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158142c2 FB |
1 | |
2 | /*============================================================================ | |
3 | ||
4 | This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic | |
5 | Package, Release 2b. | |
6 | ||
7 | Written by John R. Hauser. This work was made possible in part by the | |
8 | International Computer Science Institute, located at Suite 600, 1947 Center | |
9 | Street, Berkeley, California 94704. Funding was partially provided by the | |
10 | National Science Foundation under grant MIP-9311980. The original version | |
11 | of this code was written as part of a project to build a fixed-point vector | |
12 | processor in collaboration with the University of California at Berkeley, | |
13 | overseen by Profs. Nelson Morgan and John Wawrzynek. More information | |
14 | is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ | |
15 | arithmetic/SoftFloat.html'. | |
16 | ||
17 | THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has | |
18 | been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES | |
19 | RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS | |
20 | AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, | |
21 | COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE | |
22 | EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE | |
23 | INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR | |
24 | OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. | |
25 | ||
26 | Derivative works are acceptable, even for commercial purposes, so long as | |
27 | (1) the source code for the derivative work includes prominent notice that | |
28 | the work is derivative, and (2) the source code includes prominent notice with | |
29 | these four paragraphs for those parts of this code that are retained. | |
30 | ||
31 | =============================================================================*/ | |
32 | ||
33 | #include "softfloat.h" | |
34 | ||
35 | /*---------------------------------------------------------------------------- | |
36 | | Primitive arithmetic functions, including multi-word arithmetic, and | |
37 | | division and square root approximations. (Can be specialized to target if | |
38 | | desired.) | |
39 | *----------------------------------------------------------------------------*/ | |
40 | #include "softfloat-macros.h" | |
41 | ||
42 | /*---------------------------------------------------------------------------- | |
43 | | Functions and definitions to determine: (1) whether tininess for underflow | |
44 | | is detected before or after rounding by default, (2) what (if anything) | |
45 | | happens when exceptions are raised, (3) how signaling NaNs are distinguished | |
46 | | from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs | |
47 | | are propagated from function inputs to output. These details are target- | |
48 | | specific. | |
49 | *----------------------------------------------------------------------------*/ | |
50 | #include "softfloat-specialize.h" | |
51 | ||
52 | void set_float_rounding_mode(int val STATUS_PARAM) | |
53 | { | |
54 | STATUS(float_rounding_mode) = val; | |
55 | } | |
56 | ||
1d6bda35 FB |
57 | void set_float_exception_flags(int val STATUS_PARAM) |
58 | { | |
59 | STATUS(float_exception_flags) = val; | |
60 | } | |
61 | ||
158142c2 FB |
62 | #ifdef FLOATX80 |
63 | void set_floatx80_rounding_precision(int val STATUS_PARAM) | |
64 | { | |
65 | STATUS(floatx80_rounding_precision) = val; | |
66 | } | |
67 | #endif | |
68 | ||
69 | /*---------------------------------------------------------------------------- | |
70 | | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 | |
71 | | and 7, and returns the properly rounded 32-bit integer corresponding to the | |
72 | | input. If `zSign' is 1, the input is negated before being converted to an | |
73 | | integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input | |
74 | | is simply rounded to an integer, with the inexact exception raised if the | |
75 | | input cannot be represented exactly as an integer. However, if the fixed- | |
76 | | point input is too large, the invalid exception is raised and the largest | |
77 | | positive or negative integer is returned. | |
78 | *----------------------------------------------------------------------------*/ | |
79 | ||
80 | static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM) | |
81 | { | |
82 | int8 roundingMode; | |
83 | flag roundNearestEven; | |
84 | int8 roundIncrement, roundBits; | |
85 | int32 z; | |
86 | ||
87 | roundingMode = STATUS(float_rounding_mode); | |
88 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
89 | roundIncrement = 0x40; | |
90 | if ( ! roundNearestEven ) { | |
91 | if ( roundingMode == float_round_to_zero ) { | |
92 | roundIncrement = 0; | |
93 | } | |
94 | else { | |
95 | roundIncrement = 0x7F; | |
96 | if ( zSign ) { | |
97 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
98 | } | |
99 | else { | |
100 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
101 | } | |
102 | } | |
103 | } | |
104 | roundBits = absZ & 0x7F; | |
105 | absZ = ( absZ + roundIncrement )>>7; | |
106 | absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
107 | z = absZ; | |
108 | if ( zSign ) z = - z; | |
109 | if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { | |
110 | float_raise( float_flag_invalid STATUS_VAR); | |
111 | return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; | |
112 | } | |
113 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
114 | return z; | |
115 | ||
116 | } | |
117 | ||
118 | /*---------------------------------------------------------------------------- | |
119 | | Takes the 128-bit fixed-point value formed by concatenating `absZ0' and | |
120 | | `absZ1', with binary point between bits 63 and 64 (between the input words), | |
121 | | and returns the properly rounded 64-bit integer corresponding to the input. | |
122 | | If `zSign' is 1, the input is negated before being converted to an integer. | |
123 | | Ordinarily, the fixed-point input is simply rounded to an integer, with | |
124 | | the inexact exception raised if the input cannot be represented exactly as | |
125 | | an integer. However, if the fixed-point input is too large, the invalid | |
126 | | exception is raised and the largest positive or negative integer is | |
127 | | returned. | |
128 | *----------------------------------------------------------------------------*/ | |
129 | ||
130 | static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM) | |
131 | { | |
132 | int8 roundingMode; | |
133 | flag roundNearestEven, increment; | |
134 | int64 z; | |
135 | ||
136 | roundingMode = STATUS(float_rounding_mode); | |
137 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
138 | increment = ( (sbits64) absZ1 < 0 ); | |
139 | if ( ! roundNearestEven ) { | |
140 | if ( roundingMode == float_round_to_zero ) { | |
141 | increment = 0; | |
142 | } | |
143 | else { | |
144 | if ( zSign ) { | |
145 | increment = ( roundingMode == float_round_down ) && absZ1; | |
146 | } | |
147 | else { | |
148 | increment = ( roundingMode == float_round_up ) && absZ1; | |
149 | } | |
150 | } | |
151 | } | |
152 | if ( increment ) { | |
153 | ++absZ0; | |
154 | if ( absZ0 == 0 ) goto overflow; | |
155 | absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven ); | |
156 | } | |
157 | z = absZ0; | |
158 | if ( zSign ) z = - z; | |
159 | if ( z && ( ( z < 0 ) ^ zSign ) ) { | |
160 | overflow: | |
161 | float_raise( float_flag_invalid STATUS_VAR); | |
162 | return | |
163 | zSign ? (sbits64) LIT64( 0x8000000000000000 ) | |
164 | : LIT64( 0x7FFFFFFFFFFFFFFF ); | |
165 | } | |
166 | if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
167 | return z; | |
168 | ||
169 | } | |
170 | ||
171 | /*---------------------------------------------------------------------------- | |
172 | | Returns the fraction bits of the single-precision floating-point value `a'. | |
173 | *----------------------------------------------------------------------------*/ | |
174 | ||
175 | INLINE bits32 extractFloat32Frac( float32 a ) | |
176 | { | |
177 | ||
178 | return a & 0x007FFFFF; | |
179 | ||
180 | } | |
181 | ||
182 | /*---------------------------------------------------------------------------- | |
183 | | Returns the exponent bits of the single-precision floating-point value `a'. | |
184 | *----------------------------------------------------------------------------*/ | |
185 | ||
186 | INLINE int16 extractFloat32Exp( float32 a ) | |
187 | { | |
188 | ||
189 | return ( a>>23 ) & 0xFF; | |
190 | ||
191 | } | |
192 | ||
193 | /*---------------------------------------------------------------------------- | |
194 | | Returns the sign bit of the single-precision floating-point value `a'. | |
195 | *----------------------------------------------------------------------------*/ | |
196 | ||
197 | INLINE flag extractFloat32Sign( float32 a ) | |
198 | { | |
199 | ||
200 | return a>>31; | |
201 | ||
202 | } | |
203 | ||
204 | /*---------------------------------------------------------------------------- | |
205 | | Normalizes the subnormal single-precision floating-point value represented | |
206 | | by the denormalized significand `aSig'. The normalized exponent and | |
207 | | significand are stored at the locations pointed to by `zExpPtr' and | |
208 | | `zSigPtr', respectively. | |
209 | *----------------------------------------------------------------------------*/ | |
210 | ||
211 | static void | |
212 | normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr ) | |
213 | { | |
214 | int8 shiftCount; | |
215 | ||
216 | shiftCount = countLeadingZeros32( aSig ) - 8; | |
217 | *zSigPtr = aSig<<shiftCount; | |
218 | *zExpPtr = 1 - shiftCount; | |
219 | ||
220 | } | |
221 | ||
222 | /*---------------------------------------------------------------------------- | |
223 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
224 | | single-precision floating-point value, returning the result. After being | |
225 | | shifted into the proper positions, the three fields are simply added | |
226 | | together to form the result. This means that any integer portion of `zSig' | |
227 | | will be added into the exponent. Since a properly normalized significand | |
228 | | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
229 | | than the desired result exponent whenever `zSig' is a complete, normalized | |
230 | | significand. | |
231 | *----------------------------------------------------------------------------*/ | |
232 | ||
233 | INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig ) | |
234 | { | |
235 | ||
236 | return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig; | |
237 | ||
238 | } | |
239 | ||
240 | /*---------------------------------------------------------------------------- | |
241 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
242 | | and significand `zSig', and returns the proper single-precision floating- | |
243 | | point value corresponding to the abstract input. Ordinarily, the abstract | |
244 | | value is simply rounded and packed into the single-precision format, with | |
245 | | the inexact exception raised if the abstract input cannot be represented | |
246 | | exactly. However, if the abstract value is too large, the overflow and | |
247 | | inexact exceptions are raised and an infinity or maximal finite value is | |
248 | | returned. If the abstract value is too small, the input value is rounded to | |
249 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
250 | | the abstract input cannot be represented exactly as a subnormal single- | |
251 | | precision floating-point number. | |
252 | | The input significand `zSig' has its binary point between bits 30 | |
253 | | and 29, which is 7 bits to the left of the usual location. This shifted | |
254 | | significand must be normalized or smaller. If `zSig' is not normalized, | |
255 | | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
256 | | and it must not require rounding. In the usual case that `zSig' is | |
