2 This is a variation on dtoa.c that converts arbitary binary
3 floating-point formats to and from decimal notation. It uses
4 double-precision arithmetic internally, so there are still
5 various #ifdefs that adapt the calculations to the native
6 IEEE double-precision arithmetic.
8 Copyright (c) 2010 - 2014, Intel Corporation. All rights reserved.<BR>
9 This program and the accompanying materials are licensed and made available under
10 the terms and conditions of the BSD License that accompanies this distribution.
11 The full text of the license may be found at
12 http://opensource.org/licenses/bsd-license.
14 THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
15 WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
17 *****************************************************************
19 The author of this software is David M. Gay.
21 Copyright (C) 1998-2000 by Lucent Technologies
24 Permission to use, copy, modify, and distribute this software and
25 its documentation for any purpose and without fee is hereby
26 granted, provided that the above copyright notice appear in all
27 copies and that both that the copyright notice and this
28 permission notice and warranty disclaimer appear in supporting
29 documentation, and that the name of Lucent or any of its entities
30 not be used in advertising or publicity pertaining to
31 distribution of the software without specific, written prior
34 LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
35 INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
36 IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
37 SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
38 WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
39 IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
40 ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
43 Please send bug reports to David M. Gay (dmg at acm dot org,
44 with " at " changed at "@" and " dot " changed to ".").
46 *****************************************************************
48 NetBSD: gdtoaimp.h,v 1.5.4.1 2007/05/07 19:49:06 pavel Exp
51 /* On a machine with IEEE extended-precision registers, it is
52 * necessary to specify double-precision (53-bit) rounding precision
53 * before invoking strtod or dtoa. If the machine uses (the equivalent
54 * of) Intel 80x87 arithmetic, the call
55 * _control87(PC_53, MCW_PC);
56 * does this with many compilers. Whether this or another call is
57 * appropriate depends on the compiler; for this to work, it may be
58 * necessary to #include "float.h" or another system-dependent header
62 /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
64 * This strtod returns a nearest machine number to the input decimal
65 * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
66 * broken by the IEEE round-even rule. Otherwise ties are broken by
67 * biased rounding (add half and chop).
69 * Inspired loosely by William D. Clinger's paper "How to Read Floating
70 * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 112-126].
74 * 1. We only require IEEE, IBM, or VAX double-precision
75 * arithmetic (not IEEE double-extended).
76 * 2. We get by with floating-point arithmetic in a case that
77 * Clinger missed -- when we're computing d * 10^n
78 * for a small integer d and the integer n is not too
79 * much larger than 22 (the maximum integer k for which
80 * we can represent 10^k exactly), we may be able to
81 * compute (d*10^k) * 10^(e-k) with just one roundoff.
82 * 3. Rather than a bit-at-a-time adjustment of the binary
83 * result in the hard case, we use floating-point
84 * arithmetic to determine the adjustment to within
85 * one bit; only in really hard cases do we need to
86 * compute a second residual.
87 * 4. Because of 3., we don't need a large table of powers of 10
88 * for ten-to-e (just some small tables, e.g. of 10^k
93 * #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
94 * significant byte has the lowest address.
95 * #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
96 * significant byte has the lowest address.
97 * #define Long int on machines with 32-bit ints and 64-bit longs.
98 * #define Sudden_Underflow for IEEE-format machines without gradual
99 * underflow (i.e., that flush to zero on underflow).
100 * #define No_leftright to omit left-right logic in fast floating-point
101 * computation of dtoa.
102 * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3.
103 * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
104 * that use extended-precision instructions to compute rounded
105 * products and quotients) with IBM.
106 * #define ROUND_BIASED for IEEE-format with biased rounding.
107 * #define Inaccurate_Divide for IEEE-format with correctly rounded
108 * products but inaccurate quotients, e.g., for Intel i860.
