dn, string, 0); | |
625 | return string; | |
626 | } /* DecNumberToString */ | |
627 | ||
628 | char * decNumberToEngString(const decNumber *dn, char *string){ | |
629 | decToString(dn, string, 1); | |
630 | return string; | |
631 | } /* DecNumberToEngString */ | |
632 | ||
633 | /* ------------------------------------------------------------------ */ | |
634 | /* to-number -- conversion from numeric string */ | |
635 | /* */ | |
636 | /* decNumberFromString -- convert string to decNumber */ | |
637 | /* dn -- the number structure to fill */ | |
638 | /* chars[] -- the string to convert ('\0' terminated) */ | |
639 | /* set -- the context used for processing any error, */ | |
640 | /* determining the maximum precision available */ | |
641 | /* (set.digits), determining the maximum and minimum */ | |
642 | /* exponent (set.emax and set.emin), determining if */ | |
643 | /* extended values are allowed, and checking the */ | |
644 | /* rounding mode if overflow occurs or rounding is */ | |
645 | /* needed. */ | |
646 | /* */ | |
647 | /* The length of the coefficient and the size of the exponent are */ | |
648 | /* checked by this routine, so the correct error (Underflow or */ | |
649 | /* Overflow) can be reported or rounding applied, as necessary. */ | |
650 | /* */ | |
651 | /* If bad syntax is detected, the result will be a quiet NaN. */ | |
652 | /* ------------------------------------------------------------------ */ | |
653 | decNumber * decNumberFromString(decNumber *dn, const char chars[], | |
654 | decContext *set) { | |
655 | Int exponent=0; /* working exponent [assume 0] */ | |
656 | uByte bits=0; /* working flags [assume +ve] */ | |
657 | Unit *res; /* where result will be built */ | |
658 | Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ | |
659 | /* [+9 allows for ln() constants] */ | |
660 | Unit *allocres=NULL; /* -> allocated result, iff allocated */ | |
661 | Int d=0; /* count of digits found in decimal part */ | |
662 | const char *dotchar=NULL; /* where dot was found */ | |
663 | const char *cfirst=chars; /* -> first character of decimal part */ | |
664 | const char *last=NULL; /* -> last digit of decimal part */ | |
665 | const char *c; /* work */ | |
666 | Unit *up; /* .. */ | |
667 | #if DECDPUN>1 | |
668 | Int cut, out; /* .. */ | |
669 | #endif | |
670 | Int residue; /* rounding residue */ | |
671 | uInt status=0; /* error code */ | |
672 | ||
673 | #if DECCHECK | |
674 | if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) | |
675 | return decNumberZero(dn); | |
676 | #endif | |
677 | ||
678 | do { /* status & malloc protection */ | |
679 | for (c=chars;; c++) { /* -> input character */ | |
680 | if (*c>='0' && *c<='9') { /* test for Arabic digit */ | |
681 | last=c; | |
682 | d++; /* count of real digits */ | |
683 | continue; /* still in decimal part */ | |
684 | } | |
685 | if (*c=='.' && dotchar==NULL) { /* first '.' */ | |
686 | dotchar=c; /* record offset into decimal part */ | |
687 | if (c==cfirst) cfirst++; /* first digit must follow */ | |
688 | continue;} | |
689 | if (c==chars) { /* first in string... */ | |
690 | if (*c=='-') { /* valid - sign */ | |
691 | cfirst++; | |
692 | bits=DECNEG; | |
693 | continue;} | |
694 | if (*c=='+') { /* valid + sign */ | |
695 | cfirst++; | |
696 | continue;} | |
697 | } | |
698 | /* *c is not a digit, or a valid +, -, or '.' */ | |
699 | break; | |
700 | } /* c */ | |
701 | ||
702 | if (last==NULL) { /* no digits yet */ | |
703 | status=DEC_Conversion_syntax;/* assume the worst */ | |
704 | if (*c=='\0') break; /* and no more to come... */ | |
705 | #if DECSUBSET | |
706 | /* if subset then infinities and NaNs are not allowed */ | |
707 | if (!set->extended) break; /* hopeless */ | |
708 | #endif | |
709 | /* Infinities and NaNs are possible, here */ | |
710 | if (dotchar!=NULL) break; /* .. unless had a dot */ | |
711 | decNumberZero(dn); /* be optimistic */ | |
712 | if (decBiStr(c, "infinity", "INFINITY") | |
713 | || decBiStr(c, "inf", "INF")) { | |
714 | dn->bits=bits | DECINF; | |
715 | status=0; /* is OK */ | |
716 | break; /* all done */ | |
717 | } | |
718 | /* a NaN expected */ | |
719 | /* 2003.09.10 NaNs are now permitted to have a sign */ | |
720 | dn->bits=bits | DECNAN; /* assume simple NaN */ | |
721 | if (*c=='s' || *c=='S') { /* looks like an sNaN */ | |
722 | c++; | |
723 | dn->bits=bits | DECSNAN; | |
724 | } | |
725 | if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ | |
726 | c++; | |
727 | if (*c!='a' && *c!='A') break; /* .. */ | |
728 | c++; | |
729 | if (*c!='n' && *c!='N') break; /* .. */ | |
730 | c++; | |
731 | /* now either nothing, or nnnn payload, expected */ | |
732 | /* -> start of integer and skip leading 0s [including plain 0] */ | |
733 | for (cfirst=c; *cfirst=='0';) cfirst++; | |
734 | if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ | |
735 | status=0; /* it's good */ | |
736 | break; /* .. */ | |
737 | } | |
738 | /* something other than 0s; setup last and d as usual [no dots] */ | |
739 | for (c=cfirst;; c++, d++) { | |
740 | if (*c<'0' || *c>'9') break; /* test for Arabic digit */ | |
741 | last=c; | |
742 | } | |
743 | if (*c!='\0') break; /* not all digits */ | |
744 | if (d>set->digits-1) { | |
745 | /* [NB: payload in a decNumber can be full length unless */ | |
746 | /* clamped, in which case can only be digits-1] */ | |
747 | if (set->clamp) break; | |
748 | if (d>set->digits) break; | |
749 | } /* too many digits? */ | |
750 | /* good; drop through to convert the integer to coefficient */ | |
751 | status=0; /* syntax is OK */ | |
752 | bits=dn->bits; /* for copy-back */ | |
753 | } /* last==NULL */ | |
754 | ||
755 | else if (*c!='\0') { /* more to process... */ | |
756 | /* had some digits; exponent is only valid sequence now */ | |
757 | Flag nege; /* 1=negative exponent */ | |
758 | const char *firstexp; /* -> first significant exponent digit */ | |
759 | status=DEC_Conversion_syntax;/* assume the worst */ | |
760 | if (*c!='e' && *c!='E') break; | |
761 | /* Found 'e' or 'E' -- now process explicit exponent */ | |
762 | /* 1998.07.11: sign no longer required */ | |
763 | nege=0; | |
764 | c++; /* to (possible) sign */ | |
765 | if (*c=='-') {nege=1; c++;} | |
766 | else if (*c=='+') c++; | |
767 | if (*c=='\0') break; | |
768 | ||
769 | for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ | |
770 | firstexp=c; /* save exponent digit place */ | |
771 | for (; ;c++) { | |
772 | if (*c<'0' || *c>'9') break; /* not a digit */ | |
773 | exponent=X10(exponent)+(Int)*c-(Int)'0'; | |
774 | } /* c */ | |
775 | /* if not now on a '\0', *c must not be a digit */ | |
776 | if (*c!='\0') break; | |
777 | ||
778 | /* (this next test must be after the syntax checks) */ | |
779 | /* if it was too long the exponent may have wrapped, so check */ | |
780 | /* carefully and set it to a certain overflow if wrap possible */ | |
781 | if (c>=firstexp+9+1) { | |
782 | if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; | |
783 | /* [up to 1999999999 is OK, for example 1E-1000000998] */ | |
784 | } | |
785 | if (nege) exponent=-exponent; /* was negative */ | |
786 | status=0; /* is OK */ | |
787 | } /* stuff after digits */ | |
788 | ||
789 | /* Here when whole string has been inspected; syntax is good */ | |
790 | /* cfirst->first digit (never dot), last->last digit (ditto) */ | |
791 | ||
792 | /* strip leading zeros/dot [leave final 0 if all 0's] */ | |
793 | if (*cfirst=='0') { /* [cfirst has stepped over .] */ | |
794 | for (c=cfirst; c<last; c++, cfirst++) { | |
795 | if (*c=='.') continue; /* ignore dots */ | |
796 | if (*c!='0') break; /* non-zero found */ | |
797 | d--; /* 0 stripped */ | |
798 | } /* c */ | |
799 | #if DECSUBSET | |
800 | /* make a rapid exit for easy zeros if !extended */ | |
801 | if (*cfirst=='0' && !set->extended) { | |
802 | decNumberZero(dn); /* clean result */ | |
803 | break; /* [could be return] */ | |
804 | } | |
805 | #endif | |
806 | } /* at least one leading 0 */ | |
807 | ||
808 | /* Handle decimal point... */ | |
809 | if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ | |
810 | exponent-=(last-dotchar); /* adjust exponent */ | |
811 | /* [we can now ignore the .] */ | |
812 | ||
813 | /* OK, the digits string is good. Assemble in the decNumber, or in */ | |
814 | /* a temporary units array if rounding is needed */ | |
815 | if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ | |
816 | else { /* rounding needed */ | |
817 | Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ | |
818 | res=resbuff; /* assume use local buffer */ | |
819 | if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ | |
820 | allocres=(Unit *)malloc(needbytes); | |
821 | if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} | |
822 | res=allocres; | |
823 | } | |
824 | } | |
825 | /* res now -> number lsu, buffer, or allocated storage for Unit array */ | |
826 | ||
827 | /* Place the coefficient into the selected Unit array */ | |
828 | /* [this is often 70% of the cost of this function when DECDPUN>1] */ | |
829 | #if DECDPUN>1 | |
830 | out=0; /* accumulator */ | |
831 | up=res+D2U(d)-1; /* -> msu */ | |
832 | cut=d-(up-res)*DECDPUN; /* digits in top unit */ | |
833 | for (c=cfirst;; c++) { /* along the digits */ | |
834 | if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ | |
835 | out=X10(out)+(Int)*c-(Int)'0'; | |
836 | if (c==last) break; /* done [never get to trailing '.'] */ | |
837 | cut--; | |
838 | if (cut>0) continue; /* more for this unit */ | |
839 | *up=(Unit)out; /* write unit */ | |
840 | up--; /* prepare for unit below.. */ | |
841 | cut=DECDPUN; /* .. */ | |
842 | out=0; /* .. */ | |
843 | } /* c */ | |
844 | *up=(Unit)out; /* write lsu */ | |
845 | ||
846 | #else | |
847 | /* DECDPUN==1 */ | |
848 | up=res; /* -> lsu */ | |
849 | for (c=last; c>=cfirst; c--) { /* over each character, from least */ | |
850 | if (*c=='.') continue; /* ignore . [don't step up] */ | |
851 | *up=(Unit)((Int)*c-(Int)'0'); | |
852 | up++; | |
853 | } /* c */ | |
854 | #endif | |
855 | ||
856 | dn->bits=bits; | |
857 | dn->exponent=exponent; | |
858 | dn->digits=d; | |
859 | ||
860 | /* if not in number (too long) shorten into the number */ | |
861 | if (d>set->digits) { | |
862 | residue=0; | |
863 | decSetCoeff(dn, set, res, d, &residue, &status); | |
864 | /* always check for overflow or subnormal and round as needed */ | |
865 | decFinalize(dn, set, &residue, &status); | |
866 | } | |
867 | else { /* no rounding, but may still have overflow or subnormal */ | |
868 | /* [these tests are just for performance; finalize repeats them] */ | |
869 | if ((dn->exponent-1<set->emin-dn->digits) | |
870 | || (dn->exponent-1>set->emax-set->digits)) { | |
871 | residue=0; | |
872 | decFinalize(dn, set, &residue, &status); | |
873 | } | |
874 | } | |
875 | /* decNumberShow(dn); */ | |
876 | } while(0); /* [for break] */ | |
877 | ||
878 | if (allocres!=NULL) free(allocres); /* drop any storage used */ | |
879 | if (status!=0) decStatus(dn, status, set); | |
880 | return dn; | |
881 | } /* decNumberFromString */ | |
882 | ||
883 | /* ================================================================== */ | |
884 | /* Operators */ | |
885 | /* ================================================================== */ | |
886 | ||
887 | /* ------------------------------------------------------------------ */ | |
888 | /* decNumberAbs -- absolute value operator */ | |
889 | /* */ | |
890 | /* This computes C = abs(A) */ | |
891 | /* */ | |
892 | /* res is C, the result. C may be A */ | |
893 | /* rhs is A */ | |
894 | /* set is the context */ | |
895 | /* */ | |
896 | /* See also decNumberCopyAbs for a quiet bitwise version of this. */ | |
897 | /* C must have space for set->digits digits. */ | |
898 | /* ------------------------------------------------------------------ */ | |
899 | /* This has the same effect as decNumberPlus unless A is negative, */ | |
900 | /* in which case it has the same effect as decNumberMinus. */ | |
901 | /* ------------------------------------------------------------------ */ | |
902 | decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, | |
903 | decContext *set) { | |
904 | decNumber dzero; /* for 0 */ | |
905 | uInt status=0; /* accumulator */ | |
906 | ||
907 | #if DECCHECK | |
908 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
909 | #endif | |
910 | ||
911 | decNumberZero(&dzero); /* set 0 */ | |
912 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ | |
913 | decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); | |
914 | if (status!=0) decStatus(res, status, set); | |
915 | #if DECCHECK | |
916 | decCheckInexact(res, set); | |
917 | #endif | |
918 | return res; | |
919 | } /* decNumberAbs */ | |
920 | ||
921 | /* ------------------------------------------------------------------ */ | |
922 | /* decNumberAdd -- add two Numbers */ | |
923 | /* */ | |
924 | /* This computes C = A + B */ | |
925 | /* */ | |
926 | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ | |
927 | /* lhs is A */ | |
928 | /* rhs is B */ | |
929 | /* set is the context */ | |
930 | /* */ | |
931 | /* C must have space for set->digits digits. */ | |
932 | /* ------------------------------------------------------------------ */ | |
933 | /* This just calls the routine shared with Subtract */ | |
934 | decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, | |
935 | const decNumber *rhs, decContext *set) { | |
936 | uInt status=0; /* accumulator */ | |
937 | decAddOp(res, lhs, rhs, set, 0, &status); | |
938 | if (status!=0) decStatus(res, status, set); | |
939 | #if DECCHECK | |
940 | decCheckInexact(res, set); | |
941 | #endif | |
942 | return res; | |
943 | } /* decNumberAdd */ | |
944 | ||
945 | /* ------------------------------------------------------------------ */ | |
946 | /* decNumberAnd -- AND two Numbers, digitwise */ | |
947 | /* */ | |
948 | /* This computes C = A & B */ | |
949 | /* */ | |
950 | /* res is C, the result. C may be A and/or B (e.g., X=X&X) */ | |
951 | /* lhs is A */ | |
952 | /* rhs is B */ | |
953 | /* set is the context (used for result length and error report) */ | |
954 | /* */ | |
955 | /* C must have space for set->digits digits. */ | |
956 | /* */ | |
957 | /* Logical function restrictions apply (see above); a NaN is */ | |
958 | /* returned with Invalid_operation if a restriction is violated. */ | |
959 | /* ------------------------------------------------------------------ */ | |
960 | decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, | |
961 | const decNumber *rhs, decContext *set) { | |
962 | const Unit *ua, *ub; /* -> operands */ | |
963 | const Unit *msua, *msub; /* -> operand msus */ | |
964 | Unit *uc, *msuc; /* -> result and its msu */ | |
965 | Int msudigs; /* digits in res msu */ | |
966 | #if DECCHECK | |
967 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
968 | #endif | |
969 | ||
970 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) | |
971 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { | |
972 | decStatus(res, DEC_Invalid_operation, set); | |
973 | return res; | |
974 | } | |
975 | ||
976 | /* operands are valid */ | |
977 | ua=lhs->lsu; /* bottom-up */ | |
978 | ub=rhs->lsu; /* .. */ | |
979 | uc=res->lsu; /* .. */ | |
980 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ | |
981 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ | |
982 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ | |
983 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ | |
984 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ | |
985 | Unit a, b; /* extract units */ | |
986 | if (ua>msua) a=0; | |
987 | else a=*ua; | |
988 | if (ub>msub) b=0; | |
989 | else b=*ub; | |
990 | *uc=0; /* can now write back */ | |
991 | if (a|b) { /* maybe 1 bits to examine */ | |
992 | Int i, j; | |
993 | *uc=0; /* can now write back */ | |
994 | /* This loop could be unrolled and/or use BIN2BCD tables */ | |
995 | for (i=0; i<DECDPUN; i++) { | |
996 | if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ | |
997 | j=a%10; | |
998 | a=a/10; | |
999 | j|=b%10; | |
1000 | b=b/10; | |
1001 | if (j>1) { | |
1002 | decStatus(res, DEC_Invalid_operation, set); | |
1003 | return res; | |
1004 | } | |
1005 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ | |
1006 | } /* each digit */ | |
1007 | } /* both OK */ | |
1008 | } /* each unit */ | |
1009 | /* [here uc-1 is the msu of the result] */ | |
1010 | res->digits=decGetDigits(res->lsu, uc-res->lsu); | |
1011 | res->exponent=0; /* integer */ | |
1012 | res->bits=0; /* sign=0 */ | |
1013 | return res; /* [no status to set] */ | |
1014 | } /* decNumberAnd */ | |
1015 | ||
1016 | /* ------------------------------------------------------------------ */ | |
1017 | /* decNumberCompare -- compare two Numbers */ | |
1018 | /* */ | |
1019 | /* This computes C = A ? B */ | |
1020 | /* */ | |
1021 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1022 | /* lhs is A */ | |
1023 | /* rhs is B */ | |
1024 | /* set is the context */ | |
1025 | /* */ | |
1026 | /* C must have space for one digit (or NaN). */ | |
1027 | /* ------------------------------------------------------------------ */ | |
1028 | decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, | |
1029 | const decNumber *rhs, decContext *set) { | |
1030 | uInt status=0; /* accumulator */ | |
1031 | decCompareOp(res, lhs, rhs, set, COMPARE, &status); | |
1032 | if (status!=0) decStatus(res, status, set); | |
1033 | return res; | |
1034 | } /* decNumberCompare */ | |
1035 | ||
1036 | /* ------------------------------------------------------------------ */ | |
1037 | /* decNumberCompareSignal -- compare, signalling on all NaNs */ | |
1038 | /* */ | |
1039 | /* This computes C = A ? B */ | |
1040 | /* */ | |
1041 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1042 | /* lhs is A */ | |
1043 | /* rhs is B */ | |
1044 | /* set is the context */ | |
1045 | /* */ | |
1046 | /* C must have space for one digit (or NaN). */ | |
1047 | /* ------------------------------------------------------------------ */ | |
1048 | decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, | |
1049 | const decNumber *rhs, decContext *set) { | |
1050 | uInt status=0; /* accumulator */ | |
1051 | decCompareOp(res, lhs, rhs, set, COMPSIG, &status); | |
1052 | if (status!=0) decStatus(res, status, set); | |
1053 | return res; | |
1054 | } /* decNumberCompareSignal */ | |
1055 | ||
1056 | /* ------------------------------------------------------------------ */ | |
1057 | /* decNumberCompareTotal -- compare two Numbers, using total ordering */ | |
1058 | /* */ | |
1059 | /* This computes C = A ? B, under total ordering */ | |
1060 | /* */ | |
1061 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1062 | /* lhs is A */ | |
1063 | /* rhs is B */ | |
1064 | /* set is the context */ | |
1065 | /* */ | |
1066 | /* C must have space for one digit; the result will always be one of */ | |
1067 | /* -1, 0, or 1. */ | |
1068 | /* ------------------------------------------------------------------ */ | |
1069 | decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, | |
1070 | const decNumber *rhs, decContext *set) { | |
1071 | uInt status=0; /* accumulator */ | |
1072 | decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); | |
1073 | if (status!=0) decStatus(res, status, set); | |
1074 | return res; | |
1075 | } /* decNumberCompareTotal */ | |
1076 | ||
1077 | /* ------------------------------------------------------------------ */ | |
1078 | /* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ | |
1079 | /* */ | |
1080 | /* This computes C = |A| ? |B|, under total ordering */ | |
1081 | /* */ | |
1082 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1083 | /* lhs is A */ | |
1084 | /* rhs is B */ | |
1085 | /* set is the context */ | |
1086 | /* */ | |
1087 | /* C must have space for one digit; the result will always be one of */ | |
1088 | /* -1, 0, or 1. */ | |
1089 | /* ------------------------------------------------------------------ */ | |
1090 | decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, | |
1091 | const decNumber *rhs, decContext *set) { | |
1092 | uInt status=0; /* accumulator */ | |
1093 | uInt needbytes; /* for space calculations */ | |
1094 | decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ | |
1095 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
1096 | decNumber bufb[D2N(DECBUFFER+1)]; | |
1097 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ | |
1098 | decNumber *a, *b; /* temporary pointers */ | |
1099 | ||
1100 | #if DECCHECK | |
1101 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
1102 | #endif | |
1103 | ||
1104 | do { /* protect allocated storage */ | |
1105 | /* if either is negative, take a copy and absolute */ | |
1106 | if (decNumberIsNegative(lhs)) { /* lhs<0 */ | |
1107 | a=bufa; | |
1108 | needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); | |
1109 | if (needbytes>sizeof(bufa)) { /* need malloc space */ | |
1110 | allocbufa=(decNumber *)malloc(needbytes); | |
1111 | if (allocbufa==NULL) { /* hopeless -- abandon */ | |
1112 | status|=DEC_Insufficient_storage; | |
1113 | break;} | |
1114 | a=allocbufa; /* use the allocated space */ | |
1115 | } | |
1116 | decNumberCopy(a, lhs); /* copy content */ | |
1117 | a->bits&=~DECNEG; /* .. and clear the sign */ | |
1118 | lhs=a; /* use copy from here on */ | |
1119 | } | |
1120 | if (decNumberIsNegative(rhs)) { /* rhs<0 */ | |
1121 | b=bufb; | |
1122 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); | |
1123 | if (needbytes>sizeof(bufb)) { /* need malloc space */ | |
1124 | allocbufb=(decNumber *)malloc(needbytes); | |
1125 | if (allocbufb==NULL) { /* hopeless -- abandon */ | |
1126 | status|=DEC_Insufficient_storage; | |
1127 | break;} | |
1128 | b=allocbufb; /* use the allocated space */ | |
1129 | } | |
1130 | decNumberCopy(b, rhs); /* copy content */ | |
1131 | b->bits&=~DECNEG; /* .. and clear the sign */ | |
1132 | rhs=b; /* use copy from here on */ | |
1133 | } | |
1134 | decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); | |
1135 | } while(0); /* end protected */ | |
1136 | ||
1137 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ | |
1138 | if (allocbufb!=NULL) free(allocbufb); /* .. */ | |
1139 | if (status!=0) decStatus(res, status, set); | |
1140 | return res; | |
1141 | } /* decNumberCompareTotalMag */ | |
1142 | ||
1143 | /* ------------------------------------------------------------------ */ | |
1144 | /* decNumberDivide -- divide one number by another */ | |
1145 | /* */ | |
1146 | /* This computes C = A / B */ | |
1147 | /* */ | |
1148 | /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ | |
1149 | /* lhs is A */ | |
1150 | /* rhs is B */ | |
1151 | /* set is the context */ | |
1152 | /* */ | |
1153 | /* C must have space for set->digits digits. */ | |
1154 | /* ------------------------------------------------------------------ */ | |
1155 | decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, | |
1156 | const decNumber *rhs, decContext *set) { | |
1157 | uInt status=0; /* accumulator */ | |
1158 | decDivideOp(res, lhs, rhs, set, DIVIDE, &status); | |
1159 | if (status!=0) decStatus(res, status, set); | |
1160 | #if DECCHECK | |
1161 | decCheckInexact(res, set); | |
1162 | #endif | |
1163 | return res; | |
1164 | } /* decNumberDivide */ | |
1165 | ||
1166 | /* ------------------------------------------------------------------ */ | |
1167 | /* decNumberDivideInteger -- divide and return integer quotient */ | |
1168 | /* */ | |
1169 | /* This computes C = A # B, where # is the integer divide operator */ | |
1170 | /* */ | |
1171 | /* res is C, the result. C may be A and/or B (e.g., X=X#X) */ | |
1172 | /* lhs is A */ | |
1173 | /* rhs is B */ | |
1174 | /* set is the context */ | |
1175 | /* */ | |
1176 | /* C must have space for set->digits digits. */ | |
1177 | /* ------------------------------------------------------------------ */ | |
1178 | decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, | |
1179 | const decNumber *rhs, decContext *set) { | |
1180 | uInt status=0; /* accumulator */ | |
1181 | decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); | |
1182 | if (status!=0) decStatus(res, status, set); | |
1183 | return res; | |
1184 | } /* decNumberDivideInteger */ | |
1185 | ||
1186 | /* ------------------------------------------------------------------ */ | |
1187 | /* decNumberExp -- exponentiation */ | |
1188 | /* */ | |
1189 | /* This computes C = exp(A) */ | |
1190 | /* */ | |
1191 | /* res is C, the result. C may be A */ | |
1192 | /* rhs is A */ | |
1193 | /* set is the context; note that rounding mode has no effect */ | |
1194 | /* */ | |
1195 | /* C must have space for set->digits digits. */ | |
1196 | /* */ | |
1197 | /* Mathematical function restrictions apply (see above); a NaN is */ | |
1198 | /* returned with Invalid_operation if a restriction is violated. */ | |
1199 | /* */ | |
1200 | /* Finite results will always be full precision and Inexact, except */ | |
1201 | /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ | |
1202 | /* */ | |
1203 | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ | |
1204 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
1205 | /* error in rare cases. */ | |
1206 | /* ------------------------------------------------------------------ */ | |
1207 | /* This is a wrapper for decExpOp which can handle the slightly wider */ | |
1208 | /* (double) range needed by Ln (which has to be able to calculate */ | |
1209 | /* exp(-a) where a can be the tiniest number (Ntiny). */ | |
1210 | /* ------------------------------------------------------------------ */ | |
1211 | decNumber * decNumberExp(decNumber *res, const decNumber *rhs, | |
1212 | decContext *set) { | |
1213 | uInt status=0; /* accumulator */ | |
1214 | #if DECSUBSET | |
1215 | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ | |
1216 | #endif | |
1217 | ||
1218 | #if DECCHECK | |
1219 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1220 | #endif | |
1221 | ||
1222 | /* Check restrictions; these restrictions ensure that if h=8 (see */ | |
1223 | /* decExpOp) then the result will either overflow or underflow to 0. */ | |
1224 | /* Other math functions restrict the input range, too, for inverses. */ | |
1225 | /* If not violated then carry out the operation. */ | |
1226 | if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ | |
1227 | #if DECSUBSET | |
1228 | if (!set->extended) { | |
1229 | /* reduce operand and set lostDigits status, as needed */ | |
1230 | if (rhs->digits>set->digits) { | |
1231 | allocrhs=decRoundOperand(rhs, set, &status); | |
1232 | if (allocrhs==NULL) break; | |
1233 | rhs=allocrhs; | |
1234 | } | |
1235 | } | |
1236 | #endif | |
1237 | decExpOp(res, rhs, set, &status); | |
1238 | } while(0); /* end protected */ | |
1239 | ||
1240 | #if DECSUBSET | |
1241 | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ | |
1242 | #endif | |
1243 | /* apply significant status */ | |
1244 | if (status!=0) decStatus(res, status, set); | |
1245 | #if DECCHECK | |
1246 | decCheckInexact(res, set); | |
1247 | #endif | |
1248 | return res; | |
1249 | } /* decNumberExp */ | |
1250 | ||
1251 | /* ------------------------------------------------------------------ */ | |
1252 | /* decNumberFMA -- fused multiply add */ | |
1253 | /* */ | |
1254 | /* This computes D = (A * B) + C with only one rounding */ | |
1255 | /* */ | |
1256 | /* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ | |
1257 | /* lhs is A */ | |
1258 | /* rhs is B */ | |
1259 | /* fhs is C [far hand side] */ | |
1260 | /* set is the context */ | |
1261 | /* */ | |
1262 | /* Mathematical function restrictions apply (see above); a NaN is */ | |
1263 | /* returned with Invalid_operation if a restriction is violated. */ | |
1264 | /* */ | |
1265 | /* C must have space for set->digits digits. */ | |
1266 | /* ------------------------------------------------------------------ */ | |
1267 | decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, | |
1268 | const decNumber *rhs, const decNumber *fhs, | |
1269 | decContext *set) { | |
1270 | uInt status=0; /* accumulator */ | |
1271 | decContext dcmul; /* context for the multiplication */ | |
1272 | uInt needbytes; /* for space calculations */ | |
1273 | decNumber bufa[D2N(DECBUFFER*2+1)]; | |
1274 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
1275 | decNumber *acc; /* accumulator pointer */ | |
1276 | decNumber dzero; /* work */ | |
1277 | ||
1278 | #if DECCHECK | |
1279 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
1280 | if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; | |
1281 | #endif | |
1282 | ||
1283 | do { /* protect allocated storage */ | |
1284 | #if DECSUBSET | |
1285 | if (!set->extended) { /* [undefined if subset] */ | |
1286 | status|=DEC_Invalid_operation; | |
1287 | break;} | |
1288 | #endif | |
1289 | /* Check math restrictions [these ensure no overflow or underflow] */ | |
1290 | if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) | |
1291 | || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) | |
1292 | || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; | |
1293 | /* set up context for multiply */ | |
1294 | dcmul=*set; | |
1295 | dcmul.digits=lhs->digits+rhs->digits; /* just enough */ | |
1296 | /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ | |
1297 | dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ | |
1298 | dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ | |
1299 | /* set up decNumber space to receive the result of the multiply */ | |
1300 | acc=bufa; /* may fit */ | |
1301 | needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); | |
1302 | if (needbytes>sizeof(bufa)) { /* need malloc space */ | |
1303 | allocbufa=(decNumber *)malloc(needbytes); | |
1304 | if (allocbufa==NULL) { /* hopeless -- abandon */ | |
1305 | status|=DEC_Insufficient_storage; | |
1306 | break;} | |
1307 | acc=allocbufa; /* use the allocated space */ | |
1308 | } | |
1309 | /* multiply with extended range and necessary precision */ | |
1310 | /*printf("emin=%ld\n", dcmul.emin); */ | |
1311 | decMultiplyOp(acc, lhs, rhs, &dcmul, &status); | |
1312 | /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ | |
1313 | /* status; if either is seen than ignore fhs (in case it is */ | |
1314 | /* another sNaN) and set acc to NaN unless we had an sNaN */ | |
1315 | /* [decMultiplyOp leaves that to caller] */ | |
1316 | /* Note sNaN has to go through addOp to shorten payload if */ | |
1317 | /* necessary */ | |
1318 | if ((status&DEC_Invalid_operation)!=0) { | |
1319 | if (!(status&DEC_sNaN)) { /* but be true invalid */ | |
1320 | decNumberZero(res); /* acc not yet set */ | |
1321 | res->bits=DECNAN; | |
1322 | break; | |
1323 | } | |
1324 | decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ | |
1325 | fhs=&dzero; /* use that */ | |
1326 | } | |
1327 | #if DECCHECK | |
1328 | else { /* multiply was OK */ | |
1329 | if (status!=0) printf("Status=%08lx after FMA multiply\n", status); | |
1330 | } | |
1331 | #endif | |
1332 | /* add the third operand and result -> res, and all is done */ | |
1333 | decAddOp(res, acc, fhs, set, 0, &status); | |
1334 | } while(0); /* end protected */ | |
1335 | ||
1336 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ | |
1337 | if (status!=0) decStatus(res, status, set); | |
1338 | #if DECCHECK | |
1339 | decCheckInexact(res, set); | |
1340 | #endif | |
1341 | return res; | |
1342 | } /* decNumberFMA */ | |
1343 | ||
1344 | /* ------------------------------------------------------------------ */ | |
1345 | /* decNumberInvert -- invert a Number, digitwise */ | |
1346 | /* */ | |
1347 | /* This computes C = ~A */ | |
1348 | /* */ | |
1349 | /* res is C, the result. C may be A (e.g., X=~X) */ | |
1350 | /* rhs is A */ | |
1351 | /* set is the context (used for result length and error report) */ | |
1352 | /* */ | |
1353 | /* C must have space for set->digits digits. */ | |
1354 | /* */ | |
1355 | /* Logical function restrictions apply (see above); a NaN is */ | |
1356 | /* returned with Invalid_operation if a restriction is violated. */ | |
1357 | /* ------------------------------------------------------------------ */ | |
1358 | decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, | |
1359 | decContext *set) { | |
1360 | const Unit *ua, *msua; /* -> operand and its msu */ | |
1361 | Unit *uc, *msuc; /* -> result and its msu */ | |
1362 | Int msudigs; /* digits in res msu */ | |
1363 | #if DECCHECK | |
1364 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1365 | #endif | |
1366 | ||
1367 | if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { | |
1368 | decStatus(res, DEC_Invalid_operation, set); | |
1369 | return res; | |
1370 | } | |
1371 | /* operand is valid */ | |
1372 | ua=rhs->lsu; /* bottom-up */ | |
1373 | uc=res->lsu; /* .. */ | |
1374 | msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ | |
1375 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ | |
1376 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ | |
1377 | for (; uc<=msuc; ua++, uc++) { /* Unit loop */ | |
1378 | Unit a; /* extract unit */ | |
1379 | Int i, j; /* work */ | |
1380 | if (ua>msua) a=0; | |
1381 | else a=*ua; | |
1382 | *uc=0; /* can now write back */ | |
1383 | /* always need to examine all bits in rhs */ | |
1384 | /* This loop could be unrolled and/or use BIN2BCD tables */ | |
1385 | for (i=0; i<DECDPUN; i++) { | |
1386 | if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ | |
1387 | j=a%10; | |
1388 | a=a/10; | |
1389 | if (j>1) { | |
1390 | decStatus(res, DEC_Invalid_operation, set); | |
1391 | return res; | |
1392 | } | |
1393 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ | |
1394 | } /* each digit */ | |
1395 | } /* each unit */ | |
1396 | /* [here uc-1 is the msu of the result] */ | |
1397 | res->digits=decGetDigits(res->lsu, uc-res->lsu); | |
1398 | res->exponent=0; /* integer */ | |
1399 | res->bits=0; /* sign=0 */ | |
1400 | return res; /* [no status to set] */ | |
1401 | } /* decNumberInvert */ | |
1402 | ||
1403 | /* ------------------------------------------------------------------ */ | |
1404 | /* decNumberLn -- natural logarithm */ | |
1405 | /* */ | |
1406 | /* This computes C = ln(A) */ | |
1407 | /* */ | |
1408 | /* res is C, the result. C may be A */ | |
1409 | /* rhs is A */ | |
1410 | /* set is the context; note that rounding mode has no effect */ | |
1411 | /* */ | |
1412 | /* C must have space for set->digits digits. */ | |
1413 | /* */ | |
1414 | /* Notable cases: */ | |
1415 | /* A<0 -> Invalid */ | |
1416 | /* A=0 -> -Infinity (Exact) */ | |
1417 | /* A=+Infinity -> +Infinity (Exact) */ | |
1418 | /* A=1 exactly -> 0 (Exact) */ | |
1419 | /* */ | |
1420 | /* Mathematical function restrictions apply (see above); a NaN is */ | |
1421 | /* returned with Invalid_operation if a restriction is violated. */ | |
1422 | /* */ | |
1423 | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ | |
1424 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
1425 | /* error in rare cases. */ | |
1426 | /* ------------------------------------------------------------------ */ | |
1427 | /* This is a wrapper for decLnOp which can handle the slightly wider */ | |
1428 | /* (+11) range needed by Ln, Log10, etc. (which may have to be able */ | |
1429 | /* to calculate at p+e+2). */ | |
1430 | /* ------------------------------------------------------------------ */ | |
1431 | decNumber * decNumberLn(decNumber *res, const decNumber *rhs, | |
1432 | decContext *set) { | |
1433 | uInt status=0; /* accumulator */ | |
1434 | #if DECSUBSET | |
1435 | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ | |
1436 | #endif | |
1437 | ||
1438 | #if DECCHECK | |
1439 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1440 | #endif | |
1441 | ||
1442 | /* Check restrictions; this is a math function; if not violated */ | |
1443 | /* then carry out the operation. */ | |
1444 | if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ | |
1445 | #if DECSUBSET | |
1446 | if (!set->extended) { | |
1447 | /* reduce operand and set lostDigits status, as needed */ | |
1448 | if (rhs->digits>set->digits) { | |
1449 | allocrhs=decRoundOperand(rhs, set, &status); | |
1450 | if (allocrhs==NULL) break; | |
1451 | rhs=allocrhs; | |
1452 | } | |
1453 | /* special check in subset for rhs=0 */ | |
1454 | if (ISZERO(rhs)) { /* +/- zeros -> error */ | |
1455 | status|=DEC_Invalid_operation; | |
1456 | break;} | |
1457 | } /* extended=0 */ | |
1458 | #endif | |
1459 | decLnOp(res, rhs, set, &status); | |
1460 | } while(0); /* end protected */ | |
1461 | ||
1462 | #if DECSUBSET | |
1463 | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ | |
1464 | #endif | |
1465 | /* apply significant status */ | |
1466 | if (status!=0) decStatus(res, status, set); | |
1467 | #if DECCHECK | |
1468 | decCheckInexact(res, set); | |
1469 | #endif | |
1470 | return res; | |
1471 | } /* decNumberLn */ | |
1472 | ||
1473 | /* ------------------------------------------------------------------ */ | |
1474 | /* decNumberLogB - get adjusted exponent, by 754r rules */ | |
1475 | /* */ | |
1476 | /* This computes C = adjustedexponent(A) */ | |
1477 | /* */ | |
1478 | /* res is C, the result. C may be A */ | |
1479 | /* rhs is A */ | |
1480 | /* set is the context, used only for digits and status */ | |
1481 | /* */ | |
1482 | /* C must have space for 10 digits (A might have 10**9 digits and */ | |
1483 | /* an exponent of +999999999, or one digit and an exponent of */ | |
1484 | /* -1999999999). */ | |
1485 | /* */ | |
1486 | /* This returns the adjusted exponent of A after (in theory) padding */ | |
1487 | /* with zeros on the right to set->digits digits while keeping the */ | |
1488 | /* same value. The exponent is not limited by emin/emax. */ | |
1489 | /* */ | |
1490 | /* Notable cases: */ | |
1491 | /* A<0 -> Use |A| */ | |
1492 | /* A=0 -> -Infinity (Division by zero) */ | |
1493 | /* A=Infinite -> +Infinity (Exact) */ | |
1494 | /* A=1 exactly -> 0 (Exact) */ | |
1495 | /* NaNs are propagated as usual */ | |
1496 | /* ------------------------------------------------------------------ */ | |
1497 | decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, | |
1498 | decContext *set) { | |
1499 | uInt status=0; /* accumulator */ | |
1500 | ||
1501 | #if DECCHECK | |
1502 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1503 | #endif | |
1504 | ||
1505 | /* NaNs as usual; Infinities return +Infinity; 0->oops */ | |
1506 | if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); | |
1507 | else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); | |
1508 | else if (decNumberIsZero(rhs)) { | |
1509 | decNumberZero(res); /* prepare for Infinity */ | |
1510 | res->bits=DECNEG|DECINF; /* -Infinity */ | |
1511 | status|=DEC_Division_by_zero; /* as per 754r */ | |
1512 | } | |
1513 | else { /* finite non-zero */ | |
1514 | Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ | |
1515 | decNumberFromInt32(res, ae); /* lay it out */ | |
1516 | } | |
1517 | ||
1518 | if (status!=0) decStatus(res, status, set); | |
1519 | return res; | |
1520 | } /* decNumberLogB */ | |
1521 | ||
1522 | /* ------------------------------------------------------------------ */ | |
1523 | /* decNumberLog10 -- logarithm in base 10 */ | |
1524 | /* */ | |
1525 | /* This computes C = log10(A) */ | |
1526 | /* */ | |
1527 | /* res is C, the result. C may be A */ | |
1528 | /* rhs is A */ | |
1529 | /* set is the context; note that rounding mode has no effect */ | |
1530 | /* */ | |
1531 | /* C must have space for set->digits digits. */ | |
1532 | /* */ | |
1533 | /* Notable cases: */ | |
1534 | /* A<0 -> Invalid */ | |
1535 | /* A=0 -> -Infinity (Exact) */ | |
1536 | /* A=+Infinity -> +Infinity (Exact) */ | |
1537 | /* A=10**n (if n is an integer) -> n (Exact) */ | |
1538 | /* */ | |
1539 | /* Mathematical function restrictions apply (see above); a NaN is */ | |
1540 | /* returned with Invalid_operation if a restriction is violated. */ | |
1541 | /* */ | |
1542 | /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ | |
1543 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
1544 | /* error in rare cases. */ | |
1545 | /* ------------------------------------------------------------------ */ | |
1546 | /* This calculates ln(A)/ln(10) using appropriate precision. For */ | |
1547 | /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ | |
1548 | /* requested digits and t is the number of digits in the exponent */ | |
1549 | /* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ | |
1550 | /* fastpath in decLnOp. The final division is done to the requested */ | |
1551 | /* precision. */ | |
1552 | /* ------------------------------------------------------------------ */ | |
1553 | decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, | |
1554 | decContext *set) { | |
1555 | uInt status=0, ignore=0; /* status accumulators */ | |
1556 | uInt needbytes; /* for space calculations */ | |
1557 | Int p; /* working precision */ | |
1558 | Int t; /* digits in exponent of A */ | |
1559 | ||
1560 | /* buffers for a and b working decimals */ | |
1561 | /* (adjustment calculator, same size) */ | |
1562 | decNumber bufa[D2N(DECBUFFER+2)]; | |
1563 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
1564 | decNumber *a=bufa; /* temporary a */ | |
1565 | decNumber bufb[D2N(DECBUFFER+2)]; | |
1566 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ | |
1567 | decNumber *b=bufb; /* temporary b */ | |
1568 | decNumber bufw[D2N(10)]; /* working 2-10 digit number */ | |
1569 | decNumber *w=bufw; /* .. */ | |
1570 | #if DECSUBSET | |
1571 | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ | |
1572 | #endif | |
1573 | ||
1574 | decContext aset; /* working context */ | |
1575 | ||
1576 | #if DECCHECK | |
1577 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1578 | #endif | |
1579 | ||
1580 | /* Check restrictions; this is a math function; if not violated */ | |
1581 | /* then carry out the operation. */ | |
1582 | if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ | |
1583 | #if DECSUBSET | |
1584 | if (!set->extended) { | |
1585 | /* reduce operand and set lostDigits status, as needed */ | |
1586 | if (rhs->digits>set->digits) { | |
1587 | allocrhs=decRoundOperand(rhs, set, &status); | |
1588 | if (allocrhs==NULL) break; | |
1589 | rhs=allocrhs; | |
1590 | } | |
1591 | /* special check in subset for rhs=0 */ | |
1592 | if (ISZERO(rhs)) { /* +/- zeros -> error */ | |
1593 | status|=DEC_Invalid_operation; | |
1594 | break;} | |
1595 | } /* extended=0 */ | |
1596 | #endif | |
1597 | ||
1598 | decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ | |
1599 | ||
1600 | /* handle exact powers of 10; only check if +ve finite */ | |
1601 | if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { | |
1602 | Int residue=0; /* (no residue) */ | |
1603 | uInt copystat=0; /* clean status */ | |
1604 | ||
1605 | /* round to a single digit... */ | |
1606 | aset.digits=1; | |
1607 | decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ | |
1608 | /* if exact and the digit is 1, rhs is a power of 10 */ | |
1609 | if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { | |
1610 | /* the exponent, conveniently, is the power of 10; making */ | |
1611 | /* this the result needs a little care as it might not fit, */ | |
1612 | /* so first convert it into the working number, and then move */ | |
1613 | /* to res */ | |
1614 | decNumberFromInt32(w, w->exponent); | |
1615 | residue=0; | |
1616 | decCopyFit(res, w, set, &residue, &status); /* copy & round */ | |
1617 | decFinish(res, set, &residue, &status); /* cleanup/set flags */ | |
1618 | break; | |
1619 | } /* not a power of 10 */ | |