257 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
258 | | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
259 | | Binary Floating-Point Arithmetic. | |
260 | *----------------------------------------------------------------------------*/ | |
261 | ||
262 | static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM) | |
263 | { | |
264 | int8 roundingMode; | |
265 | flag roundNearestEven; | |
266 | int8 roundIncrement, roundBits; | |
267 | flag isTiny; | |
268 | ||
269 | roundingMode = STATUS(float_rounding_mode); | |
270 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
271 | roundIncrement = 0x40; | |
272 | if ( ! roundNearestEven ) { | |
273 | if ( roundingMode == float_round_to_zero ) { | |
274 | roundIncrement = 0; | |
275 | } | |
276 | else { | |
277 | roundIncrement = 0x7F; | |
278 | if ( zSign ) { | |
279 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
280 | } | |
281 | else { | |
282 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
283 | } | |
284 | } | |
285 | } | |
286 | roundBits = zSig & 0x7F; | |
287 | if ( 0xFD <= (bits16) zExp ) { | |
288 | if ( ( 0xFD < zExp ) | |
289 | || ( ( zExp == 0xFD ) | |
290 | && ( (sbits32) ( zSig + roundIncrement ) < 0 ) ) | |
291 | ) { | |
292 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
293 | return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 ); | |
294 | } | |
295 | if ( zExp < 0 ) { | |
296 | isTiny = | |
297 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
298 | || ( zExp < -1 ) | |
299 | || ( zSig + roundIncrement < 0x80000000 ); | |
300 | shift32RightJamming( zSig, - zExp, &zSig ); | |
301 | zExp = 0; | |
302 | roundBits = zSig & 0x7F; | |
303 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
304 | } | |
305 | } | |
306 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
307 | zSig = ( zSig + roundIncrement )>>7; | |
308 | zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
309 | if ( zSig == 0 ) zExp = 0; | |
310 | return packFloat32( zSign, zExp, zSig ); | |
311 | ||
312 | } | |
313 | ||
314 | /*---------------------------------------------------------------------------- | |
315 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
316 | | and significand `zSig', and returns the proper single-precision floating- | |
317 | | point value corresponding to the abstract input. This routine is just like | |
318 | | `roundAndPackFloat32' except that `zSig' does not have to be normalized. | |
319 | | Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' | |
320 | | floating-point exponent. | |
321 | *----------------------------------------------------------------------------*/ | |
322 | ||
323 | static float32 | |
324 | normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM) | |
325 | { | |
326 | int8 shiftCount; | |
327 | ||
328 | shiftCount = countLeadingZeros32( zSig ) - 1; | |
329 | return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); | |
330 | ||
331 | } | |
332 | ||
333 | /*---------------------------------------------------------------------------- | |
334 | | Returns the fraction bits of the double-precision floating-point value `a'. | |
335 | *----------------------------------------------------------------------------*/ | |
336 | ||
337 | INLINE bits64 extractFloat64Frac( float64 a ) | |
338 | { | |
339 | ||
340 | return a & LIT64( 0x000FFFFFFFFFFFFF ); | |
341 | ||
342 | } | |
343 | ||
344 | /*---------------------------------------------------------------------------- | |
345 | | Returns the exponent bits of the double-precision floating-point value `a'. | |
346 | *----------------------------------------------------------------------------*/ | |
347 | ||
348 | INLINE int16 extractFloat64Exp( float64 a ) | |
349 | { | |
350 | ||
351 | return ( a>>52 ) & 0x7FF; | |
352 | ||
353 | } | |
354 | ||
355 | /*---------------------------------------------------------------------------- | |
356 | | Returns the sign bit of the double-precision floating-point value `a'. | |
357 | *----------------------------------------------------------------------------*/ | |
358 | ||
359 | INLINE flag extractFloat64Sign( float64 a ) | |
360 | { | |
361 | ||
362 | return a>>63; | |
363 | ||
364 | } | |
365 | ||
366 | /*---------------------------------------------------------------------------- | |
367 | | Normalizes the subnormal double-precision floating-point value represented | |
368 | | by the denormalized significand `aSig'. The normalized exponent and | |
369 | | significand are stored at the locations pointed to by `zExpPtr' and | |
370 | | `zSigPtr', respectively. | |
371 | *----------------------------------------------------------------------------*/ | |
372 | ||
373 | static void | |
374 | normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr ) | |
375 | { | |
376 | int8 shiftCount; | |
377 | ||
378 | shiftCount = countLeadingZeros64( aSig ) - 11; | |
379 | *zSigPtr = aSig<<shiftCount; | |
380 | *zExpPtr = 1 - shiftCount; | |
381 | ||
382 | } | |
383 | ||
384 | /*---------------------------------------------------------------------------- | |
385 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
386 | | double-precision floating-point value, returning the result. After being | |
387 | | shifted into the proper positions, the three fields are simply added | |
388 | | together to form the result. This means that any integer portion of `zSig' | |
389 | | will be added into the exponent. Since a properly normalized significand | |
390 | | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
391 | | than the desired result exponent whenever `zSig' is a complete, normalized | |
392 | | significand. | |
393 | *----------------------------------------------------------------------------*/ | |
394 | ||
395 | INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig ) | |
396 | { | |
397 | ||
398 | return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig; | |
399 | ||
400 | } | |
401 | ||
402 | /*---------------------------------------------------------------------------- | |
403 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
404 | | and significand `zSig', and returns the proper double-precision floating- | |
405 | | point value corresponding to the abstract input. Ordinarily, the abstract | |
406 | | value is simply rounded and packed into the double-precision format, with | |
407 | | the inexact exception raised if the abstract input cannot be represented | |
408 | | exactly. However, if the abstract value is too large, the overflow and | |
409 | | inexact exceptions are raised and an infinity or maximal finite value is | |
410 | | returned. If the abstract value is too small, the input value is rounded | |
411 | | to a subnormal number, and the underflow and inexact exceptions are raised | |
412 | | if the abstract input cannot be represented exactly as a subnormal double- | |
413 | | precision floating-point number. | |
414 | | The input significand `zSig' has its binary point between bits 62 | |
415 | | and 61, which is 10 bits to the left of the usual location. This shifted | |
416 | | significand must be normalized or smaller. If `zSig' is not normalized, | |
417 | | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
418 | | and it must not require rounding. In the usual case that `zSig' is | |
419 | | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
420 | | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
421 | | Binary Floating-Point Arithmetic. | |
422 | *----------------------------------------------------------------------------*/ | |
423 | ||
424 | static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM) | |
425 | { | |
426 | int8 roundingMode; | |
427 | flag roundNearestEven; | |
428 | int16 roundIncrement, roundBits; | |
429 | flag isTiny; | |
430 | ||
431 | roundingMode = STATUS(float_rounding_mode); | |
432 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
433 | roundIncrement = 0x200; | |
434 | if ( ! roundNearestEven ) { | |
435 | if ( roundingMode == float_round_to_zero ) { | |
436 | roundIncrement = 0; | |
437 | } | |
438 | else { | |
439 | roundIncrement = 0x3FF; | |
440 | if ( zSign ) { | |
441 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
442 | } | |
443 | else { | |
444 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
445 | } | |
446 | } | |
447 | } | |
448 | roundBits = zSig & 0x3FF; | |
449 | if ( 0x7FD <= (bits16) zExp ) { | |
450 | if ( ( 0x7FD < zExp ) | |
451 | || ( ( zExp == 0x7FD ) | |
452 | && ( (sbits64) ( zSig + roundIncrement ) < 0 ) ) | |
453 | ) { | |
454 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
455 | return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 ); | |
456 | } | |
457 | if ( zExp < 0 ) { | |
458 | isTiny = | |
459 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
460 | || ( zExp < -1 ) | |
461 | || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); | |
462 | shift64RightJamming( zSig, - zExp, &zSig ); | |
463 | zExp = 0; | |
464 | roundBits = zSig & 0x3FF; | |
465 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
466 | } | |
467 | } | |
468 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
469 | zSig = ( zSig + roundIncrement )>>10; | |
470 | zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); | |
471 | if ( zSig == 0 ) zExp = 0; | |
472 | return packFloat64( zSign, zExp, zSig ); | |
473 | ||
474 | } | |
475 | ||
476 | /*---------------------------------------------------------------------------- | |
477 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
478 | | and significand `zSig', and returns the proper double-precision floating- | |
479 | | point value corresponding to the abstract input. This routine is just like | |
480 | | `roundAndPackFloat64' except that `zSig' does not have to be normalized. | |
481 | | Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' | |
482 | | floating-point exponent. | |
483 | *----------------------------------------------------------------------------*/ | |
484 | ||
485 | static float64 | |
486 | normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM) | |
487 | { | |
488 | int8 shiftCount; | |
489 | ||
490 | shiftCount = countLeadingZeros64( zSig ) - 1; | |
491 | return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); | |
492 | ||
493 | } | |
494 | ||
495 | #ifdef FLOATX80 | |
496 | ||
497 | /*---------------------------------------------------------------------------- | |
498 | | Returns the fraction bits of the extended double-precision floating-point | |
499 | | value `a'. | |
500 | *----------------------------------------------------------------------------*/ | |
501 | ||
502 | INLINE bits64 extractFloatx80Frac( floatx80 a ) | |
503 | { | |
504 | ||
505 | return a.low; | |
506 | ||
507 | } | |
508 | ||
509 | /*---------------------------------------------------------------------------- | |
510 | | Returns the exponent bits of the extended double-precision floating-point | |
511 | | value `a'. | |
512 | *----------------------------------------------------------------------------*/ | |
513 | ||
514 | INLINE int32 extractFloatx80Exp( floatx80 a ) | |
515 | { | |
516 | ||
517 | return a.high & 0x7FFF; | |
518 | ||
519 | } | |
520 | ||
521 | /*---------------------------------------------------------------------------- | |
522 | | Returns the sign bit of the extended double-precision floating-point value | |
523 | | `a'. | |
524 | *----------------------------------------------------------------------------*/ | |
525 | ||
526 | INLINE flag extractFloatx80Sign( floatx80 a ) | |
527 | { | |
528 | ||
529 | return a.high>>15; | |
530 | ||
531 | } | |
532 | ||
533 | /*---------------------------------------------------------------------------- | |
534 | | Normalizes the subnormal extended double-precision floating-point value | |
535 | | represented by the denormalized significand `aSig'. The normalized exponent | |
536 | | and significand are stored at the locations pointed to by `zExpPtr' and | |
537 | | `zSigPtr', respectively. | |
538 | *----------------------------------------------------------------------------*/ | |