109 * #define NO_LONG_LONG on machines that do not have a "long long"
110 * integer type (of >= 64 bits). On such machines, you can
111 * #define Just_16 to store 16 bits per 32-bit Long when doing
112 * high-precision integer arithmetic. Whether this speeds things
113 * up or slows things down depends on the machine and the number
114 * being converted. If long long is available and the name is
115 * something other than "long long", #define Llong to be the name,
116 * and if "unsigned Llong" does not work as an unsigned version of
117 * Llong, #define #ULLong to be the corresponding unsigned type.
118 * #define Bad_float_h if your system lacks a float.h or if it does not
119 * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
120 * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
121 * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
122 * if memory is available and otherwise does something you deem
123 * appropriate. If MALLOC is undefined, malloc will be invoked
124 * directly -- and assumed always to succeed.
125 * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
126 * memory allocations from a private pool of memory when possible.
127 * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
128 * unless #defined to be a different length. This default length
129 * suffices to get rid of MALLOC calls except for unusual cases,
130 * such as decimal-to-binary conversion of a very long string of
131 * digits. When converting IEEE double precision values, the
132 * longest string gdtoa can return is about 751 bytes long. For
133 * conversions by strtod of strings of 800 digits and all gdtoa
134 * conversions of IEEE doubles in single-threaded executions with
135 * 8-byte pointers, PRIVATE_MEM >= 7400 appears to suffice; with
136 * 4-byte pointers, PRIVATE_MEM >= 7112 appears adequate.
137 * #define INFNAN_CHECK on IEEE systems to cause strtod to check for
138 * Infinity and NaN (case insensitively).
139 * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
140 * strtodg also accepts (case insensitively) strings of the form
141 * NaN(x), where x is a string of hexadecimal digits and spaces;
142 * if there is only one string of hexadecimal digits, it is taken
143 * for the fraction bits of the resulting NaN; if there are two or
144 * more strings of hexadecimal digits, each string is assigned
145 * to the next available sequence of 32-bit words of fractions
146 * bits (starting with the most significant), right-aligned in
148 * #define MULTIPLE_THREADS if the system offers preemptively scheduled
149 * multiple threads. In this case, you must provide (or suitably
150 * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
151 * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
152 * in pow5mult, ensures lazy evaluation of only one copy of high
153 * powers of 5; omitting this lock would introduce a small
154 * probability of wasting memory, but would otherwise be harmless.)
155 * You must also invoke freedtoa(s) to free the value s returned by
156 * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
157 * #define IMPRECISE_INEXACT if you do not care about the setting of
158 * the STRTOG_Inexact bits in the special case of doing IEEE double
159 * precision conversions (which could also be done by the strtog in
161 * #define NO_HEX_FP to disable recognition of C9x's hexadecimal
162 * floating-point constants.
163 * #define -DNO_ERRNO to suppress setting errno (in strtod.c and
165 * #define NO_STRING_H to use private versions of memcpy.
166 * On some K&R systems, it may also be necessary to
167 * #define DECLARE_SIZE_T in this case.
168 * #define YES_ALIAS to permit aliasing certain double values with
169 * arrays of ULongs. This leads to slightly better code with
170 * some compilers and was always used prior to 19990916, but it
171 * is not strictly legal and can cause trouble with aggressively
172 * optimizing compilers (e.g., gcc 2.95.1 under -O2).
173 * #define USE_LOCALE to use the current locale's decimal_point value.