1620 | } /* not a candidate for exact */ | |
1621 | ||
1622 | /* simplify the information-content calculation to use 'total */ | |
1623 | /* number of digits in a, including exponent' as compared to the */ | |
1624 | /* requested digits, as increasing this will only rarely cost an */ | |
1625 | /* iteration in ln(a) anyway */ | |
1626 | t=6; /* it can never be >6 */ | |
1627 | ||
1628 | /* allocate space when needed... */ | |
1629 | p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; | |
1630 | needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); | |
1631 | if (needbytes>sizeof(bufa)) { /* need malloc space */ | |
1632 | allocbufa=(decNumber *)malloc(needbytes); | |
1633 | if (allocbufa==NULL) { /* hopeless -- abandon */ | |
1634 | status|=DEC_Insufficient_storage; | |
1635 | break;} | |
1636 | a=allocbufa; /* use the allocated space */ | |
1637 | } | |
1638 | aset.digits=p; /* as calculated */ | |
1639 | aset.emax=DEC_MAX_MATH; /* usual bounds */ | |
1640 | aset.emin=-DEC_MAX_MATH; /* .. */ | |
1641 | aset.clamp=0; /* and no concrete format */ | |
1642 | decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ | |
1643 | ||
1644 | /* skip the division if the result so far is infinite, NaN, or */ | |
1645 | /* zero, or there was an error; note NaN from sNaN needs copy */ | |
1646 | if (status&DEC_NaNs && !(status&DEC_sNaN)) break; | |
1647 | if (a->bits&DECSPECIAL || ISZERO(a)) { | |
1648 | decNumberCopy(res, a); /* [will fit] */ | |
1649 | break;} | |
1650 | ||
1651 | /* for ln(10) an extra 3 digits of precision are needed */ | |
1652 | p=set->digits+3; | |
1653 | needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); | |
1654 | if (needbytes>sizeof(bufb)) { /* need malloc space */ | |
1655 | allocbufb=(decNumber *)malloc(needbytes); | |
1656 | if (allocbufb==NULL) { /* hopeless -- abandon */ | |
1657 | status|=DEC_Insufficient_storage; | |
1658 | break;} | |
1659 | b=allocbufb; /* use the allocated space */ | |
1660 | } | |
1661 | decNumberZero(w); /* set up 10... */ | |
1662 | #if DECDPUN==1 | |
1663 | w->lsu[1]=1; w->lsu[0]=0; /* .. */ | |
1664 | #else | |
1665 | w->lsu[0]=10; /* .. */ | |
1666 | #endif | |
1667 | w->digits=2; /* .. */ | |
1668 | ||
1669 | aset.digits=p; | |
1670 | decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ | |
1671 | ||
1672 | aset.digits=set->digits; /* for final divide */ | |
1673 | decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ | |
1674 | } while(0); /* [for break] */ | |
1675 | ||
1676 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ | |
1677 | if (allocbufb!=NULL) free(allocbufb); /* .. */ | |
1678 | #if DECSUBSET | |
1679 | if (allocrhs !=NULL) free(allocrhs); /* .. */ | |
1680 | #endif | |
1681 | /* apply significant status */ | |
1682 | if (status!=0) decStatus(res, status, set); | |
1683 | #if DECCHECK | |
1684 | decCheckInexact(res, set); | |
1685 | #endif | |
1686 | return res; | |
1687 | } /* decNumberLog10 */ | |
1688 | ||
1689 | /* ------------------------------------------------------------------ */ | |
1690 | /* decNumberMax -- compare two Numbers and return the maximum */ | |
1691 | /* */ | |
1692 | /* This computes C = A ? B, returning the maximum by 754R rules */ | |
1693 | /* */ | |
1694 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1695 | /* lhs is A */ | |
1696 | /* rhs is B */ | |
1697 | /* set is the context */ | |
1698 | /* */ | |
1699 | /* C must have space for set->digits digits. */ | |
1700 | /* ------------------------------------------------------------------ */ | |
1701 | decNumber * decNumberMax(decNumber *res, const decNumber *lhs, | |
1702 | const decNumber *rhs, decContext *set) { | |
1703 | uInt status=0; /* accumulator */ | |
1704 | decCompareOp(res, lhs, rhs, set, COMPMAX, &status); | |
1705 | if (status!=0) decStatus(res, status, set); | |
1706 | #if DECCHECK | |
1707 | decCheckInexact(res, set); | |
1708 | #endif | |
1709 | return res; | |
1710 | } /* decNumberMax */ | |
1711 | ||
1712 | /* ------------------------------------------------------------------ */ | |
1713 | /* decNumberMaxMag -- compare and return the maximum by magnitude */ | |
1714 | /* */ | |
1715 | /* This computes C = A ? B, returning the maximum by 754R rules */ | |
1716 | /* */ | |
1717 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1718 | /* lhs is A */ | |
1719 | /* rhs is B */ | |
1720 | /* set is the context */ | |
1721 | /* */ | |
1722 | /* C must have space for set->digits digits. */ | |
1723 | /* ------------------------------------------------------------------ */ | |
1724 | decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, | |
1725 | const decNumber *rhs, decContext *set) { | |
1726 | uInt status=0; /* accumulator */ | |
1727 | decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); | |
1728 | if (status!=0) decStatus(res, status, set); | |
1729 | #if DECCHECK | |
1730 | decCheckInexact(res, set); | |
1731 | #endif | |
1732 | return res; | |
1733 | } /* decNumberMaxMag */ | |
1734 | ||
1735 | /* ------------------------------------------------------------------ */ | |
1736 | /* decNumberMin -- compare two Numbers and return the minimum */ | |
1737 | /* */ | |
1738 | /* This computes C = A ? B, returning the minimum by 754R rules */ | |
1739 | /* */ | |
1740 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1741 | /* lhs is A */ | |
1742 | /* rhs is B */ | |
1743 | /* set is the context */ | |
1744 | /* */ | |
1745 | /* C must have space for set->digits digits. */ | |
1746 | /* ------------------------------------------------------------------ */ | |
1747 | decNumber * decNumberMin(decNumber *res, const decNumber *lhs, | |
1748 | const decNumber *rhs, decContext *set) { | |
1749 | uInt status=0; /* accumulator */ | |
1750 | decCompareOp(res, lhs, rhs, set, COMPMIN, &status); | |
1751 | if (status!=0) decStatus(res, status, set); | |
1752 | #if DECCHECK | |
1753 | decCheckInexact(res, set); | |
1754 | #endif | |
1755 | return res; | |
1756 | } /* decNumberMin */ | |
1757 | ||
1758 | /* ------------------------------------------------------------------ */ | |
1759 | /* decNumberMinMag -- compare and return the minimum by magnitude */ | |
1760 | /* */ | |
1761 | /* This computes C = A ? B, returning the minimum by 754R rules */ | |
1762 | /* */ | |
1763 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
1764 | /* lhs is A */ | |
1765 | /* rhs is B */ | |
1766 | /* set is the context */ | |
1767 | /* */ | |
1768 | /* C must have space for set->digits digits. */ | |
1769 | /* ------------------------------------------------------------------ */ | |
1770 | decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, | |
1771 | const decNumber *rhs, decContext *set) { | |
1772 | uInt status=0; /* accumulator */ | |
1773 | decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); | |
1774 | if (status!=0) decStatus(res, status, set); | |
1775 | #if DECCHECK | |
1776 | decCheckInexact(res, set); | |
1777 | #endif | |
1778 | return res; | |
1779 | } /* decNumberMinMag */ | |
1780 | ||
1781 | /* ------------------------------------------------------------------ */ | |
1782 | /* decNumberMinus -- prefix minus operator */ | |
1783 | /* */ | |
1784 | /* This computes C = 0 - A */ | |
1785 | /* */ | |
1786 | /* res is C, the result. C may be A */ | |
1787 | /* rhs is A */ | |
1788 | /* set is the context */ | |
1789 | /* */ | |
1790 | /* See also decNumberCopyNegate for a quiet bitwise version of this. */ | |
1791 | /* C must have space for set->digits digits. */ | |
1792 | /* ------------------------------------------------------------------ */ | |
1793 | /* Simply use AddOp for the subtract, which will do the necessary. */ | |
1794 | /* ------------------------------------------------------------------ */ | |
1795 | decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, | |
1796 | decContext *set) { | |
1797 | decNumber dzero; | |
1798 | uInt status=0; /* accumulator */ | |
1799 | ||
1800 | #if DECCHECK | |
1801 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1802 | #endif | |
1803 | ||
1804 | decNumberZero(&dzero); /* make 0 */ | |
1805 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ | |
1806 | decAddOp(res, &dzero, rhs, set, DECNEG, &status); | |
1807 | if (status!=0) decStatus(res, status, set); | |
1808 | #if DECCHECK | |
1809 | decCheckInexact(res, set); | |
1810 | #endif | |
1811 | return res; | |
1812 | } /* decNumberMinus */ | |
1813 | ||
1814 | /* ------------------------------------------------------------------ */ | |
1815 | /* decNumberNextMinus -- next towards -Infinity */ | |
1816 | /* */ | |
1817 | /* This computes C = A - infinitesimal, rounded towards -Infinity */ | |
1818 | /* */ | |
1819 | /* res is C, the result. C may be A */ | |
1820 | /* rhs is A */ | |
1821 | /* set is the context */ | |
1822 | /* */ | |
1823 | /* This is a generalization of 754r NextDown. */ | |
1824 | /* ------------------------------------------------------------------ */ | |
1825 | decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, | |
1826 | decContext *set) { | |
1827 | decNumber dtiny; /* constant */ | |
1828 | decContext workset=*set; /* work */ | |
1829 | uInt status=0; /* accumulator */ | |
1830 | #if DECCHECK | |
1831 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1832 | #endif | |
1833 | ||
1834 | /* +Infinity is the special case */ | |
1835 | if ((rhs->bits&(DECINF|DECNEG))==DECINF) { | |
1836 | decSetMaxValue(res, set); /* is +ve */ | |
1837 | /* there is no status to set */ | |
1838 | return res; | |
1839 | } | |
1840 | decNumberZero(&dtiny); /* start with 0 */ | |
1841 | dtiny.lsu[0]=1; /* make number that is .. */ | |
1842 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ | |
1843 | workset.round=DEC_ROUND_FLOOR; | |
1844 | decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); | |
1845 | status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ | |
1846 | if (status!=0) decStatus(res, status, set); | |
1847 | return res; | |
1848 | } /* decNumberNextMinus */ | |
1849 | ||
1850 | /* ------------------------------------------------------------------ */ | |
1851 | /* decNumberNextPlus -- next towards +Infinity */ | |
1852 | /* */ | |
1853 | /* This computes C = A + infinitesimal, rounded towards +Infinity */ | |
1854 | /* */ | |
1855 | /* res is C, the result. C may be A */ | |
1856 | /* rhs is A */ | |
1857 | /* set is the context */ | |
1858 | /* */ | |
1859 | /* This is a generalization of 754r NextUp. */ | |
1860 | /* ------------------------------------------------------------------ */ | |
1861 | decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, | |
1862 | decContext *set) { | |
1863 | decNumber dtiny; /* constant */ | |
1864 | decContext workset=*set; /* work */ | |
1865 | uInt status=0; /* accumulator */ | |
1866 | #if DECCHECK | |
1867 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
1868 | #endif | |
1869 | ||
1870 | /* -Infinity is the special case */ | |
1871 | if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { | |
1872 | decSetMaxValue(res, set); | |
1873 | res->bits=DECNEG; /* negative */ | |
1874 | /* there is no status to set */ | |
1875 | return res; | |
1876 | } | |
1877 | decNumberZero(&dtiny); /* start with 0 */ | |
1878 | dtiny.lsu[0]=1; /* make number that is .. */ | |
1879 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ | |
1880 | workset.round=DEC_ROUND_CEILING; | |
1881 | decAddOp(res, rhs, &dtiny, &workset, 0, &status); | |
1882 | status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ | |
1883 | if (status!=0) decStatus(res, status, set); | |
1884 | return res; | |
1885 | } /* decNumberNextPlus */ | |
1886 | ||
1887 | /* ------------------------------------------------------------------ */ | |
1888 | /* decNumberNextToward -- next towards rhs */ | |
1889 | /* */ | |
1890 | /* This computes C = A +/- infinitesimal, rounded towards */ | |
1891 | /* +/-Infinity in the direction of B, as per 754r nextafter rules */ | |
1892 | /* */ | |
1893 | /* res is C, the result. C may be A or B. */ | |
1894 | /* lhs is A */ | |
1895 | /* rhs is B */ | |
1896 | /* set is the context */ | |
1897 | /* */ | |
1898 | /* This is a generalization of 754r NextAfter. */ | |
1899 | /* ------------------------------------------------------------------ */ | |
1900 | decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, | |
1901 | const decNumber *rhs, decContext *set) { | |
1902 | decNumber dtiny; /* constant */ | |
1903 | decContext workset=*set; /* work */ | |
1904 | Int result; /* .. */ | |
1905 | uInt status=0; /* accumulator */ | |
1906 | #if DECCHECK | |
1907 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
1908 | #endif | |
1909 | ||
1910 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { | |
1911 | decNaNs(res, lhs, rhs, set, &status); | |
1912 | } | |
1913 | else { /* Is numeric, so no chance of sNaN Invalid, etc. */ | |
1914 | result=decCompare(lhs, rhs, 0); /* sign matters */ | |
1915 | if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ | |
1916 | else { /* valid compare */ | |
1917 | if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */ | |
1918 | else { /* differ: need NextPlus or NextMinus */ | |
1919 | uByte sub; /* add or subtract */ | |
1920 | if (result<0) { /* lhs<rhs, do nextplus */ | |
1921 | /* -Infinity is the special case */ | |
1922 | if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { | |
1923 | decSetMaxValue(res, set); | |
1924 | res->bits=DECNEG; /* negative */ | |
1925 | return res; /* there is no status to set */ | |
1926 | } | |
1927 | workset.round=DEC_ROUND_CEILING; | |
1928 | sub=0; /* add, please */ | |
1929 | } /* plus */ | |
1930 | else { /* lhs>rhs, do nextminus */ | |
1931 | /* +Infinity is the special case */ | |
1932 | if ((lhs->bits&(DECINF|DECNEG))==DECINF) { | |
1933 | decSetMaxValue(res, set); | |
1934 | return res; /* there is no status to set */ | |
1935 | } | |
1936 | workset.round=DEC_ROUND_FLOOR; | |
1937 | sub=DECNEG; /* subtract, please */ | |
1938 | } /* minus */ | |
1939 | decNumberZero(&dtiny); /* start with 0 */ | |
1940 | dtiny.lsu[0]=1; /* make number that is .. */ | |
1941 | dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ | |
1942 | decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ | |
1943 | /* turn off exceptions if the result is a normal number */ | |
1944 | /* (including Nmin), otherwise let all status through */ | |
1945 | if (decNumberIsNormal(res, set)) status=0; | |
1946 | } /* unequal */ | |
1947 | } /* compare OK */ | |
1948 | } /* numeric */ | |
1949 | if (status!=0) decStatus(res, status, set); | |
1950 | return res; | |
1951 | } /* decNumberNextToward */ | |
1952 | ||
1953 | /* ------------------------------------------------------------------ */ | |
1954 | /* decNumberOr -- OR two Numbers, digitwise */ | |
1955 | /* */ | |
1956 | /* This computes C = A | B */ | |
1957 | /* */ | |
1958 | /* res is C, the result. C may be A and/or B (e.g., X=X|X) */ | |
1959 | /* lhs is A */ | |
1960 | /* rhs is B */ | |
1961 | /* set is the context (used for result length and error report) */ | |
1962 | /* */ | |
1963 | /* C must have space for set->digits digits. */ | |
1964 | /* */ | |
1965 | /* Logical function restrictions apply (see above); a NaN is */ | |
1966 | /* returned with Invalid_operation if a restriction is violated. */ | |
1967 | /* ------------------------------------------------------------------ */ | |
1968 | decNumber * decNumberOr(decNumber *res, const decNumber *lhs, | |
1969 | const decNumber *rhs, decContext *set) { | |
1970 | const Unit *ua, *ub; /* -> operands */ | |
1971 | const Unit *msua, *msub; /* -> operand msus */ | |
1972 | Unit *uc, *msuc; /* -> result and its msu */ | |
1973 | Int msudigs; /* digits in res msu */ | |
1974 | #if DECCHECK | |
1975 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
1976 | #endif | |
1977 | ||
1978 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) | |
1979 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { | |
1980 | decStatus(res, DEC_Invalid_operation, set); | |
1981 | return res; | |
1982 | } | |
1983 | /* operands are valid */ | |
1984 | ua=lhs->lsu; /* bottom-up */ | |
1985 | ub=rhs->lsu; /* .. */ | |
1986 | uc=res->lsu; /* .. */ | |
1987 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ | |
1988 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ | |
1989 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ | |
1990 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ | |
1991 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ | |
1992 | Unit a, b; /* extract units */ | |
1993 | if (ua>msua) a=0; | |
1994 | else a=*ua; | |
1995 | if (ub>msub) b=0; | |
1996 | else b=*ub; | |
1997 | *uc=0; /* can now write back */ | |
1998 | if (a|b) { /* maybe 1 bits to examine */ | |
1999 | Int i, j; | |
2000 | /* This loop could be unrolled and/or use BIN2BCD tables */ | |
2001 | for (i=0; i<DECDPUN; i++) { | |
2002 | if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ | |
2003 | j=a%10; | |
2004 | a=a/10; | |
2005 | j|=b%10; | |
2006 | b=b/10; | |
2007 | if (j>1) { | |
2008 | decStatus(res, DEC_Invalid_operation, set); | |
2009 | return res; | |
2010 | } | |
2011 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ | |
2012 | } /* each digit */ | |
2013 | } /* non-zero */ | |
2014 | } /* each unit */ | |
2015 | /* [here uc-1 is the msu of the result] */ | |
2016 | res->digits=decGetDigits(res->lsu, uc-res->lsu); | |
2017 | res->exponent=0; /* integer */ | |
2018 | res->bits=0; /* sign=0 */ | |
2019 | return res; /* [no status to set] */ | |
2020 | } /* decNumberOr */ | |
2021 | ||
2022 | /* ------------------------------------------------------------------ */ | |
2023 | /* decNumberPlus -- prefix plus operator */ | |
2024 | /* */ | |
2025 | /* This computes C = 0 + A */ | |
2026 | /* */ | |
2027 | /* res is C, the result. C may be A */ | |
2028 | /* rhs is A */ | |
2029 | /* set is the context */ | |
2030 | /* */ | |
2031 | /* See also decNumberCopy for a quiet bitwise version of this. */ | |
2032 | /* C must have space for set->digits digits. */ | |
2033 | /* ------------------------------------------------------------------ */ | |
2034 | /* This simply uses AddOp; Add will take fast path after preparing A. */ | |
2035 | /* Performance is a concern here, as this routine is often used to */ | |
2036 | /* check operands and apply rounding and overflow/underflow testing. */ | |
2037 | /* ------------------------------------------------------------------ */ | |
2038 | decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, | |
2039 | decContext *set) { | |
2040 | decNumber dzero; | |
2041 | uInt status=0; /* accumulator */ | |
2042 | #if DECCHECK | |
2043 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
2044 | #endif | |
2045 | ||
2046 | decNumberZero(&dzero); /* make 0 */ | |
2047 | dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ | |
2048 | decAddOp(res, &dzero, rhs, set, 0, &status); | |
2049 | if (status!=0) decStatus(res, status, set); | |
2050 | #if DECCHECK | |
2051 | decCheckInexact(res, set); | |
2052 | #endif | |
2053 | return res; | |
2054 | } /* decNumberPlus */ | |
2055 | ||
2056 | /* ------------------------------------------------------------------ */ | |
2057 | /* decNumberMultiply -- multiply two Numbers */ | |
2058 | /* */ | |
2059 | /* This computes C = A x B */ | |
2060 | /* */ | |
2061 | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ | |
2062 | /* lhs is A */ | |
2063 | /* rhs is B */ | |
2064 | /* set is the context */ | |
2065 | /* */ | |
2066 | /* C must have space for set->digits digits. */ | |
2067 | /* ------------------------------------------------------------------ */ | |
2068 | decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, | |
2069 | const decNumber *rhs, decContext *set) { | |
2070 | uInt status=0; /* accumulator */ | |
2071 | decMultiplyOp(res, lhs, rhs, set, &status); | |
2072 | if (status!=0) decStatus(res, status, set); | |
2073 | #if DECCHECK | |
2074 | decCheckInexact(res, set); | |
2075 | #endif | |
2076 | return res; | |
2077 | } /* decNumberMultiply */ | |
2078 | ||
2079 | /* ------------------------------------------------------------------ */ | |
2080 | /* decNumberPower -- raise a number to a power */ | |
2081 | /* */ | |
2082 | /* This computes C = A ** B */ | |
2083 | /* */ | |
2084 | /* res is C, the result. C may be A and/or B (e.g., X=X**X) */ | |
2085 | /* lhs is A */ | |
2086 | /* rhs is B */ | |
2087 | /* set is the context */ | |
2088 | /* */ | |
2089 | /* C must have space for set->digits digits. */ | |
2090 | /* */ | |
2091 | /* Mathematical function restrictions apply (see above); a NaN is */ | |
2092 | /* returned with Invalid_operation if a restriction is violated. */ | |
2093 | /* */ | |
2094 | /* However, if 1999999997<=B<=999999999 and B is an integer then the */ | |
2095 | /* restrictions on A and the context are relaxed to the usual bounds, */ | |
2096 | /* for compatibility with the earlier (integer power only) version */ | |
2097 | /* of this function. */ | |
2098 | /* */ | |
2099 | /* When B is an integer, the result may be exact, even if rounded. */ | |
2100 | /* */ | |
2101 | /* The final result is rounded according to the context; it will */ | |
2102 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
2103 | /* error in rare cases. */ | |
2104 | /* ------------------------------------------------------------------ */ | |
2105 | decNumber * decNumberPower(decNumber *res, const decNumber *lhs, | |
2106 | const decNumber *rhs, decContext *set) { | |
2107 | #if DECSUBSET | |
2108 | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ | |
2109 | decNumber *allocrhs=NULL; /* .., rhs */ | |
2110 | #endif | |
2111 | decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ | |
2112 | decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ | |
2113 | Int reqdigits=set->digits; /* requested DIGITS */ | |
2114 | Int n; /* rhs in binary */ | |
2115 | Flag rhsint=0; /* 1 if rhs is an integer */ | |
2116 | Flag useint=0; /* 1 if can use integer calculation */ | |
2117 | Flag isoddint=0; /* 1 if rhs is an integer and odd */ | |
2118 | Int i; /* work */ | |
2119 | #if DECSUBSET | |
2120 | Int dropped; /* .. */ | |
2121 | #endif | |
2122 | uInt needbytes; /* buffer size needed */ | |
2123 | Flag seenbit; /* seen a bit while powering */ | |
2124 | Int residue=0; /* rounding residue */ | |
2125 | uInt status=0; /* accumulators */ | |
2126 | uByte bits=0; /* result sign if errors */ | |
2127 | decContext aset; /* working context */ | |
2128 | decNumber dnOne; /* work value 1... */ | |
2129 | /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ | |
2130 | decNumber dacbuff[D2N(DECBUFFER+9)]; | |
2131 | decNumber *dac=dacbuff; /* -> result accumulator */ | |
2132 | /* same again for possible 1/lhs calculation */ | |
2133 | decNumber invbuff[D2N(DECBUFFER+9)]; | |
2134 | ||
2135 | #if DECCHECK | |
2136 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
2137 | #endif | |
2138 | ||
2139 | do { /* protect allocated storage */ | |
2140 | #if DECSUBSET | |
2141 | if (!set->extended) { /* reduce operands and set status, as needed */ | |
2142 | if (lhs->digits>reqdigits) { | |
2143 | alloclhs=decRoundOperand(lhs, set, &status); | |
2144 | if (alloclhs==NULL) break; | |
2145 | lhs=alloclhs; | |
2146 | } | |
2147 | if (rhs->digits>reqdigits) { | |
2148 | allocrhs=decRoundOperand(rhs, set, &status); | |
2149 | if (allocrhs==NULL) break; | |
2150 | rhs=allocrhs; | |
2151 | } | |
2152 | } | |
2153 | #endif | |
2154 | /* [following code does not require input rounding] */ | |
2155 | ||
2156 | /* handle NaNs and rhs Infinity (lhs infinity is harder) */ | |
2157 | if (SPECIALARGS) { | |
2158 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ | |
2159 | decNaNs(res, lhs, rhs, set, &status); | |
2160 | break;} | |
2161 | if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ | |
2162 | Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ | |
2163 | if (decNumberIsNegative(lhs) /* lhs<0 */ | |
2164 | && !decNumberIsZero(lhs)) /* .. */ | |
2165 | status|=DEC_Invalid_operation; | |
2166 | else { /* lhs >=0 */ | |
2167 | decNumberZero(&dnOne); /* set up 1 */ | |
2168 | dnOne.lsu[0]=1; | |
2169 | decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ | |
2170 | decNumberZero(res); /* prepare for 0/1/Infinity */ | |
2171 | if (decNumberIsNegative(dac)) { /* lhs<1 */ | |
2172 | if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ | |
2173 | } | |
2174 | else if (dac->lsu[0]==0) { /* lhs=1 */ | |
2175 | /* 1**Infinity is inexact, so return fully-padded 1.0000 */ | |
2176 | Int shift=set->digits-1; | |
2177 | *res->lsu=1; /* was 0, make int 1 */ | |
2178 | res->digits=decShiftToMost(res->lsu, 1, shift); | |
2179 | res->exponent=-shift; /* make 1.0000... */ | |
2180 | status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ | |
2181 | } | |
2182 | else { /* lhs>1 */ | |
2183 | if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ | |
2184 | } | |
2185 | } /* lhs>=0 */ | |
2186 | break;} | |
2187 | /* [lhs infinity drops through] */ | |
2188 | } /* specials */ | |
2189 | ||
2190 | /* Original rhs may be an integer that fits and is in range */ | |
2191 | n=decGetInt(rhs); | |
2192 | if (n!=BADINT) { /* it is an integer */ | |
2193 | rhsint=1; /* record the fact for 1**n */ | |
2194 | isoddint=(Flag)n&1; /* [works even if big] */ | |
2195 | if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ | |
2196 | useint=1; /* looks good */ | |
2197 | } | |
2198 | ||
2199 | if (decNumberIsNegative(lhs) /* -x .. */ | |
2200 | && isoddint) bits=DECNEG; /* .. to an odd power */ | |
2201 | ||
2202 | /* handle LHS infinity */ | |
2203 | if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ | |
2204 | uByte rbits=rhs->bits; /* save */ | |
2205 | decNumberZero(res); /* prepare */ | |
2206 | if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ | |
2207 | else { | |
2208 | /* -Inf**nonint -> error */ | |
2209 | if (!rhsint && decNumberIsNegative(lhs)) { | |
2210 | status|=DEC_Invalid_operation; /* -Inf**nonint is error */ | |
2211 | break;} | |
2212 | if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ | |
2213 | /* [otherwise will be 0 or -0] */ | |
2214 | res->bits=bits; | |
2215 | } | |
2216 | break;} | |
2217 | ||
2218 | /* similarly handle LHS zero */ | |
2219 | if (decNumberIsZero(lhs)) { | |
2220 | if (n==0) { /* 0**0 => Error */ | |
2221 | #if DECSUBSET | |
2222 | if (!set->extended) { /* [unless subset] */ | |
2223 | decNumberZero(res); | |
2224 | *res->lsu=1; /* return 1 */ | |
2225 | break;} | |
2226 | #endif | |
2227 | status|=DEC_Invalid_operation; | |
2228 | } | |
2229 | else { /* 0**x */ | |
2230 | uByte rbits=rhs->bits; /* save */ | |
2231 | if (rbits & DECNEG) { /* was a 0**(-n) */ | |
2232 | #if DECSUBSET | |
2233 | if (!set->extended) { /* [bad if subset] */ | |
2234 | status|=DEC_Invalid_operation; | |
2235 | break;} | |
2236 | #endif | |
2237 | bits|=DECINF; | |
2238 | } | |
2239 | decNumberZero(res); /* prepare */ | |
2240 | /* [otherwise will be 0 or -0] */ | |
2241 | res->bits=bits; | |
2242 | } | |
2243 | break;} | |
2244 | ||
2245 | /* here both lhs and rhs are finite; rhs==0 is handled in the */ | |
2246 | /* integer path. Next handle the non-integer cases */ | |
2247 | if (!useint) { /* non-integral rhs */ | |
2248 | /* any -ve lhs is bad, as is either operand or context out of */ | |
2249 | /* bounds */ | |
2250 | if (decNumberIsNegative(lhs)) { | |
2251 | status|=DEC_Invalid_operation; | |
2252 | break;} | |
2253 | if (decCheckMath(lhs, set, &status) | |
2254 | || decCheckMath(rhs, set, &status)) break; /* variable status */ | |
2255 | ||
2256 | decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ | |
2257 | aset.emax=DEC_MAX_MATH; /* usual bounds */ | |
2258 | aset.emin=-DEC_MAX_MATH; /* .. */ | |
2259 | aset.clamp=0; /* and no concrete format */ | |
2260 | ||
2261 | /* calculate the result using exp(ln(lhs)*rhs), which can */ | |
2262 | /* all be done into the accumulator, dac. The precision needed */ | |
2263 | /* is enough to contain the full information in the lhs (which */ | |
2264 | /* is the total digits, including exponent), or the requested */ | |
2265 | /* precision, if larger, + 4; 6 is used for the exponent */ | |
2266 | /* maximum length, and this is also used when it is shorter */ | |
2267 | /* than the requested digits as it greatly reduces the >0.5 ulp */ | |
2268 | /* cases at little cost (because Ln doubles digits each */ | |
2269 | /* iteration so a few extra digits rarely causes an extra */ | |
2270 | /* iteration) */ | |
2271 | aset.digits=MAXI(lhs->digits, set->digits)+6+4; | |
2272 | } /* non-integer rhs */ | |
2273 | ||
2274 | else { /* rhs is in-range integer */ | |
2275 | if (n==0) { /* x**0 = 1 */ | |
2276 | /* (0**0 was handled above) */ | |
2277 | decNumberZero(res); /* result=1 */ | |
2278 | *res->lsu=1; /* .. */ | |
2279 | break;} | |
2280 | /* rhs is a non-zero integer */ | |
2281 | if (n<0) n=-n; /* use abs(n) */ | |
2282 | ||
2283 | aset=*set; /* clone the context */ | |
2284 | aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ | |
2285 | /* calculate the working DIGITS */ | |
2286 | aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; | |
2287 | #if DECSUBSET | |
2288 | if (!set->extended) aset.digits--; /* use classic precision */ | |
2289 | #endif | |
2290 | /* it's an error if this is more than can be handled */ | |
2291 | if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} | |
2292 | } /* integer path */ | |
2293 | ||
2294 | /* aset.digits is the count of digits for the accumulator needed */ | |
2295 | /* if accumulator is too long for local storage, then allocate */ | |
2296 | needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); | |
2297 | /* [needbytes also used below if 1/lhs needed] */ | |
2298 | if (needbytes>sizeof(dacbuff)) { | |
2299 | allocdac=(decNumber *)malloc(needbytes); | |
2300 | if (allocdac==NULL) { /* hopeless -- abandon */ | |
2301 | status|=DEC_Insufficient_storage; | |
2302 | break;} | |
2303 | dac=allocdac; /* use the allocated space */ | |
2304 | } | |
2305 | /* here, aset is set up and accumulator is ready for use */ | |
2306 | ||
2307 | if (!useint) { /* non-integral rhs */ | |
2308 | /* x ** y; special-case x=1 here as it will otherwise always */ | |
2309 | /* reduce to integer 1; decLnOp has a fastpath which detects */ | |
2310 | /* the case of x=1 */ | |
2311 | decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ | |
2312 | /* [no error possible, as lhs 0 already handled] */ | |
2313 | if (ISZERO(dac)) { /* x==1, 1.0, etc. */ | |
2314 | /* need to return fully-padded 1.0000 etc., but rhsint->1 */ | |
2315 | *dac->lsu=1; /* was 0, make int 1 */ | |
2316 | if (!rhsint) { /* add padding */ | |
2317 | Int shift=set->digits-1; | |
2318 | dac->digits=decShiftToMost(dac->lsu, 1, shift); | |
2319 | dac->exponent=-shift; /* make 1.0000... */ | |
2320 | status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ | |
2321 | } | |
2322 | } | |
2323 | else { | |
2324 | decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ | |
2325 | decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ | |
2326 | } | |
2327 | /* and drop through for final rounding */ | |
2328 | } /* non-integer rhs */ | |
2329 | ||
2330 | else { /* carry on with integer */ | |
2331 | decNumberZero(dac); /* acc=1 */ | |
2332 | *dac->lsu=1; /* .. */ | |
2333 | ||
2334 | /* if a negative power the constant 1 is needed, and if not subset */ | |
2335 | /* invert the lhs now rather than inverting the result later */ | |
2336 | if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ | |
67cc32eb | 2337 | decNumber *inv=invbuff; /* assume use fixed buffer */ |
72ac97cd TM |
2338 | decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ |
2339 | #if DECSUBSET | |
2340 | if (set->extended) { /* need to calculate 1/lhs */ | |
2341 | #endif | |
2342 | /* divide lhs into 1, putting result in dac [dac=1/dac] */ | |
2343 | decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); | |
2344 | /* now locate or allocate space for the inverted lhs */ | |
2345 | if (needbytes>sizeof(invbuff)) { | |
2346 | allocinv=(decNumber *)malloc(needbytes); | |
2347 | if (allocinv==NULL) { /* hopeless -- abandon */ | |
2348 | status|=DEC_Insufficient_storage; | |
2349 | break;} | |
2350 | inv=allocinv; /* use the allocated space */ | |
2351 | } | |
2352 | /* [inv now points to big-enough buffer or allocated storage] */ | |
2353 | decNumberCopy(inv, dac); /* copy the 1/lhs */ | |
2354 | decNumberCopy(dac, &dnOne); /* restore acc=1 */ | |
2355 | lhs=inv; /* .. and go forward with new lhs */ | |
2356 | #if DECSUBSET | |
2357 | } | |
2358 | #endif | |
2359 | } | |
2360 | ||
2361 | /* Raise-to-the-power loop... */ | |
2362 | seenbit=0; /* set once a 1-bit is encountered */ | |
2363 | for (i=1;;i++){ /* for each bit [top bit ignored] */ | |
2364 | /* abandon if had overflow or terminal underflow */ | |
2365 | if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ | |
2366 | if (status&DEC_Overflow || ISZERO(dac)) break; | |
2367 | } | |
2368 | /* [the following two lines revealed an optimizer bug in a C++ */ | |
2369 | /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ | |
2370 | n=n<<1; /* move next bit to testable position */ | |
2371 | if (n<0) { /* top bit is set */ | |
2372 | seenbit=1; /* OK, significant bit seen */ | |
2373 | decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ | |
2374 | } | |
2375 | if (i==31) break; /* that was the last bit */ | |
2376 | if (!seenbit) continue; /* no need to square 1 */ | |
2377 | decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ | |
2378 | } /*i*/ /* 32 bits */ | |
2379 | ||
2380 | /* complete internal overflow or underflow processing */ | |
2381 | if (status & (DEC_Overflow|DEC_Underflow)) { | |
2382 | #if DECSUBSET | |
2383 | /* If subset, and power was negative, reverse the kind of -erflow */ | |
2384 | /* [1/x not yet done] */ | |
2385 | if (!set->extended && decNumberIsNegative(rhs)) { | |
2386 | if (status & DEC_Overflow) | |
2387 | status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; | |
2388 | else { /* trickier -- Underflow may or may not be set */ | |
2389 | status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ | |
2390 | status|=DEC_Overflow; | |
2391 | } | |
2392 | } | |
2393 | #endif | |
2394 | dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ | |
2395 | /* round subnormals [to set.digits rather than aset.digits] */ | |
2396 | /* or set overflow result similarly as required */ | |
2397 | decFinalize(dac, set, &residue, &status); | |
2398 | decNumberCopy(res, dac); /* copy to result (is now OK length) */ | |
2399 | break; | |
2400 | } | |
2401 | ||
2402 | #if DECSUBSET | |
2403 | if (!set->extended && /* subset math */ | |
2404 | decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ | |
2405 | /* so divide result into 1 [dac=1/dac] */ | |
2406 | decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); | |
2407 | } | |
2408 | #endif | |
2409 | } /* rhs integer path */ | |
2410 | ||
2411 | /* reduce result to the requested length and copy to result */ | |
2412 | decCopyFit(res, dac, set, &residue, &status); | |
2413 | decFinish(res, set, &residue, &status); /* final cleanup */ | |
2414 | #if DECSUBSET | |
2415 | if (!set->extended) decTrim(res, set, 0, &dropped); /* trailing zeros */ | |
2416 | #endif | |
2417 | } while(0); /* end protected */ | |
2418 | ||
2419 | if (allocdac!=NULL) free(allocdac); /* drop any storage used */ | |
2420 | if (allocinv!=NULL) free(allocinv); /* .. */ | |
2421 | #if DECSUBSET | |
2422 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
2423 | if (allocrhs!=NULL) free(allocrhs); /* .. */ | |
2424 | #endif | |
2425 | if (status!=0) decStatus(res, status, set); | |
2426 | #if DECCHECK | |
2427 | decCheckInexact(res, set); | |
2428 | #endif | |
2429 | return res; | |
2430 | } /* decNumberPower */ | |
2431 | ||
2432 | /* ------------------------------------------------------------------ */ | |
2433 | /* decNumberQuantize -- force exponent to requested value */ | |
2434 | /* */ | |
2435 | /* This computes C = op(A, B), where op adjusts the coefficient */ | |
2436 | /* of C (by rounding or shifting) such that the exponent (-scale) */ | |
2437 | /* of C has exponent of B. The numerical value of C will equal A, */ | |
2438 | /* except for the effects of any rounding that occurred. */ | |
2439 | /* */ | |
2440 | /* res is C, the result. C may be A or B */ | |
2441 | /* lhs is A, the number to adjust */ | |
2442 | /* rhs is B, the number with exponent to match */ | |
2443 | /* set is the context */ | |
2444 | /* */ | |
2445 | /* C must have space for set->digits digits. */ | |
2446 | /* */ | |
2447 | /* Unless there is an error or the result is infinite, the exponent */ | |
2448 | /* after the operation is guaranteed to be equal to that of B. */ | |
2449 | /* ------------------------------------------------------------------ */ | |
2450 | decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, | |
2451 | const decNumber *rhs, decContext *set) { | |
2452 | uInt status=0; /* accumulator */ | |
2453 | decQuantizeOp(res, lhs, rhs, set, 1, &status); | |
2454 | if (status!=0) decStatus(res, status, set); | |
2455 | return res; | |
2456 | } /* decNumberQuantize */ | |
2457 | ||
2458 | /* ------------------------------------------------------------------ */ | |
2459 | /* decNumberReduce -- remove trailing zeros */ | |
2460 | /* */ | |
2461 | /* This computes C = 0 + A, and normalizes the result */ | |
2462 | /* */ | |
2463 | /* res is C, the result. C may be A */ | |
2464 | /* rhs is A */ | |
2465 | /* set is the context */ | |
2466 | /* */ | |
2467 | /* C must have space for set->digits digits. */ | |
2468 | /* ------------------------------------------------------------------ */ | |
2469 | /* Previously known as Normalize */ | |
2470 | decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, | |
2471 | decContext *set) { | |
2472 | return decNumberReduce(res, rhs, set); | |
2473 | } /* decNumberNormalize */ | |
2474 | ||
2475 | decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, | |
2476 | decContext *set) { | |
2477 | #if DECSUBSET | |
2478 | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ | |
2479 | #endif | |
2480 | uInt status=0; /* as usual */ | |
2481 | Int residue=0; /* as usual */ | |
2482 | Int dropped; /* work */ | |
2483 | ||
2484 | #if DECCHECK | |
2485 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
2486 | #endif | |
2487 | ||
2488 | do { /* protect allocated storage */ | |
2489 | #if DECSUBSET | |
2490 | if (!set->extended) { | |
2491 | /* reduce operand and set lostDigits status, as needed */ | |
2492 | if (rhs->digits>set->digits) { | |
2493 | allocrhs=decRoundOperand(rhs, set, &status); | |
2494 | if (allocrhs==NULL) break; | |
2495 | rhs=allocrhs; | |
2496 | } | |
2497 | } | |
2498 | #endif | |
2499 | /* [following code does not require input rounding] */ | |
2500 | ||
2501 | /* Infinities copy through; NaNs need usual treatment */ | |
2502 | if (decNumberIsNaN(rhs)) { | |
2503 | decNaNs(res, rhs, NULL, set, &status); | |
2504 | break; | |
2505 | } | |
2506 | ||
2507 | /* reduce result to the requested length and copy to result */ | |
2508 | decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ | |
2509 | decFinish(res, set, &residue, &status); /* cleanup/set flags */ | |
2510 | decTrim(res, set, 1, &dropped); /* normalize in place */ | |
2511 | } while(0); /* end protected */ | |
2512 | ||
2513 | #if DECSUBSET | |
2514 | if (allocrhs !=NULL) free(allocrhs); /* .. */ | |
2515 | #endif | |
2516 | if (status!=0) decStatus(res, status, set);/* then report status */ | |
2517 | return res; | |
2518 | } /* decNumberReduce */ | |
2519 | ||
2520 | /* ------------------------------------------------------------------ */ | |
2521 | /* decNumberRescale -- force exponent to requested value */ | |
2522 | /* */ | |
2523 | /* This computes C = op(A, B), where op adjusts the coefficient */ | |
2524 | /* of C (by rounding or shifting) such that the exponent (-scale) */ | |
2525 | /* of C has the value B. The numerical value of C will equal A, */ | |
2526 | /* except for the effects of any rounding that occurred. */ | |
2527 | /* */ | |
2528 | /* res is C, the result. C may be A or B */ | |
2529 | /* lhs is A, the number to adjust */ | |
2530 | /* rhs is B, the requested exponent */ | |
2531 | /* set is the context */ | |
2532 | /* */ | |
2533 | /* C must have space for set->digits digits. */ | |
2534 | /* */ | |
2535 | /* Unless there is an error or the result is infinite, the exponent */ | |
2536 | /* after the operation is guaranteed to be equal to B. */ | |
2537 | /* ------------------------------------------------------------------ */ | |
2538 | decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, | |
2539 | const decNumber *rhs, decContext *set) { | |
2540 | uInt status=0; /* accumulator */ | |
2541 | decQuantizeOp(res, lhs, rhs, set, 0, &status); | |
2542 | if (status!=0) decStatus(res, status, set); | |
2543 | return res; | |
2544 | } /* decNumberRescale */ | |
2545 | ||
2546 | /* ------------------------------------------------------------------ */ | |
2547 | /* decNumberRemainder -- divide and return remainder */ | |
2548 | /* */ | |
2549 | /* This computes C = A % B */ | |
2550 | /* */ | |
2551 | /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ | |
2552 | /* lhs is A */ | |
2553 | /* rhs is B */ | |
2554 | /* set is the context */ | |
2555 | /* */ | |
2556 | /* C must have space for set->digits digits. */ | |
2557 | /* ------------------------------------------------------------------ */ | |
2558 | decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, | |
2559 | const decNumber *rhs, decContext *set) { | |
2560 | uInt status=0; /* accumulator */ | |
2561 | decDivideOp(res, lhs, rhs, set, REMAINDER, &status); | |
2562 | if (status!=0) decStatus(res, status, set); | |
2563 | #if DECCHECK | |
2564 | decCheckInexact(res, set); | |
2565 | #endif | |
2566 | return res; | |
2567 | } /* decNumberRemainder */ | |
2568 | ||
2569 | /* ------------------------------------------------------------------ */ | |
2570 | /* decNumberRemainderNear -- divide and return remainder from nearest */ | |
2571 | /* */ | |
2572 | /* This computes C = A % B, where % is the IEEE remainder operator */ | |
2573 | /* */ | |
2574 | /* res is C, the result. C may be A and/or B (e.g., X=X%X) */ | |
2575 | /* lhs is A */ | |
2576 | /* rhs is B */ | |
2577 | /* set is the context */ | |
2578 | /* */ | |
2579 | /* C must have space for set->digits digits. */ | |
2580 | /* ------------------------------------------------------------------ */ | |
2581 | decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, | |
2582 | const decNumber *rhs, decContext *set) { | |
2583 | uInt status=0; /* accumulator */ | |
2584 | decDivideOp(res, lhs, rhs, set, REMNEAR, &status); | |
2585 | if (status!=0) decStatus(res, status, set); | |
2586 | #if DECCHECK | |
2587 | decCheckInexact(res, set); | |
2588 | #endif | |
2589 | return res; | |
2590 | } /* decNumberRemainderNear */ | |
2591 | ||
2592 | /* ------------------------------------------------------------------ */ | |
2593 | /* decNumberRotate -- rotate the coefficient of a Number left/right */ | |
2594 | /* */ | |
2595 | /* This computes C = A rot B (in base ten and rotating set->digits */ | |
2596 | /* digits). */ | |
2597 | /* */ | |
2598 | /* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ | |
2599 | /* lhs is A */ | |
2600 | /* rhs is B, the number of digits to rotate (-ve to right) */ | |
2601 | /* set is the context */ | |
2602 | /* */ | |
2603 | /* The digits of the coefficient of A are rotated to the left (if B */ | |
2604 | /* is positive) or to the right (if B is negative) without adjusting */ | |