539 | ||
540 | static void | |
541 | normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr ) | |
542 | { | |
543 | int8 shiftCount; | |
544 | ||
545 | shiftCount = countLeadingZeros64( aSig ); | |
546 | *zSigPtr = aSig<<shiftCount; | |
547 | *zExpPtr = 1 - shiftCount; | |
548 | ||
549 | } | |
550 | ||
551 | /*---------------------------------------------------------------------------- | |
552 | | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an | |
553 | | extended double-precision floating-point value, returning the result. | |
554 | *----------------------------------------------------------------------------*/ | |
555 | ||
556 | INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig ) | |
557 | { | |
558 | floatx80 z; | |
559 | ||
560 | z.low = zSig; | |
561 | z.high = ( ( (bits16) zSign )<<15 ) + zExp; | |
562 | return z; | |
563 | ||
564 | } | |
565 | ||
566 | /*---------------------------------------------------------------------------- | |
567 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
568 | | and extended significand formed by the concatenation of `zSig0' and `zSig1', | |
569 | | and returns the proper extended double-precision floating-point value | |
570 | | corresponding to the abstract input. Ordinarily, the abstract value is | |
571 | | rounded and packed into the extended double-precision format, with the | |
572 | | inexact exception raised if the abstract input cannot be represented | |
573 | | exactly. However, if the abstract value is too large, the overflow and | |
574 | | inexact exceptions are raised and an infinity or maximal finite value is | |
575 | | returned. If the abstract value is too small, the input value is rounded to | |
576 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
577 | | the abstract input cannot be represented exactly as a subnormal extended | |
578 | | double-precision floating-point number. | |
579 | | If `roundingPrecision' is 32 or 64, the result is rounded to the same | |
580 | | number of bits as single or double precision, respectively. Otherwise, the | |
581 | | result is rounded to the full precision of the extended double-precision | |
582 | | format. | |
583 | | The input significand must be normalized or smaller. If the input | |
584 | | significand is not normalized, `zExp' must be 0; in that case, the result | |
585 | | returned is a subnormal number, and it must not require rounding. The | |
586 | | handling of underflow and overflow follows the IEC/IEEE Standard for Binary | |
587 | | Floating-Point Arithmetic. | |
588 | *----------------------------------------------------------------------------*/ | |
589 | ||
590 | static floatx80 | |
591 | roundAndPackFloatx80( | |
592 | int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 | |
593 | STATUS_PARAM) | |
594 | { | |
595 | int8 roundingMode; | |
596 | flag roundNearestEven, increment, isTiny; | |
597 | int64 roundIncrement, roundMask, roundBits; | |
598 | ||
599 | roundingMode = STATUS(float_rounding_mode); | |
600 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
601 | if ( roundingPrecision == 80 ) goto precision80; | |
602 | if ( roundingPrecision == 64 ) { | |
603 | roundIncrement = LIT64( 0x0000000000000400 ); | |
604 | roundMask = LIT64( 0x00000000000007FF ); | |
605 | } | |
606 | else if ( roundingPrecision == 32 ) { | |
607 | roundIncrement = LIT64( 0x0000008000000000 ); | |
608 | roundMask = LIT64( 0x000000FFFFFFFFFF ); | |
609 | } | |
610 | else { | |
611 | goto precision80; | |
612 | } | |
613 | zSig0 |= ( zSig1 != 0 ); | |
614 | if ( ! roundNearestEven ) { | |
615 | if ( roundingMode == float_round_to_zero ) { | |
616 | roundIncrement = 0; | |
617 | } | |
618 | else { | |
619 | roundIncrement = roundMask; | |
620 | if ( zSign ) { | |
621 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
622 | } | |
623 | else { | |
624 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
625 | } | |
626 | } | |
627 | } | |
628 | roundBits = zSig0 & roundMask; | |
629 | if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { | |
630 | if ( ( 0x7FFE < zExp ) | |
631 | || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) | |
632 | ) { | |
633 | goto overflow; | |
634 | } | |
635 | if ( zExp <= 0 ) { | |
636 | isTiny = | |
637 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
638 | || ( zExp < 0 ) | |
639 | || ( zSig0 <= zSig0 + roundIncrement ); | |
640 | shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); | |
641 | zExp = 0; | |
642 | roundBits = zSig0 & roundMask; | |
643 | if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); | |
644 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
645 | zSig0 += roundIncrement; | |
646 | if ( (sbits64) zSig0 < 0 ) zExp = 1; | |
647 | roundIncrement = roundMask + 1; | |
648 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
649 | roundMask |= roundIncrement; | |
650 | } | |
651 | zSig0 &= ~ roundMask; | |
652 | return packFloatx80( zSign, zExp, zSig0 ); | |
653 | } | |
654 | } | |
655 | if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; | |
656 | zSig0 += roundIncrement; | |
657 | if ( zSig0 < roundIncrement ) { | |
658 | ++zExp; | |
659 | zSig0 = LIT64( 0x8000000000000000 ); | |
660 | } | |
661 | roundIncrement = roundMask + 1; | |
662 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
663 | roundMask |= roundIncrement; | |
664 | } | |
665 | zSig0 &= ~ roundMask; | |
666 | if ( zSig0 == 0 ) zExp = 0; | |
667 | return packFloatx80( zSign, zExp, zSig0 ); | |
668 | precision80: | |
669 | increment = ( (sbits64) zSig1 < 0 ); | |
670 | if ( ! roundNearestEven ) { | |
671 | if ( roundingMode == float_round_to_zero ) { | |
672 | increment = 0; | |
673 | } | |
674 | else { | |
675 | if ( zSign ) { | |
676 | increment = ( roundingMode == float_round_down ) && zSig1; | |
677 | } | |
678 | else { | |
679 | increment = ( roundingMode == float_round_up ) && zSig1; | |
680 | } | |
681 | } | |
682 | } | |
683 | if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { | |
684 | if ( ( 0x7FFE < zExp ) | |
685 | || ( ( zExp == 0x7FFE ) | |
686 | && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) | |
687 | && increment | |
688 | ) | |
689 | ) { | |
690 | roundMask = 0; | |
691 | overflow: | |
692 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
693 | if ( ( roundingMode == float_round_to_zero ) | |
694 | || ( zSign && ( roundingMode == float_round_up ) ) | |
695 | || ( ! zSign && ( roundingMode == float_round_down ) ) | |
696 | ) { | |
697 | return packFloatx80( zSign, 0x7FFE, ~ roundMask ); | |
698 | } | |
699 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
700 | } | |
701 | if ( zExp <= 0 ) { | |
702 | isTiny = | |
703 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
704 | || ( zExp < 0 ) | |
705 | || ! increment | |
706 | || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); | |
707 | shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); | |
708 | zExp = 0; | |
709 | if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR); | |
710 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
711 | if ( roundNearestEven ) { | |
712 | increment = ( (sbits64) zSig1 < 0 ); | |
713 | } | |
714 | else { | |
715 | if ( zSign ) { | |
716 | increment = ( roundingMode == float_round_down ) && zSig1; | |
717 | } | |
718 | else { | |
719 | increment = ( roundingMode == float_round_up ) && zSig1; | |
720 | } | |
721 | } | |
722 | if ( increment ) { | |
723 | ++zSig0; | |
724 | zSig0 &= | |
725 | ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); | |
726 | if ( (sbits64) zSig0 < 0 ) zExp = 1; | |
727 | } | |
728 | return packFloatx80( zSign, zExp, zSig0 ); | |
729 | } | |
730 | } | |
731 | if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
732 | if ( increment ) { | |
733 | ++zSig0; | |
734 | if ( zSig0 == 0 ) { | |
735 | ++zExp; | |
736 | zSig0 = LIT64( 0x8000000000000000 ); | |
737 | } | |
738 | else { | |
739 | zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); | |
740 | } | |
741 | } | |
742 | else { | |
743 | if ( zSig0 == 0 ) zExp = 0; | |
744 | } | |
745 | return packFloatx80( zSign, zExp, zSig0 ); | |
746 | ||
747 | } | |
748 | ||
749 | /*---------------------------------------------------------------------------- | |
750 | | Takes an abstract floating-point value having sign `zSign', exponent | |
751 | | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', | |
752 | | and returns the proper extended double-precision floating-point value | |
753 | | corresponding to the abstract input. This routine is just like | |
754 | | `roundAndPackFloatx80' except that the input significand does not have to be | |
755 | | normalized. | |
756 | *----------------------------------------------------------------------------*/ | |
757 | ||
758 | static floatx80 | |
759 | normalizeRoundAndPackFloatx80( | |
760 | int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 | |
761 | STATUS_PARAM) | |
762 | { | |
763 | int8 shiftCount; | |
764 | ||
765 | if ( zSig0 == 0 ) { | |
766 | zSig0 = zSig1; | |
767 | zSig1 = 0; | |
768 | zExp -= 64; | |
769 | } | |
770 | shiftCount = countLeadingZeros64( zSig0 ); | |
771 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
772 | zExp -= shiftCount; | |
773 | return | |
774 | roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); | |
775 | ||
776 | } | |
777 | ||
778 | #endif | |
779 | ||
780 | #ifdef FLOAT128 | |
781 | ||
782 | /*---------------------------------------------------------------------------- | |
783 | | Returns the least-significant 64 fraction bits of the quadruple-precision | |
784 | | floating-point value `a'. | |
785 | *----------------------------------------------------------------------------*/ | |
786 | ||
787 | INLINE bits64 extractFloat128Frac1( float128 a ) | |
788 | { | |
789 | ||
790 | return a.low; | |
791 | ||
792 | } | |
793 | ||
794 | /*---------------------------------------------------------------------------- | |
795 | | Returns the most-significant 48 fraction bits of the quadruple-precision | |
796 | | floating-point value `a'. | |
797 | *----------------------------------------------------------------------------*/ | |
798 | ||
799 | INLINE bits64 extractFloat128Frac0( float128 a ) | |
800 | { | |
801 | ||
802 | return a.high & LIT64( 0x0000FFFFFFFFFFFF ); | |
803 | ||
804 | } | |
805 | ||
806 | /*---------------------------------------------------------------------------- | |
807 | | Returns the exponent bits of the quadruple-precision floating-point value | |
808 | | `a'. | |
809 | *----------------------------------------------------------------------------*/ | |
810 | ||
811 | INLINE int32 extractFloat128Exp( float128 a ) | |
812 | { | |
813 | ||
814 | return ( a.high>>48 ) & 0x7FFF; | |
815 | ||
816 | } | |
817 | ||
818 | /*---------------------------------------------------------------------------- | |
819 | | Returns the sign bit of the quadruple-precision floating-point value `a'. | |
820 | *----------------------------------------------------------------------------*/ | |
821 | ||
822 | INLINE flag extractFloat128Sign( float128 a ) | |
823 | { | |
824 | ||
825 | return a.high>>63; | |
826 | ||
827 | } | |
828 | ||
829 | /*---------------------------------------------------------------------------- | |
830 | | Normalizes the subnormal quadruple-precision floating-point value | |
831 | | represented by the denormalized significand formed by the concatenation of | |
832 | | `aSig0' and `aSig1'. The normalized exponent is stored at the location | |
833 | | pointed to by `zExpPtr'. The most significant 49 bits of the normalized | |
834 | | significand are stored at the location pointed to by `zSig0Ptr', and the | |
835 | | least significant 64 bits of the normalized significand are stored at the | |
836 | | location pointed to by `zSig1Ptr'. | |
837 | *----------------------------------------------------------------------------*/ | |
838 | ||
839 | static void | |
840 | normalizeFloat128Subnormal( | |
841 | bits64 aSig0, | |
842 | bits64 aSig1, | |
843 | int32 *zExpPtr, | |
844 | bits64 *zSig0Ptr, | |