176 /* #define IEEE_{BIG,LITTLE}_ENDIAN in ${ARCHDIR}/gdtoa/arith.h */
177 #include <LibConfig.h>
180 #define Short int16_t
181 #define UShort uint16_t
183 #define ULong uint32_t
184 #define LLong int64_t
185 #define ULLong uint64_t
189 #define MULTIPLE_THREADS
193 #ifndef GDTOAIMP_H_INCLUDED
194 #define GDTOAIMP_H_INCLUDED
200 #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
209 extern Char
*MALLOC
ANSI((size_t));
211 #define MALLOC malloc
215 #undef Avoid_Underflow
216 #ifdef IEEE_BIG_ENDIAN
219 #ifdef IEEE_LITTLE_ENDIAN
228 #define DBL_MAX_10_EXP 308
229 #define DBL_MAX_EXP 1024
231 #define DBL_MAX 1.7976931348623157e+308
235 #define LONG_MAX 2147483647
238 #else /* ifndef Bad_float_h */
240 #endif /* Bad_float_h */
243 #define Scale_Bit 0x10
253 #if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) != 1
254 Exactly one of IEEE_LITTLE_ENDIAN
or IEEE_BIG_ENDIAN should be defined
.
257 /* This union assumes that:
261 If this is not the case, the type and dimension of the L member will
264 typedef union { double d
; UINT32 L
[2]; } U
;
268 #ifdef IEEE_LITTLE_ENDIAN
269 #define word0(x) ((ULong *)&x)[1]
270 #define word1(x) ((ULong *)&x)[0]
272 #define word0(x) ((ULong *)&x)[0]
273 #define word1(x) ((ULong *)&x)[1]
275 #else /* !YES_ALIAS */
276 #ifdef IEEE_LITTLE_ENDIAN
277 #define word0(x) ( /* LINTED */ (U*)&x)->L[1]
278 #define word1(x) ( /* LINTED */ (U*)&x)->L[0]
280 #define word0(x) ( /* LINTED */ (U*)&x)->L[0]
281 #define word1(x) ( /* LINTED */ (U*)&x)->L[1]
283 #define dval(x) ( /* LINTED */ (U*)&x)->d
284 #endif /* YES_ALIAS */
286 /* The following definition of Storeinc is appropriate for MIPS processors.
287 * An alternative that might be better on some machines is
288 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
290 #if defined(IEEE_LITTLE_ENDIAN)
291 #define Storeinc(a,b,c) \
292 (((unsigned short *)(void *)a)[1] = (unsigned short)b, \
293 ((unsigned short *)(void *)a)[0] = (unsigned short)c, \
296 #define Storeinc(a,b,c) \
297 (((unsigned short *)(void *)a)[0] = (unsigned short)b, \
298 ((unsigned short *)(void *)a)[1] = (unsigned short)c, \
302 /* #define P DBL_MANT_DIG */
303 /* Ten_pmax = floor(P*log(2)/log(5)) */
304 /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
305 /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
306 /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
310 #define Exp_shift1 20
311 #define Exp_msk1 0x100000
312 #define Exp_msk11 0x100000
313 #define Exp_mask 0x7ff00000
317 #define Exp_1 0x3ff00000
318 #define Exp_11 0x3ff00000
320 #define Frac_mask 0xfffffU
321 #define Frac_mask1 0xfffffU
324 #define Bndry_mask 0xfffffU
325 #define Bndry_mask1 0xfffffU
327 #define Sign_bit 0x80000000
336 #define Flt_Rounds FLT_ROUNDS
340 #endif /*Flt_Rounds*/
342 #else /* ifndef IEEE_Arith */
343 #undef Sudden_Underflow
344 #define Sudden_Underflow
349 #define Exp_shift1 24
350 #define Exp_msk1 0x1000000
351 #define Exp_msk11 0x1000000
352 #define Exp_mask 0x7f000000
355 #define Exp_1 0x41000000
356 #define Exp_11 0x41000000
357 #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
358 #define Frac_mask 0xffffff
359 #define Frac_mask1 0xffffff
362 #define Bndry_mask 0xefffff
363 #define Bndry_mask1 0xffffff
365 #define Sign_bit 0x80000000
367 #define Tiny0 0x100000
376 #define Exp_msk1 0x80
377 #define Exp_msk11 0x800000
378 #define Exp_mask 0x7f80
381 #define Exp_1 0x40800000
382 #define Exp_11 0x4080
384 #define Frac_mask 0x7fffff
385 #define Frac_mask1 0xffff007f
388 #define Bndry_mask 0xffff007f
389 #define Bndry_mask1 0xffff007f
391 #define Sign_bit 0x8000
397 #endif /* IBM, VAX */
398 #endif /* IEEE_Arith */
405 #define rounded_product(a,b) a = rnd_prod(a, b)
406 #define rounded_quotient(a,b) a = rnd_quot(a, b)
407 extern double rnd_prod(double, double), rnd_quot(double, double);
409 #define rounded_product(a,b) a *= b
410 #define rounded_quotient(a,b) a /= b
413 #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
414 #define Big1 0xffffffffU
426 /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
427 * This makes some inner loops simpler and sometimes saves work
428 * during multiplications, but it often seems to make things slightly
429 * slower. Hence the default is now to store 32 bits per Long.