2605 | /* the exponent or the sign of A. If lhs->digits is less than */ | |
2606 | /* set->digits the coefficient is padded with zeros on the left */ | |
2607 | /* before the rotate. Any leading zeros in the result are removed */ | |
2608 | /* as usual. */ | |
2609 | /* */ | |
2610 | /* B must be an integer (q=0) and in the range -set->digits through */ | |
2611 | /* +set->digits. */ | |
2612 | /* C must have space for set->digits digits. */ | |
2613 | /* NaNs are propagated as usual. Infinities are unaffected (but */ | |
2614 | /* B must be valid). No status is set unless B is invalid or an */ | |
2615 | /* operand is an sNaN. */ | |
2616 | /* ------------------------------------------------------------------ */ | |
2617 | decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, | |
2618 | const decNumber *rhs, decContext *set) { | |
2619 | uInt status=0; /* accumulator */ | |
2620 | Int rotate; /* rhs as an Int */ | |
2621 | ||
2622 | #if DECCHECK | |
2623 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
2624 | #endif | |
2625 | ||
2626 | /* NaNs propagate as normal */ | |
2627 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) | |
2628 | decNaNs(res, lhs, rhs, set, &status); | |
2629 | /* rhs must be an integer */ | |
2630 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) | |
2631 | status=DEC_Invalid_operation; | |
2632 | else { /* both numeric, rhs is an integer */ | |
2633 | rotate=decGetInt(rhs); /* [cannot fail] */ | |
2634 | if (rotate==BADINT /* something bad .. */ | |
2635 | || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ | |
2636 | || abs(rotate)>set->digits) /* .. or out of range */ | |
2637 | status=DEC_Invalid_operation; | |
2638 | else { /* rhs is OK */ | |
2639 | decNumberCopy(res, lhs); | |
2640 | /* convert -ve rotate to equivalent positive rotation */ | |
2641 | if (rotate<0) rotate=set->digits+rotate; | |
2642 | if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ | |
2643 | && !decNumberIsInfinite(res)) { /* lhs was infinite */ | |
2644 | /* left-rotate to do; 0 < rotate < set->digits */ | |
2645 | uInt units, shift; /* work */ | |
2646 | uInt msudigits; /* digits in result msu */ | |
2647 | Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ | |
2648 | Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ | |
2649 | for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ | |
2650 | res->digits=set->digits; /* now full-length */ | |
2651 | msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ | |
2652 | ||
2653 | /* rotation here is done in-place, in three steps */ | |
2654 | /* 1. shift all to least up to one unit to unit-align final */ | |
2655 | /* lsd [any digits shifted out are rotated to the left, */ | |
2656 | /* abutted to the original msd (which may require split)] */ | |
2657 | /* */ | |
2658 | /* [if there are no whole units left to rotate, the */ | |
2659 | /* rotation is now complete] */ | |
2660 | /* */ | |
2661 | /* 2. shift to least, from below the split point only, so that */ | |
2662 | /* the final msd is in the right place in its Unit [any */ | |
2663 | /* digits shifted out will fit exactly in the current msu, */ | |
2664 | /* left aligned, no split required] */ | |
2665 | /* */ | |
2666 | /* 3. rotate all the units by reversing left part, right */ | |
2667 | /* part, and then whole */ | |
2668 | /* */ | |
2669 | /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ | |
2670 | /* */ | |
2671 | /* start: 00a bcd efg hij klm npq */ | |
2672 | /* */ | |
2673 | /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ | |
2674 | /* 1b 00p qab cde fgh|ijk lmn */ | |
2675 | /* */ | |
2676 | /* 2a 00p qab cde fgh|00i jkl [mn saved] */ | |
2677 | /* 2b mnp qab cde fgh|00i jkl */ | |
2678 | /* */ | |
2679 | /* 3a fgh cde qab mnp|00i jkl */ | |
2680 | /* 3b fgh cde qab mnp|jkl 00i */ | |
2681 | /* 3c 00i jkl mnp qab cde fgh */ | |
2682 | ||
2683 | /* Step 1: amount to shift is the partial right-rotate count */ | |
2684 | rotate=set->digits-rotate; /* make it right-rotate */ | |
2685 | units=rotate/DECDPUN; /* whole units to rotate */ | |
2686 | shift=rotate%DECDPUN; /* left-over digits count */ | |
2687 | if (shift>0) { /* not an exact number of units */ | |
2688 | uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ | |
2689 | decShiftToLeast(res->lsu, D2U(res->digits), shift); | |
2690 | if (shift>msudigits) { /* msumax-1 needs >0 digits */ | |
2691 | uInt rem=save%powers[shift-msudigits];/* split save */ | |
2692 | *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ | |
2693 | *(msumax-1)=*(msumax-1) | |
2694 | +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ | |
2695 | } | |
2696 | else { /* all fits in msumax */ | |
2697 | *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ | |
2698 | } | |
2699 | } /* digits shift needed */ | |
2700 | ||
2701 | /* If whole units to rotate... */ | |
2702 | if (units>0) { /* some to do */ | |
2703 | /* Step 2: the units to touch are the whole ones in rotate, */ | |
2704 | /* if any, and the shift is DECDPUN-msudigits (which may be */ | |
2705 | /* 0, again) */ | |
2706 | shift=DECDPUN-msudigits; | |
2707 | if (shift>0) { /* not an exact number of units */ | |
2708 | uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ | |
2709 | decShiftToLeast(res->lsu, units, shift); | |
2710 | *msumax=*msumax+(Unit)(save*powers[msudigits]); | |
2711 | } /* partial shift needed */ | |
2712 | ||
2713 | /* Step 3: rotate the units array using triple reverse */ | |
2714 | /* (reversing is easy and fast) */ | |
2715 | decReverse(res->lsu+units, msumax); /* left part */ | |
2716 | decReverse(res->lsu, res->lsu+units-1); /* right part */ | |
2717 | decReverse(res->lsu, msumax); /* whole */ | |
2718 | } /* whole units to rotate */ | |
2719 | /* the rotation may have left an undetermined number of zeros */ | |
2720 | /* on the left, so true length needs to be calculated */ | |
2721 | res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); | |
2722 | } /* rotate needed */ | |
2723 | } /* rhs OK */ | |
2724 | } /* numerics */ | |
2725 | if (status!=0) decStatus(res, status, set); | |
2726 | return res; | |
2727 | } /* decNumberRotate */ | |
2728 | ||
2729 | /* ------------------------------------------------------------------ */ | |
2730 | /* decNumberSameQuantum -- test for equal exponents */ | |
2731 | /* */ | |
2732 | /* res is the result number, which will contain either 0 or 1 */ | |
2733 | /* lhs is a number to test */ | |
2734 | /* rhs is the second (usually a pattern) */ | |
2735 | /* */ | |
2736 | /* No errors are possible and no context is needed. */ | |
2737 | /* ------------------------------------------------------------------ */ | |
2738 | decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, | |
2739 | const decNumber *rhs) { | |
2740 | Unit ret=0; /* return value */ | |
2741 | ||
2742 | #if DECCHECK | |
2743 | if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; | |
2744 | #endif | |
2745 | ||
2746 | if (SPECIALARGS) { | |
2747 | if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; | |
2748 | else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; | |
2749 | /* [anything else with a special gives 0] */ | |
2750 | } | |
2751 | else if (lhs->exponent==rhs->exponent) ret=1; | |
2752 | ||
2753 | decNumberZero(res); /* OK to overwrite an operand now */ | |
2754 | *res->lsu=ret; | |
2755 | return res; | |
2756 | } /* decNumberSameQuantum */ | |
2757 | ||
2758 | /* ------------------------------------------------------------------ */ | |
2759 | /* decNumberScaleB -- multiply by a power of 10 */ | |
2760 | /* */ | |
2761 | /* This computes C = A x 10**B where B is an integer (q=0) with */ | |
2762 | /* maximum magnitude 2*(emax+digits) */ | |
2763 | /* */ | |
2764 | /* res is C, the result. C may be A or B */ | |
2765 | /* lhs is A, the number to adjust */ | |
2766 | /* rhs is B, the requested power of ten to use */ | |
2767 | /* set is the context */ | |
2768 | /* */ | |
2769 | /* C must have space for set->digits digits. */ | |
2770 | /* */ | |
2771 | /* The result may underflow or overflow. */ | |
2772 | /* ------------------------------------------------------------------ */ | |
2773 | decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, | |
2774 | const decNumber *rhs, decContext *set) { | |
2775 | Int reqexp; /* requested exponent change [B] */ | |
2776 | uInt status=0; /* accumulator */ | |
2777 | Int residue; /* work */ | |
2778 | ||
2779 | #if DECCHECK | |
2780 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
2781 | #endif | |
2782 | ||
2783 | /* Handle special values except lhs infinite */ | |
2784 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) | |
2785 | decNaNs(res, lhs, rhs, set, &status); | |
2786 | /* rhs must be an integer */ | |
2787 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) | |
2788 | status=DEC_Invalid_operation; | |
2789 | else { | |
2790 | /* lhs is a number; rhs is a finite with q==0 */ | |
2791 | reqexp=decGetInt(rhs); /* [cannot fail] */ | |
2792 | if (reqexp==BADINT /* something bad .. */ | |
2793 | || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ | |
2794 | || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ | |
2795 | status=DEC_Invalid_operation; | |
2796 | else { /* rhs is OK */ | |
2797 | decNumberCopy(res, lhs); /* all done if infinite lhs */ | |
2798 | if (!decNumberIsInfinite(res)) { /* prepare to scale */ | |
2799 | res->exponent+=reqexp; /* adjust the exponent */ | |
2800 | residue=0; | |
2801 | decFinalize(res, set, &residue, &status); /* .. and check */ | |
2802 | } /* finite LHS */ | |
2803 | } /* rhs OK */ | |
2804 | } /* rhs finite */ | |
2805 | if (status!=0) decStatus(res, status, set); | |
2806 | return res; | |
2807 | } /* decNumberScaleB */ | |
2808 | ||
2809 | /* ------------------------------------------------------------------ */ | |
2810 | /* decNumberShift -- shift the coefficient of a Number left or right */ | |
2811 | /* */ | |
2812 | /* This computes C = A << B or C = A >> -B (in base ten). */ | |
2813 | /* */ | |
2814 | /* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ | |
2815 | /* lhs is A */ | |
2816 | /* rhs is B, the number of digits to shift (-ve to right) */ | |
2817 | /* set is the context */ | |
2818 | /* */ | |
2819 | /* The digits of the coefficient of A are shifted to the left (if B */ | |
2820 | /* is positive) or to the right (if B is negative) without adjusting */ | |
2821 | /* the exponent or the sign of A. */ | |
2822 | /* */ | |
2823 | /* B must be an integer (q=0) and in the range -set->digits through */ | |
2824 | /* +set->digits. */ | |
2825 | /* C must have space for set->digits digits. */ | |
2826 | /* NaNs are propagated as usual. Infinities are unaffected (but */ | |
2827 | /* B must be valid). No status is set unless B is invalid or an */ | |
2828 | /* operand is an sNaN. */ | |
2829 | /* ------------------------------------------------------------------ */ | |
2830 | decNumber * decNumberShift(decNumber *res, const decNumber *lhs, | |
2831 | const decNumber *rhs, decContext *set) { | |
2832 | uInt status=0; /* accumulator */ | |
2833 | Int shift; /* rhs as an Int */ | |
2834 | ||
2835 | #if DECCHECK | |
2836 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
2837 | #endif | |
2838 | ||
2839 | /* NaNs propagate as normal */ | |
2840 | if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) | |
2841 | decNaNs(res, lhs, rhs, set, &status); | |
2842 | /* rhs must be an integer */ | |
2843 | else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) | |
2844 | status=DEC_Invalid_operation; | |
2845 | else { /* both numeric, rhs is an integer */ | |
2846 | shift=decGetInt(rhs); /* [cannot fail] */ | |
2847 | if (shift==BADINT /* something bad .. */ | |
2848 | || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ | |
2849 | || abs(shift)>set->digits) /* .. or out of range */ | |
2850 | status=DEC_Invalid_operation; | |
2851 | else { /* rhs is OK */ | |
2852 | decNumberCopy(res, lhs); | |
2853 | if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ | |
2854 | if (shift>0) { /* to left */ | |
2855 | if (shift==set->digits) { /* removing all */ | |
2856 | *res->lsu=0; /* so place 0 */ | |
2857 | res->digits=1; /* .. */ | |
2858 | } | |
2859 | else { /* */ | |
2860 | /* first remove leading digits if necessary */ | |
2861 | if (res->digits+shift>set->digits) { | |
2862 | decDecap(res, res->digits+shift-set->digits); | |
2863 | /* that updated res->digits; may have gone to 1 (for a */ | |
2864 | /* single digit or for zero */ | |
2865 | } | |
2866 | if (res->digits>1 || *res->lsu) /* if non-zero.. */ | |
2867 | res->digits=decShiftToMost(res->lsu, res->digits, shift); | |
2868 | } /* partial left */ | |
2869 | } /* left */ | |
2870 | else { /* to right */ | |
2871 | if (-shift>=res->digits) { /* discarding all */ | |
2872 | *res->lsu=0; /* so place 0 */ | |
2873 | res->digits=1; /* .. */ | |
2874 | } | |
2875 | else { | |
2876 | decShiftToLeast(res->lsu, D2U(res->digits), -shift); | |
2877 | res->digits-=(-shift); | |
2878 | } | |
2879 | } /* to right */ | |
2880 | } /* non-0 non-Inf shift */ | |
2881 | } /* rhs OK */ | |
2882 | } /* numerics */ | |
2883 | if (status!=0) decStatus(res, status, set); | |
2884 | return res; | |
2885 | } /* decNumberShift */ | |
2886 | ||
2887 | /* ------------------------------------------------------------------ */ | |
2888 | /* decNumberSquareRoot -- square root operator */ | |
2889 | /* */ | |
2890 | /* This computes C = squareroot(A) */ | |
2891 | /* */ | |
2892 | /* res is C, the result. C may be A */ | |
2893 | /* rhs is A */ | |
2894 | /* set is the context; note that rounding mode has no effect */ | |
2895 | /* */ | |
2896 | /* C must have space for set->digits digits. */ | |
2897 | /* ------------------------------------------------------------------ */ | |
2898 | /* This uses the following varying-precision algorithm in: */ | |
2899 | /* */ | |
2900 | /* Properly Rounded Variable Precision Square Root, T. E. Hull and */ | |
2901 | /* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ | |
2902 | /* pp229-237, ACM, September 1985. */ | |
2903 | /* */ | |
2904 | /* The square-root is calculated using Newton's method, after which */ | |
2905 | /* a check is made to ensure the result is correctly rounded. */ | |
2906 | /* */ | |
2907 | /* % [Reformatted original Numerical Turing source code follows.] */ | |
2908 | /* function sqrt(x : real) : real */ | |
2909 | /* % sqrt(x) returns the properly rounded approximation to the square */ | |
2910 | /* % root of x, in the precision of the calling environment, or it */ | |
2911 | /* % fails if x < 0. */ | |
2912 | /* % t e hull and a abrham, august, 1984 */ | |
2913 | /* if x <= 0 then */ | |
2914 | /* if x < 0 then */ | |
2915 | /* assert false */ | |
2916 | /* else */ | |
2917 | /* result 0 */ | |
2918 | /* end if */ | |
2919 | /* end if */ | |
2920 | /* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ | |
2921 | /* var e := getexp(x) % exponent part of x */ | |
2922 | /* var approx : real */ | |
2923 | /* if e mod 2 = 0 then */ | |
2924 | /* approx := .259 + .819 * f % approx to root of f */ | |
2925 | /* else */ | |
2926 | /* f := f/l0 % adjustments */ | |
2927 | /* e := e + 1 % for odd */ | |
2928 | /* approx := .0819 + 2.59 * f % exponent */ | |
2929 | /* end if */ | |
2930 | /* */ | |
2931 | /* var p:= 3 */ | |
2932 | /* const maxp := currentprecision + 2 */ | |
2933 | /* loop */ | |
2934 | /* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ | |
2935 | /* precision p */ | |
2936 | /* approx := .5 * (approx + f/approx) */ | |
2937 | /* exit when p = maxp */ | |
2938 | /* end loop */ | |
2939 | /* */ | |
2940 | /* % approx is now within 1 ulp of the properly rounded square root */ | |
2941 | /* % of f; to ensure proper rounding, compare squares of (approx - */ | |
2942 | /* % l/2 ulp) and (approx + l/2 ulp) with f. */ | |
2943 | /* p := currentprecision */ | |
2944 | /* begin */ | |
2945 | /* precision p + 2 */ | |
2946 | /* const approxsubhalf := approx - setexp(.5, -p) */ | |
2947 | /* if mulru(approxsubhalf, approxsubhalf) > f then */ | |
2948 | /* approx := approx - setexp(.l, -p + 1) */ | |
2949 | /* else */ | |
2950 | /* const approxaddhalf := approx + setexp(.5, -p) */ | |
2951 | /* if mulrd(approxaddhalf, approxaddhalf) < f then */ | |
2952 | /* approx := approx + setexp(.l, -p + 1) */ | |
2953 | /* end if */ | |
2954 | /* end if */ | |
2955 | /* end */ | |
2956 | /* result setexp(approx, e div 2) % fix exponent */ | |
2957 | /* end sqrt */ | |
2958 | /* ------------------------------------------------------------------ */ | |
2959 | decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, | |
2960 | decContext *set) { | |
2961 | decContext workset, approxset; /* work contexts */ | |
2962 | decNumber dzero; /* used for constant zero */ | |
2963 | Int maxp; /* largest working precision */ | |
2964 | Int workp; /* working precision */ | |
2965 | Int residue=0; /* rounding residue */ | |
2966 | uInt status=0, ignore=0; /* status accumulators */ | |
2967 | uInt rstatus; /* .. */ | |
2968 | Int exp; /* working exponent */ | |
2969 | Int ideal; /* ideal (preferred) exponent */ | |
2970 | Int needbytes; /* work */ | |
2971 | Int dropped; /* .. */ | |
2972 | ||
2973 | #if DECSUBSET | |
2974 | decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ | |
2975 | #endif | |
2976 | /* buffer for f [needs +1 in case DECBUFFER 0] */ | |
2977 | decNumber buff[D2N(DECBUFFER+1)]; | |
2978 | /* buffer for a [needs +2 to match likely maxp] */ | |
2979 | decNumber bufa[D2N(DECBUFFER+2)]; | |
2980 | /* buffer for temporary, b [must be same size as a] */ | |
2981 | decNumber bufb[D2N(DECBUFFER+2)]; | |
2982 | decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ | |
2983 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
2984 | decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ | |
2985 | decNumber *f=buff; /* reduced fraction */ | |
2986 | decNumber *a=bufa; /* approximation to result */ | |
2987 | decNumber *b=bufb; /* intermediate result */ | |
2988 | /* buffer for temporary variable, up to 3 digits */ | |
2989 | decNumber buft[D2N(3)]; | |
2990 | decNumber *t=buft; /* up-to-3-digit constant or work */ | |
2991 | ||
2992 | #if DECCHECK | |
2993 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
2994 | #endif | |
2995 | ||
2996 | do { /* protect allocated storage */ | |
2997 | #if DECSUBSET | |
2998 | if (!set->extended) { | |
2999 | /* reduce operand and set lostDigits status, as needed */ | |
3000 | if (rhs->digits>set->digits) { | |
3001 | allocrhs=decRoundOperand(rhs, set, &status); | |
3002 | if (allocrhs==NULL) break; | |
3003 | /* [Note: 'f' allocation below could reuse this buffer if */ | |
3004 | /* used, but as this is rare they are kept separate for clarity.] */ | |
3005 | rhs=allocrhs; | |
3006 | } | |
3007 | } | |
3008 | #endif | |
3009 | /* [following code does not require input rounding] */ | |
3010 | ||
3011 | /* handle infinities and NaNs */ | |
3012 | if (SPECIALARG) { | |
3013 | if (decNumberIsInfinite(rhs)) { /* an infinity */ | |
3014 | if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; | |
3015 | else decNumberCopy(res, rhs); /* +Infinity */ | |
3016 | } | |
3017 | else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ | |
3018 | break; | |
3019 | } | |
3020 | ||
3021 | /* calculate the ideal (preferred) exponent [floor(exp/2)] */ | |
3022 | /* [We would like to write: ideal=rhs->exponent>>1, but this */ | |
3023 | /* generates a compiler warning. Generated code is the same.] */ | |
3024 | ideal=(rhs->exponent&~1)/2; /* target */ | |
3025 | ||
3026 | /* handle zeros */ | |
3027 | if (ISZERO(rhs)) { | |
3028 | decNumberCopy(res, rhs); /* could be 0 or -0 */ | |
3029 | res->exponent=ideal; /* use the ideal [safe] */ | |
3030 | /* use decFinish to clamp any out-of-range exponent, etc. */ | |
3031 | decFinish(res, set, &residue, &status); | |
3032 | break; | |
3033 | } | |
3034 | ||
3035 | /* any other -x is an oops */ | |
3036 | if (decNumberIsNegative(rhs)) { | |
3037 | status|=DEC_Invalid_operation; | |
3038 | break; | |
3039 | } | |
3040 | ||
3041 | /* space is needed for three working variables */ | |
3042 | /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ | |
3043 | /* a -- Hull's approximation -- precision, when assigned, is */ | |
3044 | /* currentprecision+1 or the input argument precision, */ | |
3045 | /* whichever is larger (+2 for use as temporary) */ | |
3046 | /* b -- intermediate temporary result (same size as a) */ | |
3047 | /* if any is too long for local storage, then allocate */ | |
3048 | workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ | |
3049 | maxp=workp+2; /* largest working precision */ | |
3050 | ||
3051 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); | |
3052 | if (needbytes>(Int)sizeof(buff)) { | |
3053 | allocbuff=(decNumber *)malloc(needbytes); | |
3054 | if (allocbuff==NULL) { /* hopeless -- abandon */ | |
3055 | status|=DEC_Insufficient_storage; | |
3056 | break;} | |
3057 | f=allocbuff; /* use the allocated space */ | |
3058 | } | |
3059 | /* a and b both need to be able to hold a maxp-length number */ | |
3060 | needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); | |
3061 | if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ | |
3062 | allocbufa=(decNumber *)malloc(needbytes); | |
3063 | allocbufb=(decNumber *)malloc(needbytes); | |
3064 | if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ | |
3065 | status|=DEC_Insufficient_storage; | |
3066 | break;} | |
3067 | a=allocbufa; /* use the allocated spaces */ | |
3068 | b=allocbufb; /* .. */ | |
3069 | } | |
3070 | ||
3071 | /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ | |
3072 | decNumberCopy(f, rhs); | |
3073 | exp=f->exponent+f->digits; /* adjusted to Hull rules */ | |
3074 | f->exponent=-(f->digits); /* to range */ | |
3075 | ||
3076 | /* set up working context */ | |
3077 | decContextDefault(&workset, DEC_INIT_DECIMAL64); | |
3078 | ||
3079 | /* [Until further notice, no error is possible and status bits */ | |
3080 | /* (Rounded, etc.) should be ignored, not accumulated.] */ | |
3081 | ||
3082 | /* Calculate initial approximation, and allow for odd exponent */ | |
3083 | workset.digits=workp; /* p for initial calculation */ | |
3084 | t->bits=0; t->digits=3; | |
3085 | a->bits=0; a->digits=3; | |
3086 | if ((exp & 1)==0) { /* even exponent */ | |
3087 | /* Set t=0.259, a=0.819 */ | |
3088 | t->exponent=-3; | |
3089 | a->exponent=-3; | |
3090 | #if DECDPUN>=3 | |
3091 | t->lsu[0]=259; | |
3092 | a->lsu[0]=819; | |
3093 | #elif DECDPUN==2 | |
3094 | t->lsu[0]=59; t->lsu[1]=2; | |
3095 | a->lsu[0]=19; a->lsu[1]=8; | |
3096 | #else | |
3097 | t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; | |
3098 | a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; | |
3099 | #endif | |
3100 | } | |
3101 | else { /* odd exponent */ | |
3102 | /* Set t=0.0819, a=2.59 */ | |
3103 | f->exponent--; /* f=f/10 */ | |
3104 | exp++; /* e=e+1 */ | |
3105 | t->exponent=-4; | |
3106 | a->exponent=-2; | |
3107 | #if DECDPUN>=3 | |
3108 | t->lsu[0]=819; | |
3109 | a->lsu[0]=259; | |
3110 | #elif DECDPUN==2 | |
3111 | t->lsu[0]=19; t->lsu[1]=8; | |
3112 | a->lsu[0]=59; a->lsu[1]=2; | |
3113 | #else | |
3114 | t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; | |
3115 | a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; | |
3116 | #endif | |
3117 | } | |
3118 | decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ | |
3119 | decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ | |
3120 | /* [a is now the initial approximation for sqrt(f), calculated with */ | |
3121 | /* currentprecision, which is also a's precision.] */ | |
3122 | ||
3123 | /* the main calculation loop */ | |
3124 | decNumberZero(&dzero); /* make 0 */ | |
3125 | decNumberZero(t); /* set t = 0.5 */ | |
3126 | t->lsu[0]=5; /* .. */ | |
3127 | t->exponent=-1; /* .. */ | |
3128 | workset.digits=3; /* initial p */ | |
3129 | for (;;) { | |
3130 | /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ | |
3131 | workset.digits=workset.digits*2-2; | |
3132 | if (workset.digits>maxp) workset.digits=maxp; | |
3133 | /* a = 0.5 * (a + f/a) */ | |
3134 | /* [calculated at p then rounded to currentprecision] */ | |
3135 | decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ | |
3136 | decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ | |
3137 | decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ | |
3138 | if (a->digits==maxp) break; /* have required digits */ | |
3139 | } /* loop */ | |
3140 | ||
3141 | /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ | |
3142 | /* now reduce to length, etc.; this needs to be done with a */ | |
3143 | /* having the correct exponent so as to handle subnormals */ | |
3144 | /* correctly */ | |
3145 | approxset=*set; /* get emin, emax, etc. */ | |
3146 | approxset.round=DEC_ROUND_HALF_EVEN; | |
3147 | a->exponent+=exp/2; /* set correct exponent */ | |
3148 | ||
3149 | rstatus=0; /* clear status */ | |
3150 | residue=0; /* .. and accumulator */ | |
3151 | decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ | |
3152 | decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ | |
3153 | ||
3154 | /* Overflow was possible if the input exponent was out-of-range, */ | |
3155 | /* in which case quit */ | |
3156 | if (rstatus&DEC_Overflow) { | |
3157 | status=rstatus; /* use the status as-is */ | |
3158 | decNumberCopy(res, a); /* copy to result */ | |
3159 | break; | |
3160 | } | |
3161 | ||
3162 | /* Preserve status except Inexact/Rounded */ | |
3163 | status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); | |
3164 | ||
3165 | /* Carry out the Hull correction */ | |
3166 | a->exponent-=exp/2; /* back to 0.1->1 */ | |
3167 | ||
3168 | /* a is now at final precision and within 1 ulp of the properly */ | |
3169 | /* rounded square root of f; to ensure proper rounding, compare */ | |
3170 | /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ | |
3171 | /* Here workset.digits=maxp and t=0.5, and a->digits determines */ | |
3172 | /* the ulp */ | |
3173 | workset.digits--; /* maxp-1 is OK now */ | |
3174 | t->exponent=-a->digits-1; /* make 0.5 ulp */ | |
3175 | decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ | |
3176 | workset.round=DEC_ROUND_UP; | |
3177 | decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ | |
3178 | decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ | |
3179 | if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ | |
3180 | /* this is the more common adjustment, though both are rare */ | |
3181 | t->exponent++; /* make 1.0 ulp */ | |
3182 | t->lsu[0]=1; /* .. */ | |
3183 | decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ | |
3184 | /* assign to approx [round to length] */ | |
3185 | approxset.emin-=exp/2; /* adjust to match a */ | |
3186 | approxset.emax-=exp/2; | |
3187 | decAddOp(a, &dzero, a, &approxset, 0, &ignore); | |
3188 | } | |
3189 | else { | |
3190 | decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ | |
3191 | workset.round=DEC_ROUND_DOWN; | |
3192 | decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ | |
3193 | decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ | |
3194 | if (decNumberIsNegative(b)) { /* b < f */ | |
3195 | t->exponent++; /* make 1.0 ulp */ | |
3196 | t->lsu[0]=1; /* .. */ | |
3197 | decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ | |
3198 | /* assign to approx [round to length] */ | |
3199 | approxset.emin-=exp/2; /* adjust to match a */ | |
3200 | approxset.emax-=exp/2; | |
3201 | decAddOp(a, &dzero, a, &approxset, 0, &ignore); | |
3202 | } | |
3203 | } | |
3204 | /* [no errors are possible in the above, and rounding/inexact during */ | |
3205 | /* estimation are irrelevant, so status was not accumulated] */ | |
3206 | ||
3207 | /* Here, 0.1 <= a < 1 (still), so adjust back */ | |
3208 | a->exponent+=exp/2; /* set correct exponent */ | |
3209 | ||
3210 | /* count droppable zeros [after any subnormal rounding] by */ | |
3211 | /* trimming a copy */ | |
3212 | decNumberCopy(b, a); | |
3213 | decTrim(b, set, 1, &dropped); /* [drops trailing zeros] */ | |
3214 | ||
3215 | /* Set Inexact and Rounded. The answer can only be exact if */ | |
3216 | /* it is short enough so that squaring it could fit in workp digits, */ | |
3217 | /* and it cannot have trailing zeros due to clamping, so these are */ | |
3218 | /* the only (relatively rare) conditions a careful check is needed */ | |
3219 | if (b->digits*2-1 > workp && !set->clamp) { /* cannot fit */ | |
3220 | status|=DEC_Inexact|DEC_Rounded; | |
3221 | } | |
3222 | else { /* could be exact/unrounded */ | |
3223 | uInt mstatus=0; /* local status */ | |
3224 | decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ | |
3225 | if (mstatus&DEC_Overflow) { /* result just won't fit */ | |
3226 | status|=DEC_Inexact|DEC_Rounded; | |
3227 | } | |
3228 | else { /* plausible */ | |
3229 | decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ | |
3230 | if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ | |
3231 | else { /* is Exact */ | |
3232 | /* here, dropped is the count of trailing zeros in 'a' */ | |
3233 | /* use closest exponent to ideal... */ | |
3234 | Int todrop=ideal-a->exponent; /* most that can be dropped */ | |
3235 | if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ | |
3236 | else { /* unrounded */ | |
3237 | if (dropped<todrop) { /* clamp to those available */ | |
3238 | todrop=dropped; | |
3239 | status|=DEC_Clamped; | |
3240 | } | |
3241 | if (todrop>0) { /* have some to drop */ | |
3242 | decShiftToLeast(a->lsu, D2U(a->digits), todrop); | |
3243 | a->exponent+=todrop; /* maintain numerical value */ | |
3244 | a->digits-=todrop; /* new length */ | |
3245 | } | |
3246 | } | |
3247 | } | |
3248 | } | |
3249 | } | |
3250 | ||
3251 | /* double-check Underflow, as perhaps the result could not have */ | |
3252 | /* been subnormal (initial argument too big), or it is now Exact */ | |
3253 | if (status&DEC_Underflow) { | |
3254 | Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ | |
3255 | /* check if truly subnormal */ | |
3256 | #if DECEXTFLAG /* DEC_Subnormal too */ | |
3257 | if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); | |
3258 | #else | |
3259 | if (ae>=set->emin*2) status&=~DEC_Underflow; | |
3260 | #endif | |
3261 | /* check if truly inexact */ | |
3262 | if (!(status&DEC_Inexact)) status&=~DEC_Underflow; | |
3263 | } | |
3264 | ||
3265 | decNumberCopy(res, a); /* a is now the result */ | |
3266 | } while(0); /* end protected */ | |
3267 | ||
3268 | if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ | |
3269 | if (allocbufa!=NULL) free(allocbufa); /* .. */ | |
3270 | if (allocbufb!=NULL) free(allocbufb); /* .. */ | |
3271 | #if DECSUBSET | |
3272 | if (allocrhs !=NULL) free(allocrhs); /* .. */ | |
3273 | #endif | |
3274 | if (status!=0) decStatus(res, status, set);/* then report status */ | |
3275 | #if DECCHECK | |
3276 | decCheckInexact(res, set); | |
3277 | #endif | |
3278 | return res; | |
3279 | } /* decNumberSquareRoot */ | |
3280 | ||
3281 | /* ------------------------------------------------------------------ */ | |
3282 | /* decNumberSubtract -- subtract two Numbers */ | |
3283 | /* */ | |
3284 | /* This computes C = A - B */ | |
3285 | /* */ | |
3286 | /* res is C, the result. C may be A and/or B (e.g., X=X-X) */ | |
3287 | /* lhs is A */ | |
3288 | /* rhs is B */ | |
3289 | /* set is the context */ | |
3290 | /* */ | |
3291 | /* C must have space for set->digits digits. */ | |
3292 | /* ------------------------------------------------------------------ */ | |
3293 | decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, | |
3294 | const decNumber *rhs, decContext *set) { | |
3295 | uInt status=0; /* accumulator */ | |
3296 | ||
3297 | decAddOp(res, lhs, rhs, set, DECNEG, &status); | |
3298 | if (status!=0) decStatus(res, status, set); | |
3299 | #if DECCHECK | |
3300 | decCheckInexact(res, set); | |
3301 | #endif | |
3302 | return res; | |
3303 | } /* decNumberSubtract */ | |
3304 | ||
3305 | /* ------------------------------------------------------------------ */ | |
3306 | /* decNumberToIntegralExact -- round-to-integral-value with InExact */ | |
3307 | /* decNumberToIntegralValue -- round-to-integral-value */ | |
3308 | /* */ | |
3309 | /* res is the result */ | |
3310 | /* rhs is input number */ | |
3311 | /* set is the context */ | |
3312 | /* */ | |
3313 | /* res must have space for any value of rhs. */ | |
3314 | /* */ | |
3315 | /* This implements the IEEE special operators and therefore treats */ | |
3316 | /* special values as valid. For finite numbers it returns */ | |
3317 | /* rescale(rhs, 0) if rhs->exponent is <0. */ | |
3318 | /* Otherwise the result is rhs (so no error is possible, except for */ | |
3319 | /* sNaN). */ | |
3320 | /* */ | |
3321 | /* The context is used for rounding mode and status after sNaN, but */ | |
3322 | /* the digits setting is ignored. The Exact version will signal */ | |
3323 | /* Inexact if the result differs numerically from rhs; the other */ | |
3324 | /* never signals Inexact. */ | |
3325 | /* ------------------------------------------------------------------ */ | |
3326 | decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, | |
3327 | decContext *set) { | |
3328 | decNumber dn; | |
3329 | decContext workset; /* working context */ | |
3330 | uInt status=0; /* accumulator */ | |
3331 | ||
3332 | #if DECCHECK | |
3333 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
3334 | #endif | |
3335 | ||
3336 | /* handle infinities and NaNs */ | |
3337 | if (SPECIALARG) { | |
3338 | if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */ | |
3339 | else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ | |
3340 | } | |
3341 | else { /* finite */ | |
3342 | /* have a finite number; no error possible (res must be big enough) */ | |
3343 | if (rhs->exponent>=0) return decNumberCopy(res, rhs); | |
3344 | /* that was easy, but if negative exponent there is work to do... */ | |
3345 | workset=*set; /* clone rounding, etc. */ | |
3346 | workset.digits=rhs->digits; /* no length rounding */ | |
3347 | workset.traps=0; /* no traps */ | |
3348 | decNumberZero(&dn); /* make a number with exponent 0 */ | |
3349 | decNumberQuantize(res, rhs, &dn, &workset); | |
3350 | status|=workset.status; | |
3351 | } | |
3352 | if (status!=0) decStatus(res, status, set); | |
3353 | return res; | |
3354 | } /* decNumberToIntegralExact */ | |
3355 | ||
3356 | decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, | |
3357 | decContext *set) { | |
3358 | decContext workset=*set; /* working context */ | |
3359 | workset.traps=0; /* no traps */ | |
3360 | decNumberToIntegralExact(res, rhs, &workset); | |
3361 | /* this never affects set, except for sNaNs; NaN will have been set */ | |
3362 | /* or propagated already, so no need to call decStatus */ | |
3363 | set->status|=workset.status&DEC_Invalid_operation; | |
3364 | return res; | |
3365 | } /* decNumberToIntegralValue */ | |
3366 | ||
3367 | /* ------------------------------------------------------------------ */ | |
3368 | /* decNumberXor -- XOR two Numbers, digitwise */ | |
3369 | /* */ | |
3370 | /* This computes C = A ^ B */ | |
3371 | /* */ | |
3372 | /* res is C, the result. C may be A and/or B (e.g., X=X^X) */ | |
3373 | /* lhs is A */ | |
3374 | /* rhs is B */ | |
3375 | /* set is the context (used for result length and error report) */ | |
3376 | /* */ | |
3377 | /* C must have space for set->digits digits. */ | |
3378 | /* */ | |
3379 | /* Logical function restrictions apply (see above); a NaN is */ | |
3380 | /* returned with Invalid_operation if a restriction is violated. */ | |
3381 | /* ------------------------------------------------------------------ */ | |
3382 | decNumber * decNumberXor(decNumber *res, const decNumber *lhs, | |
3383 | const decNumber *rhs, decContext *set) { | |
3384 | const Unit *ua, *ub; /* -> operands */ | |
3385 | const Unit *msua, *msub; /* -> operand msus */ | |
3386 | Unit *uc, *msuc; /* -> result and its msu */ | |
3387 | Int msudigs; /* digits in res msu */ | |
3388 | #if DECCHECK | |
3389 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
3390 | #endif | |
3391 | ||
3392 | if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) | |
3393 | || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { | |
3394 | decStatus(res, DEC_Invalid_operation, set); | |
3395 | return res; | |
3396 | } | |
3397 | /* operands are valid */ | |
3398 | ua=lhs->lsu; /* bottom-up */ | |
3399 | ub=rhs->lsu; /* .. */ | |
3400 | uc=res->lsu; /* .. */ | |
3401 | msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ | |
3402 | msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ | |
3403 | msuc=uc+D2U(set->digits)-1; /* -> msu of result */ | |
3404 | msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ | |
3405 | for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ | |
3406 | Unit a, b; /* extract units */ | |
3407 | if (ua>msua) a=0; | |
3408 | else a=*ua; | |
3409 | if (ub>msub) b=0; | |
3410 | else b=*ub; | |
3411 | *uc=0; /* can now write back */ | |
3412 | if (a|b) { /* maybe 1 bits to examine */ | |
3413 | Int i, j; | |
3414 | /* This loop could be unrolled and/or use BIN2BCD tables */ | |
3415 | for (i=0; i<DECDPUN; i++) { | |
3416 | if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ | |
3417 | j=a%10; | |
3418 | a=a/10; | |
3419 | j|=b%10; | |
3420 | b=b/10; | |
3421 | if (j>1) { | |
3422 | decStatus(res, DEC_Invalid_operation, set); | |
3423 | return res; | |
3424 | } | |
3425 | if (uc==msuc && i==msudigs-1) break; /* just did final digit */ | |
3426 | } /* each digit */ | |
3427 | } /* non-zero */ | |
3428 | } /* each unit */ | |
3429 | /* [here uc-1 is the msu of the result] */ | |
3430 | res->digits=decGetDigits(res->lsu, uc-res->lsu); | |
3431 | res->exponent=0; /* integer */ | |
3432 | res->bits=0; /* sign=0 */ | |
3433 | return res; /* [no status to set] */ | |
3434 | } /* decNumberXor */ | |
3435 | ||
3436 | ||
3437 | /* ================================================================== */ | |
3438 | /* Utility routines */ | |
3439 | /* ================================================================== */ | |
3440 | ||
3441 | /* ------------------------------------------------------------------ */ | |
3442 | /* decNumberClass -- return the decClass of a decNumber */ | |
3443 | /* dn -- the decNumber to test */ | |
3444 | /* set -- the context to use for Emin */ | |
3445 | /* returns the decClass enum */ | |
3446 | /* ------------------------------------------------------------------ */ | |
3447 | enum decClass decNumberClass(const decNumber *dn, decContext *set) { | |
3448 | if (decNumberIsSpecial(dn)) { | |
3449 | if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; | |
3450 | if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; | |
3451 | /* must be an infinity */ | |
3452 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; | |
3453 | return DEC_CLASS_POS_INF; | |
3454 | } | |
3455 | /* is finite */ | |
3456 | if (decNumberIsNormal(dn, set)) { /* most common */ | |
3457 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; | |
3458 | return DEC_CLASS_POS_NORMAL; | |
3459 | } | |
3460 | /* is subnormal or zero */ | |
3461 | if (decNumberIsZero(dn)) { /* most common */ | |
3462 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; | |
3463 | return DEC_CLASS_POS_ZERO; | |
3464 | } | |
3465 | if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; | |
3466 | return DEC_CLASS_POS_SUBNORMAL; | |
3467 | } /* decNumberClass */ | |
3468 | ||
3469 | /* ------------------------------------------------------------------ */ | |
3470 | /* decNumberClassToString -- convert decClass to a string */ | |
3471 | /* */ | |
3472 | /* eclass is a valid decClass */ | |
3473 | /* returns a constant string describing the class (max 13+1 chars) */ | |
3474 | /* ------------------------------------------------------------------ */ | |
3475 | const char *decNumberClassToString(enum decClass eclass) { | |
3476 | if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; | |
3477 | if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; | |
3478 | if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; | |
3479 | if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; | |
3480 | if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; | |
3481 | if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; | |
3482 | if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; | |
3483 | if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; | |
3484 | if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; | |
3485 | if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; | |
3486 | return DEC_ClassString_UN; /* Unknown */ | |
3487 | } /* decNumberClassToString */ | |
3488 | ||
3489 | /* ------------------------------------------------------------------ */ | |
3490 | /* decNumberCopy -- copy a number */ | |
3491 | /* */ | |
3492 | /* dest is the target decNumber */ | |
3493 | /* src is the source decNumber */ | |
3494 | /* returns dest */ | |
3495 | /* */ | |
3496 | /* (dest==src is allowed and is a no-op) */ | |
3497 | /* All fields are updated as required. This is a utility operation, */ | |
3498 | /* so special values are unchanged and no error is possible. */ | |
3499 | /* ------------------------------------------------------------------ */ | |
3500 | decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { | |
3501 | ||
3502 | #if DECCHECK | |
3503 | if (src==NULL) return decNumberZero(dest); | |
3504 | #endif | |
3505 | ||
3506 | if (dest==src) return dest; /* no copy required */ | |
3507 | ||
3508 | /* Use explicit assignments here as structure assignment could copy */ | |
3509 | /* more than just the lsu (for small DECDPUN). This would not affect */ | |
3510 | /* the value of the results, but could disturb test harness spill */ | |
3511 | /* checking. */ | |
3512 | dest->bits=src->bits; | |
3513 | dest->exponent=src->exponent; | |
3514 | dest->digits=src->digits; | |
3515 | dest->lsu[0]=src->lsu[0]; | |
3516 | if (src->digits>DECDPUN) { /* more Units to come */ | |
3517 | const Unit *smsup, *s; /* work */ | |
3518 | Unit *d; /* .. */ | |
3519 | /* memcpy for the remaining Units would be safe as they cannot */ | |
3520 | /* overlap. However, this explicit loop is faster in short cases. */ | |
3521 | d=dest->lsu+1; /* -> first destination */ | |
3522 | smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ | |
3523 | for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; | |
3524 | } | |
3525 | return dest; | |
3526 | } /* decNumberCopy */ | |
3527 | ||
3528 | /* ------------------------------------------------------------------ */ | |
3529 | /* decNumberCopyAbs -- quiet absolute value operator */ | |
3530 | /* */ | |
3531 | /* This sets C = abs(A) */ | |
3532 | /* */ | |
3533 | /* res is C, the result. C may be A */ | |
3534 | /* rhs is A */ | |
3535 | /* */ | |
3536 | /* C must have space for set->digits digits. */ | |
3537 | /* No exception or error can occur; this is a quiet bitwise operation.*/ | |
3538 | /* See also decNumberAbs for a checking version of this. */ | |
3539 | /* ------------------------------------------------------------------ */ | |
3540 | decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { | |
3541 | #if DECCHECK | |
3542 | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; | |
3543 | #endif | |
3544 | decNumberCopy(res, rhs); | |
3545 | res->bits&=~DECNEG; /* turn off sign */ | |
3546 | return res; | |
3547 | } /* decNumberCopyAbs */ | |
3548 | ||
3549 | /* ------------------------------------------------------------------ */ | |
3550 | /* decNumberCopyNegate -- quiet negate value operator */ | |
3551 | /* */ | |