845 | bits64 *zSig1Ptr | |
846 | ) | |
847 | { | |
848 | int8 shiftCount; | |
849 | ||
850 | if ( aSig0 == 0 ) { | |
851 | shiftCount = countLeadingZeros64( aSig1 ) - 15; | |
852 | if ( shiftCount < 0 ) { | |
853 | *zSig0Ptr = aSig1>>( - shiftCount ); | |
854 | *zSig1Ptr = aSig1<<( shiftCount & 63 ); | |
855 | } | |
856 | else { | |
857 | *zSig0Ptr = aSig1<<shiftCount; | |
858 | *zSig1Ptr = 0; | |
859 | } | |
860 | *zExpPtr = - shiftCount - 63; | |
861 | } | |
862 | else { | |
863 | shiftCount = countLeadingZeros64( aSig0 ) - 15; | |
864 | shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); | |
865 | *zExpPtr = 1 - shiftCount; | |
866 | } | |
867 | ||
868 | } | |
869 | ||
870 | /*---------------------------------------------------------------------------- | |
871 | | Packs the sign `zSign', the exponent `zExp', and the significand formed | |
872 | | by the concatenation of `zSig0' and `zSig1' into a quadruple-precision | |
873 | | floating-point value, returning the result. After being shifted into the | |
874 | | proper positions, the three fields `zSign', `zExp', and `zSig0' are simply | |
875 | | added together to form the most significant 32 bits of the result. This | |
876 | | means that any integer portion of `zSig0' will be added into the exponent. | |
877 | | Since a properly normalized significand will have an integer portion equal | |
878 | | to 1, the `zExp' input should be 1 less than the desired result exponent | |
879 | | whenever `zSig0' and `zSig1' concatenated form a complete, normalized | |
880 | | significand. | |
881 | *----------------------------------------------------------------------------*/ | |
882 | ||
883 | INLINE float128 | |
884 | packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 ) | |
885 | { | |
886 | float128 z; | |
887 | ||
888 | z.low = zSig1; | |
889 | z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0; | |
890 | return z; | |
891 | ||
892 | } | |
893 | ||
894 | /*---------------------------------------------------------------------------- | |
895 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
896 | | and extended significand formed by the concatenation of `zSig0', `zSig1', | |
897 | | and `zSig2', and returns the proper quadruple-precision floating-point value | |
898 | | corresponding to the abstract input. Ordinarily, the abstract value is | |
899 | | simply rounded and packed into the quadruple-precision format, with the | |
900 | | inexact exception raised if the abstract input cannot be represented | |
901 | | exactly. However, if the abstract value is too large, the overflow and | |
902 | | inexact exceptions are raised and an infinity or maximal finite value is | |
903 | | returned. If the abstract value is too small, the input value is rounded to | |
904 | | a subnormal number, and the underflow and inexact exceptions are raised if | |
905 | | the abstract input cannot be represented exactly as a subnormal quadruple- | |
906 | | precision floating-point number. | |
907 | | The input significand must be normalized or smaller. If the input | |
908 | | significand is not normalized, `zExp' must be 0; in that case, the result | |
909 | | returned is a subnormal number, and it must not require rounding. In the | |
910 | | usual case that the input significand is normalized, `zExp' must be 1 less | |
911 | | than the ``true'' floating-point exponent. The handling of underflow and | |
912 | | overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
913 | *----------------------------------------------------------------------------*/ | |
914 | ||
915 | static float128 | |
916 | roundAndPackFloat128( | |
917 | flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM) | |
918 | { | |
919 | int8 roundingMode; | |
920 | flag roundNearestEven, increment, isTiny; | |
921 | ||
922 | roundingMode = STATUS(float_rounding_mode); | |
923 | roundNearestEven = ( roundingMode == float_round_nearest_even ); | |
924 | increment = ( (sbits64) zSig2 < 0 ); | |
925 | if ( ! roundNearestEven ) { | |
926 | if ( roundingMode == float_round_to_zero ) { | |
927 | increment = 0; | |
928 | } | |
929 | else { | |
930 | if ( zSign ) { | |
931 | increment = ( roundingMode == float_round_down ) && zSig2; | |
932 | } | |
933 | else { | |
934 | increment = ( roundingMode == float_round_up ) && zSig2; | |
935 | } | |
936 | } | |
937 | } | |
938 | if ( 0x7FFD <= (bits32) zExp ) { | |
939 | if ( ( 0x7FFD < zExp ) | |
940 | || ( ( zExp == 0x7FFD ) | |
941 | && eq128( | |
942 | LIT64( 0x0001FFFFFFFFFFFF ), | |
943 | LIT64( 0xFFFFFFFFFFFFFFFF ), | |
944 | zSig0, | |
945 | zSig1 | |
946 | ) | |
947 | && increment | |
948 | ) | |
949 | ) { | |
950 | float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); | |
951 | if ( ( roundingMode == float_round_to_zero ) | |
952 | || ( zSign && ( roundingMode == float_round_up ) ) | |
953 | || ( ! zSign && ( roundingMode == float_round_down ) ) | |
954 | ) { | |
955 | return | |
956 | packFloat128( | |
957 | zSign, | |
958 | 0x7FFE, | |
959 | LIT64( 0x0000FFFFFFFFFFFF ), | |
960 | LIT64( 0xFFFFFFFFFFFFFFFF ) | |
961 | ); | |
962 | } | |
963 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
964 | } | |
965 | if ( zExp < 0 ) { | |
966 | isTiny = | |
967 | ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) | |
968 | || ( zExp < -1 ) | |
969 | || ! increment | |
970 | || lt128( | |
971 | zSig0, | |
972 | zSig1, | |
973 | LIT64( 0x0001FFFFFFFFFFFF ), | |
974 | LIT64( 0xFFFFFFFFFFFFFFFF ) | |
975 | ); | |
976 | shift128ExtraRightJamming( | |
977 | zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); | |
978 | zExp = 0; | |
979 | if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR); | |
980 | if ( roundNearestEven ) { | |
981 | increment = ( (sbits64) zSig2 < 0 ); | |
982 | } | |
983 | else { | |
984 | if ( zSign ) { | |
985 | increment = ( roundingMode == float_round_down ) && zSig2; | |
986 | } | |
987 | else { | |
988 | increment = ( roundingMode == float_round_up ) && zSig2; | |
989 | } | |
990 | } | |
991 | } | |
992 | } | |
993 | if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
994 | if ( increment ) { | |
995 | add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); | |
996 | zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); | |
997 | } | |
998 | else { | |
999 | if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; | |
1000 | } | |
1001 | return packFloat128( zSign, zExp, zSig0, zSig1 ); | |
1002 | ||
1003 | } | |
1004 | ||
1005 | /*---------------------------------------------------------------------------- | |
1006 | | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
1007 | | and significand formed by the concatenation of `zSig0' and `zSig1', and | |
1008 | | returns the proper quadruple-precision floating-point value corresponding | |
1009 | | to the abstract input. This routine is just like `roundAndPackFloat128' | |
1010 | | except that the input significand has fewer bits and does not have to be | |
1011 | | normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- | |
1012 | | point exponent. | |
1013 | *----------------------------------------------------------------------------*/ | |
1014 | ||
1015 | static float128 | |
1016 | normalizeRoundAndPackFloat128( | |
1017 | flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM) | |
1018 | { | |
1019 | int8 shiftCount; | |
1020 | bits64 zSig2; | |
1021 | ||
1022 | if ( zSig0 == 0 ) { | |
1023 | zSig0 = zSig1; | |
1024 | zSig1 = 0; | |
1025 | zExp -= 64; | |
1026 | } | |
1027 | shiftCount = countLeadingZeros64( zSig0 ) - 15; | |
1028 | if ( 0 <= shiftCount ) { | |
1029 | zSig2 = 0; | |
1030 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
1031 | } | |
1032 | else { | |
1033 | shift128ExtraRightJamming( | |
1034 | zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); | |
1035 | } | |
1036 | zExp -= shiftCount; | |
1037 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR); | |
1038 | ||
1039 | } | |
1040 | ||
1041 | #endif | |
1042 | ||
1043 | /*---------------------------------------------------------------------------- | |
1044 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1045 | | to the single-precision floating-point format. The conversion is performed | |
1046 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1047 | *----------------------------------------------------------------------------*/ | |
1048 | ||
1049 | float32 int32_to_float32( int32 a STATUS_PARAM ) | |
1050 | { | |
1051 | flag zSign; | |
1052 | ||
1053 | if ( a == 0 ) return 0; | |
1054 | if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); | |
1055 | zSign = ( a < 0 ); | |
1056 | return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); | |
1057 | ||
1058 | } | |
1059 | ||
1060 | /*---------------------------------------------------------------------------- | |
1061 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1062 | | to the double-precision floating-point format. The conversion is performed | |
1063 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1064 | *----------------------------------------------------------------------------*/ | |
1065 | ||
1066 | float64 int32_to_float64( int32 a STATUS_PARAM ) | |
1067 | { | |
1068 | flag zSign; | |
1069 | uint32 absA; | |
1070 | int8 shiftCount; | |
1071 | bits64 zSig; | |
1072 | ||
1073 | if ( a == 0 ) return 0; | |
1074 | zSign = ( a < 0 ); | |
1075 | absA = zSign ? - a : a; | |
1076 | shiftCount = countLeadingZeros32( absA ) + 21; | |
1077 | zSig = absA; | |
1078 | return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); | |
1079 | ||
1080 | } | |
1081 | ||
1082 | #ifdef FLOATX80 | |
1083 | ||
1084 | /*---------------------------------------------------------------------------- | |
1085 | | Returns the result of converting the 32-bit two's complement integer `a' | |
1086 | | to the extended double-precision floating-point format. The conversion | |
1087 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1088 | | Arithmetic. | |
1089 | *----------------------------------------------------------------------------*/ | |
1090 | ||
1091 | floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) | |
1092 | { | |
1093 | flag zSign; | |
1094 | uint32 absA; | |
1095 | int8 shiftCount; | |
1096 | bits64 zSig; | |
1097 | ||
1098 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); | |
1099 | zSign = ( a < 0 ); | |
1100 | absA = zSign ? - a : a; | |
1101 | shiftCount = countLeadingZeros32( absA ) + 32; | |
1102 | zSig = absA; | |
1103 | return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); | |
1104 | ||
1105 | } | |
1106 | ||
1107 | #endif | |
1108 | ||
1109 | #ifdef FLOAT128 | |
1110 | ||
1111 | /*---------------------------------------------------------------------------- | |
1112 | | Returns the result of converting the 32-bit two's complement integer `a' to | |
1113 | | the quadruple-precision floating-point format. The conversion is performed | |
1114 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1115 | *----------------------------------------------------------------------------*/ | |
1116 | ||
1117 | float128 int32_to_float128( int32 a STATUS_PARAM ) | |
1118 | { | |
1119 | flag zSign; | |
1120 | uint32 absA; | |
1121 | int8 shiftCount; | |
1122 | bits64 zSig0; | |
1123 | ||
1124 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
1125 | zSign = ( a < 0 ); | |
1126 | absA = zSign ? - a : a; | |
1127 | shiftCount = countLeadingZeros32( absA ) + 17; | |
1128 | zSig0 = absA; | |
1129 | return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); | |
1130 | ||
1131 | } | |
1132 | ||
1133 | #endif | |
1134 | ||
1135 | /*---------------------------------------------------------------------------- | |
1136 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1137 | | to the single-precision floating-point format. The conversion is performed | |
1138 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1139 | *----------------------------------------------------------------------------*/ | |
1140 | ||
1141 | float32 int64_to_float32( int64 a STATUS_PARAM ) | |
1142 | { | |