432 #else /* long long available */
434 #define Llong long long
437 #define ULLong unsigned Llong
439 #endif /* NO_LONG_LONG */
445 #define ALL_ON 0xffffffff
450 #define ALL_ON 0xffff
453 #ifndef MULTIPLE_THREADS
454 #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
455 #define FREE_DTOA_LOCK(n) /*nothing*/
457 #include "reentrant.h"
459 extern mutex_t __gdtoa_locks
[2];
461 #define ACQUIRE_DTOA_LOCK(n) \
464 mutex_lock(&__gdtoa_locks[n]); \
465 } while (/* CONSTCOND */ 0)
466 #define FREE_DTOA_LOCK(n) \
469 mutex_unlock(&__gdtoa_locks[n]); \
470 } while (/* CONSTCOND */ 0)
473 #define Kmax (sizeof(size_t) << 3)
478 int k
, maxwds
, sign
, wds
;
482 typedef struct Bigint Bigint
;
485 #ifdef DECLARE_SIZE_T
486 typedef unsigned int size_t;
488 extern void memcpy_D2A
ANSI((void*, const void*, size_t));
489 #define Bcopy(x,y) memcpy_D2A(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
490 #else /* !NO_STRING_H */
491 #define Bcopy(x,y) memcpy(&x->sign,&y->sign,y->wds*sizeof(ULong) + 2*sizeof(int))
492 #endif /* NO_STRING_H */
494 #define Balloc __Balloc_D2A
495 #define Bfree __Bfree_D2A
496 #define ULtoQ __ULtoQ_D2A
497 #define ULtof __ULtof_D2A
498 #define ULtod __ULtod_D2A
499 #define ULtodd __ULtodd_D2A
500 #define ULtox __ULtox_D2A
501 #define ULtoxL __ULtoxL_D2A
502 #define any_on __any_on_D2A
503 #define b2d __b2d_D2A
504 #define bigtens __bigtens_D2A
505 #define cmp __cmp_D2A
506 #define copybits __copybits_D2A
507 #define d2b __d2b_D2A
508 #define decrement __decrement_D2A
509 #define diff __diff_D2A
510 #define dtoa_result __dtoa_result_D2A
511 #define g__fmt __g__fmt_D2A
512 #define gethex __gethex_D2A
513 #define hexdig __hexdig_D2A
514 #define hexdig_init_D2A __hexdig_init_D2A
515 #define hexnan __hexnan_D2A
516 #define hi0bits __hi0bits_D2A
517 #define hi0bits_D2A __hi0bits_D2A
518 #define i2b __i2b_D2A
519 #define increment __increment_D2A
520 #define lo0bits __lo0bits_D2A
521 #define lshift __lshift_D2A
522 #define match __match_D2A
523 #define mult __mult_D2A
524 #define multadd __multadd_D2A
525 #define nrv_alloc __nrv_alloc_D2A
526 #define pow5mult __pow5mult_D2A
527 #define quorem __quorem_D2A
528 #define ratio __ratio_D2A
529 #define rshift __rshift_D2A
530 #define rv_alloc __rv_alloc_D2A
531 #define s2b __s2b_D2A
532 #define set_ones __set_ones_D2A
533 #define strcp __strcp_D2A
534 #define strcp_D2A __strcp_D2A
535 #define strtoIg __strtoIg_D2A
536 #define sum __sum_D2A
537 #define tens __tens_D2A
538 #define tinytens __tinytens_D2A
539 #define tinytens __tinytens_D2A
540 #define trailz __trailz_D2A
541 #define ulp __ulp_D2A
543 extern char *dtoa_result
;
544 extern CONST
double bigtens
[], tens
[], tinytens
[];