3552 | /* This sets C = negate(A) */ | |
3553 | /* */ | |
3554 | /* res is C, the result. C may be A */ | |
3555 | /* rhs is A */ | |
3556 | /* */ | |
3557 | /* C must have space for set->digits digits. */ | |
3558 | /* No exception or error can occur; this is a quiet bitwise operation.*/ | |
3559 | /* See also decNumberMinus for a checking version of this. */ | |
3560 | /* ------------------------------------------------------------------ */ | |
3561 | decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { | |
3562 | #if DECCHECK | |
3563 | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; | |
3564 | #endif | |
3565 | decNumberCopy(res, rhs); | |
3566 | res->bits^=DECNEG; /* invert the sign */ | |
3567 | return res; | |
3568 | } /* decNumberCopyNegate */ | |
3569 | ||
3570 | /* ------------------------------------------------------------------ */ | |
3571 | /* decNumberCopySign -- quiet copy and set sign operator */ | |
3572 | /* */ | |
3573 | /* This sets C = A with the sign of B */ | |
3574 | /* */ | |
3575 | /* res is C, the result. C may be A */ | |
3576 | /* lhs is A */ | |
3577 | /* rhs is B */ | |
3578 | /* */ | |
3579 | /* C must have space for set->digits digits. */ | |
3580 | /* No exception or error can occur; this is a quiet bitwise operation.*/ | |
3581 | /* ------------------------------------------------------------------ */ | |
3582 | decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, | |
3583 | const decNumber *rhs) { | |
3584 | uByte sign; /* rhs sign */ | |
3585 | #if DECCHECK | |
3586 | if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; | |
3587 | #endif | |
3588 | sign=rhs->bits & DECNEG; /* save sign bit */ | |
3589 | decNumberCopy(res, lhs); | |
3590 | res->bits&=~DECNEG; /* clear the sign */ | |
3591 | res->bits|=sign; /* set from rhs */ | |
3592 | return res; | |
3593 | } /* decNumberCopySign */ | |
3594 | ||
3595 | /* ------------------------------------------------------------------ */ | |
3596 | /* decNumberGetBCD -- get the coefficient in BCD8 */ | |
3597 | /* dn is the source decNumber */ | |
3598 | /* bcd is the uInt array that will receive dn->digits BCD bytes, */ | |
3599 | /* most-significant at offset 0 */ | |
3600 | /* returns bcd */ | |
3601 | /* */ | |
3602 | /* bcd must have at least dn->digits bytes. No error is possible; if */ | |
3603 | /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ | |
3604 | /* ------------------------------------------------------------------ */ | |
3605 | uByte * decNumberGetBCD(const decNumber *dn, uint8_t *bcd) { | |
3606 | uByte *ub=bcd+dn->digits-1; /* -> lsd */ | |
3607 | const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ | |
3608 | ||
3609 | #if DECDPUN==1 /* trivial simple copy */ | |
3610 | for (; ub>=bcd; ub--, up++) *ub=*up; | |
3611 | #else /* chopping needed */ | |
3612 | uInt u=*up; /* work */ | |
3613 | uInt cut=DECDPUN; /* downcounter through unit */ | |
3614 | for (; ub>=bcd; ub--) { | |
3615 | *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ | |
3616 | u=u/10; | |
3617 | cut--; | |
3618 | if (cut>0) continue; /* more in this unit */ | |
3619 | up++; | |
3620 | u=*up; | |
3621 | cut=DECDPUN; | |
3622 | } | |
3623 | #endif | |
3624 | return bcd; | |
3625 | } /* decNumberGetBCD */ | |
3626 | ||
3627 | /* ------------------------------------------------------------------ */ | |
3628 | /* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ | |
3629 | /* dn is the target decNumber */ | |
3630 | /* bcd is the uInt array that will source n BCD bytes, most- */ | |
3631 | /* significant at offset 0 */ | |
3632 | /* n is the number of digits in the source BCD array (bcd) */ | |
3633 | /* returns dn */ | |
3634 | /* */ | |
3635 | /* dn must have space for at least n digits. No error is possible; */ | |
3636 | /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ | |
3637 | /* and bcd[0] zero. */ | |
3638 | /* ------------------------------------------------------------------ */ | |
3639 | decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { | |
0a322e7e | 3640 | Unit *up = dn->lsu + D2U(n) - 1; /* -> msu [target pointer] */ |
72ac97cd TM |
3641 | const uByte *ub=bcd; /* -> source msd */ |
3642 | ||
3643 | #if DECDPUN==1 /* trivial simple copy */ | |
3644 | for (; ub<bcd+n; ub++, up--) *up=*ub; | |
3645 | #else /* some assembly needed */ | |
3646 | /* calculate how many digits in msu, and hence first cut */ | |
3647 | Int cut=MSUDIGITS(n); /* [faster than remainder] */ | |
3648 | for (;up>=dn->lsu; up--) { /* each Unit from msu */ | |
3649 | *up=0; /* will take <=DECDPUN digits */ | |
3650 | for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; | |
3651 | cut=DECDPUN; /* next Unit has all digits */ | |
3652 | } | |
3653 | #endif | |
3654 | dn->digits=n; /* set digit count */ | |
3655 | return dn; | |
3656 | } /* decNumberSetBCD */ | |
3657 | ||
3658 | /* ------------------------------------------------------------------ */ | |
3659 | /* decNumberIsNormal -- test normality of a decNumber */ | |
3660 | /* dn is the decNumber to test */ | |
3661 | /* set is the context to use for Emin */ | |
3662 | /* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ | |
3663 | /* ------------------------------------------------------------------ */ | |
3664 | Int decNumberIsNormal(const decNumber *dn, decContext *set) { | |
3665 | Int ae; /* adjusted exponent */ | |
3666 | #if DECCHECK | |
3667 | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; | |
3668 | #endif | |
3669 | ||
3670 | if (decNumberIsSpecial(dn)) return 0; /* not finite */ | |
3671 | if (decNumberIsZero(dn)) return 0; /* not non-zero */ | |
3672 | ||
3673 | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ | |
3674 | if (ae<set->emin) return 0; /* is subnormal */ | |
3675 | return 1; | |
3676 | } /* decNumberIsNormal */ | |
3677 | ||
3678 | /* ------------------------------------------------------------------ */ | |
3679 | /* decNumberIsSubnormal -- test subnormality of a decNumber */ | |
3680 | /* dn is the decNumber to test */ | |
3681 | /* set is the context to use for Emin */ | |
3682 | /* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ | |
3683 | /* ------------------------------------------------------------------ */ | |
3684 | Int decNumberIsSubnormal(const decNumber *dn, decContext *set) { | |
3685 | Int ae; /* adjusted exponent */ | |
3686 | #if DECCHECK | |
3687 | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; | |
3688 | #endif | |
3689 | ||
3690 | if (decNumberIsSpecial(dn)) return 0; /* not finite */ | |
3691 | if (decNumberIsZero(dn)) return 0; /* not non-zero */ | |
3692 | ||
3693 | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ | |
3694 | if (ae<set->emin) return 1; /* is subnormal */ | |
3695 | return 0; | |
3696 | } /* decNumberIsSubnormal */ | |
3697 | ||
3698 | /* ------------------------------------------------------------------ */ | |
3699 | /* decNumberTrim -- remove insignificant zeros */ | |
3700 | /* */ | |
3701 | /* dn is the number to trim */ | |
3702 | /* returns dn */ | |
3703 | /* */ | |
3704 | /* All fields are updated as required. This is a utility operation, */ | |
3705 | /* so special values are unchanged and no error is possible. */ | |
3706 | /* ------------------------------------------------------------------ */ | |
3707 | decNumber * decNumberTrim(decNumber *dn) { | |
3708 | Int dropped; /* work */ | |
3709 | decContext set; /* .. */ | |
3710 | #if DECCHECK | |
3711 | if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; | |
3712 | #endif | |
3713 | decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ | |
3714 | return decTrim(dn, &set, 0, &dropped); | |
3715 | } /* decNumberTrim */ | |
3716 | ||
3717 | /* ------------------------------------------------------------------ */ | |
3718 | /* decNumberVersion -- return the name and version of this module */ | |
3719 | /* */ | |
3720 | /* No error is possible. */ | |
3721 | /* ------------------------------------------------------------------ */ | |
3722 | const char * decNumberVersion(void) { | |
3723 | return DECVERSION; | |
3724 | } /* decNumberVersion */ | |
3725 | ||
3726 | /* ------------------------------------------------------------------ */ | |
3727 | /* decNumberZero -- set a number to 0 */ | |
3728 | /* */ | |
3729 | /* dn is the number to set, with space for one digit */ | |
3730 | /* returns dn */ | |
3731 | /* */ | |
3732 | /* No error is possible. */ | |
3733 | /* ------------------------------------------------------------------ */ | |
3734 | /* Memset is not used as it is much slower in some environments. */ | |
3735 | decNumber * decNumberZero(decNumber *dn) { | |
3736 | ||
3737 | #if DECCHECK | |
3738 | if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; | |
3739 | #endif | |
3740 | ||
3741 | dn->bits=0; | |
3742 | dn->exponent=0; | |
3743 | dn->digits=1; | |
3744 | dn->lsu[0]=0; | |
3745 | return dn; | |
3746 | } /* decNumberZero */ | |
3747 | ||
3748 | /* ================================================================== */ | |
3749 | /* Local routines */ | |
3750 | /* ================================================================== */ | |
3751 | ||
3752 | /* ------------------------------------------------------------------ */ | |
3753 | /* decToString -- lay out a number into a string */ | |
3754 | /* */ | |
3755 | /* dn is the number to lay out */ | |
3756 | /* string is where to lay out the number */ | |
3757 | /* eng is 1 if Engineering, 0 if Scientific */ | |
3758 | /* */ | |
3759 | /* string must be at least dn->digits+14 characters long */ | |
3760 | /* No error is possible. */ | |
3761 | /* */ | |
3762 | /* Note that this routine can generate a -0 or 0.000. These are */ | |
3763 | /* never generated in subset to-number or arithmetic, but can occur */ | |
3764 | /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ | |
3765 | /* ------------------------------------------------------------------ */ | |
3766 | /* If DECCHECK is enabled the string "?" is returned if a number is */ | |
3767 | /* invalid. */ | |
3768 | static void decToString(const decNumber *dn, char *string, Flag eng) { | |
3769 | Int exp=dn->exponent; /* local copy */ | |
3770 | Int e; /* E-part value */ | |
3771 | Int pre; /* digits before the '.' */ | |
3772 | Int cut; /* for counting digits in a Unit */ | |
3773 | char *c=string; /* work [output pointer] */ | |
3774 | const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ | |
3775 | uInt u, pow; /* work */ | |
3776 | ||
3777 | #if DECCHECK | |
3778 | if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { | |
3779 | strcpy(string, "?"); | |
3780 | return;} | |
3781 | #endif | |
3782 | ||
3783 | if (decNumberIsNegative(dn)) { /* Negatives get a minus */ | |
3784 | *c='-'; | |
3785 | c++; | |
3786 | } | |
3787 | if (dn->bits&DECSPECIAL) { /* Is a special value */ | |
3788 | if (decNumberIsInfinite(dn)) { | |
3789 | strcpy(c, "Inf"); | |
3790 | strcpy(c+3, "inity"); | |
3791 | return;} | |
3792 | /* a NaN */ | |
3793 | if (dn->bits&DECSNAN) { /* signalling NaN */ | |
3794 | *c='s'; | |
3795 | c++; | |
3796 | } | |
3797 | strcpy(c, "NaN"); | |
3798 | c+=3; /* step past */ | |
3799 | /* if not a clean non-zero coefficient, that's all there is in a */ | |
3800 | /* NaN string */ | |
3801 | if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; | |
3802 | /* [drop through to add integer] */ | |
3803 | } | |
3804 | ||
3805 | /* calculate how many digits in msu, and hence first cut */ | |
3806 | cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ | |
3807 | cut--; /* power of ten for digit */ | |
3808 | ||
3809 | if (exp==0) { /* simple integer [common fastpath] */ | |
3810 | for (;up>=dn->lsu; up--) { /* each Unit from msu */ | |
3811 | u=*up; /* contains DECDPUN digits to lay out */ | |
3812 | for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); | |
3813 | cut=DECDPUN-1; /* next Unit has all digits */ | |
3814 | } | |
3815 | *c='\0'; /* terminate the string */ | |
3816 | return;} | |
3817 | ||
3818 | /* non-0 exponent -- assume plain form */ | |
3819 | pre=dn->digits+exp; /* digits before '.' */ | |
3820 | e=0; /* no E */ | |
3821 | if ((exp>0) || (pre<-5)) { /* need exponential form */ | |
3822 | e=exp+dn->digits-1; /* calculate E value */ | |
3823 | pre=1; /* assume one digit before '.' */ | |
3824 | if (eng && (e!=0)) { /* engineering: may need to adjust */ | |
3825 | Int adj; /* adjustment */ | |
3826 | /* The C remainder operator is undefined for negative numbers, so */ | |
3827 | /* a positive remainder calculation must be used here */ | |
3828 | if (e<0) { | |
3829 | adj=(-e)%3; | |
3830 | if (adj!=0) adj=3-adj; | |
3831 | } | |
3832 | else { /* e>0 */ | |
3833 | adj=e%3; | |
3834 | } | |
3835 | e=e-adj; | |
3836 | /* if dealing with zero still produce an exponent which is a */ | |
3837 | /* multiple of three, as expected, but there will only be the */ | |
3838 | /* one zero before the E, still. Otherwise note the padding. */ | |
3839 | if (!ISZERO(dn)) pre+=adj; | |
3840 | else { /* is zero */ | |
3841 | if (adj!=0) { /* 0.00Esnn needed */ | |
3842 | e=e+3; | |
3843 | pre=-(2-adj); | |
3844 | } | |
3845 | } /* zero */ | |
3846 | } /* eng */ | |
3847 | } /* need exponent */ | |
3848 | ||
3849 | /* lay out the digits of the coefficient, adding 0s and . as needed */ | |
3850 | u=*up; | |
3851 | if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ | |
3852 | Int n=pre; | |
3853 | for (; pre>0; pre--, c++, cut--) { | |
3854 | if (cut<0) { /* need new Unit */ | |
3855 | if (up==dn->lsu) break; /* out of input digits (pre>digits) */ | |
3856 | up--; | |
3857 | cut=DECDPUN-1; | |
3858 | u=*up; | |
3859 | } | |
3860 | TODIGIT(u, cut, c, pow); | |
3861 | } | |
3862 | if (n<dn->digits) { /* more to come, after '.' */ | |
3863 | *c='.'; c++; | |
3864 | for (;; c++, cut--) { | |
3865 | if (cut<0) { /* need new Unit */ | |
3866 | if (up==dn->lsu) break; /* out of input digits */ | |
3867 | up--; | |
3868 | cut=DECDPUN-1; | |
3869 | u=*up; | |
3870 | } | |
3871 | TODIGIT(u, cut, c, pow); | |
3872 | } | |
3873 | } | |
3874 | else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ | |
3875 | } | |
3876 | else { /* 0.xxx or 0.000xxx form */ | |
3877 | *c='0'; c++; | |
3878 | *c='.'; c++; | |
3879 | for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ | |
3880 | for (; ; c++, cut--) { | |
3881 | if (cut<0) { /* need new Unit */ | |
3882 | if (up==dn->lsu) break; /* out of input digits */ | |
3883 | up--; | |
3884 | cut=DECDPUN-1; | |
3885 | u=*up; | |
3886 | } | |
3887 | TODIGIT(u, cut, c, pow); | |
3888 | } | |
3889 | } | |
3890 | ||
3891 | /* Finally add the E-part, if needed. It will never be 0, has a | |
3892 | base maximum and minimum of +999999999 through -999999999, but | |
3893 | could range down to -1999999998 for anormal numbers */ | |
3894 | if (e!=0) { | |
3895 | Flag had=0; /* 1=had non-zero */ | |
3896 | *c='E'; c++; | |
3897 | *c='+'; c++; /* assume positive */ | |
3898 | u=e; /* .. */ | |
3899 | if (e<0) { | |
3900 | *(c-1)='-'; /* oops, need - */ | |
3901 | u=-e; /* uInt, please */ | |
3902 | } | |
3903 | /* lay out the exponent [_itoa or equivalent is not ANSI C] */ | |
3904 | for (cut=9; cut>=0; cut--) { | |
3905 | TODIGIT(u, cut, c, pow); | |
3906 | if (*c=='0' && !had) continue; /* skip leading zeros */ | |
3907 | had=1; /* had non-0 */ | |
3908 | c++; /* step for next */ | |
3909 | } /* cut */ | |
3910 | } | |
3911 | *c='\0'; /* terminate the string (all paths) */ | |
3912 | return; | |
3913 | } /* decToString */ | |
3914 | ||
3915 | /* ------------------------------------------------------------------ */ | |
3916 | /* decAddOp -- add/subtract operation */ | |
3917 | /* */ | |
3918 | /* This computes C = A + B */ | |
3919 | /* */ | |
3920 | /* res is C, the result. C may be A and/or B (e.g., X=X+X) */ | |
3921 | /* lhs is A */ | |
3922 | /* rhs is B */ | |
3923 | /* set is the context */ | |
3924 | /* negate is DECNEG if rhs should be negated, or 0 otherwise */ | |
3925 | /* status accumulates status for the caller */ | |
3926 | /* */ | |
3927 | /* C must have space for set->digits digits. */ | |
3928 | /* Inexact in status must be 0 for correct Exact zero sign in result */ | |
3929 | /* ------------------------------------------------------------------ */ | |
3930 | /* If possible, the coefficient is calculated directly into C. */ | |
3931 | /* However, if: */ | |
3932 | /* -- a digits+1 calculation is needed because the numbers are */ | |
3933 | /* unaligned and span more than set->digits digits */ | |
3934 | /* -- a carry to digits+1 digits looks possible */ | |
3935 | /* -- C is the same as A or B, and the result would destructively */ | |
3936 | /* overlap the A or B coefficient */ | |
3937 | /* then the result must be calculated into a temporary buffer. In */ | |
3938 | /* this case a local (stack) buffer is used if possible, and only if */ | |
3939 | /* too long for that does malloc become the final resort. */ | |
3940 | /* */ | |
3941 | /* Misalignment is handled as follows: */ | |
3942 | /* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ | |
3943 | /* BPad: Apply the padding by a combination of shifting (whole */ | |
3944 | /* units) and multiplication (part units). */ | |
3945 | /* */ | |
3946 | /* Addition, especially x=x+1, is speed-critical. */ | |
3947 | /* The static buffer is larger than might be expected to allow for */ | |
67cc32eb | 3948 | /* calls from higher-level functions (notably exp). */ |
72ac97cd TM |
3949 | /* ------------------------------------------------------------------ */ |
3950 | static decNumber * decAddOp(decNumber *res, const decNumber *lhs, | |
3951 | const decNumber *rhs, decContext *set, | |
3952 | uByte negate, uInt *status) { | |
3953 | #if DECSUBSET | |
3954 | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ | |
3955 | decNumber *allocrhs=NULL; /* .., rhs */ | |
3956 | #endif | |
3957 | Int rhsshift; /* working shift (in Units) */ | |
3958 | Int maxdigits; /* longest logical length */ | |
3959 | Int mult; /* multiplier */ | |
3960 | Int residue; /* rounding accumulator */ | |
3961 | uByte bits; /* result bits */ | |
3962 | Flag diffsign; /* non-0 if arguments have different sign */ | |
3963 | Unit *acc; /* accumulator for result */ | |
3964 | Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ | |
3965 | /* allocations when called from */ | |
3966 | /* other operations, notable exp] */ | |
3967 | Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ | |
3968 | Int reqdigits=set->digits; /* local copy; requested DIGITS */ | |
3969 | Int padding; /* work */ | |
3970 | ||
3971 | #if DECCHECK | |
3972 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
3973 | #endif | |
3974 | ||
3975 | do { /* protect allocated storage */ | |
3976 | #if DECSUBSET | |
3977 | if (!set->extended) { | |
3978 | /* reduce operands and set lostDigits status, as needed */ | |
3979 | if (lhs->digits>reqdigits) { | |
3980 | alloclhs=decRoundOperand(lhs, set, status); | |
3981 | if (alloclhs==NULL) break; | |
3982 | lhs=alloclhs; | |
3983 | } | |
3984 | if (rhs->digits>reqdigits) { | |
3985 | allocrhs=decRoundOperand(rhs, set, status); | |
3986 | if (allocrhs==NULL) break; | |
3987 | rhs=allocrhs; | |
3988 | } | |
3989 | } | |
3990 | #endif | |
3991 | /* [following code does not require input rounding] */ | |
3992 | ||
3993 | /* note whether signs differ [used all paths] */ | |
3994 | diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); | |
3995 | ||
3996 | /* handle infinities and NaNs */ | |
3997 | if (SPECIALARGS) { /* a special bit set */ | |
3998 | if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ | |
3999 | decNaNs(res, lhs, rhs, set, status); | |
4000 | else { /* one or two infinities */ | |
4001 | if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ | |
4002 | /* two infinities with different signs is invalid */ | |
4003 | if (decNumberIsInfinite(rhs) && diffsign) { | |
4004 | *status|=DEC_Invalid_operation; | |
4005 | break; | |
4006 | } | |
4007 | bits=lhs->bits & DECNEG; /* get sign from LHS */ | |
4008 | } | |
4009 | else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ | |
4010 | bits|=DECINF; | |
4011 | decNumberZero(res); | |
4012 | res->bits=bits; /* set +/- infinity */ | |
4013 | } /* an infinity */ | |
4014 | break; | |
4015 | } | |
4016 | ||
4017 | /* Quick exit for add 0s; return the non-0, modified as need be */ | |
4018 | if (ISZERO(lhs)) { | |
4019 | Int adjust; /* work */ | |
4020 | Int lexp=lhs->exponent; /* save in case LHS==RES */ | |
4021 | bits=lhs->bits; /* .. */ | |
4022 | residue=0; /* clear accumulator */ | |
4023 | decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ | |
4024 | res->bits^=negate; /* flip if rhs was negated */ | |
4025 | #if DECSUBSET | |
4026 | if (set->extended) { /* exponents on zeros count */ | |
4027 | #endif | |
4028 | /* exponent will be the lower of the two */ | |
4029 | adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ | |
4030 | if (ISZERO(res)) { /* both 0: special IEEE 854 rules */ | |
4031 | if (adjust<0) res->exponent=lexp; /* set exponent */ | |
4032 | /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ | |
4033 | if (diffsign) { | |
4034 | if (set->round!=DEC_ROUND_FLOOR) res->bits=0; | |
4035 | else res->bits=DECNEG; /* preserve 0 sign */ | |
4036 | } | |
4037 | } | |
4038 | else { /* non-0 res */ | |
4039 | if (adjust<0) { /* 0-padding needed */ | |
4040 | if ((res->digits-adjust)>set->digits) { | |
4041 | adjust=res->digits-set->digits; /* to fit exactly */ | |
4042 | *status|=DEC_Rounded; /* [but exact] */ | |
4043 | } | |
4044 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); | |
4045 | res->exponent+=adjust; /* set the exponent. */ | |
4046 | } | |
4047 | } /* non-0 res */ | |
4048 | #if DECSUBSET | |
4049 | } /* extended */ | |
4050 | #endif | |
4051 | decFinish(res, set, &residue, status); /* clean and finalize */ | |
4052 | break;} | |
4053 | ||
4054 | if (ISZERO(rhs)) { /* [lhs is non-zero] */ | |
4055 | Int adjust; /* work */ | |
4056 | Int rexp=rhs->exponent; /* save in case RHS==RES */ | |
4057 | bits=rhs->bits; /* be clean */ | |
4058 | residue=0; /* clear accumulator */ | |
4059 | decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ | |
4060 | #if DECSUBSET | |
4061 | if (set->extended) { /* exponents on zeros count */ | |
4062 | #endif | |
4063 | /* exponent will be the lower of the two */ | |
4064 | /* [0-0 case handled above] */ | |
4065 | adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ | |
4066 | if (adjust<0) { /* 0-padding needed */ | |
4067 | if ((res->digits-adjust)>set->digits) { | |
4068 | adjust=res->digits-set->digits; /* to fit exactly */ | |
4069 | *status|=DEC_Rounded; /* [but exact] */ | |
4070 | } | |
4071 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); | |
4072 | res->exponent+=adjust; /* set the exponent. */ | |
4073 | } | |
4074 | #if DECSUBSET | |
4075 | } /* extended */ | |
4076 | #endif | |
4077 | decFinish(res, set, &residue, status); /* clean and finalize */ | |
4078 | break;} | |
4079 | ||
4080 | /* [NB: both fastpath and mainpath code below assume these cases */ | |
4081 | /* (notably 0-0) have already been handled] */ | |
4082 | ||
4083 | /* calculate the padding needed to align the operands */ | |
4084 | padding=rhs->exponent-lhs->exponent; | |
4085 | ||
4086 | /* Fastpath cases where the numbers are aligned and normal, the RHS */ | |
4087 | /* is all in one unit, no operand rounding is needed, and no carry, */ | |
4088 | /* lengthening, or borrow is needed */ | |
4089 | if (padding==0 | |
4090 | && rhs->digits<=DECDPUN | |
4091 | && rhs->exponent>=set->emin /* [some normals drop through] */ | |
4092 | && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ | |
4093 | && rhs->digits<=reqdigits | |
4094 | && lhs->digits<=reqdigits) { | |
4095 | Int partial=*lhs->lsu; | |
4096 | if (!diffsign) { /* adding */ | |
4097 | partial+=*rhs->lsu; | |
4098 | if ((partial<=DECDPUNMAX) /* result fits in unit */ | |
4099 | && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ | |
4100 | partial<(Int)powers[lhs->digits])) { /* .. */ | |
4101 | if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ | |
4102 | *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ | |
4103 | break; | |
4104 | } | |
4105 | /* else drop out for careful add */ | |
4106 | } | |
4107 | else { /* signs differ */ | |
4108 | partial-=*rhs->lsu; | |
4109 | if (partial>0) { /* no borrow needed, and non-0 result */ | |
4110 | if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ | |
4111 | *res->lsu=(Unit)partial; | |
4112 | /* this could have reduced digits [but result>0] */ | |
4113 | res->digits=decGetDigits(res->lsu, D2U(res->digits)); | |
4114 | break; | |
4115 | } | |
4116 | /* else drop out for careful subtract */ | |
4117 | } | |
4118 | } | |
4119 | ||
4120 | /* Now align (pad) the lhs or rhs so they can be added or */ | |
4121 | /* subtracted, as necessary. If one number is much larger than */ | |
4122 | /* the other (that is, if in plain form there is a least one */ | |
4123 | /* digit between the lowest digit of one and the highest of the */ | |
4124 | /* other) padding with up to DIGITS-1 trailing zeros may be */ | |
4125 | /* needed; then apply rounding (as exotic rounding modes may be */ | |
4126 | /* affected by the residue). */ | |
4127 | rhsshift=0; /* rhs shift to left (padding) in Units */ | |
4128 | bits=lhs->bits; /* assume sign is that of LHS */ | |
4129 | mult=1; /* likely multiplier */ | |
4130 | ||
4131 | /* [if padding==0 the operands are aligned; no padding is needed] */ | |
4132 | if (padding!=0) { | |
4133 | /* some padding needed; always pad the RHS, as any required */ | |
4134 | /* padding can then be effected by a simple combination of */ | |
4135 | /* shifts and a multiply */ | |
4136 | Flag swapped=0; | |
4137 | if (padding<0) { /* LHS needs the padding */ | |
4138 | const decNumber *t; | |
4139 | padding=-padding; /* will be +ve */ | |
4140 | bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ | |
4141 | t=lhs; lhs=rhs; rhs=t; | |
4142 | swapped=1; | |
4143 | } | |
4144 | ||
4145 | /* If, after pad, rhs would be longer than lhs by digits+1 or */ | |
4146 | /* more then lhs cannot affect the answer, except as a residue, */ | |
4147 | /* so only need to pad up to a length of DIGITS+1. */ | |
4148 | if (rhs->digits+padding > lhs->digits+reqdigits+1) { | |
4149 | /* The RHS is sufficient */ | |
4150 | /* for residue use the relative sign indication... */ | |
4151 | Int shift=reqdigits-rhs->digits; /* left shift needed */ | |
4152 | residue=1; /* residue for rounding */ | |
4153 | if (diffsign) residue=-residue; /* signs differ */ | |
4154 | /* copy, shortening if necessary */ | |
4155 | decCopyFit(res, rhs, set, &residue, status); | |
4156 | /* if it was already shorter, then need to pad with zeros */ | |
4157 | if (shift>0) { | |
4158 | res->digits=decShiftToMost(res->lsu, res->digits, shift); | |
4159 | res->exponent-=shift; /* adjust the exponent. */ | |
4160 | } | |
4161 | /* flip the result sign if unswapped and rhs was negated */ | |
4162 | if (!swapped) res->bits^=negate; | |
4163 | decFinish(res, set, &residue, status); /* done */ | |
4164 | break;} | |
4165 | ||
4166 | /* LHS digits may affect result */ | |
4167 | rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ | |
4168 | mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ | |
4169 | } /* padding needed */ | |
4170 | ||
4171 | if (diffsign) mult=-mult; /* signs differ */ | |
4172 | ||
4173 | /* determine the longer operand */ | |
4174 | maxdigits=rhs->digits+padding; /* virtual length of RHS */ | |
4175 | if (lhs->digits>maxdigits) maxdigits=lhs->digits; | |
4176 | ||
4177 | /* Decide on the result buffer to use; if possible place directly */ | |
4178 | /* into result. */ | |
4179 | acc=res->lsu; /* assume add direct to result */ | |
4180 | /* If destructive overlap, or the number is too long, or a carry or */ | |
4181 | /* borrow to DIGITS+1 might be possible, a buffer must be used. */ | |
4182 | /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ | |
4183 | if ((maxdigits>=reqdigits) /* is, or could be, too large */ | |
4184 | || (res==rhs && rhsshift>0)) { /* destructive overlap */ | |
4185 | /* buffer needed, choose it; units for maxdigits digits will be */ | |
4186 | /* needed, +1 Unit for carry or borrow */ | |
4187 | Int need=D2U(maxdigits)+1; | |
4188 | acc=accbuff; /* assume use local buffer */ | |
4189 | if (need*sizeof(Unit)>sizeof(accbuff)) { | |
4190 | /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ | |
4191 | allocacc=(Unit *)malloc(need*sizeof(Unit)); | |
4192 | if (allocacc==NULL) { /* hopeless -- abandon */ | |
4193 | *status|=DEC_Insufficient_storage; | |
4194 | break;} | |
4195 | acc=allocacc; | |
4196 | } | |
4197 | } | |
4198 | ||
4199 | res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ | |
4200 | res->exponent=lhs->exponent; /* .. operands (even if aliased) */ | |
4201 | ||
4202 | #if DECTRACE | |
4203 | decDumpAr('A', lhs->lsu, D2U(lhs->digits)); | |
4204 | decDumpAr('B', rhs->lsu, D2U(rhs->digits)); | |
4205 | printf(" :h: %ld %ld\n", rhsshift, mult); | |
4206 | #endif | |
4207 | ||
4208 | /* add [A+B*m] or subtract [A+B*(-m)] */ | |
4209 | res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), | |
4210 | rhs->lsu, D2U(rhs->digits), | |
4211 | rhsshift, acc, mult) | |
4212 | *DECDPUN; /* [units -> digits] */ | |
4213 | if (res->digits<0) { /* borrowed... */ | |
4214 | res->digits=-res->digits; | |
4215 | res->bits^=DECNEG; /* flip the sign */ | |
4216 | } | |
4217 | #if DECTRACE | |
4218 | decDumpAr('+', acc, D2U(res->digits)); | |
4219 | #endif | |
4220 | ||
4221 | /* If a buffer was used the result must be copied back, possibly */ | |
4222 | /* shortening. (If no buffer was used then the result must have */ | |
4223 | /* fit, so can't need rounding and residue must be 0.) */ | |
4224 | residue=0; /* clear accumulator */ | |
4225 | if (acc!=res->lsu) { | |
4226 | #if DECSUBSET | |
4227 | if (set->extended) { /* round from first significant digit */ | |
4228 | #endif | |
4229 | /* remove leading zeros that were added due to rounding up to */ | |
4230 | /* integral Units -- before the test for rounding. */ | |
4231 | if (res->digits>reqdigits) | |
4232 | res->digits=decGetDigits(acc, D2U(res->digits)); | |
4233 | decSetCoeff(res, set, acc, res->digits, &residue, status); | |
4234 | #if DECSUBSET | |
4235 | } | |
4236 | else { /* subset arithmetic rounds from original significant digit */ | |
4237 | /* May have an underestimate. This only occurs when both */ | |
4238 | /* numbers fit in DECDPUN digits and are padding with a */ | |
4239 | /* negative multiple (-10, -100...) and the top digit(s) become */ | |
4240 | /* 0. (This only matters when using X3.274 rules where the */ | |
4241 | /* leading zero could be included in the rounding.) */ | |
4242 | if (res->digits<maxdigits) { | |
4243 | *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ | |
4244 | res->digits=maxdigits; | |
4245 | } | |
4246 | else { | |
4247 | /* remove leading zeros that added due to rounding up to */ | |
4248 | /* integral Units (but only those in excess of the original */ | |
4249 | /* maxdigits length, unless extended) before test for rounding. */ | |
4250 | if (res->digits>reqdigits) { | |
4251 | res->digits=decGetDigits(acc, D2U(res->digits)); | |
4252 | if (res->digits<maxdigits) res->digits=maxdigits; | |
4253 | } | |
4254 | } | |
4255 | decSetCoeff(res, set, acc, res->digits, &residue, status); | |
4256 | /* Now apply rounding if needed before removing leading zeros. */ | |
4257 | /* This is safe because subnormals are not a possibility */ | |
4258 | if (residue!=0) { | |
4259 | decApplyRound(res, set, residue, status); | |
4260 | residue=0; /* did what needed to be done */ | |
4261 | } | |
4262 | } /* subset */ | |
4263 | #endif | |
4264 | } /* used buffer */ | |
4265 | ||
4266 | /* strip leading zeros [these were left on in case of subset subtract] */ | |
4267 | res->digits=decGetDigits(res->lsu, D2U(res->digits)); | |
4268 | ||
4269 | /* apply checks and rounding */ | |
4270 | decFinish(res, set, &residue, status); | |
4271 | ||
4272 | /* "When the sum of two operands with opposite signs is exactly */ | |
4273 | /* zero, the sign of that sum shall be '+' in all rounding modes */ | |
4274 | /* except round toward -Infinity, in which mode that sign shall be */ | |
4275 | /* '-'." [Subset zeros also never have '-', set by decFinish.] */ | |
4276 | if (ISZERO(res) && diffsign | |
4277 | #if DECSUBSET | |
4278 | && set->extended | |
4279 | #endif | |
4280 | && (*status&DEC_Inexact)==0) { | |
4281 | if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ | |
4282 | else res->bits&=~DECNEG; /* sign + */ | |
4283 | } | |
4284 | } while(0); /* end protected */ | |
4285 | ||
4286 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ | |
4287 | #if DECSUBSET | |
4288 | if (allocrhs!=NULL) free(allocrhs); /* .. */ | |
4289 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
4290 | #endif | |
4291 | return res; | |
4292 | } /* decAddOp */ | |
4293 | ||
4294 | /* ------------------------------------------------------------------ */ | |
4295 | /* decDivideOp -- division operation */ | |
4296 | /* */ | |
4297 | /* This routine performs the calculations for all four division */ | |
4298 | /* operators (divide, divideInteger, remainder, remainderNear). */ | |
4299 | /* */ | |
4300 | /* C=A op B */ | |
4301 | /* */ | |
4302 | /* res is C, the result. C may be A and/or B (e.g., X=X/X) */ | |
4303 | /* lhs is A */ | |
4304 | /* rhs is B */ | |
4305 | /* set is the context */ | |
4306 | /* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ | |
4307 | /* status is the usual accumulator */ | |
4308 | /* */ | |
4309 | /* C must have space for set->digits digits. */ | |
4310 | /* */ | |
4311 | /* ------------------------------------------------------------------ */ | |
4312 | /* The underlying algorithm of this routine is the same as in the */ | |
4313 | /* 1981 S/370 implementation, that is, non-restoring long division */ | |
4314 | /* with bi-unit (rather than bi-digit) estimation for each unit */ | |
4315 | /* multiplier. In this pseudocode overview, complications for the */ | |
4316 | /* Remainder operators and division residues for exact rounding are */ | |
4317 | /* omitted for clarity. */ | |
4318 | /* */ | |
4319 | /* Prepare operands and handle special values */ | |
4320 | /* Test for x/0 and then 0/x */ | |
4321 | /* Exp =Exp1 - Exp2 */ | |
4322 | /* Exp =Exp +len(var1) -len(var2) */ | |
4323 | /* Sign=Sign1 * Sign2 */ | |
4324 | /* Pad accumulator (Var1) to double-length with 0's (pad1) */ | |
4325 | /* Pad Var2 to same length as Var1 */ | |
4326 | /* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ | |
4327 | /* have=0 */ | |
4328 | /* Do until (have=digits+1 OR residue=0) */ | |
4329 | /* if exp<0 then if integer divide/residue then leave */ | |
4330 | /* this_unit=0 */ | |
4331 | /* Do forever */ | |
4332 | /* compare numbers */ | |
4333 | /* if <0 then leave inner_loop */ | |
4334 | /* if =0 then (* quick exit without subtract *) do */ | |
4335 | /* this_unit=this_unit+1; output this_unit */ | |
4336 | /* leave outer_loop; end */ | |
4337 | /* Compare lengths of numbers (mantissae): */ | |
4338 | /* If same then tops2=msu2pair -- {units 1&2 of var2} */ | |
4339 | /* else tops2=msu2plus -- {0, unit 1 of var2} */ | |
4340 | /* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ | |
4341 | /* mult=tops1/tops2 -- Good and safe guess at divisor */ | |
4342 | /* if mult=0 then mult=1 */ | |
4343 | /* this_unit=this_unit+mult */ | |
4344 | /* subtract */ | |
4345 | /* end inner_loop */ | |
4346 | /* if have\=0 | this_unit\=0 then do */ | |
4347 | /* output this_unit */ | |
4348 | /* have=have+1; end */ | |
4349 | /* var2=var2/10 */ | |
4350 | /* exp=exp-1 */ | |
4351 | /* end outer_loop */ | |
4352 | /* exp=exp+1 -- set the proper exponent */ | |
4353 | /* if have=0 then generate answer=0 */ | |
4354 | /* Return (Result is defined by Var1) */ | |
4355 | /* */ | |
4356 | /* ------------------------------------------------------------------ */ | |
4357 | /* Two working buffers are needed during the division; one (digits+ */ | |
4358 | /* 1) to accumulate the result, and the other (up to 2*digits+1) for */ | |
4359 | /* long subtractions. These are acc and var1 respectively. */ | |
4360 | /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ | |
4361 | /* The static buffers may be larger than might be expected to allow */ | |
67cc32eb | 4362 | /* for calls from higher-level functions (notably exp). */ |
72ac97cd TM |
4363 | /* ------------------------------------------------------------------ */ |
4364 | static decNumber * decDivideOp(decNumber *res, | |
4365 | const decNumber *lhs, const decNumber *rhs, | |
4366 | decContext *set, Flag op, uInt *status) { | |
4367 | #if DECSUBSET | |
4368 | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ | |
4369 | decNumber *allocrhs=NULL; /* .., rhs */ | |
4370 | #endif | |
4371 | Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ | |
4372 | Unit *acc=accbuff; /* -> accumulator array for result */ | |
4373 | Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ | |
4374 | Unit *accnext; /* -> where next digit will go */ | |
4375 | Int acclength; /* length of acc needed [Units] */ | |
4376 | Int accunits; /* count of units accumulated */ | |
4377 | Int accdigits; /* count of digits accumulated */ | |
4378 | ||
4379 | Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)*sizeof(Unit)]; /* buffer for var1 */ | |
4380 | Unit *var1=varbuff; /* -> var1 array for long subtraction */ | |
4381 | Unit *varalloc=NULL; /* -> allocated buffer, iff used */ | |
4382 | Unit *msu1; /* -> msu of var1 */ | |
4383 | ||
4384 | const Unit *var2; /* -> var2 array */ | |
4385 | const Unit *msu2; /* -> msu of var2 */ | |
4386 | Int msu2plus; /* msu2 plus one [does not vary] */ | |
4387 | eInt msu2pair; /* msu2 pair plus one [does not vary] */ | |
4388 | ||
4389 | Int var1units, var2units; /* actual lengths */ | |
4390 | Int var2ulen; /* logical length (units) */ | |
4391 | Int var1initpad=0; /* var1 initial padding (digits) */ | |
4392 | Int maxdigits; /* longest LHS or required acc length */ | |
4393 | Int mult; /* multiplier for subtraction */ | |
4394 | Unit thisunit; /* current unit being accumulated */ | |
4395 | Int residue; /* for rounding */ | |
4396 | Int reqdigits=set->digits; /* requested DIGITS */ | |
4397 | Int exponent; /* working exponent */ | |
4398 | Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ | |
4399 | uByte bits; /* working sign */ | |
4400 | Unit *target; /* work */ | |
4401 | const Unit *source; /* .. */ | |
79af3572 | 4402 | uLong const *pow; /* .. */ |
72ac97cd TM |
4403 | Int shift, cut; /* .. */ |
4404 | #if DECSUBSET | |
4405 | Int dropped; /* work */ | |
4406 | #endif | |
4407 | ||
4408 | #if DECCHECK | |
4409 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
4410 | #endif | |
4411 | ||
4412 | do { /* protect allocated storage */ | |
4413 | #if DECSUBSET | |
4414 | if (!set->extended) { | |
4415 | /* reduce operands and set lostDigits status, as needed */ | |
4416 | if (lhs->digits>reqdigits) { | |
4417 | alloclhs=decRoundOperand(lhs, set, status); | |
4418 | if (alloclhs==NULL) break; | |
4419 | lhs=alloclhs; | |
4420 | } | |
4421 | if (rhs->digits>reqdigits) { | |
4422 | allocrhs=decRoundOperand(rhs, set, status); | |
4423 | if (allocrhs==NULL) break; | |
4424 | rhs=allocrhs; | |
4425 | } | |
4426 | } | |
4427 | #endif | |
4428 | /* [following code does not require input rounding] */ | |
4429 | ||
4430 | bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ | |
4431 | ||
4432 | /* handle infinities and NaNs */ | |
4433 | if (SPECIALARGS) { /* a special bit set */ | |
4434 | if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ | |
4435 | decNaNs(res, lhs, rhs, set, status); | |
4436 | break; | |
4437 | } | |
4438 | /* one or two infinities */ | |
4439 | if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ | |
4440 | if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ | |
4441 | op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ | |
4442 | *status|=DEC_Invalid_operation; | |
4443 | break; | |
4444 | } | |
4445 | /* [Note that infinity/0 raises no exceptions] */ | |
4446 | decNumberZero(res); | |
4447 | res->bits=bits|DECINF; /* set +/- infinity */ | |
4448 | break; | |
4449 | } | |
4450 | else { /* RHS (divisor) is infinite */ | |
4451 | residue=0; | |
4452 | if (op&(REMAINDER|REMNEAR)) { | |
4453 | /* result is [finished clone of] lhs */ | |
4454 | decCopyFit(res, lhs, set, &residue, status); | |
4455 | } | |
4456 | else { /* a division */ | |
4457 | decNumberZero(res); | |
4458 | res->bits=bits; /* set +/- zero */ | |
4459 | /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ | |
4460 | /* is a 0 with infinitely negative exponent, clamped to minimum */ | |
4461 | if (op&DIVIDE) { | |
4462 | res->exponent=set->emin-set->digits+1; | |
4463 | *status|=DEC_Clamped; | |
4464 | } | |
4465 | } | |
4466 | decFinish(res, set, &residue, status); | |
4467 | break; | |
4468 | } | |
4469 | } | |
4470 | ||
4471 | /* handle 0 rhs (x/0) */ | |
4472 | if (ISZERO(rhs)) { /* x/0 is always exceptional */ | |
4473 | if (ISZERO(lhs)) { | |
4474 | decNumberZero(res); /* [after lhs test] */ | |
4475 | *status|=DEC_Division_undefined;/* 0/0 will become NaN */ | |
4476 | } | |
4477 | else { | |
4478 | decNumberZero(res); | |
4479 | if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; | |
4480 | else { | |
4481 | *status|=DEC_Division_by_zero; /* x/0 */ | |
4482 | res->bits=bits|DECINF; /* .. is +/- Infinity */ | |
4483 | } | |
4484 | } | |
4485 | break;} | |
4486 | ||
4487 | /* handle 0 lhs (0/x) */ | |
4488 | if (ISZERO(lhs)) { /* 0/x [x!=0] */ | |
4489 | #if DECSUBSET | |
4490 | if (!set->extended) decNumberZero(res); | |
4491 | else { | |
4492 | #endif | |
4493 | if (op&DIVIDE) { | |
4494 | residue=0; | |
4495 | exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ | |
4496 | decNumberCopy(res, lhs); /* [zeros always fit] */ | |
4497 | res->bits=bits; /* sign as computed */ | |
4498 | res->exponent=exponent; /* exponent, too */ | |
4499 | decFinalize(res, set, &residue, status); /* check exponent */ | |
4500 | } | |
4501 | else if (op&DIVIDEINT) { | |
4502 | decNumberZero(res); /* integer 0 */ | |
4503 | res->bits=bits; /* sign as computed */ | |
4504 | } | |
4505 | else { /* a remainder */ | |
4506 | exponent=rhs->exponent; /* [save in case overwrite] */ | |
4507 | decNumberCopy(res, lhs); /* [zeros always fit] */ | |
4508 | if (exponent<res->exponent) res->exponent=exponent; /* use lower */ | |
4509 | } | |
4510 | #if DECSUBSET | |
4511 | } | |
4512 | #endif | |
4513 | break;} | |
4514 | ||
4515 | /* Precalculate exponent. This starts off adjusted (and hence fits */ | |
4516 | /* in 31 bits) and becomes the usual unadjusted exponent as the */ | |
4517 | /* division proceeds. The order of evaluation is important, here, */ | |
4518 | /* to avoid wrap. */ | |
4519 | exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); | |
4520 | ||
4521 | /* If the working exponent is -ve, then some quick exits are */ | |
4522 | /* possible because the quotient is known to be <1 */ | |
4523 | /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ | |
4524 | if (exponent<0 && !(op==DIVIDE)) { | |
4525 | if (op&DIVIDEINT) { | |
4526 | decNumberZero(res); /* integer part is 0 */ | |
4527 | #if DECSUBSET | |
4528 | if (set->extended) | |
4529 | #endif | |
4530 | res->bits=bits; /* set +/- zero */ | |
4531 | break;} | |
4532 | /* fastpath remainders so long as the lhs has the smaller */ | |
4533 | /* (or equal) exponent */ | |
4534 | if (lhs->exponent<=rhs->exponent) { | |
4535 | if (op&REMAINDER || exponent<-1) { | |