1143 | flag zSign; | |
1144 | uint64 absA; | |
1145 | int8 shiftCount; | |
1146 | ||
1147 | if ( a == 0 ) return 0; | |
1148 | zSign = ( a < 0 ); | |
1149 | absA = zSign ? - a : a; | |
1150 | shiftCount = countLeadingZeros64( absA ) - 40; | |
1151 | if ( 0 <= shiftCount ) { | |
1152 | return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); | |
1153 | } | |
1154 | else { | |
1155 | shiftCount += 7; | |
1156 | if ( shiftCount < 0 ) { | |
1157 | shift64RightJamming( absA, - shiftCount, &absA ); | |
1158 | } | |
1159 | else { | |
1160 | absA <<= shiftCount; | |
1161 | } | |
1162 | return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); | |
1163 | } | |
1164 | ||
1165 | } | |
1166 | ||
3430b0be | 1167 | float32 uint64_to_float32( uint64 a STATUS_PARAM ) |
75d62a58 JM |
1168 | { |
1169 | int8 shiftCount; | |
1170 | ||
1171 | if ( a == 0 ) return 0; | |
1172 | shiftCount = countLeadingZeros64( a ) - 40; | |
1173 | if ( 0 <= shiftCount ) { | |
1174 | return packFloat32( 1 > 0, 0x95 - shiftCount, a<<shiftCount ); | |
1175 | } | |
1176 | else { | |
1177 | shiftCount += 7; | |
1178 | if ( shiftCount < 0 ) { | |
1179 | shift64RightJamming( a, - shiftCount, &a ); | |
1180 | } | |
1181 | else { | |
1182 | a <<= shiftCount; | |
1183 | } | |
1184 | return roundAndPackFloat32( 1 > 0, 0x9C - shiftCount, a STATUS_VAR ); | |
1185 | } | |
1186 | } | |
1187 | ||
158142c2 FB |
1188 | /*---------------------------------------------------------------------------- |
1189 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1190 | | to the double-precision floating-point format. The conversion is performed | |
1191 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1192 | *----------------------------------------------------------------------------*/ | |
1193 | ||
1194 | float64 int64_to_float64( int64 a STATUS_PARAM ) | |
1195 | { | |
1196 | flag zSign; | |
1197 | ||
1198 | if ( a == 0 ) return 0; | |
1199 | if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) { | |
1200 | return packFloat64( 1, 0x43E, 0 ); | |
1201 | } | |
1202 | zSign = ( a < 0 ); | |
1203 | return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); | |
1204 | ||
1205 | } | |
1206 | ||
75d62a58 JM |
1207 | float64 uint64_to_float64( uint64 a STATUS_PARAM ) |
1208 | { | |
1209 | if ( a == 0 ) return 0; | |
1210 | return normalizeRoundAndPackFloat64( 0, 0x43C, a STATUS_VAR ); | |
1211 | ||
1212 | } | |
1213 | ||
158142c2 FB |
1214 | #ifdef FLOATX80 |
1215 | ||
1216 | /*---------------------------------------------------------------------------- | |
1217 | | Returns the result of converting the 64-bit two's complement integer `a' | |
1218 | | to the extended double-precision floating-point format. The conversion | |
1219 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1220 | | Arithmetic. | |
1221 | *----------------------------------------------------------------------------*/ | |
1222 | ||
1223 | floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) | |
1224 | { | |
1225 | flag zSign; | |
1226 | uint64 absA; | |
1227 | int8 shiftCount; | |
1228 | ||
1229 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); | |
1230 | zSign = ( a < 0 ); | |
1231 | absA = zSign ? - a : a; | |
1232 | shiftCount = countLeadingZeros64( absA ); | |
1233 | return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); | |
1234 | ||
1235 | } | |
1236 | ||
1237 | #endif | |
1238 | ||
1239 | #ifdef FLOAT128 | |
1240 | ||
1241 | /*---------------------------------------------------------------------------- | |
1242 | | Returns the result of converting the 64-bit two's complement integer `a' to | |
1243 | | the quadruple-precision floating-point format. The conversion is performed | |
1244 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1245 | *----------------------------------------------------------------------------*/ | |
1246 | ||
1247 | float128 int64_to_float128( int64 a STATUS_PARAM ) | |
1248 | { | |
1249 | flag zSign; | |
1250 | uint64 absA; | |
1251 | int8 shiftCount; | |
1252 | int32 zExp; | |
1253 | bits64 zSig0, zSig1; | |
1254 | ||
1255 | if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
1256 | zSign = ( a < 0 ); | |
1257 | absA = zSign ? - a : a; | |
1258 | shiftCount = countLeadingZeros64( absA ) + 49; | |
1259 | zExp = 0x406E - shiftCount; | |
1260 | if ( 64 <= shiftCount ) { | |
1261 | zSig1 = 0; | |
1262 | zSig0 = absA; | |
1263 | shiftCount -= 64; | |
1264 | } | |
1265 | else { | |
1266 | zSig1 = absA; | |
1267 | zSig0 = 0; | |
1268 | } | |
1269 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
1270 | return packFloat128( zSign, zExp, zSig0, zSig1 ); | |
1271 | ||
1272 | } | |
1273 | ||
1274 | #endif | |
1275 | ||
1276 | /*---------------------------------------------------------------------------- | |
1277 | | Returns the result of converting the single-precision floating-point value | |
1278 | | `a' to the 32-bit two's complement integer format. The conversion is | |
1279 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1280 | | Arithmetic---which means in particular that the conversion is rounded | |
1281 | | according to the current rounding mode. If `a' is a NaN, the largest | |
1282 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
1283 | | largest integer with the same sign as `a' is returned. | |
1284 | *----------------------------------------------------------------------------*/ | |
1285 | ||
1286 | int32 float32_to_int32( float32 a STATUS_PARAM ) | |
1287 | { | |
1288 | flag aSign; | |
1289 | int16 aExp, shiftCount; | |
1290 | bits32 aSig; | |
1291 | bits64 aSig64; | |
1292 | ||
1293 | aSig = extractFloat32Frac( a ); | |
1294 | aExp = extractFloat32Exp( a ); | |
1295 | aSign = extractFloat32Sign( a ); | |
1296 | if ( ( aExp == 0xFF ) && aSig ) aSign = 0; | |
1297 | if ( aExp ) aSig |= 0x00800000; | |
1298 | shiftCount = 0xAF - aExp; | |
1299 | aSig64 = aSig; | |
1300 | aSig64 <<= 32; | |
1301 | if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); | |
1302 | return roundAndPackInt32( aSign, aSig64 STATUS_VAR ); | |
1303 | ||
1304 | } | |
1305 | ||
1306 | /*---------------------------------------------------------------------------- | |
1307 | | Returns the result of converting the single-precision floating-point value | |
1308 | | `a' to the 32-bit two's complement integer format. The conversion is | |
1309 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1310 | | Arithmetic, except that the conversion is always rounded toward zero. | |
1311 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
1312 | | the conversion overflows, the largest integer with the same sign as `a' is | |
1313 | | returned. | |
1314 | *----------------------------------------------------------------------------*/ | |
1315 | ||
1316 | int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) | |
1317 | { | |
1318 | flag aSign; | |
1319 | int16 aExp, shiftCount; | |
1320 | bits32 aSig; | |
1321 | int32 z; | |
1322 | ||
1323 | aSig = extractFloat32Frac( a ); | |
1324 | aExp = extractFloat32Exp( a ); | |
1325 | aSign = extractFloat32Sign( a ); | |
1326 | shiftCount = aExp - 0x9E; | |
1327 | if ( 0 <= shiftCount ) { | |
1328 | if ( a != 0xCF000000 ) { | |
1329 | float_raise( float_flag_invalid STATUS_VAR); | |
1330 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; | |
1331 | } | |
1332 | return (sbits32) 0x80000000; | |
1333 | } | |
1334 | else if ( aExp <= 0x7E ) { | |
1335 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1336 | return 0; | |
1337 | } | |
1338 | aSig = ( aSig | 0x00800000 )<<8; | |
1339 | z = aSig>>( - shiftCount ); | |
1340 | if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) { | |
1341 | STATUS(float_exception_flags) |= float_flag_inexact; | |
1342 | } | |
1343 | if ( aSign ) z = - z; | |
1344 | return z; | |
1345 | ||
1346 | } | |
1347 | ||
1348 | /*---------------------------------------------------------------------------- | |
1349 | | Returns the result of converting the single-precision floating-point value | |
1350 | | `a' to the 64-bit two's complement integer format. The conversion is | |
1351 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1352 | | Arithmetic---which means in particular that the conversion is rounded | |
1353 | | according to the current rounding mode. If `a' is a NaN, the largest | |
1354 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
1355 | | largest integer with the same sign as `a' is returned. | |
1356 | *----------------------------------------------------------------------------*/ | |
1357 | ||
1358 | int64 float32_to_int64( float32 a STATUS_PARAM ) | |
1359 | { | |
1360 | flag aSign; | |
1361 | int16 aExp, shiftCount; | |
1362 | bits32 aSig; | |
1363 | bits64 aSig64, aSigExtra; | |
1364 | ||
1365 | aSig = extractFloat32Frac( a ); | |
1366 | aExp = extractFloat32Exp( a ); | |
1367 | aSign = extractFloat32Sign( a ); | |
1368 | shiftCount = 0xBE - aExp; | |
1369 | if ( shiftCount < 0 ) { | |
1370 | float_raise( float_flag_invalid STATUS_VAR); | |
1371 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { | |
1372 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
1373 | } | |
1374 | return (sbits64) LIT64( 0x8000000000000000 ); | |
1375 | } | |
1376 | if ( aExp ) aSig |= 0x00800000; | |
1377 | aSig64 = aSig; | |
1378 | aSig64 <<= 40; | |
1379 | shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); | |
1380 | return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR ); | |
1381 | ||
1382 | } | |
1383 | ||
1384 | /*---------------------------------------------------------------------------- | |
1385 | | Returns the result of converting the single-precision floating-point value | |
1386 | | `a' to the 64-bit two's complement integer format. The conversion is | |
1387 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1388 | | Arithmetic, except that the conversion is always rounded toward zero. If | |
1389 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
1390 | | conversion overflows, the largest integer with the same sign as `a' is | |
1391 | | returned. | |
1392 | *----------------------------------------------------------------------------*/ | |
1393 | ||
1394 | int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) | |
1395 | { | |
1396 | flag aSign; | |
1397 | int16 aExp, shiftCount; | |
1398 | bits32 aSig; | |
1399 | bits64 aSig64; | |
1400 | int64 z; | |
1401 | ||
1402 | aSig = extractFloat32Frac( a ); | |
1403 | aExp = extractFloat32Exp( a ); | |
1404 | aSign = extractFloat32Sign( a ); | |
1405 | shiftCount = aExp - 0xBE; | |
1406 | if ( 0 <= shiftCount ) { | |
1407 | if ( a != 0xDF000000 ) { | |
1408 | float_raise( float_flag_invalid STATUS_VAR); | |
1409 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { | |
1410 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
1411 | } | |
1412 | } | |
1413 | return (sbits64) LIT64( 0x8000000000000000 ); | |
1414 | } | |
1415 | else if ( aExp <= 0x7E ) { | |
1416 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1417 | return 0; | |
1418 | } | |
1419 | aSig64 = aSig | 0x00800000; | |
1420 | aSig64 <<= 40; | |
1421 | z = aSig64>>( - shiftCount ); | |
1422 | if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) { | |
1423 | STATUS(float_exception_flags) |= float_flag_inexact; | |
1424 | } | |
1425 | if ( aSign ) z = - z; | |
1426 | return z; | |
1427 | ||
1428 | } | |
1429 | ||
1430 | /*---------------------------------------------------------------------------- | |
1431 | | Returns the result of converting the single-precision floating-point value | |
1432 | | `a' to the double-precision floating-point format. The conversion is | |
1433 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1434 | | Arithmetic. | |
1435 | *----------------------------------------------------------------------------*/ | |
1436 | ||
1437 | float64 float32_to_float64( float32 a STATUS_PARAM ) | |
1438 | { | |
1439 | flag aSign; | |
1440 | int16 aExp; | |
1441 | bits32 aSig; | |
1442 | ||
1443 | aSig = extractFloat32Frac( a ); | |
1444 | aExp = extractFloat32Exp( a ); | |
1445 | aSign = extractFloat32Sign( a ); | |