545 extern unsigned char hexdig
[];
547 extern Bigint
*Balloc (int);
548 extern void Bfree (Bigint
*);
549 extern void ULtof (ULong
*, ULong
*, Long
, int);
550 extern void ULtod (ULong
*, ULong
*, Long
, int);
551 extern void ULtodd (ULong
*, ULong
*, Long
, int);
552 extern void ULtoQ (ULong
*, ULong
*, Long
, int);
553 extern void ULtox (UShort
*, ULong
*, Long
, int);
554 extern void ULtoxL (ULong
*, ULong
*, Long
, int);
555 extern ULong
any_on (Bigint
*, int);
556 extern double b2d (Bigint
*, int*);
557 extern int cmp (Bigint
*, Bigint
*);
558 extern void copybits (ULong
*, int, Bigint
*);
559 extern Bigint
*d2b (double, int*, int*);
560 extern int decrement (Bigint
*);
561 extern Bigint
*diff (Bigint
*, Bigint
*);
562 extern char *dtoa (double d
, int mode
, int ndigits
,
563 int *decpt
, int *sign
, char **rve
);
564 extern char *g__fmt (char*, char*, char*, int, ULong
);
565 extern int gethex (CONST
char**, CONST FPI
*, Long
*, Bigint
**, int);
566 extern void hexdig_init_D2A(Void
);
567 extern int hexnan (CONST
char**, CONST FPI
*, ULong
*);
568 extern int hi0bits_D2A (ULong
);
569 extern Bigint
*i2b (int);
570 extern Bigint
*increment (Bigint
*);
571 extern int lo0bits (ULong
*);
572 extern Bigint
*lshift (Bigint
*, int);
573 extern int match (CONST
char**, CONST
char*);
574 extern Bigint
*mult (Bigint
*, Bigint
*);
575 extern Bigint
*multadd (Bigint
*, int, int);
576 extern char *nrv_alloc (CONST
char*, char **, size_t);
577 extern Bigint
*pow5mult (Bigint
*, int);
578 extern int quorem (Bigint
*, Bigint
*);
579 extern double ratio (Bigint
*, Bigint
*);
580 extern void rshift (Bigint
*, int);
581 extern char *rv_alloc (size_t);
582 extern Bigint
*s2b (CONST
char*, int, int, ULong
);
583 extern Bigint
*set_ones (Bigint
*, int);
584 extern char *strcp (char*, const char*);
585 extern int strtoIg (CONST
char*, char**, FPI
*, Long
*, Bigint
**, int*);
586 extern double strtod (const char *s00
, char **se
);
587 extern Bigint
*sum (Bigint
*, Bigint
*);
588 extern int trailz (CONST Bigint
*);
589 extern double ulp (double);
595 * NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
596 * 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
597 * respectively), but now are determined by compiling and running
598 * qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
599 * Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
600 * and -DNAN_WORD1=... values if necessary. This should still work.
601 * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
604 #ifdef IEEE_BIG_ENDIAN
608 #define NAN_WORD0 d_QNAN0
611 #define NAN_WORD1 d_QNAN1
617 #define NAN_WORD0 d_QNAN1
620 #define NAN_WORD1 d_QNAN0
628 #ifdef Sudden_Underflow
634 #endif /* GDTOAIMP_H_INCLUDED */