4536 | /* It is REMAINDER or safe REMNEAR; result is [finished */ | |
4537 | /* clone of] lhs (r = x - 0*y) */ | |
4538 | residue=0; | |
4539 | decCopyFit(res, lhs, set, &residue, status); | |
4540 | decFinish(res, set, &residue, status); | |
4541 | break; | |
4542 | } | |
4543 | /* [unsafe REMNEAR drops through] */ | |
4544 | } | |
4545 | } /* fastpaths */ | |
4546 | ||
4547 | /* Long (slow) division is needed; roll up the sleeves... */ | |
4548 | ||
4549 | /* The accumulator will hold the quotient of the division. */ | |
4550 | /* If it needs to be too long for stack storage, then allocate. */ | |
4551 | acclength=D2U(reqdigits+DECDPUN); /* in Units */ | |
4552 | if (acclength*sizeof(Unit)>sizeof(accbuff)) { | |
4553 | /* printf("malloc dvacc %ld units\n", acclength); */ | |
4554 | allocacc=(Unit *)malloc(acclength*sizeof(Unit)); | |
4555 | if (allocacc==NULL) { /* hopeless -- abandon */ | |
4556 | *status|=DEC_Insufficient_storage; | |
4557 | break;} | |
4558 | acc=allocacc; /* use the allocated space */ | |
4559 | } | |
4560 | ||
4561 | /* var1 is the padded LHS ready for subtractions. */ | |
4562 | /* If it needs to be too long for stack storage, then allocate. */ | |
4563 | /* The maximum units needed for var1 (long subtraction) is: */ | |
4564 | /* Enough for */ | |
4565 | /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ | |
4566 | /* or (lhs->digits) -- to allow for long lhs */ | |
4567 | /* whichever is larger */ | |
4568 | /* +1 -- for rounding of slide to right */ | |
4569 | /* +1 -- for leading 0s */ | |
4570 | /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ | |
4571 | /* [Note: unused units do not participate in decUnitAddSub data] */ | |
4572 | maxdigits=rhs->digits+reqdigits-1; | |
4573 | if (lhs->digits>maxdigits) maxdigits=lhs->digits; | |
4574 | var1units=D2U(maxdigits)+2; | |
4575 | /* allocate a guard unit above msu1 for REMAINDERNEAR */ | |
4576 | if (!(op&DIVIDE)) var1units++; | |
4577 | if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { | |
4578 | /* printf("malloc dvvar %ld units\n", var1units+1); */ | |
4579 | varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); | |
4580 | if (varalloc==NULL) { /* hopeless -- abandon */ | |
4581 | *status|=DEC_Insufficient_storage; | |
4582 | break;} | |
4583 | var1=varalloc; /* use the allocated space */ | |
4584 | } | |
4585 | ||
4586 | /* Extend the lhs and rhs to full long subtraction length. The lhs */ | |
4587 | /* is truly extended into the var1 buffer, with 0 padding, so a */ | |
4588 | /* subtract in place is always possible. The rhs (var2) has */ | |
4589 | /* virtual padding (implemented by decUnitAddSub). */ | |
4590 | /* One guard unit was allocated above msu1 for rem=rem+rem in */ | |
4591 | /* REMAINDERNEAR. */ | |
4592 | msu1=var1+var1units-1; /* msu of var1 */ | |
4593 | source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ | |
4594 | for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; | |
4595 | for (; target>=var1; target--) *target=0; | |
4596 | ||
4597 | /* rhs (var2) is left-aligned with var1 at the start */ | |
4598 | var2ulen=var1units; /* rhs logical length (units) */ | |
4599 | var2units=D2U(rhs->digits); /* rhs actual length (units) */ | |
4600 | var2=rhs->lsu; /* -> rhs array */ | |
4601 | msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ | |
4602 | /* now set up the variables which will be used for estimating the */ | |
4603 | /* multiplication factor. If these variables are not exact, add */ | |
4604 | /* 1 to make sure that the multiplier is never overestimated. */ | |
4605 | msu2plus=*msu2; /* it's value .. */ | |
4606 | if (var2units>1) msu2plus++; /* .. +1 if any more */ | |
4607 | msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ | |
4608 | if (var2units>1) { /* .. [else treat 2nd as 0] */ | |
4609 | msu2pair+=*(msu2-1); /* .. */ | |
4610 | if (var2units>2) msu2pair++; /* .. +1 if any more */ | |
4611 | } | |
4612 | ||
4613 | /* The calculation is working in units, which may have leading zeros, */ | |
4614 | /* but the exponent was calculated on the assumption that they are */ | |
4615 | /* both left-aligned. Adjust the exponent to compensate: add the */ | |
4616 | /* number of leading zeros in var1 msu and subtract those in var2 msu. */ | |
4617 | /* [This is actually done by counting the digits and negating, as */ | |
4618 | /* lead1=DECDPUN-digits1, and similarly for lead2.] */ | |
4619 | for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; | |
4620 | for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; | |
4621 | ||
4622 | /* Now, if doing an integer divide or remainder, ensure that */ | |
4623 | /* the result will be Unit-aligned. To do this, shift the var1 */ | |
4624 | /* accumulator towards least if need be. (It's much easier to */ | |
4625 | /* do this now than to reassemble the residue afterwards, if */ | |
4626 | /* doing a remainder.) Also ensure the exponent is not negative. */ | |
4627 | if (!(op&DIVIDE)) { | |
4628 | Unit *u; /* work */ | |
4629 | /* save the initial 'false' padding of var1, in digits */ | |
4630 | var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; | |
4631 | /* Determine the shift to do. */ | |
4632 | if (exponent<0) cut=-exponent; | |
4633 | else cut=DECDPUN-exponent%DECDPUN; | |
4634 | decShiftToLeast(var1, var1units, cut); | |
4635 | exponent+=cut; /* maintain numerical value */ | |
4636 | var1initpad-=cut; /* .. and reduce padding */ | |
4637 | /* clean any most-significant units which were just emptied */ | |
4638 | for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; | |
4639 | } /* align */ | |
4640 | else { /* is DIVIDE */ | |
4641 | maxexponent=lhs->exponent-rhs->exponent; /* save */ | |
4642 | /* optimization: if the first iteration will just produce 0, */ | |
4643 | /* preadjust to skip it [valid for DIVIDE only] */ | |
4644 | if (*msu1<*msu2) { | |
4645 | var2ulen--; /* shift down */ | |
4646 | exponent-=DECDPUN; /* update the exponent */ | |
4647 | } | |
4648 | } | |
4649 | ||
4650 | /* ---- start the long-division loops ------------------------------ */ | |
4651 | accunits=0; /* no units accumulated yet */ | |
4652 | accdigits=0; /* .. or digits */ | |
4653 | accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ | |
4654 | for (;;) { /* outer forever loop */ | |
4655 | thisunit=0; /* current unit assumed 0 */ | |
4656 | /* find the next unit */ | |
4657 | for (;;) { /* inner forever loop */ | |
4658 | /* strip leading zero units [from either pre-adjust or from */ | |
4659 | /* subtract last time around]. Leave at least one unit. */ | |
4660 | for (; *msu1==0 && msu1>var1; msu1--) var1units--; | |
4661 | ||
4662 | if (var1units<var2ulen) break; /* var1 too low for subtract */ | |
4663 | if (var1units==var2ulen) { /* unit-by-unit compare needed */ | |
4664 | /* compare the two numbers, from msu */ | |
4665 | const Unit *pv1, *pv2; | |
4666 | Unit v2; /* units to compare */ | |
4667 | pv2=msu2; /* -> msu */ | |
4668 | for (pv1=msu1; ; pv1--, pv2--) { | |
4669 | /* v1=*pv1 -- always OK */ | |
4670 | v2=0; /* assume in padding */ | |
4671 | if (pv2>=var2) v2=*pv2; /* in range */ | |
4672 | if (*pv1!=v2) break; /* no longer the same */ | |
4673 | if (pv1==var1) break; /* done; leave pv1 as is */ | |
4674 | } | |
4675 | /* here when all inspected or a difference seen */ | |
4676 | if (*pv1<v2) break; /* var1 too low to subtract */ | |
4677 | if (*pv1==v2) { /* var1 == var2 */ | |
4678 | /* reach here if var1 and var2 are identical; subtraction */ | |
4679 | /* would increase digit by one, and the residue will be 0 so */ | |
4680 | /* the calculation is done; leave the loop with residue=0. */ | |
4681 | thisunit++; /* as though subtracted */ | |
4682 | *var1=0; /* set var1 to 0 */ | |
4683 | var1units=1; /* .. */ | |
4684 | break; /* from inner */ | |
4685 | } /* var1 == var2 */ | |
4686 | /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ | |
4687 | /* Estimate the multiplier (there's always a msu1-1)... */ | |
4688 | /* Bring in two units of var2 to provide a good estimate. */ | |
4689 | mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); | |
4690 | } /* lengths the same */ | |
4691 | else { /* var1units > var2ulen, so subtraction is safe */ | |
4692 | /* The var2 msu is one unit towards the lsu of the var1 msu, */ | |
4693 | /* so only one unit for var2 can be used. */ | |
4694 | mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); | |
4695 | } | |
4696 | if (mult==0) mult=1; /* must always be at least 1 */ | |
4697 | /* subtraction needed; var1 is > var2 */ | |
4698 | thisunit=(Unit)(thisunit+mult); /* accumulate */ | |
4699 | /* subtract var1-var2, into var1; only the overlap needs */ | |
4700 | /* processing, as this is an in-place calculation */ | |
4701 | shift=var2ulen-var2units; | |
4702 | #if DECTRACE | |
4703 | decDumpAr('1', &var1[shift], var1units-shift); | |
4704 | decDumpAr('2', var2, var2units); | |
4705 | printf("m=%ld\n", -mult); | |
4706 | #endif | |
4707 | decUnitAddSub(&var1[shift], var1units-shift, | |
4708 | var2, var2units, 0, | |
4709 | &var1[shift], -mult); | |
4710 | #if DECTRACE | |
4711 | decDumpAr('#', &var1[shift], var1units-shift); | |
4712 | #endif | |
4713 | /* var1 now probably has leading zeros; these are removed at the */ | |
4714 | /* top of the inner loop. */ | |
4715 | } /* inner loop */ | |
4716 | ||
4717 | /* The next unit has been calculated in full; unless it's a */ | |
4718 | /* leading zero, add to acc */ | |
4719 | if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ | |
4720 | *accnext=thisunit; /* store in accumulator */ | |
4721 | /* account exactly for the new digits */ | |
4722 | if (accunits==0) { | |
4723 | accdigits++; /* at least one */ | |
4724 | for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; | |
4725 | } | |
4726 | else accdigits+=DECDPUN; | |
4727 | accunits++; /* update count */ | |
4728 | accnext--; /* ready for next */ | |
4729 | if (accdigits>reqdigits) break; /* have enough digits */ | |
4730 | } | |
4731 | ||
4732 | /* if the residue is zero, the operation is done (unless divide */ | |
4733 | /* or divideInteger and still not enough digits yet) */ | |
4734 | if (*var1==0 && var1units==1) { /* residue is 0 */ | |
4735 | if (op&(REMAINDER|REMNEAR)) break; | |
4736 | if ((op&DIVIDE) && (exponent<=maxexponent)) break; | |
4737 | /* [drop through if divideInteger] */ | |
4738 | } | |
4739 | /* also done enough if calculating remainder or integer */ | |
4740 | /* divide and just did the last ('units') unit */ | |
4741 | if (exponent==0 && !(op&DIVIDE)) break; | |
4742 | ||
4743 | /* to get here, var1 is less than var2, so divide var2 by the per- */ | |
4744 | /* Unit power of ten and go for the next digit */ | |
4745 | var2ulen--; /* shift down */ | |
4746 | exponent-=DECDPUN; /* update the exponent */ | |
4747 | } /* outer loop */ | |
4748 | ||
4749 | /* ---- division is complete --------------------------------------- */ | |
4750 | /* here: acc has at least reqdigits+1 of good results (or fewer */ | |
4751 | /* if early stop), starting at accnext+1 (its lsu) */ | |
4752 | /* var1 has any residue at the stopping point */ | |
4753 | /* accunits is the number of digits collected in acc */ | |
4754 | if (accunits==0) { /* acc is 0 */ | |
4755 | accunits=1; /* show have a unit .. */ | |
4756 | accdigits=1; /* .. */ | |
4757 | *accnext=0; /* .. whose value is 0 */ | |
4758 | } | |
4759 | else accnext++; /* back to last placed */ | |
4760 | /* accnext now -> lowest unit of result */ | |
4761 | ||
4762 | residue=0; /* assume no residue */ | |
4763 | if (op&DIVIDE) { | |
4764 | /* record the presence of any residue, for rounding */ | |
4765 | if (*var1!=0 || var1units>1) residue=1; | |
4766 | else { /* no residue */ | |
4767 | /* Had an exact division; clean up spurious trailing 0s. */ | |
4768 | /* There will be at most DECDPUN-1, from the final multiply, */ | |
4769 | /* and then only if the result is non-0 (and even) and the */ | |
4770 | /* exponent is 'loose'. */ | |
4771 | #if DECDPUN>1 | |
4772 | Unit lsu=*accnext; | |
4773 | if (!(lsu&0x01) && (lsu!=0)) { | |
4774 | /* count the trailing zeros */ | |
4775 | Int drop=0; | |
4776 | for (;; drop++) { /* [will terminate because lsu!=0] */ | |
4777 | if (exponent>=maxexponent) break; /* don't chop real 0s */ | |
4778 | #if DECDPUN<=4 | |
4779 | if ((lsu-QUOT10(lsu, drop+1) | |
4780 | *powers[drop+1])!=0) break; /* found non-0 digit */ | |
4781 | #else | |
4782 | if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ | |
4783 | #endif | |
4784 | exponent++; | |
4785 | } | |
4786 | if (drop>0) { | |
4787 | accunits=decShiftToLeast(accnext, accunits, drop); | |
4788 | accdigits=decGetDigits(accnext, accunits); | |
4789 | accunits=D2U(accdigits); | |
4790 | /* [exponent was adjusted in the loop] */ | |
4791 | } | |
4792 | } /* neither odd nor 0 */ | |
4793 | #endif | |
4794 | } /* exact divide */ | |
4795 | } /* divide */ | |
4796 | else /* op!=DIVIDE */ { | |
4797 | /* check for coefficient overflow */ | |
4798 | if (accdigits+exponent>reqdigits) { | |
4799 | *status|=DEC_Division_impossible; | |
4800 | break; | |
4801 | } | |
4802 | if (op & (REMAINDER|REMNEAR)) { | |
4803 | /* [Here, the exponent will be 0, because var1 was adjusted */ | |
4804 | /* appropriately.] */ | |
4805 | Int postshift; /* work */ | |
4806 | Flag wasodd=0; /* integer was odd */ | |
4807 | Unit *quotlsu; /* for save */ | |
4808 | Int quotdigits; /* .. */ | |
4809 | ||
4810 | bits=lhs->bits; /* remainder sign is always as lhs */ | |
4811 | ||
4812 | /* Fastpath when residue is truly 0 is worthwhile [and */ | |
4813 | /* simplifies the code below] */ | |
4814 | if (*var1==0 && var1units==1) { /* residue is 0 */ | |
4815 | Int exp=lhs->exponent; /* save min(exponents) */ | |
4816 | if (rhs->exponent<exp) exp=rhs->exponent; | |
4817 | decNumberZero(res); /* 0 coefficient */ | |
4818 | #if DECSUBSET | |
4819 | if (set->extended) | |
4820 | #endif | |
4821 | res->exponent=exp; /* .. with proper exponent */ | |
4822 | res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ | |
4823 | decFinish(res, set, &residue, status); /* might clamp */ | |
4824 | break; | |
4825 | } | |
4826 | /* note if the quotient was odd */ | |
4827 | if (*accnext & 0x01) wasodd=1; /* acc is odd */ | |
4828 | quotlsu=accnext; /* save in case need to reinspect */ | |
4829 | quotdigits=accdigits; /* .. */ | |
4830 | ||
4831 | /* treat the residue, in var1, as the value to return, via acc */ | |
4832 | /* calculate the unused zero digits. This is the smaller of: */ | |
4833 | /* var1 initial padding (saved above) */ | |
4834 | /* var2 residual padding, which happens to be given by: */ | |
4835 | postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; | |
4836 | /* [the 'exponent' term accounts for the shifts during divide] */ | |
4837 | if (var1initpad<postshift) postshift=var1initpad; | |
4838 | ||
4839 | /* shift var1 the requested amount, and adjust its digits */ | |
4840 | var1units=decShiftToLeast(var1, var1units, postshift); | |
4841 | accnext=var1; | |
4842 | accdigits=decGetDigits(var1, var1units); | |
4843 | accunits=D2U(accdigits); | |
4844 | ||
4845 | exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ | |
4846 | if (rhs->exponent<exponent) exponent=rhs->exponent; | |
4847 | ||
4848 | /* Now correct the result if doing remainderNear; if it */ | |
4849 | /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ | |
4850 | /* the integer was odd then the result should be rem-rhs. */ | |
4851 | if (op&REMNEAR) { | |
4852 | Int compare, tarunits; /* work */ | |
4853 | Unit *up; /* .. */ | |
4854 | /* calculate remainder*2 into the var1 buffer (which has */ | |
4855 | /* 'headroom' of an extra unit and hence enough space) */ | |
4856 | /* [a dedicated 'double' loop would be faster, here] */ | |
4857 | tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, | |
4858 | 0, accnext, 1); | |
4859 | /* decDumpAr('r', accnext, tarunits); */ | |
4860 | ||
4861 | /* Here, accnext (var1) holds tarunits Units with twice the */ | |
4862 | /* remainder's coefficient, which must now be compared to the */ | |
4863 | /* RHS. The remainder's exponent may be smaller than the RHS's. */ | |
4864 | compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), | |
4865 | rhs->exponent-exponent); | |
4866 | if (compare==BADINT) { /* deep trouble */ | |
4867 | *status|=DEC_Insufficient_storage; | |
4868 | break;} | |
4869 | ||
4870 | /* now restore the remainder by dividing by two; the lsu */ | |
4871 | /* is known to be even. */ | |
4872 | for (up=accnext; up<accnext+tarunits; up++) { | |
4873 | Int half; /* half to add to lower unit */ | |
4874 | half=*up & 0x01; | |
4875 | *up/=2; /* [shift] */ | |
4876 | if (!half) continue; | |
6402cbbb | 4877 | *(up-1)+=DIV_ROUND_UP(DECDPUNMAX, 2); |
72ac97cd TM |
4878 | } |
4879 | /* [accunits still describes the original remainder length] */ | |
4880 | ||
4881 | if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ | |
4882 | Int exp, expunits, exprem; /* work */ | |
4883 | /* This is effectively causing round-up of the quotient, */ | |
4884 | /* so if it was the rare case where it was full and all */ | |
4885 | /* nines, it would overflow and hence division-impossible */ | |
4886 | /* should be raised */ | |
4887 | Flag allnines=0; /* 1 if quotient all nines */ | |
4888 | if (quotdigits==reqdigits) { /* could be borderline */ | |
4889 | for (up=quotlsu; ; up++) { | |
4890 | if (quotdigits>DECDPUN) { | |
4891 | if (*up!=DECDPUNMAX) break;/* non-nines */ | |
4892 | } | |
4893 | else { /* this is the last Unit */ | |
4894 | if (*up==powers[quotdigits]-1) allnines=1; | |
4895 | break; | |
4896 | } | |
4897 | quotdigits-=DECDPUN; /* checked those digits */ | |
4898 | } /* up */ | |
4899 | } /* borderline check */ | |
4900 | if (allnines) { | |
4901 | *status|=DEC_Division_impossible; | |
4902 | break;} | |
4903 | ||
4904 | /* rem-rhs is needed; the sign will invert. Again, var1 */ | |
4905 | /* can safely be used for the working Units array. */ | |
4906 | exp=rhs->exponent-exponent; /* RHS padding needed */ | |
4907 | /* Calculate units and remainder from exponent. */ | |
4908 | expunits=exp/DECDPUN; | |
4909 | exprem=exp%DECDPUN; | |
4910 | /* subtract [A+B*(-m)]; the result will always be negative */ | |
4911 | accunits=-decUnitAddSub(accnext, accunits, | |
4912 | rhs->lsu, D2U(rhs->digits), | |
4913 | expunits, accnext, -(Int)powers[exprem]); | |
4914 | accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ | |
4915 | accunits=D2U(accdigits); /* and recalculate the units for copy */ | |
4916 | /* [exponent is as for original remainder] */ | |
4917 | bits^=DECNEG; /* flip the sign */ | |
4918 | } | |
4919 | } /* REMNEAR */ | |
4920 | } /* REMAINDER or REMNEAR */ | |
4921 | } /* not DIVIDE */ | |
4922 | ||
4923 | /* Set exponent and bits */ | |
4924 | res->exponent=exponent; | |
4925 | res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ | |
4926 | ||
4927 | /* Now the coefficient. */ | |
4928 | decSetCoeff(res, set, accnext, accdigits, &residue, status); | |
4929 | ||
4930 | decFinish(res, set, &residue, status); /* final cleanup */ | |
4931 | ||
4932 | #if DECSUBSET | |
4933 | /* If a divide then strip trailing zeros if subset [after round] */ | |
4934 | if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, &dropped); | |
4935 | #endif | |
4936 | } while(0); /* end protected */ | |
4937 | ||
4938 | if (varalloc!=NULL) free(varalloc); /* drop any storage used */ | |
4939 | if (allocacc!=NULL) free(allocacc); /* .. */ | |
4940 | #if DECSUBSET | |
4941 | if (allocrhs!=NULL) free(allocrhs); /* .. */ | |
4942 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
4943 | #endif | |
4944 | return res; | |
4945 | } /* decDivideOp */ | |
4946 | ||
4947 | /* ------------------------------------------------------------------ */ | |
4948 | /* decMultiplyOp -- multiplication operation */ | |
4949 | /* */ | |
4950 | /* This routine performs the multiplication C=A x B. */ | |
4951 | /* */ | |
4952 | /* res is C, the result. C may be A and/or B (e.g., X=X*X) */ | |
4953 | /* lhs is A */ | |
4954 | /* rhs is B */ | |
4955 | /* set is the context */ | |
4956 | /* status is the usual accumulator */ | |
4957 | /* */ | |
4958 | /* C must have space for set->digits digits. */ | |
4959 | /* */ | |
4960 | /* ------------------------------------------------------------------ */ | |
4961 | /* 'Classic' multiplication is used rather than Karatsuba, as the */ | |
4962 | /* latter would give only a minor improvement for the short numbers */ | |
4963 | /* expected to be handled most (and uses much more memory). */ | |
4964 | /* */ | |
4965 | /* There are two major paths here: the general-purpose ('old code') */ | |
4966 | /* path which handles all DECDPUN values, and a fastpath version */ | |
4967 | /* which is used if 64-bit ints are available, DECDPUN<=4, and more */ | |
4968 | /* than two calls to decUnitAddSub would be made. */ | |
4969 | /* */ | |
4970 | /* The fastpath version lumps units together into 8-digit or 9-digit */ | |
4971 | /* chunks, and also uses a lazy carry strategy to minimise expensive */ | |
4972 | /* 64-bit divisions. The chunks are then broken apart again into */ | |
4973 | /* units for continuing processing. Despite this overhead, the */ | |
4974 | /* fastpath can speed up some 16-digit operations by 10x (and much */ | |
4975 | /* more for higher-precision calculations). */ | |
4976 | /* */ | |
4977 | /* A buffer always has to be used for the accumulator; in the */ | |
4978 | /* fastpath, buffers are also always needed for the chunked copies of */ | |
4979 | /* of the operand coefficients. */ | |
4980 | /* Static buffers are larger than needed just for multiply, to allow */ | |
4981 | /* for calls from other operations (notably exp). */ | |
4982 | /* ------------------------------------------------------------------ */ | |
4983 | #define FASTMUL (DECUSE64 && DECDPUN<5) | |
4984 | static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, | |
4985 | const decNumber *rhs, decContext *set, | |
4986 | uInt *status) { | |
4987 | Int accunits; /* Units of accumulator in use */ | |
4988 | Int exponent; /* work */ | |
4989 | Int residue=0; /* rounding residue */ | |
4990 | uByte bits; /* result sign */ | |
4991 | Unit *acc; /* -> accumulator Unit array */ | |
4992 | Int needbytes; /* size calculator */ | |
4993 | void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ | |
4994 | Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ | |
4995 | /* *4 for calls from other operations) */ | |
4996 | const Unit *mer, *mermsup; /* work */ | |
4997 | Int madlength; /* Units in multiplicand */ | |
4998 | Int shift; /* Units to shift multiplicand by */ | |
4999 | ||
5000 | #if FASTMUL | |
5001 | /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ | |
5002 | /* (DECDPUN is 2 or 4) then work in base 10**8 */ | |
5003 | #if DECDPUN & 1 /* odd */ | |
5004 | #define FASTBASE 1000000000 /* base */ | |
5005 | #define FASTDIGS 9 /* digits in base */ | |
5006 | #define FASTLAZY 18 /* carry resolution point [1->18] */ | |
5007 | #else | |
5008 | #define FASTBASE 100000000 | |
5009 | #define FASTDIGS 8 | |
5010 | #define FASTLAZY 1844 /* carry resolution point [1->1844] */ | |
5011 | #endif | |
5012 | /* three buffers are used, two for chunked copies of the operands */ | |
5013 | /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ | |
5014 | /* lazy carry evaluation */ | |
5015 | uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ | |
5016 | uInt *zlhi=zlhibuff; /* -> lhs array */ | |
5017 | uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ | |
5018 | uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ | |
5019 | uInt *zrhi=zrhibuff; /* -> rhs array */ | |
5020 | uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ | |
5021 | uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ | |
5022 | /* [allocacc is shared for both paths, as only one will run] */ | |
5023 | uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ | |
5024 | #if DECDPUN==1 | |
5025 | Int zoff; /* accumulator offset */ | |
5026 | #endif | |
5027 | uInt *lip, *rip; /* item pointers */ | |
5028 | uInt *lmsi, *rmsi; /* most significant items */ | |
5029 | Int ilhs, irhs, iacc; /* item counts in the arrays */ | |
5030 | Int lazy; /* lazy carry counter */ | |
5031 | uLong lcarry; /* uLong carry */ | |
5032 | uInt carry; /* carry (NB not uLong) */ | |
5033 | Int count; /* work */ | |
5034 | const Unit *cup; /* .. */ | |
5035 | Unit *up; /* .. */ | |
5036 | uLong *lp; /* .. */ | |
5037 | Int p; /* .. */ | |
5038 | #endif | |
5039 | ||
5040 | #if DECSUBSET | |
5041 | decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ | |
5042 | decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ | |
5043 | #endif | |
5044 | ||
5045 | #if DECCHECK | |
5046 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
5047 | #endif | |
5048 | ||
5049 | /* precalculate result sign */ | |
5050 | bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); | |
5051 | ||
5052 | /* handle infinities and NaNs */ | |
5053 | if (SPECIALARGS) { /* a special bit set */ | |
5054 | if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ | |
5055 | decNaNs(res, lhs, rhs, set, status); | |
5056 | return res;} | |
5057 | /* one or two infinities; Infinity * 0 is invalid */ | |
5058 | if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) | |
5059 | ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { | |
5060 | *status|=DEC_Invalid_operation; | |
5061 | return res;} | |
5062 | decNumberZero(res); | |
5063 | res->bits=bits|DECINF; /* infinity */ | |
5064 | return res;} | |
5065 | ||
5066 | /* For best speed, as in DMSRCN [the original Rexx numerics */ | |
5067 | /* module], use the shorter number as the multiplier (rhs) and */ | |
5068 | /* the longer as the multiplicand (lhs) to minimise the number of */ | |
5069 | /* adds (partial products) */ | |
5070 | if (lhs->digits<rhs->digits) { /* swap... */ | |
5071 | const decNumber *hold=lhs; | |
5072 | lhs=rhs; | |
5073 | rhs=hold; | |
5074 | } | |
5075 | ||
5076 | do { /* protect allocated storage */ | |
5077 | #if DECSUBSET | |
5078 | if (!set->extended) { | |
5079 | /* reduce operands and set lostDigits status, as needed */ | |
5080 | if (lhs->digits>set->digits) { | |
5081 | alloclhs=decRoundOperand(lhs, set, status); | |
5082 | if (alloclhs==NULL) break; | |
5083 | lhs=alloclhs; | |
5084 | } | |
5085 | if (rhs->digits>set->digits) { | |
5086 | allocrhs=decRoundOperand(rhs, set, status); | |
5087 | if (allocrhs==NULL) break; | |
5088 | rhs=allocrhs; | |
5089 | } | |
5090 | } | |
5091 | #endif | |
5092 | /* [following code does not require input rounding] */ | |
5093 | ||
5094 | #if FASTMUL /* fastpath can be used */ | |
5095 | /* use the fast path if there are enough digits in the shorter */ | |
5096 | /* operand to make the setup and takedown worthwhile */ | |
5097 | #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ | |
5098 | if (rhs->digits>NEEDTWO) { /* use fastpath... */ | |
5099 | /* calculate the number of elements in each array */ | |
5100 | ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ | |
5101 | irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ | |
5102 | iacc=ilhs+irhs; | |
5103 | ||
5104 | /* allocate buffers if required, as usual */ | |
5105 | needbytes=ilhs*sizeof(uInt); | |
5106 | if (needbytes>(Int)sizeof(zlhibuff)) { | |
5107 | alloclhi=(uInt *)malloc(needbytes); | |
5108 | zlhi=alloclhi;} | |
5109 | needbytes=irhs*sizeof(uInt); | |
5110 | if (needbytes>(Int)sizeof(zrhibuff)) { | |
5111 | allocrhi=(uInt *)malloc(needbytes); | |
5112 | zrhi=allocrhi;} | |
5113 | ||
5114 | /* Allocating the accumulator space needs a special case when */ | |
5115 | /* DECDPUN=1 because when converting the accumulator to Units */ | |
5116 | /* after the multiplication each 8-byte item becomes 9 1-byte */ | |
5117 | /* units. Therefore iacc extra bytes are needed at the front */ | |
5118 | /* (rounded up to a multiple of 8 bytes), and the uLong */ | |
5119 | /* accumulator starts offset the appropriate number of units */ | |
5120 | /* to the right to avoid overwrite during the unchunking. */ | |
5121 | needbytes=iacc*sizeof(uLong); | |
5122 | #if DECDPUN==1 | |
5123 | zoff=(iacc+7)/8; /* items to offset by */ | |
5124 | needbytes+=zoff*8; | |
5125 | #endif | |
5126 | if (needbytes>(Int)sizeof(zaccbuff)) { | |
5127 | allocacc=(uLong *)malloc(needbytes); | |
5128 | zacc=(uLong *)allocacc;} | |
5129 | if (zlhi==NULL||zrhi==NULL||zacc==NULL) { | |
5130 | *status|=DEC_Insufficient_storage; | |
5131 | break;} | |
5132 | ||
5133 | acc=(Unit *)zacc; /* -> target Unit array */ | |
5134 | #if DECDPUN==1 | |
5135 | zacc+=zoff; /* start uLong accumulator to right */ | |
5136 | #endif | |
5137 | ||
5138 | /* assemble the chunked copies of the left and right sides */ | |
5139 | for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) | |
5140 | for (p=0, *lip=0; p<FASTDIGS && count>0; | |
5141 | p+=DECDPUN, cup++, count-=DECDPUN) | |
5142 | *lip+=*cup*powers[p]; | |
5143 | lmsi=lip-1; /* save -> msi */ | |
5144 | for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) | |
5145 | for (p=0, *rip=0; p<FASTDIGS && count>0; | |
5146 | p+=DECDPUN, cup++, count-=DECDPUN) | |
5147 | *rip+=*cup*powers[p]; | |
5148 | rmsi=rip-1; /* save -> msi */ | |
5149 | ||
5150 | /* zero the accumulator */ | |
5151 | for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; | |
5152 | ||
5153 | /* Start the multiplication */ | |
5154 | /* Resolving carries can dominate the cost of accumulating the */ | |
5155 | /* partial products, so this is only done when necessary. */ | |
5156 | /* Each uLong item in the accumulator can hold values up to */ | |
5157 | /* 2**64-1, and each partial product can be as large as */ | |
5158 | /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ | |
5159 | /* itself 18.4 times in a uLong without overflowing, so during */ | |
5160 | /* the main calculation resolution is carried out every 18th */ | |
5161 | /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ | |
5162 | /* partial products can be added to themselves 1844.6 times in */ | |
5163 | /* a uLong without overflowing, so intermediate carry */ | |
5164 | /* resolution occurs only every 14752 digits. Hence for common */ | |
5165 | /* short numbers usually only the one final carry resolution */ | |
5166 | /* occurs. */ | |
5167 | /* (The count is set via FASTLAZY to simplify experiments to */ | |
5168 | /* measure the value of this approach: a 35% improvement on a */ | |
5169 | /* [34x34] multiply.) */ | |
5170 | lazy=FASTLAZY; /* carry delay count */ | |
5171 | for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ | |
5172 | lp=zacc+(rip-zrhi); /* where to add the lhs */ | |
5173 | for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ | |
5174 | *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ | |
5175 | } /* lip loop */ | |
5176 | lazy--; | |
5177 | if (lazy>0 && rip!=rmsi) continue; | |
5178 | lazy=FASTLAZY; /* reset delay count */ | |
5179 | /* spin up the accumulator resolving overflows */ | |
5180 | for (lp=zacc; lp<zacc+iacc; lp++) { | |
5181 | if (*lp<FASTBASE) continue; /* it fits */ | |
5182 | lcarry=*lp/FASTBASE; /* top part [slow divide] */ | |
5183 | /* lcarry can exceed 2**32-1, so check again; this check */ | |
5184 | /* and occasional extra divide (slow) is well worth it, as */ | |
5185 | /* it allows FASTLAZY to be increased to 18 rather than 4 */ | |
5186 | /* in the FASTDIGS=9 case */ | |
5187 | if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ | |
5188 | else { /* two-place carry [fairly rare] */ | |
5189 | uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ | |
5190 | *(lp+2)+=carry2; /* add to item+2 */ | |
5191 | *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ | |
5192 | carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ | |
5193 | } | |
5194 | *(lp+1)+=carry; /* add to item above [inline] */ | |
5195 | *lp-=((uLong)FASTBASE*carry); /* [inline] */ | |
5196 | } /* carry resolution */ | |
5197 | } /* rip loop */ | |
5198 | ||
5199 | /* The multiplication is complete; time to convert back into */ | |
5200 | /* units. This can be done in-place in the accumulator and in */ | |
5201 | /* 32-bit operations, because carries were resolved after the */ | |
5202 | /* final add. This needs N-1 divides and multiplies for */ | |
5203 | /* each item in the accumulator (which will become up to N */ | |
5204 | /* units, where 2<=N<=9). */ | |
5205 | for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { | |
5206 | uInt item=(uInt)*lp; /* decapitate to uInt */ | |
5207 | for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { | |
5208 | uInt part=item/(DECDPUNMAX+1); | |
5209 | *up=(Unit)(item-(part*(DECDPUNMAX+1))); | |
5210 | item=part; | |
5211 | } /* p */ | |
5212 | *up=(Unit)item; up++; /* [final needs no division] */ | |
5213 | } /* lp */ | |
5214 | accunits=up-acc; /* count of units */ | |
5215 | } | |
5216 | else { /* here to use units directly, without chunking ['old code'] */ | |
5217 | #endif | |
5218 | ||
5219 | /* if accumulator will be too long for local storage, then allocate */ | |
5220 | acc=accbuff; /* -> assume buffer for accumulator */ | |
5221 | needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); | |
5222 | if (needbytes>(Int)sizeof(accbuff)) { | |
5223 | allocacc=(Unit *)malloc(needbytes); | |
5224 | if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} | |
5225 | acc=(Unit *)allocacc; /* use the allocated space */ | |
5226 | } | |
5227 | ||
5228 | /* Now the main long multiplication loop */ | |
5229 | /* Unlike the equivalent in the IBM Java implementation, there */ | |
5230 | /* is no advantage in calculating from msu to lsu. So, do it */ | |
5231 | /* by the book, as it were. */ | |
5232 | /* Each iteration calculates ACC=ACC+MULTAND*MULT */ | |
5233 | accunits=1; /* accumulator starts at '0' */ | |
5234 | *acc=0; /* .. (lsu=0) */ | |
5235 | shift=0; /* no multiplicand shift at first */ | |
5236 | madlength=D2U(lhs->digits); /* this won't change */ | |
5237 | mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ | |
5238 | ||
5239 | for (mer=rhs->lsu; mer<mermsup; mer++) { | |
5240 | /* Here, *mer is the next Unit in the multiplier to use */ | |
5241 | /* If non-zero [optimization] add it... */ | |
5242 | if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, | |
5243 | lhs->lsu, madlength, 0, | |
5244 | &acc[shift], *mer) | |
5245 | + shift; | |
5246 | else { /* extend acc with a 0; it will be used shortly */ | |
5247 | *(acc+accunits)=0; /* [this avoids length of <=0 later] */ | |
5248 | accunits++; | |
5249 | } | |
5250 | /* multiply multiplicand by 10**DECDPUN for next Unit to left */ | |
5251 | shift++; /* add this for 'logical length' */ | |
5252 | } /* n */ | |
5253 | #if FASTMUL | |
5254 | } /* unchunked units */ | |
5255 | #endif | |
5256 | /* common end-path */ | |
5257 | #if DECTRACE | |
5258 | decDumpAr('*', acc, accunits); /* Show exact result */ | |
5259 | #endif | |
5260 | ||
5261 | /* acc now contains the exact result of the multiplication, */ | |
5262 | /* possibly with a leading zero unit; build the decNumber from */ | |
5263 | /* it, noting if any residue */ | |
5264 | res->bits=bits; /* set sign */ | |
5265 | res->digits=decGetDigits(acc, accunits); /* count digits exactly */ | |
5266 | ||
5267 | /* There can be a 31-bit wrap in calculating the exponent. */ | |
5268 | /* This can only happen if both input exponents are negative and */ | |
5269 | /* both their magnitudes are large. If there was a wrap, set a */ | |
5270 | /* safe very negative exponent, from which decFinalize() will */ | |
5271 | /* raise a hard underflow shortly. */ | |
5272 | exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ | |
5273 | if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) | |
5274 | exponent=-2*DECNUMMAXE; /* force underflow */ | |
5275 | res->exponent=exponent; /* OK to overwrite now */ | |
5276 | ||
5277 | ||
5278 | /* Set the coefficient. If any rounding, residue records */ | |
5279 | decSetCoeff(res, set, acc, res->digits, &residue, status); | |
5280 | decFinish(res, set, &residue, status); /* final cleanup */ | |
5281 | } while(0); /* end protected */ | |
5282 | ||
5283 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ | |
5284 | #if DECSUBSET | |
5285 | if (allocrhs!=NULL) free(allocrhs); /* .. */ | |
5286 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
5287 | #endif | |
5288 | #if FASTMUL | |
5289 | if (allocrhi!=NULL) free(allocrhi); /* .. */ | |
5290 | if (alloclhi!=NULL) free(alloclhi); /* .. */ | |
5291 | #endif | |
5292 | return res; | |
5293 | } /* decMultiplyOp */ | |
5294 | ||
5295 | /* ------------------------------------------------------------------ */ | |
5296 | /* decExpOp -- effect exponentiation */ | |
5297 | /* */ | |
5298 | /* This computes C = exp(A) */ | |
5299 | /* */ | |
5300 | /* res is C, the result. C may be A */ | |
5301 | /* rhs is A */ | |
5302 | /* set is the context; note that rounding mode has no effect */ | |
5303 | /* */ | |
5304 | /* C must have space for set->digits digits. status is updated but */ | |
5305 | /* not set. */ | |
5306 | /* */ | |
5307 | /* Restrictions: */ | |
5308 | /* */ | |
5309 | /* digits, emax, and -emin in the context must be less than */ | |
5310 | /* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ | |
5311 | /* bounds or a zero. This is an internal routine, so these */ | |
5312 | /* restrictions are contractual and not enforced. */ | |
5313 | /* */ | |
5314 | /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ | |
5315 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
5316 | /* error in rare cases. */ | |
5317 | /* */ | |
5318 | /* Finite results will always be full precision and Inexact, except */ | |
5319 | /* when A is a zero or -Infinity (giving 1 or 0 respectively). */ | |
5320 | /* ------------------------------------------------------------------ */ | |
5321 | /* This approach used here is similar to the algorithm described in */ | |
5322 | /* */ | |
5323 | /* Variable Precision Exponential Function, T. E. Hull and */ | |
5324 | /* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ | |
5325 | /* pp79-91, ACM, June 1986. */ | |
5326 | /* */ | |
5327 | /* with the main difference being that the iterations in the series */ | |
5328 | /* evaluation are terminated dynamically (which does not require the */ | |
5329 | /* extra variable-precision variables which are expensive in this */ | |
5330 | /* context). */ | |
5331 | /* */ | |
5332 | /* The error analysis in Hull & Abrham's paper applies except for the */ | |
5333 | /* round-off error accumulation during the series evaluation. This */ | |
5334 | /* code does not precalculate the number of iterations and so cannot */ | |
5335 | /* use Horner's scheme. Instead, the accumulation is done at double- */ | |
5336 | /* precision, which ensures that the additions of the terms are exact */ | |
5337 | /* and do not accumulate round-off (and any round-off errors in the */ | |
5338 | /* terms themselves move 'to the right' faster than they can */ | |
5339 | /* accumulate). This code also extends the calculation by allowing, */ | |
5340 | /* in the spirit of other decNumber operators, the input to be more */ | |
5341 | /* precise than the result (the precision used is based on the more */ | |
5342 | /* precise of the input or requested result). */ | |
5343 | /* */ | |
5344 | /* Implementation notes: */ | |
5345 | /* */ | |
5346 | /* 1. This is separated out as decExpOp so it can be called from */ | |
5347 | /* other Mathematical functions (notably Ln) with a wider range */ | |
5348 | /* than normal. In particular, it can handle the slightly wider */ | |
5349 | /* (double) range needed by Ln (which has to be able to calculate */ | |
5350 | /* exp(-x) where x can be the tiniest number (Ntiny). */ | |
5351 | /* */ | |
5352 | /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ | |
67cc32eb | 5353 | /* iterations by approximately a third with additional (although */ |
72ac97cd TM |
5354 | /* diminishing) returns as the range is reduced to even smaller */ |
5355 | /* fractions. However, h (the power of 10 used to correct the */ | |
5356 | /* result at the end, see below) must be kept <=8 as otherwise */ | |
5357 | /* the final result cannot be computed. Hence the leverage is a */ | |
5358 | /* sliding value (8-h), where potentially the range is reduced */ | |
5359 | /* more for smaller values. */ | |
5360 | /* */ | |
5361 | /* The leverage that can be applied in this way is severely */ | |
5362 | /* limited by the cost of the raise-to-the power at the end, */ | |
5363 | /* which dominates when the number of iterations is small (less */ | |
5364 | /* than ten) or when rhs is short. As an example, the adjustment */ | |
5365 | /* x**10,000,000 needs 31 multiplications, all but one full-width. */ | |
5366 | /* */ | |
5367 | /* 3. The restrictions (especially precision) could be raised with */ | |
5368 | /* care, but the full decNumber range seems very hard within the */ | |
5369 | /* 32-bit limits. */ | |
5370 | /* */ | |
5371 | /* 4. The working precisions for the static buffers are twice the */ | |
5372 | /* obvious size to allow for calls from decNumberPower. */ | |
5373 | /* ------------------------------------------------------------------ */ | |
d072cdf3 SW |
5374 | static decNumber *decExpOp(decNumber *res, const decNumber *rhs, |
5375 | decContext *set, uInt *status) { | |
72ac97cd TM |
5376 | uInt ignore=0; /* working status */ |
5377 | Int h; /* adjusted exponent for 0.xxxx */ | |
5378 | Int p; /* working precision */ | |
5379 | Int residue; /* rounding residue */ | |
5380 | uInt needbytes; /* for space calculations */ | |
5381 | const decNumber *x=rhs; /* (may point to safe copy later) */ | |
5382 | decContext aset, tset, dset; /* working contexts */ | |
5383 | Int comp; /* work */ | |
5384 | ||
5385 | /* the argument is often copied to normalize it, so (unusually) it */ | |
5386 | /* is treated like other buffers, using DECBUFFER, +1 in case */ | |
5387 | /* DECBUFFER is 0 */ | |
5388 | decNumber bufr[D2N(DECBUFFER*2+1)]; | |
5389 | decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ | |
5390 | ||
5391 | /* the working precision will be no more than set->digits+8+1 */ | |
5392 | /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ | |
5393 | /* is 0 (and twice that for the accumulator) */ | |
5394 | ||
5395 | /* buffer for t, term (working precision plus) */ | |
5396 | decNumber buft[D2N(DECBUFFER*2+9+1)]; | |
5397 | decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ | |
5398 | decNumber *t=buft; /* term */ | |
5399 | /* buffer for a, accumulator (working precision * 2), at least 9 */ | |
5400 | decNumber bufa[D2N(DECBUFFER*4+18+1)]; | |
5401 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
5402 | decNumber *a=bufa; /* accumulator */ | |
5403 | /* decNumber for the divisor term; this needs at most 9 digits */ | |
5404 | /* and so can be fixed size [16 so can use standard context] */ | |
5405 | decNumber bufd[D2N(16)]; | |
5406 | decNumber *d=bufd; /* divisor */ | |
5407 | decNumber numone; /* constant 1 */ | |
5408 | ||
5409 | #if DECCHECK | |
5410 | Int iterations=0; /* for later sanity check */ | |
5411 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
5412 | #endif | |
5413 | ||
5414 | do { /* protect allocated storage */ | |
5415 | if (SPECIALARG) { /* handle infinities and NaNs */ | |
5416 | if (decNumberIsInfinite(rhs)) { /* an infinity */ | |
5417 | if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ | |
5418 | decNumberZero(res); | |
5419 | else decNumberCopy(res, rhs); /* +Infinity -> self */ | |
5420 | } | |
5421 | else decNaNs(res, rhs, NULL, set, status); /* a NaN */ | |
5422 | break;} | |
5423 | ||