1446 | if ( aExp == 0xFF ) { | |
1447 | if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR )); | |
1448 | return packFloat64( aSign, 0x7FF, 0 ); | |
1449 | } | |
1450 | if ( aExp == 0 ) { | |
1451 | if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); | |
1452 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1453 | --aExp; | |
1454 | } | |
1455 | return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 ); | |
1456 | ||
1457 | } | |
1458 | ||
1459 | #ifdef FLOATX80 | |
1460 | ||
1461 | /*---------------------------------------------------------------------------- | |
1462 | | Returns the result of converting the single-precision floating-point value | |
1463 | | `a' to the extended double-precision floating-point format. The conversion | |
1464 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1465 | | Arithmetic. | |
1466 | *----------------------------------------------------------------------------*/ | |
1467 | ||
1468 | floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) | |
1469 | { | |
1470 | flag aSign; | |
1471 | int16 aExp; | |
1472 | bits32 aSig; | |
1473 | ||
1474 | aSig = extractFloat32Frac( a ); | |
1475 | aExp = extractFloat32Exp( a ); | |
1476 | aSign = extractFloat32Sign( a ); | |
1477 | if ( aExp == 0xFF ) { | |
1478 | if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) ); | |
1479 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
1480 | } | |
1481 | if ( aExp == 0 ) { | |
1482 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
1483 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1484 | } | |
1485 | aSig |= 0x00800000; | |
1486 | return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 ); | |
1487 | ||
1488 | } | |
1489 | ||
1490 | #endif | |
1491 | ||
1492 | #ifdef FLOAT128 | |
1493 | ||
1494 | /*---------------------------------------------------------------------------- | |
1495 | | Returns the result of converting the single-precision floating-point value | |
1496 | | `a' to the double-precision floating-point format. The conversion is | |
1497 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
1498 | | Arithmetic. | |
1499 | *----------------------------------------------------------------------------*/ | |
1500 | ||
1501 | float128 float32_to_float128( float32 a STATUS_PARAM ) | |
1502 | { | |
1503 | flag aSign; | |
1504 | int16 aExp; | |
1505 | bits32 aSig; | |
1506 | ||
1507 | aSig = extractFloat32Frac( a ); | |
1508 | aExp = extractFloat32Exp( a ); | |
1509 | aSign = extractFloat32Sign( a ); | |
1510 | if ( aExp == 0xFF ) { | |
1511 | if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) ); | |
1512 | return packFloat128( aSign, 0x7FFF, 0, 0 ); | |
1513 | } | |
1514 | if ( aExp == 0 ) { | |
1515 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); | |
1516 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1517 | --aExp; | |
1518 | } | |
1519 | return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 ); | |
1520 | ||
1521 | } | |
1522 | ||
1523 | #endif | |
1524 | ||
1525 | /*---------------------------------------------------------------------------- | |
1526 | | Rounds the single-precision floating-point value `a' to an integer, and | |
1527 | | returns the result as a single-precision floating-point value. The | |
1528 | | operation is performed according to the IEC/IEEE Standard for Binary | |
1529 | | Floating-Point Arithmetic. | |
1530 | *----------------------------------------------------------------------------*/ | |
1531 | ||
1532 | float32 float32_round_to_int( float32 a STATUS_PARAM) | |
1533 | { | |
1534 | flag aSign; | |
1535 | int16 aExp; | |
1536 | bits32 lastBitMask, roundBitsMask; | |
1537 | int8 roundingMode; | |
1538 | float32 z; | |
1539 | ||
1540 | aExp = extractFloat32Exp( a ); | |
1541 | if ( 0x96 <= aExp ) { | |
1542 | if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { | |
1543 | return propagateFloat32NaN( a, a STATUS_VAR ); | |
1544 | } | |
1545 | return a; | |
1546 | } | |
1547 | if ( aExp <= 0x7E ) { | |
1548 | if ( (bits32) ( a<<1 ) == 0 ) return a; | |
1549 | STATUS(float_exception_flags) |= float_flag_inexact; | |
1550 | aSign = extractFloat32Sign( a ); | |
1551 | switch ( STATUS(float_rounding_mode) ) { | |
1552 | case float_round_nearest_even: | |
1553 | if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { | |
1554 | return packFloat32( aSign, 0x7F, 0 ); | |
1555 | } | |
1556 | break; | |
1557 | case float_round_down: | |
1558 | return aSign ? 0xBF800000 : 0; | |
1559 | case float_round_up: | |
1560 | return aSign ? 0x80000000 : 0x3F800000; | |
1561 | } | |
1562 | return packFloat32( aSign, 0, 0 ); | |
1563 | } | |
1564 | lastBitMask = 1; | |
1565 | lastBitMask <<= 0x96 - aExp; | |
1566 | roundBitsMask = lastBitMask - 1; | |
1567 | z = a; | |
1568 | roundingMode = STATUS(float_rounding_mode); | |
1569 | if ( roundingMode == float_round_nearest_even ) { | |
1570 | z += lastBitMask>>1; | |
1571 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
1572 | } | |
1573 | else if ( roundingMode != float_round_to_zero ) { | |
1574 | if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
1575 | z += roundBitsMask; | |
1576 | } | |
1577 | } | |
1578 | z &= ~ roundBitsMask; | |
1579 | if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact; | |
1580 | return z; | |
1581 | ||
1582 | } | |
1583 | ||
1584 | /*---------------------------------------------------------------------------- | |
1585 | | Returns the result of adding the absolute values of the single-precision | |
1586 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
1587 | | before being returned. `zSign' is ignored if the result is a NaN. | |
1588 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
1589 | | Floating-Point Arithmetic. | |
1590 | *----------------------------------------------------------------------------*/ | |
1591 | ||
1592 | static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) | |
1593 | { | |
1594 | int16 aExp, bExp, zExp; | |
1595 | bits32 aSig, bSig, zSig; | |
1596 | int16 expDiff; | |
1597 | ||
1598 | aSig = extractFloat32Frac( a ); | |
1599 | aExp = extractFloat32Exp( a ); | |
1600 | bSig = extractFloat32Frac( b ); | |
1601 | bExp = extractFloat32Exp( b ); | |
1602 | expDiff = aExp - bExp; | |
1603 | aSig <<= 6; | |
1604 | bSig <<= 6; | |
1605 | if ( 0 < expDiff ) { | |
1606 | if ( aExp == 0xFF ) { | |
1607 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1608 | return a; | |
1609 | } | |
1610 | if ( bExp == 0 ) { | |
1611 | --expDiff; | |
1612 | } | |
1613 | else { | |
1614 | bSig |= 0x20000000; | |
1615 | } | |
1616 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1617 | zExp = aExp; | |
1618 | } | |
1619 | else if ( expDiff < 0 ) { | |
1620 | if ( bExp == 0xFF ) { | |
1621 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1622 | return packFloat32( zSign, 0xFF, 0 ); | |
1623 | } | |
1624 | if ( aExp == 0 ) { | |
1625 | ++expDiff; | |
1626 | } | |
1627 | else { | |
1628 | aSig |= 0x20000000; | |
1629 | } | |
1630 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1631 | zExp = bExp; | |
1632 | } | |
1633 | else { | |
1634 | if ( aExp == 0xFF ) { | |
1635 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1636 | return a; | |
1637 | } | |
1638 | if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); | |
1639 | zSig = 0x40000000 + aSig + bSig; | |
1640 | zExp = aExp; | |
1641 | goto roundAndPack; | |
1642 | } | |
1643 | aSig |= 0x20000000; | |
1644 | zSig = ( aSig + bSig )<<1; | |
1645 | --zExp; | |
1646 | if ( (sbits32) zSig < 0 ) { | |
1647 | zSig = aSig + bSig; | |
1648 | ++zExp; | |
1649 | } | |
1650 | roundAndPack: | |
1651 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1652 | ||
1653 | } | |
1654 | ||
1655 | /*---------------------------------------------------------------------------- | |
1656 | | Returns the result of subtracting the absolute values of the single- | |
1657 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
1658 | | difference is negated before being returned. `zSign' is ignored if the | |
1659 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
1660 | | Standard for Binary Floating-Point Arithmetic. | |
1661 | *----------------------------------------------------------------------------*/ | |
1662 | ||
1663 | static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) | |
1664 | { | |
1665 | int16 aExp, bExp, zExp; | |
1666 | bits32 aSig, bSig, zSig; | |
1667 | int16 expDiff; | |
1668 | ||
1669 | aSig = extractFloat32Frac( a ); | |
1670 | aExp = extractFloat32Exp( a ); | |
1671 | bSig = extractFloat32Frac( b ); | |
1672 | bExp = extractFloat32Exp( b ); | |
1673 | expDiff = aExp - bExp; | |
1674 | aSig <<= 7; | |
1675 | bSig <<= 7; | |
1676 | if ( 0 < expDiff ) goto aExpBigger; | |
1677 | if ( expDiff < 0 ) goto bExpBigger; | |
1678 | if ( aExp == 0xFF ) { | |
1679 | if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1680 | float_raise( float_flag_invalid STATUS_VAR); | |
1681 | return float32_default_nan; | |
1682 | } | |
1683 | if ( aExp == 0 ) { | |
1684 | aExp = 1; | |
1685 | bExp = 1; | |
1686 | } | |
1687 | if ( bSig < aSig ) goto aBigger; | |
1688 | if ( aSig < bSig ) goto bBigger; | |
1689 | return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
1690 | bExpBigger: | |
1691 | if ( bExp == 0xFF ) { | |
1692 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1693 | return packFloat32( zSign ^ 1, 0xFF, 0 ); | |
1694 | } | |
1695 | if ( aExp == 0 ) { | |
1696 | ++expDiff; | |
1697 | } | |
1698 | else { | |
1699 | aSig |= 0x40000000; | |
1700 | } | |
1701 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1702 | bSig |= 0x40000000; | |
1703 | bBigger: | |
1704 | zSig = bSig - aSig; | |
1705 | zExp = bExp; | |
1706 | zSign ^= 1; | |
1707 | goto normalizeRoundAndPack; | |
1708 | aExpBigger: | |
1709 | if ( aExp == 0xFF ) { | |
1710 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1711 | return a; | |
1712 | } | |
1713 | if ( bExp == 0 ) { | |
1714 | --expDiff; | |
1715 | } | |
1716 | else { | |
1717 | bSig |= 0x40000000; | |
1718 | } | |
1719 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1720 | aSig |= 0x40000000; | |
1721 | aBigger: | |
1722 | zSig = aSig - bSig; | |
1723 | zExp = aExp; | |
1724 | normalizeRoundAndPack: | |
1725 | --zExp; | |
1726 | return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1727 | ||
1728 | } | |
1729 | ||
1730 | /*---------------------------------------------------------------------------- | |
1731 | | Returns the result of adding the single-precision floating-point values `a' | |
1732 | | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
1733 | | Binary Floating-Point Arithmetic. | |
1734 | *----------------------------------------------------------------------------*/ | |
1735 | ||
1736 | float32 float32_add( float32 a, float32 b STATUS_PARAM ) | |
1737 | { | |
1738 | flag aSign, bSign; | |
1739 | ||
1740 | aSign = extractFloat32Sign( a ); | |
1741 | bSign = extractFloat32Sign( b ); | |
1742 | if ( aSign == bSign ) { | |
1743 | return addFloat32Sigs( a, b, aSign STATUS_VAR); | |
1744 | } | |
1745 | else { | |
1746 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1747 | } | |
1748 | ||
1749 | } | |
1750 | ||
1751 | /*---------------------------------------------------------------------------- | |
1752 | | Returns the result of subtracting the single-precision floating-point values | |
1753 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1754 | | for Binary Floating-Point Arithmetic. | |
1755 | *----------------------------------------------------------------------------*/ | |
1756 | ||
1757 | float32 float32_sub( float32 a, float32 b STATUS_PARAM ) | |
1758 | { | |
1759 | flag aSign, bSign; | |
1760 | ||
1761 | aSign = extractFloat32Sign( a ); | |
1762 | bSign = extractFloat32Sign( b ); | |
1763 | if ( aSign == bSign ) { | |
1764 | return subFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1765 | } | |
1766 | else { | |
1767 | return addFloat32Sigs( a, b, aSign STATUS_VAR ); | |
1768 | } | |
1769 | ||
1770 | } | |
1771 | ||
1772 | /*---------------------------------------------------------------------------- | |
1773 | | Returns the result of multiplying the single-precision floating-point values | |
1774 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1775 | | for Binary Floating-Point Arithmetic. | |
1776 | *----------------------------------------------------------------------------*/ | |
1777 | ||
1778 | float32 float32_mul( float32 a, float32 b STATUS_PARAM ) | |
1779 | { | |
1780 | flag aSign, bSign, zSign; | |
1781 | int16 aExp, bExp, zExp; | |
1782 | bits32 aSig, bSig; | |
1783 | bits64 zSig64; | |
1784 | bits32 zSig; | |
1785 | ||
1786 | aSig = extractFloat32Frac( a ); | |
1787 | aExp = extractFloat32Exp( a ); | |
1788 | aSign = extractFloat32Sign( a ); | |
1789 | bSig = extractFloat32Frac( b ); | |
1790 | bExp = extractFloat32Exp( b ); | |
1791 | bSign = extractFloat32Sign( b ); | |
1792 | zSign = aSign ^ bSign; | |
1793 | if ( aExp == 0xFF ) { | |
1794 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
1795 | return propagateFloat32NaN( a, b STATUS_VAR ); | |
1796 | } | |
1797 | if ( ( bExp | bSig ) == 0 ) { | |
1798 | float_raise( float_flag_invalid STATUS_VAR); | |
1799 | return float32_default_nan; | |
1800 | } | |
1801 | return packFloat32( zSign, 0xFF, 0 ); | |
1802 | } | |
1803 | if ( bExp == 0xFF ) { | |
1804 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1805 | if ( ( aExp | aSig ) == 0 ) { | |
1806 | float_raise( float_flag_invalid STATUS_VAR); | |
1807 | return float32_default_nan; | |
1808 | } | |
1809 | return packFloat32( zSign, 0xFF, 0 ); | |
1810 | } | |
1811 | if ( aExp == 0 ) { | |
1812 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1813 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1814 | } | |
1815 | if ( bExp == 0 ) { | |
1816 | if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1817 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1818 | } | |
1819 | zExp = aExp + bExp - 0x7F; | |
1820 | aSig = ( aSig | 0x00800000 )<<7; | |
1821 | bSig = ( bSig | 0x00800000 )<<8; | |
1822 | shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 ); | |
1823 | zSig = zSig64; | |
1824 | if ( 0 <= (sbits32) ( zSig<<1 ) ) { | |
1825 | zSig <<= 1; | |
1826 | --zExp; | |
1827 | } | |
1828 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1829 | ||
1830 | } | |
1831 | ||
1832 | /*---------------------------------------------------------------------------- | |
1833 | | Returns the result of dividing the single-precision floating-point value `a' | |
1834 | | by the corresponding value `b'. The operation is performed according to the | |
1835 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1836 | *----------------------------------------------------------------------------*/ | |
1837 | ||
1838 | float32 float32_div( float32 a, float32 b STATUS_PARAM ) | |
1839 | { | |
1840 | flag aSign, bSign, zSign; | |
1841 | int16 aExp, bExp, zExp; | |
1842 | bits32 aSig, bSig, zSig; | |
1843 | ||
1844 | aSig = extractFloat32Frac( a ); | |
1845 | aExp = extractFloat32Exp( a ); | |
1846 | aSign = extractFloat32Sign( a ); | |
1847 | bSig = extractFloat32Frac( b ); | |
1848 | bExp = extractFloat32Exp( b ); | |
1849 | bSign = extractFloat32Sign( b ); | |
1850 | zSign = aSign ^ bSign; | |
1851 | if ( aExp == 0xFF ) { | |
1852 | if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1853 | if ( bExp == 0xFF ) { | |
1854 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1855 | float_raise( float_flag_invalid STATUS_VAR); | |
1856 | return float32_default_nan; | |
1857 | } | |
1858 | return packFloat32( zSign, 0xFF, 0 ); | |
1859 | } | |
1860 | if ( bExp == 0xFF ) { | |
1861 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1862 | return packFloat32( zSign, 0, 0 ); | |
1863 | } | |
1864 | if ( bExp == 0 ) { | |
1865 | if ( bSig == 0 ) { | |
1866 | if ( ( aExp | aSig ) == 0 ) { | |
1867 | float_raise( float_flag_invalid STATUS_VAR); | |
1868 | return float32_default_nan; | |
1869 | } | |
1870 | float_raise( float_flag_divbyzero STATUS_VAR); | |
1871 | return packFloat32( zSign, 0xFF, 0 ); | |
1872 | } | |
1873 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1874 | } | |
1875 | if ( aExp == 0 ) { | |
1876 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1877 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1878 | } | |
1879 | zExp = aExp - bExp + 0x7D; | |
1880 | aSig = ( aSig | 0x00800000 )<<7; | |
1881 | bSig = ( bSig | 0x00800000 )<<8; | |
1882 | if ( bSig <= ( aSig + aSig ) ) { | |
1883 | aSig >>= 1; | |
1884 | ++zExp; | |
1885 | } | |
1886 | zSig = ( ( (bits64) aSig )<<32 ) / bSig; | |
1887 | if ( ( zSig & 0x3F ) == 0 ) { | |
1888 | zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 ); | |
1889 | } | |
1890 | return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); | |
1891 | ||
1892 | } | |
1893 | ||
1894 | /*---------------------------------------------------------------------------- | |
1895 | | Returns the remainder of the single-precision floating-point value `a' | |
1896 | | with respect to the corresponding value `b'. The operation is performed | |
1897 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
1898 | *----------------------------------------------------------------------------*/ | |
1899 | ||
1900 | float32 float32_rem( float32 a, float32 b STATUS_PARAM ) | |
1901 | { | |
1902 | flag aSign, bSign, zSign; | |
1903 | int16 aExp, bExp, expDiff; | |
1904 | bits32 aSig, bSig; | |
1905 | bits32 q; | |
1906 | bits64 aSig64, bSig64, q64; | |
1907 | bits32 alternateASig; | |
1908 | sbits32 sigMean; | |
1909 | ||
1910 | aSig = extractFloat32Frac( a ); | |
1911 | aExp = extractFloat32Exp( a ); | |
1912 | aSign = extractFloat32Sign( a ); | |
1913 | bSig = extractFloat32Frac( b ); | |
1914 | bExp = extractFloat32Exp( b ); | |
1915 | bSign = extractFloat32Sign( b ); | |
1916 | if ( aExp == 0xFF ) { | |
1917 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
1918 | return propagateFloat32NaN( a, b STATUS_VAR ); | |
1919 | } | |
1920 | float_raise( float_flag_invalid STATUS_VAR); | |
1921 | return float32_default_nan; | |
1922 | } | |
1923 | if ( bExp == 0xFF ) { | |
1924 | if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); | |
1925 | return a; | |
1926 | } | |
1927 | if ( bExp == 0 ) { | |
1928 | if ( bSig == 0 ) { | |
1929 | float_raise( float_flag_invalid STATUS_VAR); | |
1930 | return float32_default_nan; | |
1931 | } | |
1932 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1933 | } | |
1934 | if ( aExp == 0 ) { | |
1935 | if ( aSig == 0 ) return a; | |
1936 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1937 | } | |
1938 | expDiff = aExp - bExp; | |
1939 | aSig |= 0x00800000; | |
1940 | bSig |= 0x00800000; | |
1941 | if ( expDiff < 32 ) { | |
1942 | aSig <<= 8; | |
1943 | bSig <<= 8; | |
1944 | if ( expDiff < 0 ) { | |
1945 | if ( expDiff < -1 ) return a; | |
1946 | aSig >>= 1; | |
1947 | } | |
1948 | q = ( bSig <= aSig ); | |
1949 | if ( q ) aSig -= bSig; | |
1950 | if ( 0 < expDiff ) { | |
1951 | q = ( ( (bits64) aSig )<<32 ) / bSig; | |
1952 | q >>= 32 - expDiff; | |
1953 | bSig >>= 2; | |
1954 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
1955 | } | |
1956 | else { | |
1957 | aSig >>= 2; | |
1958 | bSig >>= 2; | |
1959 | } | |
1960 | } | |
1961 | else { | |
1962 | if ( bSig <= aSig ) aSig -= bSig; | |
1963 | aSig64 = ( (bits64) aSig )<<40; | |
1964 | bSig64 = ( (bits64) bSig )<<40; | |
1965 | expDiff -= 64; | |
1966 | while ( 0 < expDiff ) { | |
1967 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
1968 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
1969 | aSig64 = - ( ( bSig * q64 )<<38 ); | |
1970 | expDiff -= 62; | |
1971 | } | |
1972 | expDiff += 64; | |
1973 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
1974 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
1975 | q = q64>>( 64 - expDiff ); | |
1976 | bSig <<= 6; | |
1977 | aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; | |
1978 | } | |
1979 | do { | |
1980 | alternateASig = aSig; | |
1981 | ++q; | |
1982 | aSig -= bSig; | |
1983 | } while ( 0 <= (sbits32) aSig ); | |
1984 | sigMean = aSig + alternateASig; | |
1985 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
1986 | aSig = alternateASig; | |
1987 | } | |
1988 | zSign = ( (sbits32) aSig < 0 ); | |
1989 | if ( zSign ) aSig = - aSig; | |
1990 | return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR ); | |
1991 | ||
1992 | } | |
1993 | ||
1994 | /*---------------------------------------------------------------------------- | |
1995 | | Returns the square root of the single-precision floating-point value `a'. | |
1996 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
1997 | | Floating-Point Arithmetic. | |
1998 | *----------------------------------------------------------------------------*/ | |
1999 | ||
2000 | float32 float32_sqrt( float32 a STATUS_PARAM ) | |
2001 | { | |
2002 | flag aSign; | |
2003 | int16 aExp, zExp; | |
2004 | bits32 aSig, zSig; | |
2005 | bits64 rem, term; | |
2006 | ||
2007 | aSig = extractFloat32Frac( a ); | |
2008 | aExp = extractFloat32Exp( a ); | |
2009 | aSign = extractFloat32Sign( a ); | |
2010 | if ( aExp == 0xFF ) { | |
2011 | if ( aSig ) return propagateFloat32NaN( a, 0 STATUS_VAR ); | |
2012 | if ( ! aSign ) return a; | |
2013 | float_raise( float_flag_invalid STATUS_VAR); | |
2014 | return float32_default_nan; | |
2015 | } | |
2016 | if ( aSign ) { | |
2017 | if ( ( aExp | aSig ) == 0 ) return a; | |
2018 | float_raise( float_flag_invalid STATUS_VAR); | |
2019 | return float32_default_nan; | |
2020 | } | |
2021 | if ( aExp == 0 ) { | |
2022 | if ( aSig == 0 ) return 0; | |
2023 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
2024 | } | |
2025 | zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; | |
2026 | aSig = ( aSig | 0x00800000 )<<8; | |
2027 | zSig = estimateSqrt32( aExp, aSig ) + 2; | |
2028 | if ( ( zSig & 0x7F ) <= 5 ) { | |
2029 | if ( zSig < 2 ) { | |
2030 | zSig = 0x7FFFFFFF; | |
2031 | goto roundAndPack; | |
2032 | } | |
2033 | aSig >>= aExp & 1; | |
2034 | term = ( (bits64) zSig ) * zSig; | |
2035 | rem = ( ( (bits64) aSig )<<32 ) - term; | |
2036 | while ( (sbits64) rem < 0 ) { | |
2037 | --zSig; | |
2038 | rem += ( ( (bits64) zSig )<<1 ) | 1; | |
2039 | } | |
2040 | zSig |= ( rem != 0 ); | |
2041 | } | |
2042 | shift32RightJamming( zSig, 1, &zSig ); | |
2043 | roundAndPack: | |
2044 | return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); | |
2045 | ||
2046 | } | |
2047 | ||
2048 | /*---------------------------------------------------------------------------- | |
2049 | | Returns 1 if the single-precision floating-point value `a' is equal to | |
2050 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
2051 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2052 | *----------------------------------------------------------------------------*/ | |
2053 | ||
750afe93 | 2054 | int float32_eq( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2055 | { |
2056 | ||
2057 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2058 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2059 | ) { | |
2060 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2061 | float_raise( float_flag_invalid STATUS_VAR); | |
2062 | } | |
2063 | return 0; | |
2064 | } | |
2065 | return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
2066 | ||
2067 | } | |
2068 | ||
2069 | /*---------------------------------------------------------------------------- | |
2070 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2071 | | or equal to the corresponding value `b', and 0 otherwise. The comparison | |
2072 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2073 | | Arithmetic. | |
2074 | *----------------------------------------------------------------------------*/ | |
2075 | ||
750afe93 | 2076 | int float32_le( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2077 | { |
2078 | flag aSign, bSign; | |
2079 | ||
2080 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2081 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2082 | ) { | |