5424 | if (ISZERO(rhs)) { /* zeros -> exact 1 */ | |
5425 | decNumberZero(res); /* make clean 1 */ | |
5426 | *res->lsu=1; /* .. */ | |
5427 | break;} /* [no status to set] */ | |
5428 | ||
5429 | /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ | |
5430 | /* positive and negative tiny cases which will result in inexact */ | |
5431 | /* 1. This also allows the later add-accumulate to always be */ | |
5432 | /* exact (because its length will never be more than twice the */ | |
5433 | /* working precision). */ | |
5434 | /* The comparator (tiny) needs just one digit, so use the */ | |
5435 | /* decNumber d for it (reused as the divisor, etc., below); its */ | |
5436 | /* exponent is such that if x is positive it will have */ | |
5437 | /* set->digits-1 zeros between the decimal point and the digit, */ | |
5438 | /* which is 4, and if x is negative one more zero there as the */ | |
5439 | /* more precise result will be of the form 0.9999999 rather than */ | |
5440 | /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ | |
5441 | /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ | |
5442 | /* this then the result will be 1.000000 */ | |
5443 | decNumberZero(d); /* clean */ | |
5444 | *d->lsu=4; /* set 4 .. */ | |
5445 | d->exponent=-set->digits; /* * 10**(-d) */ | |
5446 | if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ | |
5447 | comp=decCompare(d, rhs, 1); /* signless compare */ | |
5448 | if (comp==BADINT) { | |
5449 | *status|=DEC_Insufficient_storage; | |
5450 | break;} | |
5451 | if (comp>=0) { /* rhs < d */ | |
5452 | Int shift=set->digits-1; | |
5453 | decNumberZero(res); /* set 1 */ | |
5454 | *res->lsu=1; /* .. */ | |
5455 | res->digits=decShiftToMost(res->lsu, 1, shift); | |
5456 | res->exponent=-shift; /* make 1.0000... */ | |
5457 | *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ | |
5458 | break;} /* tiny */ | |
5459 | ||
5460 | /* set up the context to be used for calculating a, as this is */ | |
5461 | /* used on both paths below */ | |
5462 | decContextDefault(&aset, DEC_INIT_DECIMAL64); | |
5463 | /* accumulator bounds are as requested (could underflow) */ | |
5464 | aset.emax=set->emax; /* usual bounds */ | |
5465 | aset.emin=set->emin; /* .. */ | |
5466 | aset.clamp=0; /* and no concrete format */ | |
5467 | ||
5468 | /* calculate the adjusted (Hull & Abrham) exponent (where the */ | |
5469 | /* decimal point is just to the left of the coefficient msd) */ | |
5470 | h=rhs->exponent+rhs->digits; | |
5471 | /* if h>8 then 10**h cannot be calculated safely; however, when */ | |
5472 | /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ | |
5473 | /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ | |
5474 | /* overflow (or underflow to 0) is guaranteed -- so this case can */ | |
5475 | /* be handled by simply forcing the appropriate excess */ | |
5476 | if (h>8) { /* overflow/underflow */ | |
5477 | /* set up here so Power call below will over or underflow to */ | |
5478 | /* zero; set accumulator to either 2 or 0.02 */ | |
5479 | /* [stack buffer for a is always big enough for this] */ | |
5480 | decNumberZero(a); | |
5481 | *a->lsu=2; /* not 1 but < exp(1) */ | |
5482 | if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ | |
5483 | h=8; /* clamp so 10**h computable */ | |
5484 | p=9; /* set a working precision */ | |
5485 | } | |
5486 | else { /* h<=8 */ | |
5487 | Int maxlever=(rhs->digits>8?1:0); | |
5488 | /* [could/should increase this for precisions >40 or so, too] */ | |
5489 | ||
5490 | /* if h is 8, cannot normalize to a lower upper limit because */ | |
5491 | /* the final result will not be computable (see notes above), */ | |
5492 | /* but leverage can be applied whenever h is less than 8. */ | |
5493 | /* Apply as much as possible, up to a MAXLEVER digits, which */ | |
5494 | /* sets the tradeoff against the cost of the later a**(10**h). */ | |
5495 | /* As h is increased, the working precision below also */ | |
5496 | /* increases to compensate for the "constant digits at the */ | |
5497 | /* front" effect. */ | |
5498 | Int lever=MINI(8-h, maxlever); /* leverage attainable */ | |
5499 | Int use=-rhs->digits-lever; /* exponent to use for RHS */ | |
5500 | h+=lever; /* apply leverage selected */ | |
5501 | if (h<0) { /* clamp */ | |
5502 | use+=h; /* [may end up subnormal] */ | |
5503 | h=0; | |
5504 | } | |
5505 | /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ | |
5506 | if (rhs->exponent!=use) { | |
5507 | decNumber *newrhs=bufr; /* assume will fit on stack */ | |
5508 | needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); | |
5509 | if (needbytes>sizeof(bufr)) { /* need malloc space */ | |
5510 | allocrhs=(decNumber *)malloc(needbytes); | |
5511 | if (allocrhs==NULL) { /* hopeless -- abandon */ | |
5512 | *status|=DEC_Insufficient_storage; | |
5513 | break;} | |
5514 | newrhs=allocrhs; /* use the allocated space */ | |
5515 | } | |
5516 | decNumberCopy(newrhs, rhs); /* copy to safe space */ | |
5517 | newrhs->exponent=use; /* normalize; now <1 */ | |
5518 | x=newrhs; /* ready for use */ | |
5519 | /* decNumberShow(x); */ | |
5520 | } | |
5521 | ||
5522 | /* Now use the usual power series to evaluate exp(x). The */ | |
5523 | /* series starts as 1 + x + x^2/2 ... so prime ready for the */ | |
5524 | /* third term by setting the term variable t=x, the accumulator */ | |
5525 | /* a=1, and the divisor d=2. */ | |
5526 | ||
5527 | /* First determine the working precision. From Hull & Abrham */ | |
5528 | /* this is set->digits+h+2. However, if x is 'over-precise' we */ | |
5529 | /* need to allow for all its digits to potentially participate */ | |
5530 | /* (consider an x where all the excess digits are 9s) so in */ | |
5531 | /* this case use x->digits+h+2 */ | |
5532 | p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ | |
5533 | ||
5534 | /* a and t are variable precision, and depend on p, so space */ | |
5535 | /* must be allocated for them if necessary */ | |
5536 | ||
5537 | /* the accumulator needs to be able to hold 2p digits so that */ | |
5538 | /* the additions on the second and subsequent iterations are */ | |
5539 | /* sufficiently exact. */ | |
5540 | needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); | |
5541 | if (needbytes>sizeof(bufa)) { /* need malloc space */ | |
5542 | allocbufa=(decNumber *)malloc(needbytes); | |
5543 | if (allocbufa==NULL) { /* hopeless -- abandon */ | |
5544 | *status|=DEC_Insufficient_storage; | |
5545 | break;} | |
5546 | a=allocbufa; /* use the allocated space */ | |
5547 | } | |
5548 | /* the term needs to be able to hold p digits (which is */ | |
5549 | /* guaranteed to be larger than x->digits, so the initial copy */ | |
5550 | /* is safe); it may also be used for the raise-to-power */ | |
5551 | /* calculation below, which needs an extra two digits */ | |
5552 | needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); | |
5553 | if (needbytes>sizeof(buft)) { /* need malloc space */ | |
5554 | allocbuft=(decNumber *)malloc(needbytes); | |
5555 | if (allocbuft==NULL) { /* hopeless -- abandon */ | |
5556 | *status|=DEC_Insufficient_storage; | |
5557 | break;} | |
5558 | t=allocbuft; /* use the allocated space */ | |
5559 | } | |
5560 | ||
5561 | decNumberCopy(t, x); /* term=x */ | |
5562 | decNumberZero(a); *a->lsu=1; /* accumulator=1 */ | |
5563 | decNumberZero(d); *d->lsu=2; /* divisor=2 */ | |
5564 | decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ | |
5565 | ||
5566 | /* set up the contexts for calculating a, t, and d */ | |
5567 | decContextDefault(&tset, DEC_INIT_DECIMAL64); | |
5568 | dset=tset; | |
5569 | /* accumulator bounds are set above, set precision now */ | |
5570 | aset.digits=p*2; /* double */ | |
5571 | /* term bounds avoid any underflow or overflow */ | |
5572 | tset.digits=p; | |
5573 | tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ | |
5574 | /* [dset.digits=16, etc., are sufficient] */ | |
5575 | ||
5576 | /* finally ready to roll */ | |
5577 | for (;;) { | |
5578 | #if DECCHECK | |
5579 | iterations++; | |
5580 | #endif | |
5581 | /* only the status from the accumulation is interesting */ | |
5582 | /* [but it should remain unchanged after first add] */ | |
5583 | decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ | |
5584 | decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ | |
5585 | decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ | |
5586 | /* the iteration ends when the term cannot affect the result, */ | |
5587 | /* if rounded to p digits, which is when its value is smaller */ | |
5588 | /* than the accumulator by p+1 digits. There must also be */ | |
5589 | /* full precision in a. */ | |
5590 | if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) | |
5591 | && (a->digits>=p)) break; | |
5592 | decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ | |
5593 | } /* iterate */ | |
5594 | ||
5595 | #if DECCHECK | |
5596 | /* just a sanity check; comment out test to show always */ | |
5597 | if (iterations>p+3) | |
5598 | printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", | |
5599 | iterations, *status, p, x->digits); | |
5600 | #endif | |
5601 | } /* h<=8 */ | |
5602 | ||
5603 | /* apply postconditioning: a=a**(10**h) -- this is calculated */ | |
5604 | /* at a slightly higher precision than Hull & Abrham suggest */ | |
5605 | if (h>0) { | |
5606 | Int seenbit=0; /* set once a 1-bit is seen */ | |
5607 | Int i; /* counter */ | |
5608 | Int n=powers[h]; /* always positive */ | |
5609 | aset.digits=p+2; /* sufficient precision */ | |
5610 | /* avoid the overhead and many extra digits of decNumberPower */ | |
5611 | /* as all that is needed is the short 'multipliers' loop; here */ | |
5612 | /* accumulate the answer into t */ | |
5613 | decNumberZero(t); *t->lsu=1; /* acc=1 */ | |
5614 | for (i=1;;i++){ /* for each bit [top bit ignored] */ | |
5615 | /* abandon if have had overflow or terminal underflow */ | |
5616 | if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ | |
5617 | if (*status&DEC_Overflow || ISZERO(t)) break;} | |
5618 | n=n<<1; /* move next bit to testable position */ | |
5619 | if (n<0) { /* top bit is set */ | |
5620 | seenbit=1; /* OK, have a significant bit */ | |
5621 | decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ | |
5622 | } | |
5623 | if (i==31) break; /* that was the last bit */ | |
5624 | if (!seenbit) continue; /* no need to square 1 */ | |
5625 | decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ | |
5626 | } /*i*/ /* 32 bits */ | |
5627 | /* decNumberShow(t); */ | |
5628 | a=t; /* and carry on using t instead of a */ | |
5629 | } | |
5630 | ||
5631 | /* Copy and round the result to res */ | |
5632 | residue=1; /* indicate dirt to right .. */ | |
5633 | if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ | |
5634 | aset.digits=set->digits; /* [use default rounding] */ | |
5635 | decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ | |
5636 | decFinish(res, set, &residue, status); /* cleanup/set flags */ | |
5637 | } while(0); /* end protected */ | |
5638 | ||
5639 | if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ | |
5640 | if (allocbufa!=NULL) free(allocbufa); /* .. */ | |
5641 | if (allocbuft!=NULL) free(allocbuft); /* .. */ | |
5642 | /* [status is handled by caller] */ | |
5643 | return res; | |
5644 | } /* decExpOp */ | |
5645 | ||
5646 | /* ------------------------------------------------------------------ */ | |
5647 | /* Initial-estimate natural logarithm table */ | |
5648 | /* */ | |
5649 | /* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ | |
5650 | /* The result is a 4-digit encode of the coefficient (c=the */ | |
5651 | /* top 14 bits encoding 0-9999) and a 2-digit encode of the */ | |
5652 | /* exponent (e=the bottom 2 bits encoding 0-3) */ | |
5653 | /* */ | |
5654 | /* The resulting value is given by: */ | |
5655 | /* */ | |
5656 | /* v = -c * 10**(-e-3) */ | |
5657 | /* */ | |
5658 | /* where e and c are extracted from entry k = LNnn[x-10] */ | |
5659 | /* where x is truncated (NB) into the range 10 through 99, */ | |
5660 | /* and then c = k>>2 and e = k&3. */ | |
5661 | /* ------------------------------------------------------------------ */ | |
d072cdf3 SW |
5662 | static const uShort LNnn[90] = { |
5663 | 9016, 8652, 8316, 8008, 7724, 7456, 7208, | |
72ac97cd TM |
5664 | 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, |
5665 | 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, | |
5666 | 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, | |
5667 | 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, | |
5668 | 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, | |
5669 | 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, | |
5670 | 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, | |
5671 | 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, | |
5672 | 10130, 6046, 20055}; | |
5673 | ||
5674 | /* ------------------------------------------------------------------ */ | |
5675 | /* decLnOp -- effect natural logarithm */ | |
5676 | /* */ | |
5677 | /* This computes C = ln(A) */ | |
5678 | /* */ | |
5679 | /* res is C, the result. C may be A */ | |
5680 | /* rhs is A */ | |
5681 | /* set is the context; note that rounding mode has no effect */ | |
5682 | /* */ | |
5683 | /* C must have space for set->digits digits. */ | |
5684 | /* */ | |
5685 | /* Notable cases: */ | |
5686 | /* A<0 -> Invalid */ | |
5687 | /* A=0 -> -Infinity (Exact) */ | |
5688 | /* A=+Infinity -> +Infinity (Exact) */ | |
5689 | /* A=1 exactly -> 0 (Exact) */ | |
5690 | /* */ | |
5691 | /* Restrictions (as for Exp): */ | |
5692 | /* */ | |
5693 | /* digits, emax, and -emin in the context must be less than */ | |
5694 | /* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ | |
5695 | /* bounds or a zero. This is an internal routine, so these */ | |
5696 | /* restrictions are contractual and not enforced. */ | |
5697 | /* */ | |
5698 | /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ | |
5699 | /* almost always be correctly rounded, but may be up to 1 ulp in */ | |
5700 | /* error in rare cases. */ | |
5701 | /* ------------------------------------------------------------------ */ | |
5702 | /* The result is calculated using Newton's method, with each */ | |
5703 | /* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ | |
5704 | /* Epperson 1989. */ | |
5705 | /* */ | |
5706 | /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ | |
5707 | /* This has to be calculated at the sum of the precision of x and the */ | |
5708 | /* working precision. */ | |
5709 | /* */ | |
5710 | /* Implementation notes: */ | |
5711 | /* */ | |
5712 | /* 1. This is separated out as decLnOp so it can be called from */ | |
5713 | /* other Mathematical functions (e.g., Log 10) with a wider range */ | |
5714 | /* than normal. In particular, it can handle the slightly wider */ | |
5715 | /* (+9+2) range needed by a power function. */ | |
5716 | /* */ | |
5717 | /* 2. The speed of this function is about 10x slower than exp, as */ | |
5718 | /* it typically needs 4-6 iterations for short numbers, and the */ | |
5719 | /* extra precision needed adds a squaring effect, twice. */ | |
5720 | /* */ | |
5721 | /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ | |
5722 | /* as these are common requests. ln(10) is used by log10(x). */ | |
5723 | /* */ | |
5724 | /* 4. An iteration might be saved by widening the LNnn table, and */ | |
5725 | /* would certainly save at least one if it were made ten times */ | |
5726 | /* bigger, too (for truncated fractions 0.100 through 0.999). */ | |
5727 | /* However, for most practical evaluations, at least four or five */ | |
e3a6e0da | 5728 | /* iterations will be needed -- so this would only speed up by */ |
72ac97cd TM |
5729 | /* 20-25% and that probably does not justify increasing the table */ |
5730 | /* size. */ | |
5731 | /* */ | |
5732 | /* 5. The static buffers are larger than might be expected to allow */ | |
5733 | /* for calls from decNumberPower. */ | |
5734 | /* ------------------------------------------------------------------ */ | |
d072cdf3 SW |
5735 | static decNumber *decLnOp(decNumber *res, const decNumber *rhs, |
5736 | decContext *set, uInt *status) { | |
72ac97cd TM |
5737 | uInt ignore=0; /* working status accumulator */ |
5738 | uInt needbytes; /* for space calculations */ | |
5739 | Int residue; /* rounding residue */ | |
5740 | Int r; /* rhs=f*10**r [see below] */ | |
5741 | Int p; /* working precision */ | |
5742 | Int pp; /* precision for iteration */ | |
5743 | Int t; /* work */ | |
5744 | ||
5745 | /* buffers for a (accumulator, typically precision+2) and b */ | |
5746 | /* (adjustment calculator, same size) */ | |
5747 | decNumber bufa[D2N(DECBUFFER+12)]; | |
5748 | decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ | |
5749 | decNumber *a=bufa; /* accumulator/work */ | |
5750 | decNumber bufb[D2N(DECBUFFER*2+2)]; | |
5751 | decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ | |
5752 | decNumber *b=bufb; /* adjustment/work */ | |
5753 | ||
5754 | decNumber numone; /* constant 1 */ | |
5755 | decNumber cmp; /* work */ | |
5756 | decContext aset, bset; /* working contexts */ | |
5757 | ||
5758 | #if DECCHECK | |
5759 | Int iterations=0; /* for later sanity check */ | |
5760 | if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; | |
5761 | #endif | |
5762 | ||
5763 | do { /* protect allocated storage */ | |
5764 | if (SPECIALARG) { /* handle infinities and NaNs */ | |
5765 | if (decNumberIsInfinite(rhs)) { /* an infinity */ | |
5766 | if (decNumberIsNegative(rhs)) /* -Infinity -> error */ | |
5767 | *status|=DEC_Invalid_operation; | |
5768 | else decNumberCopy(res, rhs); /* +Infinity -> self */ | |
5769 | } | |
5770 | else decNaNs(res, rhs, NULL, set, status); /* a NaN */ | |
5771 | break;} | |
5772 | ||
5773 | if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ | |
5774 | decNumberZero(res); /* make clean */ | |
5775 | res->bits=DECINF|DECNEG; /* set - infinity */ | |
5776 | break;} /* [no status to set] */ | |
5777 | ||
5778 | /* Non-zero negatives are bad... */ | |
5779 | if (decNumberIsNegative(rhs)) { /* -x -> error */ | |
5780 | *status|=DEC_Invalid_operation; | |
5781 | break;} | |
5782 | ||
5783 | /* Here, rhs is positive, finite, and in range */ | |
5784 | ||
5785 | /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ | |
5786 | if (rhs->exponent==0 && set->digits<=40) { | |
5787 | #if DECDPUN==1 | |
5788 | if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ | |
5789 | #else | |
5790 | if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ | |
5791 | #endif | |
5792 | aset=*set; aset.round=DEC_ROUND_HALF_EVEN; | |
5793 | #define LN10 "2.302585092994045684017991454684364207601" | |
5794 | decNumberFromString(res, LN10, &aset); | |
5795 | *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ | |
5796 | break;} | |
5797 | if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ | |
5798 | aset=*set; aset.round=DEC_ROUND_HALF_EVEN; | |
5799 | #define LN2 "0.6931471805599453094172321214581765680755" | |
5800 | decNumberFromString(res, LN2, &aset); | |
5801 | *status|=(DEC_Inexact | DEC_Rounded); | |
5802 | break;} | |
5803 | } /* integer and short */ | |
5804 | ||
5805 | /* Determine the working precision. This is normally the */ | |
5806 | /* requested precision + 2, with a minimum of 9. However, if */ | |
5807 | /* the rhs is 'over-precise' then allow for all its digits to */ | |
5808 | /* potentially participate (consider an rhs where all the excess */ | |
5809 | /* digits are 9s) so in this case use rhs->digits+2. */ | |
5810 | p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; | |
5811 | ||
5812 | /* Allocate space for the accumulator and the high-precision */ | |
5813 | /* adjustment calculator, if necessary. The accumulator must */ | |
5814 | /* be able to hold p digits, and the adjustment up to */ | |
5815 | /* rhs->digits+p digits. They are also made big enough for 16 */ | |
5816 | /* digits so that they can be used for calculating the initial */ | |
5817 | /* estimate. */ | |
5818 | needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); | |
5819 | if (needbytes>sizeof(bufa)) { /* need malloc space */ | |
5820 | allocbufa=(decNumber *)malloc(needbytes); | |
5821 | if (allocbufa==NULL) { /* hopeless -- abandon */ | |
5822 | *status|=DEC_Insufficient_storage; | |
5823 | break;} | |
5824 | a=allocbufa; /* use the allocated space */ | |
5825 | } | |
5826 | pp=p+rhs->digits; | |
5827 | needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); | |
5828 | if (needbytes>sizeof(bufb)) { /* need malloc space */ | |
5829 | allocbufb=(decNumber *)malloc(needbytes); | |
5830 | if (allocbufb==NULL) { /* hopeless -- abandon */ | |
5831 | *status|=DEC_Insufficient_storage; | |
5832 | break;} | |
5833 | b=allocbufb; /* use the allocated space */ | |
5834 | } | |
5835 | ||
5836 | /* Prepare an initial estimate in acc. Calculate this by */ | |
5837 | /* considering the coefficient of x to be a normalized fraction, */ | |
5838 | /* f, with the decimal point at far left and multiplied by */ | |
5839 | /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ | |
5840 | /* ln(x) = ln(f) + ln(10)*r */ | |
5841 | /* Get the initial estimate for ln(f) from a small lookup */ | |
5842 | /* table (see above) indexed by the first two digits of f, */ | |
5843 | /* truncated. */ | |
5844 | ||
5845 | decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ | |
5846 | r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ | |
5847 | decNumberFromInt32(a, r); /* a=r */ | |
5848 | decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ | |
5849 | b->exponent=-6; /* .. */ | |
5850 | decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ | |
5851 | /* now get top two digits of rhs into b by simple truncate and */ | |
5852 | /* force to integer */ | |
5853 | residue=0; /* (no residue) */ | |
5854 | aset.digits=2; aset.round=DEC_ROUND_DOWN; | |
5855 | decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ | |
5856 | b->exponent=0; /* make integer */ | |
5857 | t=decGetInt(b); /* [cannot fail] */ | |
5858 | if (t<10) t=X10(t); /* adjust single-digit b */ | |
5859 | t=LNnn[t-10]; /* look up ln(b) */ | |
5860 | decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ | |
5861 | b->exponent=-(t&3)-3; /* set exponent */ | |
5862 | b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ | |
5863 | aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ | |
5864 | decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ | |
5865 | /* the initial estimate is now in a, with up to 4 digits correct. */ | |
5866 | /* When rhs is at or near Nmax the estimate will be low, so we */ | |
5867 | /* will approach it from below, avoiding overflow when calling exp. */ | |
5868 | ||
5869 | decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ | |
5870 | ||
5871 | /* accumulator bounds are as requested (could underflow, but */ | |
5872 | /* cannot overflow) */ | |
5873 | aset.emax=set->emax; | |
5874 | aset.emin=set->emin; | |
5875 | aset.clamp=0; /* no concrete format */ | |
5876 | /* set up a context to be used for the multiply and subtract */ | |
5877 | bset=aset; | |
5878 | bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ | |
5879 | bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ | |
5880 | /* [see decExpOp call below] */ | |
5881 | /* for each iteration double the number of digits to calculate, */ | |
5882 | /* up to a maximum of p */ | |
5883 | pp=9; /* initial precision */ | |
5884 | /* [initially 9 as then the sequence starts 7+2, 16+2, and */ | |
5885 | /* 34+2, which is ideal for standard-sized numbers] */ | |
5886 | aset.digits=pp; /* working context */ | |
5887 | bset.digits=pp+rhs->digits; /* wider context */ | |
5888 | for (;;) { /* iterate */ | |
5889 | #if DECCHECK | |
5890 | iterations++; | |
5891 | if (iterations>24) break; /* consider 9 * 2**24 */ | |
5892 | #endif | |
5893 | /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ | |
5894 | /* catastrophic subtraction but it really is the difference */ | |
5895 | /* from 1 that is of interest. */ | |
5896 | /* Use the internal entry point to Exp as it allows the double */ | |
5897 | /* range for calculating exp(-a) when a is the tiniest subnormal. */ | |
5898 | a->bits^=DECNEG; /* make -a */ | |
5899 | decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ | |
5900 | a->bits^=DECNEG; /* restore sign of a */ | |
5901 | /* now multiply by rhs and subtract 1, at the wider precision */ | |
5902 | decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ | |
5903 | decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ | |
5904 | ||
5905 | /* the iteration ends when the adjustment cannot affect the */ | |
5906 | /* result by >=0.5 ulp (at the requested digits), which */ | |
5907 | /* is when its value is smaller than the accumulator by */ | |
5908 | /* set->digits+1 digits (or it is zero) -- this is a looser */ | |
5909 | /* requirement than for Exp because all that happens to the */ | |
5910 | /* accumulator after this is the final rounding (but note that */ | |
5911 | /* there must also be full precision in a, or a=0). */ | |
5912 | ||
5913 | if (decNumberIsZero(b) || | |
5914 | (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { | |
5915 | if (a->digits==p) break; | |
5916 | if (decNumberIsZero(a)) { | |
5917 | decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ | |
5918 | if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ | |
5919 | else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ | |
5920 | break; | |
5921 | } | |
5922 | /* force padding if adjustment has gone to 0 before full length */ | |
5923 | if (decNumberIsZero(b)) b->exponent=a->exponent-p; | |
5924 | } | |
5925 | ||
5926 | /* not done yet ... */ | |
5927 | decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ | |
5928 | if (pp==p) continue; /* precision is at maximum */ | |
5929 | /* lengthen the next calculation */ | |
5930 | pp=pp*2; /* double precision */ | |
5931 | if (pp>p) pp=p; /* clamp to maximum */ | |
5932 | aset.digits=pp; /* working context */ | |
5933 | bset.digits=pp+rhs->digits; /* wider context */ | |
5934 | } /* Newton's iteration */ | |
5935 | ||
5936 | #if DECCHECK | |
5937 | /* just a sanity check; remove the test to show always */ | |
5938 | if (iterations>24) | |
5939 | printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", | |
5940 | iterations, *status, p, rhs->digits); | |
5941 | #endif | |
5942 | ||
5943 | /* Copy and round the result to res */ | |
5944 | residue=1; /* indicate dirt to right */ | |
5945 | if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ | |
5946 | aset.digits=set->digits; /* [use default rounding] */ | |
5947 | decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ | |
5948 | decFinish(res, set, &residue, status); /* cleanup/set flags */ | |
5949 | } while(0); /* end protected */ | |
5950 | ||
5951 | if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ | |
5952 | if (allocbufb!=NULL) free(allocbufb); /* .. */ | |
5953 | /* [status is handled by caller] */ | |
5954 | return res; | |
5955 | } /* decLnOp */ | |
5956 | ||
5957 | /* ------------------------------------------------------------------ */ | |
5958 | /* decQuantizeOp -- force exponent to requested value */ | |
5959 | /* */ | |
5960 | /* This computes C = op(A, B), where op adjusts the coefficient */ | |
5961 | /* of C (by rounding or shifting) such that the exponent (-scale) */ | |
5962 | /* of C has the value B or matches the exponent of B. */ | |
5963 | /* The numerical value of C will equal A, except for the effects of */ | |
5964 | /* any rounding that occurred. */ | |
5965 | /* */ | |
5966 | /* res is C, the result. C may be A or B */ | |
5967 | /* lhs is A, the number to adjust */ | |
5968 | /* rhs is B, the requested exponent */ | |
5969 | /* set is the context */ | |
5970 | /* quant is 1 for quantize or 0 for rescale */ | |
5971 | /* status is the status accumulator (this can be called without */ | |
5972 | /* risk of control loss) */ | |
5973 | /* */ | |
5974 | /* C must have space for set->digits digits. */ | |
5975 | /* */ | |
5976 | /* Unless there is an error or the result is infinite, the exponent */ | |
5977 | /* after the operation is guaranteed to be that requested. */ | |
5978 | /* ------------------------------------------------------------------ */ | |
5979 | static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, | |
5980 | const decNumber *rhs, decContext *set, | |
5981 | Flag quant, uInt *status) { | |
5982 | #if DECSUBSET | |
5983 | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ | |
5984 | decNumber *allocrhs=NULL; /* .., rhs */ | |
5985 | #endif | |
5986 | const decNumber *inrhs=rhs; /* save original rhs */ | |
5987 | Int reqdigits=set->digits; /* requested DIGITS */ | |
5988 | Int reqexp; /* requested exponent [-scale] */ | |
5989 | Int residue=0; /* rounding residue */ | |
5990 | Int etiny=set->emin-(reqdigits-1); | |
5991 | ||
5992 | #if DECCHECK | |
5993 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
5994 | #endif | |
5995 | ||
5996 | do { /* protect allocated storage */ | |
5997 | #if DECSUBSET | |
5998 | if (!set->extended) { | |
5999 | /* reduce operands and set lostDigits status, as needed */ | |
6000 | if (lhs->digits>reqdigits) { | |
6001 | alloclhs=decRoundOperand(lhs, set, status); | |
6002 | if (alloclhs==NULL) break; | |
6003 | lhs=alloclhs; | |
6004 | } | |
6005 | if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ | |
6006 | allocrhs=decRoundOperand(rhs, set, status); | |
6007 | if (allocrhs==NULL) break; | |
6008 | rhs=allocrhs; | |
6009 | } | |
6010 | } | |
6011 | #endif | |
6012 | /* [following code does not require input rounding] */ | |
6013 | ||
6014 | /* Handle special values */ | |
6015 | if (SPECIALARGS) { | |
6016 | /* NaNs get usual processing */ | |
6017 | if (SPECIALARGS & (DECSNAN | DECNAN)) | |
6018 | decNaNs(res, lhs, rhs, set, status); | |
6019 | /* one infinity but not both is bad */ | |
6020 | else if ((lhs->bits ^ rhs->bits) & DECINF) | |
6021 | *status|=DEC_Invalid_operation; | |
6022 | /* both infinity: return lhs */ | |
6023 | else decNumberCopy(res, lhs); /* [nop if in place] */ | |
6024 | break; | |
6025 | } | |
6026 | ||
6027 | /* set requested exponent */ | |
6028 | if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ | |
6029 | else { /* rescale -- use value of rhs */ | |
6030 | /* Original rhs must be an integer that fits and is in range, */ | |
6031 | /* which could be from -1999999997 to +999999999, thanks to */ | |
6032 | /* subnormals */ | |
6033 | reqexp=decGetInt(inrhs); /* [cannot fail] */ | |
6034 | } | |
6035 | ||
6036 | #if DECSUBSET | |
6037 | if (!set->extended) etiny=set->emin; /* no subnormals */ | |
6038 | #endif | |
6039 | ||
6040 | if (reqexp==BADINT /* bad (rescale only) or .. */ | |
6041 | || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ | |
6042 | || (reqexp<etiny) /* < lowest */ | |
6043 | || (reqexp>set->emax)) { /* > emax */ | |
6044 | *status|=DEC_Invalid_operation; | |
6045 | break;} | |
6046 | ||
6047 | /* the RHS has been processed, so it can be overwritten now if necessary */ | |
6048 | if (ISZERO(lhs)) { /* zero coefficient unchanged */ | |
6049 | decNumberCopy(res, lhs); /* [nop if in place] */ | |
6050 | res->exponent=reqexp; /* .. just set exponent */ | |
6051 | #if DECSUBSET | |
6052 | if (!set->extended) res->bits=0; /* subset specification; no -0 */ | |
6053 | #endif | |
6054 | } | |
6055 | else { /* non-zero lhs */ | |
6056 | Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ | |
6057 | /* if adjusted coefficient will definitely not fit, give up now */ | |
6058 | if ((lhs->digits-adjust)>reqdigits) { | |
6059 | *status|=DEC_Invalid_operation; | |
6060 | break; | |
6061 | } | |
6062 | ||
6063 | if (adjust>0) { /* increasing exponent */ | |
6064 | /* this will decrease the length of the coefficient by adjust */ | |
6065 | /* digits, and must round as it does so */ | |
6066 | decContext workset; /* work */ | |
6067 | workset=*set; /* clone rounding, etc. */ | |
6068 | workset.digits=lhs->digits-adjust; /* set requested length */ | |
6069 | /* [note that the latter can be <1, here] */ | |
6070 | decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ | |
6071 | decApplyRound(res, &workset, residue, status); /* .. and round */ | |
6072 | residue=0; /* [used] */ | |
6073 | /* If just rounded a 999s case, exponent will be off by one; */ | |
6074 | /* adjust back (after checking space), if so. */ | |
6075 | if (res->exponent>reqexp) { | |
6076 | /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ | |
6077 | /* set->digits==3 */ | |
6078 | if (res->digits==reqdigits) { /* cannot shift by 1 */ | |
6079 | *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ | |
6080 | *status|=DEC_Invalid_operation; | |
6081 | break; | |
6082 | } | |
6083 | res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ | |
6084 | res->exponent--; /* (re)adjust the exponent. */ | |
6085 | } | |
6086 | #if DECSUBSET | |
6087 | if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ | |
6088 | #endif | |
6089 | } /* increase */ | |
6090 | else /* adjust<=0 */ { /* decreasing or = exponent */ | |
6091 | /* this will increase the length of the coefficient by -adjust */ | |
6092 | /* digits, by adding zero or more trailing zeros; this is */ | |
6093 | /* already checked for fit, above */ | |
6094 | decNumberCopy(res, lhs); /* [it will fit] */ | |
6095 | /* if padding needed (adjust<0), add it now... */ | |
6096 | if (adjust<0) { | |
6097 | res->digits=decShiftToMost(res->lsu, res->digits, -adjust); | |
6098 | res->exponent+=adjust; /* adjust the exponent */ | |
6099 | } | |
6100 | } /* decrease */ | |
6101 | } /* non-zero */ | |
6102 | ||
6103 | /* Check for overflow [do not use Finalize in this case, as an */ | |
6104 | /* overflow here is a "don't fit" situation] */ | |
6105 | if (res->exponent>set->emax-res->digits+1) { /* too big */ | |
6106 | *status|=DEC_Invalid_operation; | |
6107 | break; | |
6108 | } | |
6109 | else { | |
6110 | decFinalize(res, set, &residue, status); /* set subnormal flags */ | |
6111 | *status&=~DEC_Underflow; /* suppress Underflow [754r] */ | |
6112 | } | |
6113 | } while(0); /* end protected */ | |
6114 | ||
6115 | #if DECSUBSET | |
6116 | if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ | |
6117 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
6118 | #endif | |
6119 | return res; | |
6120 | } /* decQuantizeOp */ | |
6121 | ||
6122 | /* ------------------------------------------------------------------ */ | |
6123 | /* decCompareOp -- compare, min, or max two Numbers */ | |
6124 | /* */ | |
6125 | /* This computes C = A ? B and carries out one of four operations: */ | |
6126 | /* COMPARE -- returns the signum (as a number) giving the */ | |
6127 | /* result of a comparison unless one or both */ | |
6128 | /* operands is a NaN (in which case a NaN results) */ | |
6129 | /* COMPSIG -- as COMPARE except that a quiet NaN raises */ | |
6130 | /* Invalid operation. */ | |
6131 | /* COMPMAX -- returns the larger of the operands, using the */ | |
6132 | /* 754r maxnum operation */ | |
6133 | /* COMPMAXMAG -- ditto, comparing absolute values */ | |
6134 | /* COMPMIN -- the 754r minnum operation */ | |
6135 | /* COMPMINMAG -- ditto, comparing absolute values */ | |
6136 | /* COMTOTAL -- returns the signum (as a number) giving the */ | |
6137 | /* result of a comparison using 754r total ordering */ | |
6138 | /* */ | |
6139 | /* res is C, the result. C may be A and/or B (e.g., X=X?X) */ | |
6140 | /* lhs is A */ | |
6141 | /* rhs is B */ | |
6142 | /* set is the context */ | |
6143 | /* op is the operation flag */ | |
6144 | /* status is the usual accumulator */ | |
6145 | /* */ | |
6146 | /* C must have space for one digit for COMPARE or set->digits for */ | |
6147 | /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ | |
6148 | /* ------------------------------------------------------------------ */ | |
6149 | /* The emphasis here is on speed for common cases, and avoiding */ | |
6150 | /* coefficient comparison if possible. */ | |
6151 | /* ------------------------------------------------------------------ */ | |
d072cdf3 SW |
6152 | static decNumber *decCompareOp(decNumber *res, const decNumber *lhs, |
6153 | const decNumber *rhs, decContext *set, | |
6154 | Flag op, uInt *status) { | |
72ac97cd TM |
6155 | #if DECSUBSET |
6156 | decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ | |
6157 | decNumber *allocrhs=NULL; /* .., rhs */ | |
6158 | #endif | |
6159 | Int result=0; /* default result value */ | |
6160 | uByte merged; /* work */ | |
6161 | ||
6162 | #if DECCHECK | |
6163 | if (decCheckOperands(res, lhs, rhs, set)) return res; | |
6164 | #endif | |
6165 | ||
6166 | do { /* protect allocated storage */ | |
6167 | #if DECSUBSET | |
6168 | if (!set->extended) { | |
6169 | /* reduce operands and set lostDigits status, as needed */ | |
6170 | if (lhs->digits>set->digits) { | |
6171 | alloclhs=decRoundOperand(lhs, set, status); | |
6172 | if (alloclhs==NULL) {result=BADINT; break;} | |
6173 | lhs=alloclhs; | |
6174 | } | |
6175 | if (rhs->digits>set->digits) { | |
6176 | allocrhs=decRoundOperand(rhs, set, status); | |
6177 | if (allocrhs==NULL) {result=BADINT; break;} | |
6178 | rhs=allocrhs; | |
6179 | } | |
6180 | } | |
6181 | #endif | |
6182 | /* [following code does not require input rounding] */ | |
6183 | ||
6184 | /* If total ordering then handle differing signs 'up front' */ | |
6185 | if (op==COMPTOTAL) { /* total ordering */ | |
d072cdf3 | 6186 | if (decNumberIsNegative(lhs) && !decNumberIsNegative(rhs)) { |
72ac97cd TM |
6187 | result=-1; |
6188 | break; | |
6189 | } | |
d072cdf3 | 6190 | if (!decNumberIsNegative(lhs) && decNumberIsNegative(rhs)) { |
72ac97cd TM |
6191 | result=+1; |
6192 | break; | |
6193 | } | |
6194 | } | |
6195 | ||
6196 | /* handle NaNs specially; let infinities drop through */ | |
6197 | /* This assumes sNaN (even just one) leads to NaN. */ | |
6198 | merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); | |
6199 | if (merged) { /* a NaN bit set */ | |
6200 | if (op==COMPARE); /* result will be NaN */ | |
6201 | else if (op==COMPSIG) /* treat qNaN as sNaN */ | |
6202 | *status|=DEC_Invalid_operation | DEC_sNaN; | |
6203 | else if (op==COMPTOTAL) { /* total ordering, always finite */ | |
6204 | /* signs are known to be the same; compute the ordering here */ | |
6205 | /* as if the signs are both positive, then invert for negatives */ | |
6206 | if (!decNumberIsNaN(lhs)) result=-1; | |
6207 | else if (!decNumberIsNaN(rhs)) result=+1; | |
6208 | /* here if both NaNs */ | |
6209 | else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; | |
6210 | else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; | |
6211 | else { /* both NaN or both sNaN */ | |
6212 | /* now it just depends on the payload */ | |
6213 | result=decUnitCompare(lhs->lsu, D2U(lhs->digits), | |
6214 | rhs->lsu, D2U(rhs->digits), 0); | |
6215 | /* [Error not possible, as these are 'aligned'] */ | |
6216 | } /* both same NaNs */ | |
6217 | if (decNumberIsNegative(lhs)) result=-result; | |
6218 | break; | |
6219 | } /* total order */ | |
6220 | ||
6221 | else if (merged & DECSNAN); /* sNaN -> qNaN */ | |
6222 | else { /* here if MIN or MAX and one or two quiet NaNs */ | |
6223 | /* min or max -- 754r rules ignore single NaN */ | |
6224 | if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { | |
6225 | /* just one NaN; force choice to be the non-NaN operand */ | |
6226 | op=COMPMAX; | |
6227 | if (lhs->bits & DECNAN) result=-1; /* pick rhs */ | |
6228 | else result=+1; /* pick lhs */ | |
6229 | break; | |
6230 | } | |
6231 | } /* max or min */ | |
6232 | op=COMPNAN; /* use special path */ | |
6233 | decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ | |
6234 | break; | |
6235 | } | |
6236 | /* have numbers */ | |
6237 | if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); | |
6238 | else result=decCompare(lhs, rhs, 0); /* sign matters */ | |
6239 | } while(0); /* end protected */ | |
6240 | ||
6241 | if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ | |
6242 | else { | |
6243 | if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ | |
6244 | if (op==COMPTOTAL && result==0) { | |
6245 | /* operands are numerically equal or same NaN (and same sign, */ | |
6246 | /* tested first); if identical, leave result 0 */ | |
6247 | if (lhs->exponent!=rhs->exponent) { | |
6248 | if (lhs->exponent<rhs->exponent) result=-1; | |
6249 | else result=+1; | |
6250 | if (decNumberIsNegative(lhs)) result=-result; | |
6251 | } /* lexp!=rexp */ | |
6252 | } /* total-order by exponent */ | |
6253 | decNumberZero(res); /* [always a valid result] */ | |
6254 | if (result!=0) { /* must be -1 or +1 */ | |
6255 | *res->lsu=1; | |
6256 | if (result<0) res->bits=DECNEG; | |
6257 | } | |
6258 | } | |
6259 | else if (op==COMPNAN); /* special, drop through */ | |
6260 | else { /* MAX or MIN, non-NaN result */ | |
6261 | Int residue=0; /* rounding accumulator */ | |
6262 | /* choose the operand for the result */ | |
6263 | const decNumber *choice; | |
6264 | if (result==0) { /* operands are numerically equal */ | |
6265 | /* choose according to sign then exponent (see 754r) */ | |
6266 | uByte slhs=(lhs->bits & DECNEG); | |
6267 | uByte srhs=(rhs->bits & DECNEG); | |
6268 | #if DECSUBSET | |
6269 | if (!set->extended) { /* subset: force left-hand */ | |
6270 | op=COMPMAX; | |
6271 | result=+1; | |
6272 | } | |
6273 | else | |
6274 | #endif | |
6275 | if (slhs!=srhs) { /* signs differ */ | |
6276 | if (slhs) result=-1; /* rhs is max */ | |
6277 | else result=+1; /* lhs is max */ | |
6278 | } | |
6279 | else if (slhs && srhs) { /* both negative */ | |
6280 | if (lhs->exponent<rhs->exponent) result=+1; | |
6281 | else result=-1; | |
6282 | /* [if equal, use lhs, technically identical] */ | |
6283 | } | |
6284 | else { /* both positive */ | |
6285 | if (lhs->exponent>rhs->exponent) result=+1; | |
6286 | else result=-1; | |
6287 | /* [ditto] */ | |
6288 | } | |
6289 | } /* numerically equal */ | |
6290 | /* here result will be non-0; reverse if looking for MIN */ | |
6291 | if (op==COMPMIN || op==COMPMINMAG) result=-result; | |
6292 | choice=(result>0 ? lhs : rhs); /* choose */ | |
6293 | /* copy chosen to result, rounding if need be */ | |
6294 | decCopyFit(res, choice, set, &residue, status); | |
6295 | decFinish(res, set, &residue, status); | |
6296 | } | |
6297 | } | |
6298 | #if DECSUBSET | |
6299 | if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ | |
6300 | if (alloclhs!=NULL) free(alloclhs); /* .. */ | |
6301 | #endif | |
6302 | return res; | |
6303 | } /* decCompareOp */ | |
6304 | ||
6305 | /* ------------------------------------------------------------------ */ | |
6306 | /* decCompare -- compare two decNumbers by numerical value */ | |
6307 | /* */ | |
6308 | /* This routine compares A ? B without altering them. */ | |
6309 | /* */ | |
6310 | /* Arg1 is A, a decNumber which is not a NaN */ | |
6311 | /* Arg2 is B, a decNumber which is not a NaN */ | |
6312 | /* Arg3 is 1 for a sign-independent compare, 0 otherwise */ | |
6313 | /* */ | |
6314 | /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ | |
6315 | /* (the only possible failure is an allocation error) */ | |
6316 | /* ------------------------------------------------------------------ */ | |
6317 | static Int decCompare(const decNumber *lhs, const decNumber *rhs, | |
6318 | Flag abs) { | |
6319 | Int result; /* result value */ | |
6320 | Int sigr; /* rhs signum */ | |
6321 | Int compare; /* work */ | |
6322 | ||
6323 | result=1; /* assume signum(lhs) */ | |
6324 | if (ISZERO(lhs)) result=0; | |
6325 | if (abs) { | |
6326 | if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ | |
6327 | /* RHS is non-zero */ | |
6328 | if (result==0) return -1; /* LHS is 0; RHS wins */ | |
6329 | /* [here, both non-zero, result=1] */ | |
6330 | } | |
6331 | else { /* signs matter */ | |
6332 | if (result && decNumberIsNegative(lhs)) result=-1; | |
6333 | sigr=1; /* compute signum(rhs) */ | |
6334 | if (ISZERO(rhs)) sigr=0; | |
6335 | else if (decNumberIsNegative(rhs)) sigr=-1; | |
6336 | if (result > sigr) return +1; /* L > R, return 1 */ | |
6337 | if (result < sigr) return -1; /* L < R, return -1 */ | |
6338 | if (result==0) return 0; /* both 0 */ | |
6339 | } | |
6340 | ||
6341 | /* signums are the same; both are non-zero */ | |
6342 | if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ | |
6343 | if (decNumberIsInfinite(rhs)) { | |
6344 | if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ | |
6345 | else result=-result; /* only rhs infinite */ | |
6346 | } | |
6347 | return result; | |
6348 | } | |
6349 | /* must compare the coefficients, allowing for exponents */ | |
6350 | if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ | |
6351 | /* swap sides, and sign */ | |
6352 | const decNumber *temp=lhs; | |
6353 | lhs=rhs; | |
6354 | rhs=temp; | |
6355 | result=-result; | |
6356 | } | |
6357 | compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), | |
6358 | rhs->lsu, D2U(rhs->digits), | |
6359 | rhs->exponent-lhs->exponent); | |
6360 | if (compare!=BADINT) compare*=result; /* comparison succeeded */ | |
6361 | return compare; | |
6362 | } /* decCompare */ | |
6363 | ||
6364 | /* ------------------------------------------------------------------ */ | |
6365 | /* decUnitCompare -- compare two >=0 integers in Unit arrays */ | |
6366 | /* */ | |
6367 | /* This routine compares A ? B*10**E where A and B are unit arrays */ | |
6368 | /* A is a plain integer */ | |
6369 | /* B has an exponent of E (which must be non-negative) */ | |
6370 | /* */ | |
6371 | /* Arg1 is A first Unit (lsu) */ | |
6372 | /* Arg2 is A length in Units */ | |
6373 | /* Arg3 is B first Unit (lsu) */ | |
6374 | /* Arg4 is B length in Units */ | |
6375 | /* Arg5 is E (0 if the units are aligned) */ | |
6376 | /* */ | |
6377 | /* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ | |
6378 | /* (the only possible failure is an allocation error, which can */ | |
6379 | /* only occur if E!=0) */ | |
6380 | /* ------------------------------------------------------------------ */ | |
6381 | static Int decUnitCompare(const Unit *a, Int alength, | |
6382 | const Unit *b, Int blength, Int exp) { | |
6383 | Unit *acc; /* accumulator for result */ | |
6384 | Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ | |
6385 | Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ | |
6386 | Int accunits, need; /* units in use or needed for acc */ | |
6387 | const Unit *l, *r, *u; /* work */ | |
6388 | Int expunits, exprem, result; /* .. */ | |
6389 | ||
6390 | if (exp==0) { /* aligned; fastpath */ | |
6391 | if (alength>blength) return 1; | |
6392 | if (alength<blength) return -1; | |
6393 | /* same number of units in both -- need unit-by-unit compare */ | |
6394 | l=a+alength-1; | |
6395 | r=b+alength-1; | |
6396 | for (;l>=a; l--, r--) { | |
6397 | if (*l>*r) return 1; | |
6398 | if (*l<*r) return -1; | |
6399 | } | |
6400 | return 0; /* all units match */ | |
6401 | } /* aligned */ | |
6402 | ||
6403 | /* Unaligned. If one is >1 unit longer than the other, padded */ | |
6404 | /* approximately, then can return easily */ | |
6405 | if (alength>blength+(Int)D2U(exp)) return 1; | |
6406 | if (alength+1<blength+(Int)D2U(exp)) return -1; | |
6407 | ||
6408 | /* Need to do a real subtract. For this, a result buffer is needed */ | |
6409 | /* even though only the sign is of interest. Its length needs */ | |
6410 | /* to be the larger of alength and padded blength, +2 */ | |
6411 | need=blength+D2U(exp); /* maximum real length of B */ | |
6412 | if (need<alength) need=alength; | |
6413 | need+=2; | |
6414 | acc=accbuff; /* assume use local buffer */ | |
6415 | if (need*sizeof(Unit)>sizeof(accbuff)) { | |
6416 | allocacc=(Unit *)malloc(need*sizeof(Unit)); | |
6417 | if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ | |
6418 | acc=allocacc; | |
6419 | } | |
6420 | /* Calculate units and remainder from exponent. */ | |
6421 | expunits=exp/DECDPUN; | |
6422 | exprem=exp%DECDPUN; | |
6423 | /* subtract [A+B*(-m)] */ | |
6424 | accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, | |
6425 | -(Int)powers[exprem]); | |
6426 | /* [UnitAddSub result may have leading zeros, even on zero] */ | |
6427 | if (accunits<0) result=-1; /* negative result */ | |
6428 | else { /* non-negative result */ | |
6429 | /* check units of the result before freeing any storage */ | |
6430 | for (u=acc; u<acc+accunits-1 && *u==0;) u++; | |
6431 | result=(*u==0 ? 0 : +1); | |
6432 | } | |
6433 | /* clean up and return the result */ | |
6434 | if (allocacc!=NULL) free(allocacc); /* drop any storage used */ | |
6435 | return result; | |
6436 | } /* decUnitCompare */ | |
6437 | ||
6438 | /* ------------------------------------------------------------------ */ | |
6439 | /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ | |
6440 | /* */ | |
6441 | /* This routine performs the calculation: */ | |
6442 | /* */ | |
6443 | /* C=A+(B*M) */ | |
6444 | /* */ | |
6445 | /* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ | |
6446 | /* */ | |
6447 | /* A may be shorter or longer than B. */ | |
6448 | /* */ | |
6449 | /* Leading zeros are not removed after a calculation. The result is */ | |
6450 | /* either the same length as the longer of A and B (adding any */ | |
6451 | /* shift), or one Unit longer than that (if a Unit carry occurred). */ | |
6452 | /* */ | |
6453 | /* A and B content are not altered unless C is also A or B. */ | |
6454 | /* C may be the same array as A or B, but only if no zero padding is */ | |
6455 | /* requested (that is, C may be B only if bshift==0). */ | |
6456 | /* C is filled from the lsu; only those units necessary to complete */ | |
6457 | /* the calculation are referenced. */ | |
6458 | /* */ | |
6459 | /* Arg1 is A first Unit (lsu) */ | |
6460 | /* Arg2 is A length in Units */ | |
6461 | /* Arg3 is B first Unit (lsu) */ | |
6462 | /* Arg4 is B length in Units */ | |
6463 | /* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ | |
6464 | /* Arg6 is C first Unit (lsu) */ | |
6465 | /* Arg7 is M, the multiplier */ | |
6466 | /* */ | |
6467 | /* returns the count of Units written to C, which will be non-zero */ | |
6468 | /* and negated if the result is negative. That is, the sign of the */ | |
6469 | /* returned Int is the sign of the result (positive for zero) and */ | |
6470 | /* the absolute value of the Int is the count of Units. */ | |
6471 | /* */ | |
6472 | /* It is the caller's responsibility to make sure that C size is */ | |
6473 | /* safe, allowing space if necessary for a one-Unit carry. */ | |
6474 | /* */ | |
6475 | /* This routine is severely performance-critical; *any* change here */ | |
6476 | /* must be measured (timed) to assure no performance degradation. */ | |
6477 | /* In particular, trickery here tends to be counter-productive, as */ | |
6478 | /* increased complexity of code hurts register optimizations on */ | |
6479 | /* register-poor architectures. Avoiding divisions is nearly */ | |
6480 | /* always a Good Idea, however. */ | |
6481 | /* */ | |
6482 | /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ | |
6483 | /* (IBM Warwick, UK) for some of the ideas used in this routine. */ | |
6484 | /* ------------------------------------------------------------------ */ | |
6485 | static Int decUnitAddSub(const Unit *a, Int alength, | |
6486 | const Unit *b, Int blength, Int bshift, | |
6487 | Unit *c, Int m) { | |
6488 | const Unit *alsu=a; /* A lsu [need to remember it] */ | |
6489 | Unit *clsu=c; /* C ditto */ | |
6490 | Unit *minC; /* low water mark for C */ | |
6491 | Unit *maxC; /* high water mark for C */ | |
6492 | eInt carry=0; /* carry integer (could be Long) */ | |
6493 | Int add; /* work */ | |
6494 | #if DECDPUN<=4 /* myriadal, millenary, etc. */ | |
6495 | Int est; /* estimated quotient */ | |
6496 | #endif | |
6497 | ||
6498 | #if DECTRACE | |
6499 | if (alength<1 || blength<1) | |
6500 | printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); | |
6501 | #endif | |
6502 | ||
6503 | maxC=c+alength; /* A is usually the longer */ | |
6504 | minC=c+blength; /* .. and B the shorter */ | |
6505 | if (bshift!=0) { /* B is shifted; low As copy across */ | |
6506 | minC+=bshift; | |
6507 | /* if in place [common], skip copy unless there's a gap [rare] */ | |
6508 | if (a==c && bshift<=alength) { | |
6509 | c+=bshift; | |
6510 | a+=bshift; | |
6511 | } | |
6512 | else for (; c<clsu+bshift; a++, c++) { /* copy needed */ | |
6513 | if (a<alsu+alength) *c=*a; | |
6514 | else *c=0; | |
6515 | } | |
6516 | } | |
6517 | if (minC>maxC) { /* swap */ | |
6518 | Unit *hold=minC; | |
6519 | minC=maxC; | |
6520 | maxC=hold; | |
6521 | } | |
6522 | ||
6523 | /* For speed, do the addition as two loops; the first where both A */ | |
6524 | /* and B contribute, and the second (if necessary) where only one or */ | |
6525 | /* other of the numbers contribute. */ | |
6526 | /* Carry handling is the same (i.e., duplicated) in each case. */ | |
6527 | for (; c<minC; c++) { | |
6528 | carry+=*a; | |
6529 | a++; | |
6530 | carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ | |
6531 | b++; /* here is not a win] */ | |
6532 | /* here carry is new Unit of digits; it could be +ve or -ve */ | |
6533 | if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ | |
6534 | *c=(Unit)carry; | |
6535 | carry=0; | |
6536 | continue; | |
6537 | } | |
6538 | #if DECDPUN==4 /* use divide-by-multiply */ | |
6539 | if (carry>=0) { | |
6540 | est=(((ueInt)carry>>11)*53687)>>18; | |
6541 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6542 | carry=est; /* likely quotient [89%] */ | |
6543 | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ | |
6544 | carry++; | |
6545 | *c-=DECDPUNMAX+1; | |
6546 | continue; | |
6547 | } | |
6548 | /* negative case */ | |
6549 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6550 | est=(((ueInt)carry>>11)*53687)>>18; | |
6551 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6552 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6553 | if (*c<DECDPUNMAX+1) continue; /* was OK */ | |
6554 | carry++; | |
6555 | *c-=DECDPUNMAX+1; | |
6556 | #elif DECDPUN==3 | |
6557 | if (carry>=0) { | |
6558 | est=(((ueInt)carry>>3)*16777)>>21; | |
6559 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6560 | carry=est; /* likely quotient [99%] */ | |
6561 | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ | |
6562 | carry++; | |
6563 | *c-=DECDPUNMAX+1; | |
6564 | continue; | |
6565 | } | |
6566 | /* negative case */ | |
6567 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6568 | est=(((ueInt)carry>>3)*16777)>>21; | |
6569 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6570 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6571 | if (*c<DECDPUNMAX+1) continue; /* was OK */ | |
6572 | carry++; | |
6573 | *c-=DECDPUNMAX+1; | |
6574 | #elif DECDPUN<=2 | |
6575 | /* Can use QUOT10 as carry <= 4 digits */ | |
6576 | if (carry>=0) { | |
6577 | est=QUOT10(carry, DECDPUN); | |
6578 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6579 | carry=est; /* quotient */ | |
6580 | continue; | |
6581 | } | |
6582 | /* negative case */ | |
6583 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6584 | est=QUOT10(carry, DECDPUN); | |
6585 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6586 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6587 | #else | |
6588 | /* remainder operator is undefined if negative, so must test */ | |
6589 | if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ | |
6590 | *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ | |
6591 | carry=1; | |
6592 | continue; | |
6593 | } | |
6594 | if (carry>=0) { | |
6595 | *c=(Unit)(carry%(DECDPUNMAX+1)); | |
6596 | carry=carry/(DECDPUNMAX+1); | |
6597 | continue; | |
6598 | } | |
6599 | /* negative case */ | |
6600 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6601 | *c=(Unit)(carry%(DECDPUNMAX+1)); | |
6602 | carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); | |
6603 | #endif | |
6604 | } /* c */ | |
6605 | ||
6606 | /* now may have one or other to complete */ | |
6607 | /* [pretest to avoid loop setup/shutdown] */ | |
6608 | if (c<maxC) for (; c<maxC; c++) { | |
6609 | if (a<alsu+alength) { /* still in A */ | |
6610 | carry+=*a; | |
6611 | a++; | |
6612 | } | |
6613 | else { /* inside B */ | |
6614 | carry+=((eInt)*b)*m; | |
6615 | b++; | |
6616 | } | |
6617 | /* here carry is new Unit of digits; it could be +ve or -ve and */ | |
6618 | /* magnitude up to DECDPUNMAX squared */ | |
6619 | if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ | |
6620 | *c=(Unit)carry; | |
6621 | carry=0; | |
6622 | continue; | |
6623 | } | |
6624 | /* result for this unit is negative or >DECDPUNMAX */ | |
6625 | #if DECDPUN==4 /* use divide-by-multiply */ | |
6626 | if (carry>=0) { | |
6627 | est=(((ueInt)carry>>11)*53687)>>18; | |
6628 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6629 | carry=est; /* likely quotient [79.7%] */ | |
6630 | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ | |
6631 | carry++; | |
6632 | *c-=DECDPUNMAX+1; | |
6633 | continue; | |
6634 | } | |
6635 | /* negative case */ | |
6636 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6637 | est=(((ueInt)carry>>11)*53687)>>18; | |
6638 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6639 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6640 | if (*c<DECDPUNMAX+1) continue; /* was OK */ | |
6641 | carry++; | |
6642 | *c-=DECDPUNMAX+1; | |
6643 | #elif DECDPUN==3 | |
6644 | if (carry>=0) { | |
6645 | est=(((ueInt)carry>>3)*16777)>>21; | |
6646 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6647 | carry=est; /* likely quotient [99%] */ | |
6648 | if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ | |
6649 | carry++; | |
6650 | *c-=DECDPUNMAX+1; | |
6651 | continue; | |
6652 | } | |
6653 | /* negative case */ | |
6654 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6655 | est=(((ueInt)carry>>3)*16777)>>21; | |
6656 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6657 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6658 | if (*c<DECDPUNMAX+1) continue; /* was OK */ | |
6659 | carry++; | |
6660 | *c-=DECDPUNMAX+1; | |
6661 | #elif DECDPUN<=2 | |
6662 | if (carry>=0) { | |
6663 | est=QUOT10(carry, DECDPUN); | |
6664 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ | |
6665 | carry=est; /* quotient */ | |
6666 | continue; | |
6667 | } | |
6668 | /* negative case */ | |
6669 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6670 | est=QUOT10(carry, DECDPUN); | |
6671 | *c=(Unit)(carry-est*(DECDPUNMAX+1)); | |
6672 | carry=est-(DECDPUNMAX+1); /* correctly negative */ | |
6673 | #else | |
6674 | if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ | |
6675 | *c=(Unit)(carry-(DECDPUNMAX+1)); | |
6676 | carry=1; | |
6677 | continue; | |
6678 | } | |
6679 | /* remainder operator is undefined if negative, so must test */ | |
6680 | if (carry>=0) { | |
6681 | *c=(Unit)(carry%(DECDPUNMAX+1)); | |
6682 | carry=carry/(DECDPUNMAX+1); | |
6683 | continue; | |
6684 | } | |
6685 | /* negative case */ | |
6686 | carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ | |
6687 | *c=(Unit)(carry%(DECDPUNMAX+1)); | |
6688 | carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); | |
6689 | #endif | |
6690 | } /* c */ | |
6691 | ||
6692 | /* OK, all A and B processed; might still have carry or borrow */ | |
6693 | /* return number of Units in the result, negated if a borrow */ | |
6694 | if (carry==0) return c-clsu; /* no carry, so no more to do */ | |
6695 | if (carry>0) { /* positive carry */ | |
6696 | *c=(Unit)carry; /* place as new unit */ | |
6697 | c++; /* .. */ | |
6698 | return c-clsu; | |
6699 | } | |
6700 | /* -ve carry: it's a borrow; complement needed */ | |
6701 | add=1; /* temporary carry... */ | |
6702 | for (c=clsu; c<maxC; c++) { | |
6703 | add=DECDPUNMAX+add-*c; | |
6704 | if (add<=DECDPUNMAX) { | |
6705 | *c=(Unit)add; | |
6706 | add=0; | |
6707 | } | |
6708 | else { | |
6709 | *c=0; | |
6710 | add=1; | |
6711 | } | |
6712 | } | |
6713 | /* add an extra unit iff it would be non-zero */ | |
6714 | #if DECTRACE | |
6715 | printf("UAS borrow: add %ld, carry %ld\n", add, carry); | |
6716 | #endif | |
6717 | if ((add-carry-1)!=0) { | |
6718 | *c=(Unit)(add-carry-1); | |
6719 | c++; /* interesting, include it */ | |
6720 | } | |
6721 | return clsu-c; /* -ve result indicates borrowed */ | |
6722 | } /* decUnitAddSub */ | |
6723 | ||
6724 | /* ------------------------------------------------------------------ */ | |
6725 | /* decTrim -- trim trailing zeros or normalize */ | |
6726 | /* */ | |
6727 | /* dn is the number to trim or normalize */ | |
6728 | /* set is the context to use to check for clamp */ | |
6729 | /* all is 1 to remove all trailing zeros, 0 for just fraction ones */ | |
6730 | /* dropped returns the number of discarded trailing zeros */ | |
6731 | /* returns dn */ | |
6732 | /* */ | |
6733 | /* If clamp is set in the context then the number of zeros trimmed */ | |
6734 | /* may be limited if the exponent is high. */ | |
6735 | /* All fields are updated as required. This is a utility operation, */ | |
6736 | /* so special values are unchanged and no error is possible. */ | |
6737 | /* ------------------------------------------------------------------ */ | |
6738 | static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, | |
6739 | Int *dropped) { | |
6740 | Int d, exp; /* work */ | |
6741 | uInt cut; /* .. */ | |
6742 | Unit *up; /* -> current Unit */ | |
6743 | ||
6744 | #if DECCHECK | |
6745 | if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; | |
6746 | #endif | |
6747 | ||
6748 | *dropped=0; /* assume no zeros dropped */ | |
6749 | if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ | |
6750 | || (*dn->lsu & 0x01)) return dn; /* .. or odd */ | |
6751 | if (ISZERO(dn)) { /* .. or 0 */ | |
6752 | dn->exponent=0; /* (sign is preserved) */ | |
6753 | return dn; | |
6754 | } | |
6755 | ||
6756 | /* have a finite number which is even */ | |
6757 | exp=dn->exponent; | |
6758 | cut=1; /* digit (1-DECDPUN) in Unit */ | |
6759 | up=dn->lsu; /* -> current Unit */ | |
6760 | for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ | |
6761 | /* slice by powers */ | |
6762 | #if DECDPUN<=4 | |
6763 | uInt quot=QUOT10(*up, cut); | |
6764 | if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ | |
6765 | #else | |
6766 | if (*up%powers[cut]!=0) break; /* found non-0 digit */ | |
6767 | #endif | |
6768 | /* have a trailing 0 */ | |
6769 | if (!all) { /* trimming */ | |
6770 | /* [if exp>0 then all trailing 0s are significant for trim] */ | |
6771 | if (exp<=0) { /* if digit might be significant */ | |
6772 | if (exp==0) break; /* then quit */ | |
6773 | exp++; /* next digit might be significant */ | |
6774 | } | |
6775 | } | |
6776 | cut++; /* next power */ | |
6777 | if (cut>DECDPUN) { /* need new Unit */ | |
6778 | up++; | |
6779 | cut=1; | |
6780 | } | |
6781 | } /* d */ | |
6782 | if (d==0) return dn; /* none to drop */ | |
6783 | ||
6784 | /* may need to limit drop if clamping */ | |
6785 | if (set->clamp) { | |
6786 | Int maxd=set->emax-set->digits+1-dn->exponent; | |
6787 | if (maxd<=0) return dn; /* nothing possible */ | |
6788 | if (d>maxd) d=maxd; | |
6789 | } | |
6790 | ||
6791 | /* effect the drop */ | |
6792 | decShiftToLeast(dn->lsu, D2U(dn->digits), d); | |
6793 | dn->exponent+=d; /* maintain numerical value */ | |
6794 | dn->digits-=d; /* new length */ | |
6795 | *dropped=d; /* report the count */ | |
6796 | return dn; | |
6797 | } /* decTrim */ | |
6798 | ||
6799 | /* ------------------------------------------------------------------ */ | |
6800 | /* decReverse -- reverse a Unit array in place */ | |
6801 | /* */ | |
6802 | /* ulo is the start of the array */ | |
6803 | /* uhi is the end of the array (highest Unit to include) */ | |
6804 | /* */ | |
6805 | /* The units ulo through uhi are reversed in place (if the number */ | |
6806 | /* of units is odd, the middle one is untouched). Note that the */ | |
6807 | /* digit(s) in each unit are unaffected. */ | |
6808 | /* ------------------------------------------------------------------ */ | |
6809 | static void decReverse(Unit *ulo, Unit *uhi) { | |
6810 | Unit temp; | |
6811 | for (; ulo<uhi; ulo++, uhi--) { | |
6812 | temp=*ulo; | |
6813 | *ulo=*uhi; | |
6814 | *uhi=temp; | |
6815 | } | |
6816 | return; | |
6817 | } /* decReverse */ | |
6818 | ||
6819 | /* ------------------------------------------------------------------ */ | |
6820 | /* decShiftToMost -- shift digits in array towards most significant */ | |
6821 | /* */ | |
6822 | /* uar is the array */ | |
6823 | /* digits is the count of digits in use in the array */ | |
6824 | /* shift is the number of zeros to pad with (least significant); */ | |
6825 | /* it must be zero or positive */ | |
6826 | /* */ | |
6827 | /* returns the new length of the integer in the array, in digits */ | |
6828 | /* */ | |
6829 | /* No overflow is permitted (that is, the uar array must be known to */ | |
6830 | /* be large enough to hold the result, after shifting). */ | |
6831 | /* ------------------------------------------------------------------ */ | |
6832 | static Int decShiftToMost(Unit *uar, Int digits, Int shift) { | |
6833 | Unit *target, *source, *first; /* work */ | |
6834 | Int cut; /* odd 0's to add */ | |
6835 | uInt next; /* work */ | |
6836 | ||
6837 | if (shift==0) return digits; /* [fastpath] nothing to do */ | |
6838 | if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ | |
6839 | *uar=(Unit)(*uar*powers[shift]); | |
6840 | return digits+shift; | |
6841 | } | |
6842 | ||
6843 | next=0; /* all paths */ | |
6844 | source=uar+D2U(digits)-1; /* where msu comes from */ | |
6845 | target=source+D2U(shift); /* where upper part of first cut goes */ | |
6846 | cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ | |
6847 | if (cut==0) { /* unit-boundary case */ | |
6848 | for (; source>=uar; source--, target--) *target=*source; | |
6849 | } | |
6850 | else { | |
6851 | first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ | |
6852 | for (; source>=uar; source--, target--) { | |
6853 | /* split the source Unit and accumulate remainder for next */ | |
6854 | #if DECDPUN<=4 | |
6855 | uInt quot=QUOT10(*source, cut); | |
6856 | uInt rem=*source-quot*powers[cut]; | |
6857 | next+=quot; | |
6858 | #else | |
6859 | uInt rem=*source%powers[cut]; | |
6860 | next+=*source/powers[cut]; | |
6861 | #endif | |
6862 | if (target<=first) *target=(Unit)next; /* write to target iff valid */ | |
6863 | next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ | |
6864 | } | |
6865 | } /* shift-move */ | |
6866 | ||
6867 | /* propagate any partial unit to one below and clear the rest */ | |
6868 | for (; target>=uar; target--) { | |
6869 | *target=(Unit)next; | |
6870 | next=0; | |
6871 | } | |
6872 | return digits+shift; | |
6873 | } /* decShiftToMost */ | |
6874 | ||
6875 | /* ------------------------------------------------------------------ */ | |
6876 | /* decShiftToLeast -- shift digits in array towards least significant */ | |
6877 | /* */ | |
6878 | /* uar is the array */ | |
6879 | /* units is length of the array, in units */ | |
6880 | /* shift is the number of digits to remove from the lsu end; it */ | |
6881 | /* must be zero or positive and <= than units*DECDPUN. */ | |
6882 | /* */ | |
6883 | /* returns the new length of the integer in the array, in units */ | |
6884 | /* */ | |
6885 | /* Removed digits are discarded (lost). Units not required to hold */ | |
6886 | /* the final result are unchanged. */ | |
6887 | /* ------------------------------------------------------------------ */ | |
6888 | static Int decShiftToLeast(Unit *uar, Int units, Int shift) { | |
6889 | Unit *target, *up; /* work */ | |
6890 | Int cut, count; /* work */ | |
6891 | Int quot, rem; /* for division */ | |
6892 | ||
6893 | if (shift==0) return units; /* [fastpath] nothing to do */ | |
6894 | if (shift==units*DECDPUN) { /* [fastpath] little to do */ | |
6895 | *uar=0; /* all digits cleared gives zero */ | |
6896 | return 1; /* leaves just the one */ | |
6897 | } | |
6898 | ||
6899 | target=uar; /* both paths */ | |
6900 | cut=MSUDIGITS(shift); | |
6901 | if (cut==DECDPUN) { /* unit-boundary case; easy */ | |
6902 | up=uar+D2U(shift); | |
6903 | for (; up<uar+units; target++, up++) *target=*up; | |
6904 | return target-uar; | |
6905 | } | |
6906 | ||
6907 | /* messier */ | |
6908 | up=uar+D2U(shift-cut); /* source; correct to whole Units */ | |
6909 | count=units*DECDPUN-shift; /* the maximum new length */ | |
6910 | #if DECDPUN<=4 | |
6911 | quot=QUOT10(*up, cut); | |
6912 | #else | |
6913 | quot=*up/powers[cut]; | |
6914 | #endif | |
6915 | for (; ; target++) { | |
6916 | *target=(Unit)quot; | |
6917 | count-=(DECDPUN-cut); | |
6918 | if (count<=0) break; | |
6919 | up++; | |
6920 | quot=*up; | |
6921 | #if DECDPUN<=4 | |
6922 | quot=QUOT10(quot, cut); | |
6923 | rem=*up-quot*powers[cut]; | |
6924 | #else | |
6925 | rem=quot%powers[cut]; | |
6926 | quot=quot/powers[cut]; | |
6927 | #endif | |
6928 | *target=(Unit)(*target+rem*powers[DECDPUN-cut]); | |
6929 | count-=cut; | |
6930 | if (count<=0) break; | |
6931 | } | |
6932 | return target-uar+1; | |
6933 | } /* decShiftToLeast */ | |
6934 | ||
6935 | #if DECSUBSET | |
6936 | /* ------------------------------------------------------------------ */ | |
6937 | /* decRoundOperand -- round an operand [used for subset only] */ | |
6938 | /* */ | |
6939 | /* dn is the number to round (dn->digits is > set->digits) */ | |
6940 | /* set is the relevant context */ | |
6941 | /* status is the status accumulator */ | |
6942 | /* */ | |
6943 | /* returns an allocated decNumber with the rounded result. */ | |
6944 | /* */ | |
6945 | /* lostDigits and other status may be set by this. */ | |
6946 | /* */ | |
6947 | /* Since the input is an operand, it must not be modified. */ | |
6948 | /* Instead, return an allocated decNumber, rounded as required. */ | |
6949 | /* It is the caller's responsibility to free the allocated storage. */ | |
6950 | /* */ | |
6951 | /* If no storage is available then the result cannot be used, so NULL */ | |
6952 | /* is returned. */ | |
6953 | /* ------------------------------------------------------------------ */ | |
6954 | static decNumber *decRoundOperand(const decNumber *dn, decContext *set, | |
6955 | uInt *status) { | |
6956 | decNumber *res; /* result structure */ | |
6957 | uInt newstatus=0; /* status from round */ | |
6958 | Int residue=0; /* rounding accumulator */ | |
6959 | ||
6960 | /* Allocate storage for the returned decNumber, big enough for the */ | |
6961 | /* length specified by the context */ | |
6962 | res=(decNumber *)malloc(sizeof(decNumber) | |
6963 | +(D2U(set->digits)-1)*sizeof(Unit)); | |
6964 | if (res==NULL) { | |
6965 | *status|=DEC_Insufficient_storage; | |
6966 | return NULL; | |
6967 | } | |
6968 | decCopyFit(res, dn, set, &residue, &newstatus); | |
6969 | decApplyRound(res, set, residue, &newstatus); | |
6970 | ||
6971 | /* If that set Inexact then "lost digits" is raised... */ | |
6972 | if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; | |
6973 | *status|=newstatus; | |
6974 | return res; | |
6975 | } /* decRoundOperand */ | |
6976 | #endif | |
6977 | ||
6978 | /* ------------------------------------------------------------------ */ | |
6979 | /* decCopyFit -- copy a number, truncating the coefficient if needed */ | |
6980 | /* */ | |
6981 | /* dest is the target decNumber */ | |
6982 | /* src is the source decNumber */ | |
6983 | /* set is the context [used for length (digits) and rounding mode] */ | |
6984 | /* residue is the residue accumulator */ | |
6985 | /* status contains the current status to be updated */ | |
6986 | /* */ | |
6987 | /* (dest==src is allowed and will be a no-op if fits) */ | |
6988 | /* All fields are updated as required. */ | |
6989 | /* ------------------------------------------------------------------ */ | |
6990 | static void decCopyFit(decNumber *dest, const decNumber *src, | |
6991 | decContext *set, Int *residue, uInt *status) { | |
6992 | dest->bits=src->bits; | |
6993 | dest->exponent=src->exponent; | |
6994 | decSetCoeff(dest, set, src->lsu, src->digits, residue, status); | |
6995 | } /* decCopyFit */ | |
6996 | ||
6997 | /* ------------------------------------------------------------------ */ | |
6998 | /* decSetCoeff -- set the coefficient of a number */ | |
6999 | /* */ | |
7000 | /* dn is the number whose coefficient array is to be set. */ | |
7001 | /* It must have space for set->digits digits */ | |
7002 | /* set is the context [for size] */ | |
7003 | /* lsu -> lsu of the source coefficient [may be dn->lsu] */ | |
7004 | /* len is digits in the source coefficient [may be dn->digits] */ | |
7005 | /* residue is the residue accumulator. This has values as in */ | |
7006 | /* decApplyRound, and will be unchanged unless the */ | |
7007 | /* target size is less than len. In this case, the */ | |
7008 | /* coefficient is truncated and the residue is updated to */ | |
7009 | /* reflect the previous residue and the dropped digits. */ | |
7010 | /* status is the status accumulator, as usual */ | |
7011 | /* */ | |
7012 | /* The coefficient may already be in the number, or it can be an */ | |
7013 | /* external intermediate array. If it is in the number, lsu must == */ | |
7014 | /* dn->lsu and len must == dn->digits. */ | |
7015 | /* */ | |
7016 | /* Note that the coefficient length (len) may be < set->digits, and */ | |
7017 | /* in this case this merely copies the coefficient (or is a no-op */ | |
7018 | /* if dn->lsu==lsu). */ | |
7019 | /* */ | |
7020 | /* Note also that (only internally, from decQuantizeOp and */ | |
7021 | /* decSetSubnormal) the value of set->digits may be less than one, */ | |
7022 | /* indicating a round to left. This routine handles that case */ | |
7023 | /* correctly; caller ensures space. */ | |
7024 | /* */ | |
7025 | /* dn->digits, dn->lsu (and as required), and dn->exponent are */ | |
7026 | /* updated as necessary. dn->bits (sign) is unchanged. */ | |
7027 | /* */ | |
7028 | /* DEC_Rounded status is set if any digits are discarded. */ | |
7029 | /* DEC_Inexact status is set if any non-zero digits are discarded, or */ | |
7030 | /* incoming residue was non-0 (implies rounded) */ | |
7031 | /* ------------------------------------------------------------------ */ | |
7032 | /* mapping array: maps 0-9 to canonical residues, so that a residue */ | |
7033 | /* can be adjusted in the range [-1, +1] and achieve correct rounding */ | |
7034 | /* 0 1 2 3 4 5 6 7 8 9 */ | |
7035 | static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; | |
7036 | static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, | |
7037 | Int len, Int *residue, uInt *status) { | |
7038 | Int discard; /* number of digits to discard */ | |
7039 | uInt cut; /* cut point in Unit */ | |
7040 | const Unit *up; /* work */ | |
7041 | Unit *target; /* .. */ | |
7042 | Int count; /* .. */ | |
7043 | #if DECDPUN<=4 | |
7044 | uInt temp; /* .. */ | |
7045 | #endif | |
7046 | ||
7047 | discard=len-set->digits; /* digits to discard */ | |
7048 | if (discard<=0) { /* no digits are being discarded */ | |
7049 | if (dn->lsu!=lsu) { /* copy needed */ | |
7050 | /* copy the coefficient array to the result number; no shift needed */ | |
7051 | count=len; /* avoids D2U */ | |
7052 | up=lsu; | |
7053 | for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) | |
7054 | *target=*up; | |
7055 | dn->digits=len; /* set the new length */ | |
7056 | } | |
7057 | /* dn->exponent and residue are unchanged, record any inexactitude */ | |
7058 | if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); | |
7059 | return; | |
7060 | } | |
7061 | ||
7062 | /* some digits must be discarded ... */ | |
7063 | dn->exponent+=discard; /* maintain numerical value */ | |
7064 | *status|=DEC_Rounded; /* accumulate Rounded status */ | |
7065 | if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ | |
7066 | ||
7067 | if (discard>len) { /* everything, +1, is being discarded */ | |
7068 | /* guard digit is 0 */ | |
7069 | /* residue is all the number [NB could be all 0s] */ | |
7070 | if (*residue<=0) { /* not already positive */ | |
7071 | count=len; /* avoids D2U */ | |
7072 | for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ | |
7073 | *residue=1; | |
7074 | break; /* no need to check any others */ | |
7075 | } | |
7076 | } | |
7077 | if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ | |
7078 | *dn->lsu=0; /* coefficient will now be 0 */ | |
7079 | dn->digits=1; /* .. */ | |
7080 | return; | |
7081 | } /* total discard */ | |
7082 | ||
7083 | /* partial discard [most common case] */ | |
7084 | /* here, at least the first (most significant) discarded digit exists */ | |
7085 | ||
7086 | /* spin up the number, noting residue during the spin, until get to */ | |
7087 | /* the Unit with the first discarded digit. When reach it, extract */ | |
7088 | /* it and remember its position */ | |
7089 | count=0; | |
7090 | for (up=lsu;; up++) { | |
7091 | count+=DECDPUN; | |
7092 | if (count>=discard) break; /* full ones all checked */ | |
7093 | if (*up!=0) *residue=1; | |
7094 | } /* up */ | |
7095 | ||
7096 | /* here up -> Unit with first discarded digit */ | |
7097 | cut=discard-(count-DECDPUN)-1; | |
7098 | if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ | |
7099 | Unit half=(Unit)powers[DECDPUN]>>1; | |
7100 | /* set residue directly */ | |
7101 | if (*up>=half) { | |
7102 | if (*up>half) *residue=7; | |
7103 | else *residue+=5; /* add sticky bit */ | |
7104 | } | |
7105 | else { /* <half */ | |
7106 | if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ | |
7107 | } | |
7108 | if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ | |
7109 | *dn->lsu=0; /* .. result is 0 */ | |
7110 | dn->digits=1; /* .. */ | |
7111 | } | |
7112 | else { /* shift to least */ | |
7113 | count=set->digits; /* now digits to end up with */ | |
7114 | dn->digits=count; /* set the new length */ | |
7115 | up++; /* move to next */ | |
7116 | /* on unit boundary, so shift-down copy loop is simple */ | |
7117 | for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) | |
7118 | *target=*up; | |
7119 | } | |
7120 | } /* unit-boundary case */ | |
7121 | ||
7122 | else { /* discard digit is in low digit(s), and not top digit */ | |
7123 | uInt discard1; /* first discarded digit */ | |
7124 | uInt quot, rem; /* for divisions */ | |
7125 | if (cut==0) quot=*up; /* is at bottom of unit */ | |
7126 | else /* cut>0 */ { /* it's not at bottom of unit */ | |
7127 | #if DECDPUN<=4 | |
7128 | quot=QUOT10(*up, cut); | |
7129 | rem=*up-quot*powers[cut]; | |
7130 | #else | |
7131 | rem=*up%powers[cut]; | |
7132 | quot=*up/powers[cut]; | |
7133 | #endif | |
7134 | if (rem!=0) *residue=1; | |
7135 | } | |
7136 | /* discard digit is now at bottom of quot */ | |
7137 | #if DECDPUN<=4 | |
7138 | temp=(quot*6554)>>16; /* fast /10 */ | |
7139 | /* Vowels algorithm here not a win (9 instructions) */ | |
7140 | discard1=quot-X10(temp); | |
7141 | quot=temp; | |
7142 | #else | |
7143 | discard1=quot%10; | |
7144 | quot=quot/10; | |
7145 | #endif | |
7146 | /* here, discard1 is the guard digit, and residue is everything */ | |
7147 | /* else [use mapping array to accumulate residue safely] */ | |
7148 | *residue+=resmap[discard1]; | |
7149 | cut++; /* update cut */ | |
7150 | /* here: up -> Unit of the array with bottom digit */ | |
7151 | /* cut is the division point for each Unit */ | |
7152 | /* quot holds the uncut high-order digits for the current unit */ | |
7153 | if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ | |
7154 | *dn->lsu=0; /* .. result is 0 */ | |
7155 | dn->digits=1; /* .. */ | |
7156 | } | |
7157 | else { /* shift to least needed */ | |
7158 | count=set->digits; /* now digits to end up with */ | |
7159 | dn->digits=count; /* set the new length */ | |
7160 | /* shift-copy the coefficient array to the result number */ | |
7161 | for (target=dn->lsu; ; target++) { | |
7162 | *target=(Unit)quot; | |
7163 | count-=(DECDPUN-cut); | |
7164 | if (count<=0) break; | |
7165 | up++; | |
7166 | quot=*up; | |
7167 | #if DECDPUN<=4 | |
7168 | quot=QUOT10(quot, cut); | |
7169 | rem=*up-quot*powers[cut]; | |
7170 | #else | |
7171 | rem=quot%powers[cut]; | |
7172 | quot=quot/powers[cut]; | |
7173 | #endif | |
7174 | *target=(Unit)(*target+rem*powers[DECDPUN-cut]); | |
7175 | count-=cut; | |
7176 | if (count<=0) break; | |
7177 | } /* shift-copy loop */ | |
7178 | } /* shift to least */ | |
7179 | } /* not unit boundary */ | |
7180 | ||
7181 | if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ | |
7182 | return; | |
7183 | } /* decSetCoeff */ | |
7184 | ||
7185 | /* ------------------------------------------------------------------ */ | |
7186 | /* decApplyRound -- apply pending rounding to a number */ | |
7187 | /* */ | |
7188 | /* dn is the number, with space for set->digits digits */ | |
7189 | /* set is the context [for size and rounding mode] */ | |
7190 | /* residue indicates pending rounding, being any accumulated */ | |
7191 | /* guard and sticky information. It may be: */ | |
7192 | /* 6-9: rounding digit is >5 */ | |
7193 | /* 5: rounding digit is exactly half-way */ | |
7194 | /* 1-4: rounding digit is <5 and >0 */ | |
7195 | /* 0: the coefficient is exact */ | |
7196 | /* -1: as 1, but the hidden digits are subtractive, that */ | |
7197 | /* is, of the opposite sign to dn. In this case the */ | |
7198 | /* coefficient must be non-0. This case occurs when */ | |
7199 | /* subtracting a small number (which can be reduced to */ | |
7200 | /* a sticky bit); see decAddOp. */ | |
7201 | /* status is the status accumulator, as usual */ | |
7202 | /* */ | |
7203 | /* This routine applies rounding while keeping the length of the */ | |
7204 | /* coefficient constant. The exponent and status are unchanged */ | |
7205 | /* except if: */ | |
7206 | /* */ | |
7207 | /* -- the coefficient was increased and is all nines (in which */ | |
7208 | /* case Overflow could occur, and is handled directly here so */ | |
7209 | /* the caller does not need to re-test for overflow) */ | |
7210 | /* */ | |
7211 | /* -- the coefficient was decreased and becomes all nines (in which */ | |
7212 | /* case Underflow could occur, and is also handled directly). */ | |
7213 | /* */ | |
7214 | /* All fields in dn are updated as required. */ | |
7215 | /* */ | |
7216 | /* ------------------------------------------------------------------ */ | |
7217 | static void decApplyRound(decNumber *dn, decContext *set, Int residue, | |
7218 | uInt *status) { | |
7219 | Int bump; /* 1 if coefficient needs to be incremented */ | |
7220 | /* -1 if coefficient needs to be decremented */ | |
7221 | ||
7222 | if (residue==0) return; /* nothing to apply */ | |
7223 | ||
7224 | bump=0; /* assume a smooth ride */ | |
7225 | ||
7226 | /* now decide whether, and how, to round, depending on mode */ | |
7227 | switch (set->round) { | |
7228 | case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ | |
7229 | /* This is the same as DEC_ROUND_DOWN unless there is a */ | |
7230 | /* positive residue and the lsd of dn is 0 or 5, in which case */ | |
7231 | /* it is bumped; when residue is <0, the number is therefore */ | |
7232 | /* bumped down unless the final digit was 1 or 6 (in which */ | |
7233 | /* case it is bumped down and then up -- a no-op) */ | |
7234 | Int lsd5=*dn->lsu%5; /* get lsd and quintate */ | |
7235 | if (residue<0 && lsd5!=1) bump=-1; | |
7236 | else if (residue>0 && lsd5==0) bump=1; | |
7237 | /* [bump==1 could be applied directly; use common path for clarity] */ | |
7238 | break;} /* r-05 */ | |
7239 | ||
7240 | case DEC_ROUND_DOWN: { | |
7241 | /* no change, except if negative residue */ | |
7242 | if (residue<0) bump=-1; | |
7243 | break;} /* r-d */ | |
7244 | ||
7245 | case DEC_ROUND_HALF_DOWN: { | |
7246 | if (residue>5) bump=1; | |
7247 | break;} /* r-h-d */ | |
7248 | ||
7249 | case DEC_ROUND_HALF_EVEN: { | |
7250 | if (residue>5) bump=1; /* >0.5 goes up */ | |
7251 | else if (residue==5) { /* exactly 0.5000... */ | |
7252 | /* 0.5 goes up iff [new] lsd is odd */ | |
7253 | if (*dn->lsu & 0x01) bump=1; | |
7254 | } | |
7255 | break;} /* r-h-e */ | |
7256 | ||
7257 | case DEC_ROUND_HALF_UP: { | |
7258 | if (residue>=5) bump=1; | |
7259 | break;} /* r-h-u */ | |
7260 | ||
7261 | case DEC_ROUND_UP: { | |
7262 | if (residue>0) bump=1; | |
7263 | break;} /* r-u */ | |
7264 | ||
7265 | case DEC_ROUND_CEILING: { | |
7266 | /* same as _UP for positive numbers, and as _DOWN for negatives */ | |
7267 | /* [negative residue cannot occur on 0] */ | |
7268 | if (decNumberIsNegative(dn)) { | |
7269 | if (residue<0) bump=-1; | |
7270 | } | |
7271 | else { | |
7272 | if (residue>0) bump=1; | |
7273 | } | |
7274 | break;} /* r-c */ | |
7275 | ||
7276 | case DEC_ROUND_FLOOR: { | |
7277 | /* same as _UP for negative numbers, and as _DOWN for positive */ | |
7278 | /* [negative residue cannot occur on 0] */ | |
7279 | if (!decNumberIsNegative(dn)) { | |
7280 | if (residue<0) bump=-1; | |
7281 | } | |
7282 | else { | |
7283 | if (residue>0) bump=1; | |
7284 | } | |
7285 | break;} /* r-f */ | |
7286 | ||
7287 | default: { /* e.g., DEC_ROUND_MAX */ | |
7288 | *status|=DEC_Invalid_context; | |
7289 | #if DECTRACE || (DECCHECK && DECVERB) | |
7290 | printf("Unknown rounding mode: %d\n", set->round); | |
7291 | #endif | |
7292 | break;} | |
7293 | } /* switch */ | |
7294 | ||
7295 | /* now bump the number, up or down, if need be */ | |
7296 | if (bump==0) return; /* no action required */ | |
7297 | ||
7298 | /* Simply use decUnitAddSub unless bumping up and the number is */ | |
7299 | /* all nines. In this special case set to 100... explicitly */ | |
7300 | /* and adjust the exponent by one (as otherwise could overflow */ | |
7301 | /* the array) */ | |
7302 | /* Similarly handle all-nines result if bumping down. */ | |
7303 | if (bump>0) { | |
7304 | Unit *up; /* work */ | |
7305 | uInt count=dn->digits; /* digits to be checked */ | |
7306 | for (up=dn->lsu; ; up++) { | |
7307 | if (count<=DECDPUN) { | |
7308 | /* this is the last Unit (the msu) */ | |
7309 | if (*up!=powers[count]-1) break; /* not still 9s */ | |
7310 | /* here if it, too, is all nines */ | |
7311 | *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ | |
7312 | for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ | |
7313 | dn->exponent++; /* and bump exponent */ | |
7314 | /* [which, very rarely, could cause Overflow...] */ | |
7315 | if ((dn->exponent+dn->digits)>set->emax+1) { | |
7316 | decSetOverflow(dn, set, status); | |
7317 | } | |
7318 | return; /* done */ | |
7319 | } | |
7320 | /* a full unit to check, with more to come */ | |
7321 | if (*up!=DECDPUNMAX) break; /* not still 9s */ | |
7322 | count-=DECDPUN; | |
7323 | } /* up */ | |
7324 | } /* bump>0 */ | |
7325 | else { /* -1 */ | |
7326 | /* here checking for a pre-bump of 1000... (leading 1, all */ | |
7327 | /* other digits zero) */ | |
7328 | Unit *up, *sup; /* work */ | |
7329 | uInt count=dn->digits; /* digits to be checked */ | |
7330 | for (up=dn->lsu; ; up++) { | |
7331 | if (count<=DECDPUN) { | |
7332 | /* this is the last Unit (the msu) */ | |
7333 | if (*up!=powers[count-1]) break; /* not 100.. */ | |
7334 | /* here if have the 1000... case */ | |
7335 | sup=up; /* save msu pointer */ | |
7336 | *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ | |
7337 | /* others all to all-nines, too */ | |
7338 | for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; | |
7339 | dn->exponent--; /* and bump exponent */ | |
7340 | ||
7341 | /* iff the number was at the subnormal boundary (exponent=etiny) */ | |
7342 | /* then the exponent is now out of range, so it will in fact get */ | |
7343 | /* clamped to etiny and the final 9 dropped. */ | |
7344 | /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ | |
7345 | /* dn->exponent, set->digits); */ | |
7346 | if (dn->exponent+1==set->emin-set->digits+1) { | |
7347 | if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ | |
7348 | else { | |
7349 | *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ | |
7350 | dn->digits--; | |
7351 | } | |
7352 | dn->exponent++; | |
7353 | *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; | |
7354 | } | |
7355 | return; /* done */ | |
7356 | } | |
7357 | ||
7358 | /* a full unit to check, with more to come */ | |
7359 | if (*up!=0) break; /* not still 0s */ | |
7360 | count-=DECDPUN; | |
7361 | } /* up */ | |
7362 | ||
7363 | } /* bump<0 */ | |
7364 | ||
7365 | /* Actual bump needed. Do it. */ | |
7366 | decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); | |
7367 | } /* decApplyRound */ | |
7368 | ||
7369 | #if DECSUBSET | |
7370 | /* ------------------------------------------------------------------ */ | |
7371 | /* decFinish -- finish processing a number */ | |
7372 | /* */ | |
7373 | /* dn is the number */ | |
7374 | /* set is the context */ | |
7375 | /* residue is the rounding accumulator (as in decApplyRound) */ | |
7376 | /* status is the accumulator */ | |
7377 | /* */ | |
7378 | /* This finishes off the current number by: */ | |
7379 | /* 1. If not extended: */ | |
7380 | /* a. Converting a zero result to clean '0' */ | |
7381 | /* b. Reducing positive exponents to 0, if would fit in digits */ | |
7382 | /* 2. Checking for overflow and subnormals (always) */ | |
7383 | /* Note this is just Finalize when no subset arithmetic. */ | |
7384 | /* All fields are updated as required. */ | |
7385 | /* ------------------------------------------------------------------ */ | |
7386 | static void decFinish(decNumber *dn, decContext *set, Int *residue, | |
7387 | uInt *status) { | |
7388 | if (!set->extended) { | |
7389 | if ISZERO(dn) { /* value is zero */ | |
7390 | dn->exponent=0; /* clean exponent .. */ | |
7391 | dn->bits=0; /* .. and sign */ | |
7392 | return; /* no error possible */ | |
7393 | } | |
7394 | if (dn->exponent>=0) { /* non-negative exponent */ | |
7395 | /* >0; reduce to integer if possible */ | |
7396 | if (set->digits >= (dn->exponent+dn->digits)) { | |
7397 | dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); | |
7398 | dn->exponent=0; | |
7399 | } | |
7400 | } | |
7401 | } /* !extended */ | |
7402 | ||
7403 | decFinalize(dn, set, residue, status); | |
7404 | } /* decFinish */ | |
7405 | #endif | |
7406 | ||
7407 | /* ------------------------------------------------------------------ */ | |
7408 | /* decFinalize -- final check, clamp, and round of a number */ | |
7409 | /* */ | |
7410 | /* dn is the number */ | |
7411 | /* set is the context */ | |
7412 | /* residue is the rounding accumulator (as in decApplyRound) */ | |
7413 | /* status is the status accumulator */ | |
7414 | /* */ | |
7415 | /* This finishes off the current number by checking for subnormal */ | |
7416 | /* results, applying any pending rounding, checking for overflow, */ | |
7417 | /* and applying any clamping. */ | |
7418 | /* Underflow and overflow conditions are raised as appropriate. */ | |
7419 | /* All fields are updated as required. */ | |
7420 | /* ------------------------------------------------------------------ */ | |
7421 | static void decFinalize(decNumber *dn, decContext *set, Int *residue, | |
7422 | uInt *status) { | |
7423 | Int shift; /* shift needed if clamping */ | |
7424 | Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ | |
7425 | ||
7426 | /* Must be careful, here, when checking the exponent as the */ | |
7427 | /* adjusted exponent could overflow 31 bits [because it may already */ | |
7428 | /* be up to twice the expected]. */ | |
7429 | ||
7430 | /* First test for subnormal. This must be done before any final */ | |
7431 | /* round as the result could be rounded to Nmin or 0. */ | |
7432 | if (dn->exponent<=tinyexp) { /* prefilter */ | |
7433 | Int comp; | |
7434 | decNumber nmin; | |
7435 | /* A very nasty case here is dn == Nmin and residue<0 */ | |
7436 | if (dn->exponent<tinyexp) { | |
7437 | /* Go handle subnormals; this will apply round if needed. */ | |
7438 | decSetSubnormal(dn, set, residue, status); | |
7439 | return; | |
7440 | } | |
7441 | /* Equals case: only subnormal if dn=Nmin and negative residue */ | |
7442 | decNumberZero(&nmin); | |
7443 | nmin.lsu[0]=1; | |
7444 | nmin.exponent=set->emin; | |
7445 | comp=decCompare(dn, &nmin, 1); /* (signless compare) */ | |
7446 | if (comp==BADINT) { /* oops */ | |
7447 | *status|=DEC_Insufficient_storage; /* abandon... */ | |
7448 | return; | |
7449 | } | |
7450 | if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ | |
7451 | decApplyRound(dn, set, *residue, status); /* might force down */ | |
7452 | decSetSubnormal(dn, set, residue, status); | |
7453 | return; | |
7454 | } | |
7455 | } | |
7456 | ||
7457 | /* now apply any pending round (this could raise overflow). */ | |
7458 | if (*residue!=0) decApplyRound(dn, set, *residue, status); | |
7459 | ||
7460 | /* Check for overflow [redundant in the 'rare' case] or clamp */ | |
7461 | if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ | |
7462 | ||
7463 | ||
7464 | /* here when might have an overflow or clamp to do */ | |
7465 | if (dn->exponent>set->emax-dn->digits+1) { /* too big */ | |
7466 | decSetOverflow(dn, set, status); | |
7467 | return; | |
7468 | } | |
7469 | /* here when the result is normal but in clamp range */ | |
7470 | if (!set->clamp) return; | |
7471 | ||
7472 | /* here when need to apply the IEEE exponent clamp (fold-down) */ | |
7473 | shift=dn->exponent-(set->emax-set->digits+1); | |
7474 | ||
7475 | /* shift coefficient (if non-zero) */ | |
7476 | if (!ISZERO(dn)) { | |
7477 | dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); | |
7478 | } | |
7479 | dn->exponent-=shift; /* adjust the exponent to match */ | |
7480 | *status|=DEC_Clamped; /* and record the dirty deed */ | |
7481 | return; | |
7482 | } /* decFinalize */ | |
7483 | ||
7484 | /* ------------------------------------------------------------------ */ | |
7485 | /* decSetOverflow -- set number to proper overflow value */ | |
7486 | /* */ | |
7487 | /* dn is the number (used for sign [only] and result) */ | |
7488 | /* set is the context [used for the rounding mode, etc.] */ | |
7489 | /* status contains the current status to be updated */ | |
7490 | /* */ | |
7491 | /* This sets the sign of a number and sets its value to either */ | |
7492 | /* Infinity or the maximum finite value, depending on the sign of */ | |
7493 | /* dn and the rounding mode, following IEEE 854 rules. */ | |
7494 | /* ------------------------------------------------------------------ */ | |
7495 | static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { | |
7496 | Flag needmax=0; /* result is maximum finite value */ | |
7497 | uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ | |
7498 | ||
7499 | if (ISZERO(dn)) { /* zero does not overflow magnitude */ | |
7500 | Int emax=set->emax; /* limit value */ | |
7501 | if (set->clamp) emax-=set->digits-1; /* lower if clamping */ | |
7502 | if (dn->exponent>emax) { /* clamp required */ | |
7503 | dn->exponent=emax; | |
7504 | *status|=DEC_Clamped; | |
7505 | } | |
7506 | return; | |
7507 | } | |
7508 | ||
7509 | decNumberZero(dn); | |
7510 | switch (set->round) { | |
7511 | case DEC_ROUND_DOWN: { | |
7512 | needmax=1; /* never Infinity */ | |
7513 | break;} /* r-d */ | |
7514 | case DEC_ROUND_05UP: { | |
7515 | needmax=1; /* never Infinity */ | |
7516 | break;} /* r-05 */ | |
7517 | case DEC_ROUND_CEILING: { | |
7518 | if (sign) needmax=1; /* Infinity if non-negative */ | |
7519 | break;} /* r-c */ | |
7520 | case DEC_ROUND_FLOOR: { | |
7521 | if (!sign) needmax=1; /* Infinity if negative */ | |
7522 | break;} /* r-f */ | |
7523 | default: break; /* Infinity in all other cases */ | |
7524 | } | |
7525 | if (needmax) { | |
7526 | decSetMaxValue(dn, set); | |
7527 | dn->bits=sign; /* set sign */ | |
7528 | } | |
7529 | else dn->bits=sign|DECINF; /* Value is +/-Infinity */ | |
7530 | *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; | |
7531 | } /* decSetOverflow */ | |
7532 | ||
7533 | /* ------------------------------------------------------------------ */ | |
7534 | /* decSetMaxValue -- set number to +Nmax (maximum normal value) */ | |
7535 | /* */ | |
7536 | /* dn is the number to set */ | |
7537 | /* set is the context [used for digits and emax] */ | |
7538 | /* */ | |
7539 | /* This sets the number to the maximum positive value. */ | |
7540 | /* ------------------------------------------------------------------ */ | |
7541 | static void decSetMaxValue(decNumber *dn, decContext *set) { | |
7542 | Unit *up; /* work */ | |
7543 | Int count=set->digits; /* nines to add */ | |
7544 | dn->digits=count; | |
7545 | /* fill in all nines to set maximum value */ | |
7546 | for (up=dn->lsu; ; up++) { | |
7547 | if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ | |
7548 | else { /* this is the msu */ | |
7549 | *up=(Unit)(powers[count]-1); | |
7550 | break; | |
7551 | } | |
7552 | count-=DECDPUN; /* filled those digits */ | |
7553 | } /* up */ | |
7554 | dn->bits=0; /* + sign */ | |
7555 | dn->exponent=set->emax-set->digits+1; | |
7556 | } /* decSetMaxValue */ | |
7557 | ||
7558 | /* ------------------------------------------------------------------ */ | |
7559 | /* decSetSubnormal -- process value whose exponent is <Emin */ | |
7560 | /* */ | |
7561 | /* dn is the number (used as input as well as output; it may have */ | |
7562 | /* an allowed subnormal value, which may need to be rounded) */ | |
7563 | /* set is the context [used for the rounding mode] */ | |
7564 | /* residue is any pending residue */ | |
7565 | /* status contains the current status to be updated */ | |
7566 | /* */ | |
7567 | /* If subset mode, set result to zero and set Underflow flags. */ | |
7568 | /* */ | |
7569 | /* Value may be zero with a low exponent; this does not set Subnormal */ | |
7570 | /* but the exponent will be clamped to Etiny. */ | |
7571 | /* */ | |
7572 | /* Otherwise ensure exponent is not out of range, and round as */ | |
7573 | /* necessary. Underflow is set if the result is Inexact. */ | |
7574 | /* ------------------------------------------------------------------ */ | |
7575 | static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, | |
7576 | uInt *status) { | |
72ac97cd TM |
7577 | decContext workset; /* work */ |
7578 | Int etiny, adjust; /* .. */ | |
7579 | ||
7580 | #if DECSUBSET | |
7581 | /* simple set to zero and 'hard underflow' for subset */ | |
7582 | if (!set->extended) { | |
7583 | decNumberZero(dn); | |
7584 | /* always full overflow */ | |
7585 | *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; | |
7586 | return; | |
7587 | } | |
7588 | #endif | |
7589 | ||
7590 | /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ | |
7591 | /* (Etiny) if needed */ | |
7592 | etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ | |
7593 | ||
7594 | if ISZERO(dn) { /* value is zero */ | |
7595 | /* residue can never be non-zero here */ | |
7596 | #if DECCHECK | |
7597 | if (*residue!=0) { | |
7598 | printf("++ Subnormal 0 residue %ld\n", (LI)*residue); | |
7599 | *status|=DEC_Invalid_operation; | |
7600 | } | |
7601 | #endif | |
7602 | if (dn->exponent<etiny) { /* clamp required */ | |
7603 | dn->exponent=etiny; | |
7604 | *status|=DEC_Clamped; | |
7605 | } | |
7606 | return; | |
7607 | } | |
7608 | ||
7609 | *status|=DEC_Subnormal; /* have a non-zero subnormal */ | |
7610 | adjust=etiny-dn->exponent; /* calculate digits to remove */ | |
7611 | if (adjust<=0) { /* not out of range; unrounded */ | |
7612 | /* residue can never be non-zero here, except in the Nmin-residue */ | |
7613 | /* case (which is a subnormal result), so can take fast-path here */ | |
7614 | /* it may already be inexact (from setting the coefficient) */ | |
7615 | if (*status&DEC_Inexact) *status|=DEC_Underflow; | |
7616 | return; | |
7617 | } | |
7618 | ||
7619 | /* adjust>0, so need to rescale the result so exponent becomes Etiny */ | |
7620 | /* [this code is similar to that in rescale] */ | |
72ac97cd TM |
7621 | workset=*set; /* clone rounding, etc. */ |
7622 | workset.digits=dn->digits-adjust; /* set requested length */ | |
7623 | workset.emin-=adjust; /* and adjust emin to match */ | |
7624 | /* [note that the latter can be <1, here, similar to Rescale case] */ | |
7625 | decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); | |
7626 | decApplyRound(dn, &workset, *residue, status); | |
7627 | ||
7628 | /* Use 754R/854 default rule: Underflow is set iff Inexact */ | |
7629 | /* [independent of whether trapped] */ | |
7630 | if (*status&DEC_Inexact) *status|=DEC_Underflow; | |
7631 | ||
7632 | /* if rounded up a 999s case, exponent will be off by one; adjust */ | |
7633 | /* back if so [it will fit, because it was shortened earlier] */ | |
7634 | if (dn->exponent>etiny) { | |
7635 | dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); | |
7636 | dn->exponent--; /* (re)adjust the exponent. */ | |
7637 | } | |
7638 | ||
7639 | /* if rounded to zero, it is by definition clamped... */ | |
7640 | if (ISZERO(dn)) *status|=DEC_Clamped; | |
7641 | } /* decSetSubnormal */ | |
7642 | ||
7643 | /* ------------------------------------------------------------------ */ | |
7644 | /* decCheckMath - check entry conditions for a math function */ | |
7645 | /* */ | |
7646 | /* This checks the context and the operand */ | |
7647 | /* */ | |
7648 | /* rhs is the operand to check */ | |
7649 | /* set is the context to check */ | |
7650 | /* status is unchanged if both are good */ | |
7651 | /* */ | |
7652 | /* returns non-zero if status is changed, 0 otherwise */ | |
7653 | /* */ | |
7654 | /* Restrictions enforced: */ | |
7655 | /* */ | |
7656 | /* digits, emax, and -emin in the context must be less than */ | |
7657 | /* DEC_MAX_MATH (999999), and A must be within these bounds if */ | |
7658 | /* non-zero. Invalid_operation is set in the status if a */ | |
7659 | /* restriction is violated. */ | |
7660 | /* ------------------------------------------------------------------ */ | |
7661 | static uInt decCheckMath(const decNumber *rhs, decContext *set, | |
7662 | uInt *status) { | |
7663 | uInt save=*status; /* record */ | |
7664 | if (set->digits>DEC_MAX_MATH | |
7665 | || set->emax>DEC_MAX_MATH | |
7666 | || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; | |
7667 | else if ((rhs->digits>DEC_MAX_MATH | |
7668 | || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 | |
7669 | || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) | |
7670 | && !ISZERO(rhs)) *status|=DEC_Invalid_operation; | |
7671 | return (*status!=save); | |
7672 | } /* decCheckMath */ | |
7673 | ||
7674 | /* ------------------------------------------------------------------ */ | |
7675 | /* decGetInt -- get integer from a number */ | |
7676 | /* */ | |
7677 | /* dn is the number [which will not be altered] */ | |
7678 | /* */ | |
7679 | /* returns one of: */ | |
7680 | /* BADINT if there is a non-zero fraction */ | |
7681 | /* the converted integer */ | |
7682 | /* BIGEVEN if the integer is even and magnitude > 2*10**9 */ | |
7683 | /* BIGODD if the integer is odd and magnitude > 2*10**9 */ | |
7684 | /* */ | |
7685 | /* This checks and gets a whole number from the input decNumber. */ | |
7686 | /* The sign can be determined from dn by the caller when BIGEVEN or */ | |
7687 | /* BIGODD is returned. */ | |
7688 | /* ------------------------------------------------------------------ */ | |
7689 | static Int decGetInt(const decNumber *dn) { | |
7690 | Int theInt; /* result accumulator */ | |
7691 | const Unit *up; /* work */ | |
7692 | Int got; /* digits (real or not) processed */ | |
7693 | Int ilength=dn->digits+dn->exponent; /* integral length */ | |
7694 | Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ | |
7695 | ||
7696 | /* The number must be an integer that fits in 10 digits */ | |
7697 | /* Assert, here, that 10 is enough for any rescale Etiny */ | |
7698 | #if DEC_MAX_EMAX > 999999999 | |
7699 | #error GetInt may need updating [for Emax] | |
7700 | #endif | |
7701 | #if DEC_MIN_EMIN < -999999999 | |
7702 | #error GetInt may need updating [for Emin] | |
7703 | #endif | |
7704 | if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ | |
7705 | ||
7706 | up=dn->lsu; /* ready for lsu */ | |
7707 | theInt=0; /* ready to accumulate */ | |
7708 | if (dn->exponent>=0) { /* relatively easy */ | |
7709 | /* no fractional part [usual]; allow for positive exponent */ | |
7710 | got=dn->exponent; | |
7711 | } | |
7712 | else { /* -ve exponent; some fractional part to check and discard */ | |
7713 | Int count=-dn->exponent; /* digits to discard */ | |
7714 | /* spin up whole units until reach the Unit with the unit digit */ | |
7715 | for (; count>=DECDPUN; up++) { | |
7716 | if (*up!=0) return BADINT; /* non-zero Unit to discard */ | |
7717 | count-=DECDPUN; | |
7718 | } | |
7719 | if (count==0) got=0; /* [a multiple of DECDPUN] */ | |
7720 | else { /* [not multiple of DECDPUN] */ | |
7721 | Int rem; /* work */ | |
7722 | /* slice off fraction digits and check for non-zero */ | |
7723 | #if DECDPUN<=4 | |
7724 | theInt=QUOT10(*up, count); | |
7725 | rem=*up-theInt*powers[count]; | |
7726 | #else | |
7727 | rem=*up%powers[count]; /* slice off discards */ | |
7728 | theInt=*up/powers[count]; | |
7729 | #endif | |
7730 | if (rem!=0) return BADINT; /* non-zero fraction */ | |
7731 | /* it looks good */ | |
7732 | got=DECDPUN-count; /* number of digits so far */ | |
7733 | up++; /* ready for next */ | |
7734 | } | |
7735 | } | |
7736 | /* now it's known there's no fractional part */ | |
7737 | ||
7738 | /* tricky code now, to accumulate up to 9.3 digits */ | |
7739 | if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ | |
7740 | ||
7741 | if (ilength<11) { | |
7742 | Int save=theInt; | |
7743 | /* collect any remaining unit(s) */ | |
7744 | for (; got<ilength; up++) { | |
7745 | theInt+=*up*powers[got]; | |
7746 | got+=DECDPUN; | |
7747 | } | |
7748 | if (ilength==10) { /* need to check for wrap */ | |
7749 | if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; | |
7750 | /* [that test also disallows the BADINT result case] */ | |
7751 | else if (neg && theInt>1999999997) ilength=11; | |
7752 | else if (!neg && theInt>999999999) ilength=11; | |
7753 | if (ilength==11) theInt=save; /* restore correct low bit */ | |
7754 | } | |
7755 | } | |
7756 | ||
7757 | if (ilength>10) { /* too big */ | |
7758 | if (theInt&1) return BIGODD; /* bottom bit 1 */ | |
7759 | return BIGEVEN; /* bottom bit 0 */ | |
7760 | } | |
7761 | ||
7762 | if (neg) theInt=-theInt; /* apply sign */ | |
7763 | return theInt; | |
7764 | } /* decGetInt */ | |
7765 | ||
7766 | /* ------------------------------------------------------------------ */ | |
7767 | /* decDecap -- decapitate the coefficient of a number */ | |
7768 | /* */ | |
7769 | /* dn is the number to be decapitated */ | |
7770 | /* drop is the number of digits to be removed from the left of dn; */ | |
7771 | /* this must be <= dn->digits (if equal, the coefficient is */ | |
7772 | /* set to 0) */ | |
7773 | /* */ | |
7774 | /* Returns dn; dn->digits will be <= the initial digits less drop */ | |
7775 | /* (after removing drop digits there may be leading zero digits */ | |
7776 | /* which will also be removed). Only dn->lsu and dn->digits change. */ | |
7777 | /* ------------------------------------------------------------------ */ | |
7778 | static decNumber *decDecap(decNumber *dn, Int drop) { | |
7779 | Unit *msu; /* -> target cut point */ | |
7780 | Int cut; /* work */ | |
7781 | if (drop>=dn->digits) { /* losing the whole thing */ | |
7782 | #if DECCHECK | |
7783 | if (drop>dn->digits) | |
7784 | printf("decDecap called with drop>digits [%ld>%ld]\n", | |
7785 | (LI)drop, (LI)dn->digits); | |
7786 | #endif | |
7787 | dn->lsu[0]=0; | |
7788 | dn->digits=1; | |
7789 | return dn; | |
7790 | } | |
7791 | msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ | |
7792 | cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ | |
7793 | if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ | |
7794 | /* that may have left leading zero digits, so do a proper count... */ | |
7795 | dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); | |
7796 | return dn; | |
7797 | } /* decDecap */ | |
7798 | ||
7799 | /* ------------------------------------------------------------------ */ | |
7800 | /* decBiStr -- compare string with pairwise options */ | |
7801 | /* */ | |
7802 | /* targ is the string to compare */ | |
7803 | /* str1 is one of the strings to compare against (length may be 0) */ | |
7804 | /* str2 is the other; it must be the same length as str1 */ | |
7805 | /* */ | |
7806 | /* returns 1 if strings compare equal, (that is, it is the same */ | |
7807 | /* length as str1 and str2, and each character of targ is in either */ | |
7808 | /* str1 or str2 in the corresponding position), or 0 otherwise */ | |
7809 | /* */ | |
7810 | /* This is used for generic caseless compare, including the awkward */ | |
7811 | /* case of the Turkish dotted and dotless Is. Use as (for example): */ | |
7812 | /* if (decBiStr(test, "mike", "MIKE")) ... */ | |
7813 | /* ------------------------------------------------------------------ */ | |
7814 | static Flag decBiStr(const char *targ, const char *str1, const char *str2) { | |
7815 | for (;;targ++, str1++, str2++) { | |
7816 | if (*targ!=*str1 && *targ!=*str2) return 0; | |
7817 | /* *targ has a match in one (or both, if terminator) */ | |
7818 | if (*targ=='\0') break; | |
7819 | } /* forever */ | |
7820 | return 1; | |
7821 | } /* decBiStr */ | |
7822 | ||
7823 | /* ------------------------------------------------------------------ */ | |
7824 | /* decNaNs -- handle NaN operand or operands */ | |
7825 | /* */ | |
7826 | /* res is the result number */ | |
7827 | /* lhs is the first operand */ | |
7828 | /* rhs is the second operand, or NULL if none */ | |
7829 | /* context is used to limit payload length */ | |
7830 | /* status contains the current status */ | |
7831 | /* returns res in case convenient */ | |
7832 | /* */ | |
7833 | /* Called when one or both operands is a NaN, and propagates the */ | |
7834 | /* appropriate result to res. When an sNaN is found, it is changed */ | |
7835 | /* to a qNaN and Invalid operation is set. */ | |
7836 | /* ------------------------------------------------------------------ */ | |
7837 | static decNumber * decNaNs(decNumber *res, const decNumber *lhs, | |
7838 | const decNumber *rhs, decContext *set, | |
7839 | uInt *status) { | |
7840 | /* This decision tree ends up with LHS being the source pointer, */ | |
7841 | /* and status updated if need be */ | |
7842 | if (lhs->bits & DECSNAN) | |
7843 | *status|=DEC_Invalid_operation | DEC_sNaN; | |
7844 | else if (rhs==NULL); | |
7845 | else if (rhs->bits & DECSNAN) { | |
7846 | lhs=rhs; | |
7847 | *status|=DEC_Invalid_operation | DEC_sNaN; | |
7848 | } | |
7849 | else if (lhs->bits & DECNAN); | |
7850 | else lhs=rhs; | |
7851 | ||
7852 | /* propagate the payload */ | |
7853 | if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */ | |
7854 | else { /* too long */ | |
7855 | const Unit *ul; | |
7856 | Unit *ur, *uresp1; | |
7857 | /* copy safe number of units, then decapitate */ | |
7858 | res->bits=lhs->bits; /* need sign etc. */ | |
7859 | uresp1=res->lsu+D2U(set->digits); | |
7860 | for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; | |
7861 | res->digits=D2U(set->digits)*DECDPUN; | |
7862 | /* maybe still too long */ | |
7863 | if (res->digits>set->digits) decDecap(res, res->digits-set->digits); | |
7864 | } | |
7865 | ||
7866 | res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ | |
7867 | res->bits|=DECNAN; /* .. preserving sign */ | |
7868 | res->exponent=0; /* clean exponent */ | |
7869 | /* [coefficient was copied/decapitated] */ | |
7870 | return res; | |
7871 | } /* decNaNs */ | |
7872 | ||
7873 | /* ------------------------------------------------------------------ */ | |
7874 | /* decStatus -- apply non-zero status */ | |
7875 | /* */ | |
7876 | /* dn is the number to set if error */ | |
7877 | /* status contains the current status (not yet in context) */ | |
7878 | /* set is the context */ | |
7879 | /* */ | |
7880 | /* If the status is an error status, the number is set to a NaN, */ | |
7881 | /* unless the error was an overflow, divide-by-zero, or underflow, */ | |
7882 | /* in which case the number will have already been set. */ | |
7883 | /* */ | |
7884 | /* The context status is then updated with the new status. Note that */ | |
7885 | /* this may raise a signal, so control may never return from this */ | |
7886 | /* routine (hence resources must be recovered before it is called). */ | |
7887 | /* ------------------------------------------------------------------ */ | |
7888 | static void decStatus(decNumber *dn, uInt status, decContext *set) { | |
7889 | if (status & DEC_NaNs) { /* error status -> NaN */ | |
7890 | /* if cause was an sNaN, clear and propagate [NaN is already set up] */ | |
7891 | if (status & DEC_sNaN) status&=~DEC_sNaN; | |
7892 | else { | |
7893 | decNumberZero(dn); /* other error: clean throughout */ | |
7894 | dn->bits=DECNAN; /* and make a quiet NaN */ | |
7895 | } | |
7896 | } | |
7897 | decContextSetStatus(set, status); /* [may not return] */ | |
7898 | return; | |
7899 | } /* decStatus */ | |
7900 | ||
7901 | /* ------------------------------------------------------------------ */ | |
7902 | /* decGetDigits -- count digits in a Units array */ | |
7903 | /* */ | |
7904 | /* uar is the Unit array holding the number (this is often an */ | |
7905 | /* accumulator of some sort) */ | |
7906 | /* len is the length of the array in units [>=1] */ | |
7907 | /* */ | |
7908 | /* returns the number of (significant) digits in the array */ | |
7909 | /* */ | |
7910 | /* All leading zeros are excluded, except the last if the array has */ | |
7911 | /* only zero Units. */ | |
7912 | /* ------------------------------------------------------------------ */ | |
7913 | /* This may be called twice during some operations. */ | |
7914 | static Int decGetDigits(Unit *uar, Int len) { | |
7915 | Unit *up=uar+(len-1); /* -> msu */ | |
7916 | Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ | |
7917 | #if DECDPUN>4 | |
7918 | uInt const *pow; /* work */ | |
7919 | #endif | |
7920 | /* (at least 1 in final msu) */ | |
7921 | #if DECCHECK | |
7922 | if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); | |
7923 | #endif | |
7924 | ||
7925 | for (; up>=uar; up--) { | |
7926 | if (*up==0) { /* unit is all 0s */ | |
7927 | if (digits==1) break; /* a zero has one digit */ | |
7928 | digits-=DECDPUN; /* adjust for 0 unit */ | |
7929 | continue;} | |
7930 | /* found the first (most significant) non-zero Unit */ | |
7931 | #if DECDPUN>1 /* not done yet */ | |
7932 | if (*up<10) break; /* is 1-9 */ | |
7933 | digits++; | |
7934 | #if DECDPUN>2 /* not done yet */ | |
7935 | if (*up<100) break; /* is 10-99 */ | |
7936 | digits++; | |
7937 | #if DECDPUN>3 /* not done yet */ | |
7938 | if (*up<1000) break; /* is 100-999 */ | |
7939 | digits++; | |
7940 | #if DECDPUN>4 /* count the rest ... */ | |
7941 | for (pow=&powers[4]; *up>=*pow; pow++) digits++; | |
7942 | #endif | |
7943 | #endif | |
7944 | #endif | |
7945 | #endif | |
7946 | break; | |
7947 | } /* up */ | |
7948 | return digits; | |
7949 | } /* decGetDigits */ | |
7950 | ||
21d7826f LP |
7951 | /* ------------------------------------------------------------------ */ |
7952 | /* mulUInt128ByPowOf10 -- multiply a 128-bit unsigned integer by a */ | |
7953 | /* power of 10. */ | |
7954 | /* */ | |
7955 | /* The 128-bit factor composed of plow and phigh is multiplied */ | |
7956 | /* by 10^exp. */ | |
7957 | /* */ | |
7958 | /* plow pointer to the low 64 bits of the first factor */ | |
7959 | /* phigh pointer to the high 64 bits of the first factor */ | |
7960 | /* exp the exponent of the power of 10 of the second factor */ | |
7961 | /* */ | |
7962 | /* If the result fits in 128 bits, returns false and the */ | |
7963 | /* multiplication result through plow and phigh. */ | |
7964 | /* Otherwise, returns true. */ | |
7965 | /* ------------------------------------------------------------------ */ | |
7966 | static bool mulUInt128ByPowOf10(uLong *plow, uLong *phigh, uInt pow10) | |
7967 | { | |
7968 | while (pow10 >= ARRAY_SIZE(powers)) { | |
7969 | if (mulu128(plow, phigh, powers[ARRAY_SIZE(powers) - 1])) { | |
7970 | /* Overflow */ | |
7971 | return true; | |
7972 | } | |
7973 | pow10 -= ARRAY_SIZE(powers) - 1; | |
7974 | } | |
7975 | ||
7976 | if (pow10 > 0) { | |
7977 | return mulu128(plow, phigh, powers[pow10]); | |
7978 | } else { | |
7979 | return false; | |
7980 | } | |
7981 | } | |
7982 | ||
72ac97cd TM |
7983 | #if DECTRACE | DECCHECK |
7984 | /* ------------------------------------------------------------------ */ | |
7985 | /* decNumberShow -- display a number [debug aid] */ | |
7986 | /* dn is the number to show */ | |
7987 | /* */ | |
7988 | /* Shows: sign, exponent, coefficient (msu first), digits */ | |
7989 | /* or: sign, special-value */ | |
7990 | /* ------------------------------------------------------------------ */ | |
7991 | /* this is public so other modules can use it */ | |
7992 | void decNumberShow(const decNumber *dn) { | |
7993 | const Unit *up; /* work */ | |
7994 | uInt u, d; /* .. */ | |
7995 | Int cut; /* .. */ | |
7996 | char isign='+'; /* main sign */ | |
7997 | if (dn==NULL) { | |
7998 | printf("NULL\n"); | |
7999 | return;} | |
8000 | if (decNumberIsNegative(dn)) isign='-'; | |
8001 | printf(" >> %c ", isign); | |
8002 | if (dn->bits&DECSPECIAL) { /* Is a special value */ | |
8003 | if (decNumberIsInfinite(dn)) printf("Infinity"); | |
8004 | else { /* a NaN */ | |
8005 | if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ | |
8006 | else printf("NaN"); | |
8007 | } | |
8008 | /* if coefficient and exponent are 0, no more to do */ | |
8009 | if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { | |
8010 | printf("\n"); | |
8011 | return;} | |
8012 | /* drop through to report other information */ | |
8013 | printf(" "); | |
8014 | } | |
8015 | ||
8016 | /* now carefully display the coefficient */ | |
8017 | up=dn->lsu+D2U(dn->digits)-1; /* msu */ | |
8018 | printf("%ld", (LI)*up); | |
8019 | for (up=up-1; up>=dn->lsu; up--) { | |
8020 | u=*up; | |
8021 | printf(":"); | |
8022 | for (cut=DECDPUN-1; cut>=0; cut--) { | |
8023 | d=u/powers[cut]; | |
8024 | u-=d*powers[cut]; | |
8025 | printf("%ld", (LI)d); | |
8026 | } /* cut */ | |
8027 | } /* up */ | |
8028 | if (dn->exponent!=0) { | |
8029 | char esign='+'; | |
8030 | if (dn->exponent<0) esign='-'; | |
8031 | printf(" E%c%ld", esign, (LI)abs(dn->exponent)); | |
8032 | } | |
8033 | printf(" [%ld]\n", (LI)dn->digits); | |
8034 | } /* decNumberShow */ | |
8035 | #endif | |
8036 | ||
8037 | #if DECTRACE || DECCHECK | |
8038 | /* ------------------------------------------------------------------ */ | |
8039 | /* decDumpAr -- display a unit array [debug/check aid] */ | |
8040 | /* name is a single-character tag name */ | |
8041 | /* ar is the array to display */ | |
8042 | /* len is the length of the array in Units */ | |
8043 | /* ------------------------------------------------------------------ */ | |
8044 | static void decDumpAr(char name, const Unit *ar, Int len) { | |
8045 | Int i; | |
8046 | const char *spec; | |
8047 | #if DECDPUN==9 | |
8048 | spec="%09d "; | |
8049 | #elif DECDPUN==8 | |
8050 | spec="%08d "; | |
8051 | #elif DECDPUN==7 | |
8052 | spec="%07d "; | |
8053 | #elif DECDPUN==6 | |
8054 | spec="%06d "; | |
8055 | #elif DECDPUN==5 | |
8056 | spec="%05d "; | |
8057 | #elif DECDPUN==4 | |
8058 | spec="%04d "; | |
8059 | #elif DECDPUN==3 | |
8060 | spec="%03d "; | |
8061 | #elif DECDPUN==2 | |
8062 | spec="%02d "; | |
8063 | #else | |
8064 | spec="%d "; | |
8065 | #endif | |
8066 | printf(" :%c: ", name); | |
8067 | for (i=len-1; i>=0; i--) { | |
8068 | if (i==len-1) printf("%ld ", (LI)ar[i]); | |
8069 | else printf(spec, ar[i]); | |
8070 | } | |
8071 | printf("\n"); | |
8072 | return;} | |
8073 | #endif | |
8074 | ||
8075 | #if DECCHECK | |
8076 | /* ------------------------------------------------------------------ */ | |
8077 | /* decCheckOperands -- check operand(s) to a routine */ | |
8078 | /* res is the result structure (not checked; it will be set to */ | |
8079 | /* quiet NaN if error found (and it is not NULL)) */ | |
8080 | /* lhs is the first operand (may be DECUNRESU) */ | |
8081 | /* rhs is the second (may be DECUNUSED) */ | |
8082 | /* set is the context (may be DECUNCONT) */ | |
8083 | /* returns 0 if both operands, and the context are clean, or 1 */ | |
8084 | /* otherwise (in which case the context will show an error, */ | |
8085 | /* unless NULL). Note that res is not cleaned; caller should */ | |
8086 | /* handle this so res=NULL case is safe. */ | |
8087 | /* The caller is expected to abandon immediately if 1 is returned. */ | |
8088 | /* ------------------------------------------------------------------ */ | |
8089 | static Flag decCheckOperands(decNumber *res, const decNumber *lhs, | |
8090 | const decNumber *rhs, decContext *set) { | |
8091 | Flag bad=0; | |
8092 | if (set==NULL) { /* oops; hopeless */ | |
8093 | #if DECTRACE || DECVERB | |
8094 | printf("Reference to context is NULL.\n"); | |
8095 | #endif | |
8096 | bad=1; | |
8097 | return 1;} | |
8098 | else if (set!=DECUNCONT | |
8099 | && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { | |
8100 | bad=1; | |
8101 | #if DECTRACE || DECVERB | |
8102 | printf("Bad context [digits=%ld round=%ld].\n", | |
8103 | (LI)set->digits, (LI)set->round); | |
8104 | #endif | |
8105 | } | |
8106 | else { | |
8107 | if (res==NULL) { | |
8108 | bad=1; | |
8109 | #if DECTRACE | |
8110 | /* this one not DECVERB as standard tests include NULL */ | |
8111 | printf("Reference to result is NULL.\n"); | |
8112 | #endif | |
8113 | } | |
8114 | if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); | |
8115 | if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); | |
8116 | } | |
8117 | if (bad) { | |
8118 | if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); | |
8119 | if (res!=DECUNRESU && res!=NULL) { | |
8120 | decNumberZero(res); | |
8121 | res->bits=DECNAN; /* qNaN */ | |
8122 | } | |
8123 | } | |
8124 | return bad; | |
8125 | } /* decCheckOperands */ | |
8126 | ||
8127 | /* ------------------------------------------------------------------ */ | |
8128 | /* decCheckNumber -- check a number */ | |
8129 | /* dn is the number to check */ | |
8130 | /* returns 0 if the number is clean, or 1 otherwise */ | |
8131 | /* */ | |
8132 | /* The number is considered valid if it could be a result from some */ | |
8133 | /* operation in some valid context. */ | |
8134 | /* ------------------------------------------------------------------ */ | |
8135 | static Flag decCheckNumber(const decNumber *dn) { | |
8136 | const Unit *up; /* work */ | |
8137 | uInt maxuint; /* .. */ | |
8138 | Int ae, d, digits; /* .. */ | |
8139 | Int emin, emax; /* .. */ | |
8140 | ||
8141 | if (dn==NULL) { /* hopeless */ | |
8142 | #if DECTRACE | |
8143 | /* this one not DECVERB as standard tests include NULL */ | |
8144 | printf("Reference to decNumber is NULL.\n"); | |
8145 | #endif | |
8146 | return 1;} | |
8147 | ||
8148 | /* check special values */ | |
8149 | if (dn->bits & DECSPECIAL) { | |
8150 | if (dn->exponent!=0) { | |
8151 | #if DECTRACE || DECVERB | |
8152 | printf("Exponent %ld (not 0) for a special value [%02x].\n", | |
8153 | (LI)dn->exponent, dn->bits); | |
8154 | #endif | |
8155 | return 1;} | |
8156 | ||
8157 | /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ | |
8158 | if (decNumberIsInfinite(dn)) { | |
8159 | if (dn->digits!=1) { | |
8160 | #if DECTRACE || DECVERB | |
8161 | printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); | |
8162 | #endif | |
8163 | return 1;} | |
8164 | if (*dn->lsu!=0) { | |
8165 | #if DECTRACE || DECVERB | |
8166 | printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); | |
8167 | #endif | |
8168 | decDumpAr('I', dn->lsu, D2U(dn->digits)); | |
8169 | return 1;} | |
8170 | } /* Inf */ | |
8171 | /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ | |
8172 | /* concrete formats (decimal64, etc.). */ | |
8173 | return 0; | |
8174 | } | |
8175 | ||
8176 | /* check the coefficient */ | |
8177 | if (dn->digits<1 || dn->digits>DECNUMMAXP) { | |
8178 | #if DECTRACE || DECVERB | |
8179 | printf("Digits %ld in number.\n", (LI)dn->digits); | |
8180 | #endif | |
8181 | return 1;} | |
8182 | ||
8183 | d=dn->digits; | |
8184 | ||
8185 | for (up=dn->lsu; d>0; up++) { | |
8186 | if (d>DECDPUN) maxuint=DECDPUNMAX; | |
8187 | else { /* reached the msu */ | |
8188 | maxuint=powers[d]-1; | |
8189 | if (dn->digits>1 && *up<powers[d-1]) { | |
8190 | #if DECTRACE || DECVERB | |
8191 | printf("Leading 0 in number.\n"); | |
8192 | decNumberShow(dn); | |
8193 | #endif | |
8194 | return 1;} | |
8195 | } | |
8196 | if (*up>maxuint) { | |
8197 | #if DECTRACE || DECVERB | |
8198 | printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", | |
8199 | (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); | |
8200 | #endif | |
8201 | return 1;} | |
8202 | d-=DECDPUN; | |
8203 | } | |
8204 | ||
8205 | /* check the exponent. Note that input operands can have exponents */ | |
8206 | /* which are out of the set->emin/set->emax and set->digits range */ | |
8207 | /* (just as they can have more digits than set->digits). */ | |
8208 | ae=dn->exponent+dn->digits-1; /* adjusted exponent */ | |
8209 | emax=DECNUMMAXE; | |
8210 | emin=DECNUMMINE; | |
8211 | digits=DECNUMMAXP; | |
8212 | if (ae<emin-(digits-1)) { | |
8213 | #if DECTRACE || DECVERB | |
8214 | printf("Adjusted exponent underflow [%ld].\n", (LI)ae); | |
8215 | decNumberShow(dn); | |
8216 | #endif | |
8217 | return 1;} | |
8218 | if (ae>+emax) { | |
8219 | #if DECTRACE || DECVERB | |
8220 | printf("Adjusted exponent overflow [%ld].\n", (LI)ae); | |
8221 | decNumberShow(dn); | |
8222 | #endif | |
8223 | return 1;} | |
8224 | ||
8225 | return 0; /* it's OK */ | |
8226 | } /* decCheckNumber */ | |
8227 | ||
8228 | /* ------------------------------------------------------------------ */ | |
8229 | /* decCheckInexact -- check a normal finite inexact result has digits */ | |
8230 | /* dn is the number to check */ | |
8231 | /* set is the context (for status and precision) */ | |
8232 | /* sets Invalid operation, etc., if some digits are missing */ | |
8233 | /* [this check is not made for DECSUBSET compilation or when */ | |
8234 | /* subnormal is not set] */ | |
8235 | /* ------------------------------------------------------------------ */ | |
8236 | static void decCheckInexact(const decNumber *dn, decContext *set) { | |
8237 | #if !DECSUBSET && DECEXTFLAG | |
8238 | if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact | |
8239 | && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { | |
8240 | #if DECTRACE || DECVERB | |
8241 | printf("Insufficient digits [%ld] on normal Inexact result.\n", | |
8242 | (LI)dn->digits); | |
8243 | decNumberShow(dn); | |
8244 | #endif | |
8245 | decContextSetStatus(set, DEC_Invalid_operation); | |
8246 | } | |
8247 | #else | |
8248 | /* next is a noop for quiet compiler */ | |
8249 | if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; | |
8250 | #endif | |
8251 | return; | |
8252 | } /* decCheckInexact */ | |
8253 | #endif | |
8254 | ||
8255 | #if DECALLOC | |
8256 | #undef malloc | |
8257 | #undef free | |
8258 | /* ------------------------------------------------------------------ */ | |
8259 | /* decMalloc -- accountable allocation routine */ | |
8260 | /* n is the number of bytes to allocate */ | |
8261 | /* */ | |
8262 | /* Semantics is the same as the stdlib malloc routine, but bytes */ | |
8263 | /* allocated are accounted for globally, and corruption fences are */ | |
8264 | /* added before and after the 'actual' storage. */ | |
8265 | /* ------------------------------------------------------------------ */ | |
8266 | /* This routine allocates storage with an extra twelve bytes; 8 are */ | |
8267 | /* at the start and hold: */ | |
8268 | /* 0-3 the original length requested */ | |
8269 | /* 4-7 buffer corruption detection fence (DECFENCE, x4) */ | |
8270 | /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ | |
8271 | /* ------------------------------------------------------------------ */ | |
8272 | static void *decMalloc(size_t n) { | |
8273 | uInt size=n+12; /* true size */ | |
8274 | void *alloc; /* -> allocated storage */ | |
8275 | uInt *j; /* work */ | |
8276 | uByte *b, *b0; /* .. */ | |
8277 | ||
8278 | alloc=malloc(size); /* -> allocated storage */ | |
8279 | if (alloc==NULL) return NULL; /* out of strorage */ | |
8280 | b0=(uByte *)alloc; /* as bytes */ | |
8281 | decAllocBytes+=n; /* account for storage */ | |
8282 | j=(uInt *)alloc; /* -> first four bytes */ | |
8283 | *j=n; /* save n */ | |
8284 | /* printf(" alloc ++ dAB: %ld (%d)\n", decAllocBytes, n); */ | |
8285 | for (b=b0+4; b<b0+8; b++) *b=DECFENCE; | |
8286 | for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; | |
8287 | return b0+8; /* -> play area */ | |
8288 | } /* decMalloc */ | |
8289 | ||
8290 | /* ------------------------------------------------------------------ */ | |
8291 | /* decFree -- accountable free routine */ | |
8292 | /* alloc is the storage to free */ | |
8293 | /* */ | |
8294 | /* Semantics is the same as the stdlib malloc routine, except that */ | |
8295 | /* the global storage accounting is updated and the fences are */ | |
8296 | /* checked to ensure that no routine has written 'out of bounds'. */ | |
8297 | /* ------------------------------------------------------------------ */ | |
8298 | /* This routine first checks that the fences have not been corrupted. */ | |
8299 | /* It then frees the storage using the 'truw' storage address (that */ | |
8300 | /* is, offset by 8). */ | |
8301 | /* ------------------------------------------------------------------ */ | |
8302 | static void decFree(void *alloc) { | |
8303 | uInt *j, n; /* pointer, original length */ | |
8304 | uByte *b, *b0; /* work */ | |
8305 | ||
8306 | if (alloc==NULL) return; /* allowed; it's a nop */ | |
8307 | b0=(uByte *)alloc; /* as bytes */ | |
8308 | b0-=8; /* -> true start of storage */ | |
8309 | j=(uInt *)b0; /* -> first four bytes */ | |
8310 | n=*j; /* lift */ | |
8311 | for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) | |
8312 | printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, | |
8313 | b-b0-8, (Int)b0); | |
8314 | for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) | |
8315 | printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, | |
8316 | b-b0-8, (Int)b0, n); | |
8317 | free(b0); /* drop the storage */ | |
8318 | decAllocBytes-=n; /* account for storage */ | |
8319 | /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ | |
8320 | } /* decFree */ | |
8321 | #define malloc(a) decMalloc(a) | |
8322 | #define free(a) decFree(a) | |
8323 | #endif |