2083 | float_raise( float_flag_invalid STATUS_VAR); | |
2084 | return 0; | |
2085 | } | |
2086 | aSign = extractFloat32Sign( a ); | |
2087 | bSign = extractFloat32Sign( b ); | |
2088 | if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
2089 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
2090 | ||
2091 | } | |
2092 | ||
2093 | /*---------------------------------------------------------------------------- | |
2094 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2095 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
2096 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2097 | *----------------------------------------------------------------------------*/ | |
2098 | ||
750afe93 | 2099 | int float32_lt( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2100 | { |
2101 | flag aSign, bSign; | |
2102 | ||
2103 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2104 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2105 | ) { | |
2106 | float_raise( float_flag_invalid STATUS_VAR); | |
2107 | return 0; | |
2108 | } | |
2109 | aSign = extractFloat32Sign( a ); | |
2110 | bSign = extractFloat32Sign( b ); | |
2111 | if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); | |
2112 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
2113 | ||
2114 | } | |
2115 | ||
2116 | /*---------------------------------------------------------------------------- | |
2117 | | Returns 1 if the single-precision floating-point value `a' is equal to | |
2118 | | the corresponding value `b', and 0 otherwise. The invalid exception is | |
2119 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
2120 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2121 | *----------------------------------------------------------------------------*/ | |
2122 | ||
750afe93 | 2123 | int float32_eq_signaling( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2124 | { |
2125 | ||
2126 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2127 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2128 | ) { | |
2129 | float_raise( float_flag_invalid STATUS_VAR); | |
2130 | return 0; | |
2131 | } | |
2132 | return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
2133 | ||
2134 | } | |
2135 | ||
2136 | /*---------------------------------------------------------------------------- | |
2137 | | Returns 1 if the single-precision floating-point value `a' is less than or | |
2138 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
2139 | | cause an exception. Otherwise, the comparison is performed according to the | |
2140 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2141 | *----------------------------------------------------------------------------*/ | |
2142 | ||
750afe93 | 2143 | int float32_le_quiet( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2144 | { |
2145 | flag aSign, bSign; | |
2146 | ||
2147 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2148 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2149 | ) { | |
2150 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2151 | float_raise( float_flag_invalid STATUS_VAR); | |
2152 | } | |
2153 | return 0; | |
2154 | } | |
2155 | aSign = extractFloat32Sign( a ); | |
2156 | bSign = extractFloat32Sign( b ); | |
2157 | if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
2158 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
2159 | ||
2160 | } | |
2161 | ||
2162 | /*---------------------------------------------------------------------------- | |
2163 | | Returns 1 if the single-precision floating-point value `a' is less than | |
2164 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
2165 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
2166 | | Standard for Binary Floating-Point Arithmetic. | |
2167 | *----------------------------------------------------------------------------*/ | |
2168 | ||
750afe93 | 2169 | int float32_lt_quiet( float32 a, float32 b STATUS_PARAM ) |
158142c2 FB |
2170 | { |
2171 | flag aSign, bSign; | |
2172 | ||
2173 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
2174 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
2175 | ) { | |
2176 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
2177 | float_raise( float_flag_invalid STATUS_VAR); | |
2178 | } | |
2179 | return 0; | |
2180 | } | |
2181 | aSign = extractFloat32Sign( a ); | |
2182 | bSign = extractFloat32Sign( b ); | |
2183 | if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); | |
2184 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
2185 | ||
2186 | } | |
2187 | ||
2188 | /*---------------------------------------------------------------------------- | |
2189 | | Returns the result of converting the double-precision floating-point value | |
2190 | | `a' to the 32-bit two's complement integer format. The conversion is | |
2191 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2192 | | Arithmetic---which means in particular that the conversion is rounded | |
2193 | | according to the current rounding mode. If `a' is a NaN, the largest | |
2194 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
2195 | | largest integer with the same sign as `a' is returned. | |
2196 | *----------------------------------------------------------------------------*/ | |
2197 | ||
2198 | int32 float64_to_int32( float64 a STATUS_PARAM ) | |
2199 | { | |
2200 | flag aSign; | |
2201 | int16 aExp, shiftCount; | |
2202 | bits64 aSig; | |
2203 | ||
2204 | aSig = extractFloat64Frac( a ); | |
2205 | aExp = extractFloat64Exp( a ); | |
2206 | aSign = extractFloat64Sign( a ); | |
2207 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
2208 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2209 | shiftCount = 0x42C - aExp; | |
2210 | if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); | |
2211 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); | |
2212 | ||
2213 | } | |
2214 | ||
2215 | /*---------------------------------------------------------------------------- | |
2216 | | Returns the result of converting the double-precision floating-point value | |
2217 | | `a' to the 32-bit two's complement integer format. The conversion is | |
2218 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2219 | | Arithmetic, except that the conversion is always rounded toward zero. | |
2220 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
2221 | | the conversion overflows, the largest integer with the same sign as `a' is | |
2222 | | returned. | |
2223 | *----------------------------------------------------------------------------*/ | |
2224 | ||
2225 | int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) | |
2226 | { | |
2227 | flag aSign; | |
2228 | int16 aExp, shiftCount; | |
2229 | bits64 aSig, savedASig; | |
2230 | int32 z; | |
2231 | ||
2232 | aSig = extractFloat64Frac( a ); | |
2233 | aExp = extractFloat64Exp( a ); | |
2234 | aSign = extractFloat64Sign( a ); | |
2235 | if ( 0x41E < aExp ) { | |
2236 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
2237 | goto invalid; | |
2238 | } | |
2239 | else if ( aExp < 0x3FF ) { | |
2240 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
2241 | return 0; | |
2242 | } | |
2243 | aSig |= LIT64( 0x0010000000000000 ); | |
2244 | shiftCount = 0x433 - aExp; | |
2245 | savedASig = aSig; | |
2246 | aSig >>= shiftCount; | |
2247 | z = aSig; | |
2248 | if ( aSign ) z = - z; | |
2249 | if ( ( z < 0 ) ^ aSign ) { | |
2250 | invalid: | |
2251 | float_raise( float_flag_invalid STATUS_VAR); | |
2252 | return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; | |
2253 | } | |
2254 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
2255 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2256 | } | |
2257 | return z; | |
2258 | ||
2259 | } | |
2260 | ||
2261 | /*---------------------------------------------------------------------------- | |
2262 | | Returns the result of converting the double-precision floating-point value | |
2263 | | `a' to the 64-bit two's complement integer format. The conversion is | |
2264 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2265 | | Arithmetic---which means in particular that the conversion is rounded | |
2266 | | according to the current rounding mode. If `a' is a NaN, the largest | |
2267 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
2268 | | largest integer with the same sign as `a' is returned. | |
2269 | *----------------------------------------------------------------------------*/ | |
2270 | ||
2271 | int64 float64_to_int64( float64 a STATUS_PARAM ) | |
2272 | { | |
2273 | flag aSign; | |
2274 | int16 aExp, shiftCount; | |
2275 | bits64 aSig, aSigExtra; | |
2276 | ||
2277 | aSig = extractFloat64Frac( a ); | |
2278 | aExp = extractFloat64Exp( a ); | |
2279 | aSign = extractFloat64Sign( a ); | |
2280 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2281 | shiftCount = 0x433 - aExp; | |
2282 | if ( shiftCount <= 0 ) { | |
2283 | if ( 0x43E < aExp ) { | |
2284 | float_raise( float_flag_invalid STATUS_VAR); | |
2285 | if ( ! aSign | |
2286 | || ( ( aExp == 0x7FF ) | |
2287 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) | |
2288 | ) { | |
2289 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
2290 | } | |
2291 | return (sbits64) LIT64( 0x8000000000000000 ); | |
2292 | } | |
2293 | aSigExtra = 0; | |
2294 | aSig <<= - shiftCount; | |
2295 | } | |
2296 | else { | |
2297 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); | |
2298 | } | |
2299 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); | |
2300 | ||
2301 | } | |
2302 | ||
2303 | /*---------------------------------------------------------------------------- | |
2304 | | Returns the result of converting the double-precision floating-point value | |
2305 | | `a' to the 64-bit two's complement integer format. The conversion is | |
2306 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2307 | | Arithmetic, except that the conversion is always rounded toward zero. | |
2308 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
2309 | | the conversion overflows, the largest integer with the same sign as `a' is | |
2310 | | returned. | |
2311 | *----------------------------------------------------------------------------*/ | |
2312 | ||
2313 | int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) | |
2314 | { | |
2315 | flag aSign; | |
2316 | int16 aExp, shiftCount; | |
2317 | bits64 aSig; | |
2318 | int64 z; | |
2319 | ||
2320 | aSig = extractFloat64Frac( a ); | |
2321 | aExp = extractFloat64Exp( a ); | |
2322 | aSign = extractFloat64Sign( a ); | |
2323 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
2324 | shiftCount = aExp - 0x433; | |
2325 | if ( 0 <= shiftCount ) { | |
2326 | if ( 0x43E <= aExp ) { | |
2327 | if ( a != LIT64( 0xC3E0000000000000 ) ) { | |
2328 | float_raise( float_flag_invalid STATUS_VAR); | |
2329 | if ( ! aSign | |
2330 | || ( ( aExp == 0x7FF ) | |
2331 | && ( aSig != LIT64( 0x0010000000000000 ) ) ) | |
2332 | ) { | |
2333 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
2334 | } | |
2335 | } | |
2336 | return (sbits64) LIT64( 0x8000000000000000 ); | |
2337 | } | |
2338 | z = aSig<<shiftCount; | |
2339 | } | |
2340 | else { | |
2341 | if ( aExp < 0x3FE ) { | |
2342 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
2343 | return 0; | |
2344 | } | |
2345 | z = aSig>>( - shiftCount ); | |
2346 | if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { | |
2347 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2348 | } | |
2349 | } | |
2350 | if ( aSign ) z = - z; | |
2351 | return z; | |
2352 | ||
2353 | } | |
2354 | ||
2355 | /*---------------------------------------------------------------------------- | |
2356 | | Returns the result of converting the double-precision floating-point value | |
2357 | | `a' to the single-precision floating-point format. The conversion is | |
2358 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2359 | | Arithmetic. | |
2360 | *----------------------------------------------------------------------------*/ | |
2361 | ||
2362 | float32 float64_to_float32( float64 a STATUS_PARAM ) | |
2363 | { | |
2364 | flag aSign; | |
2365 | int16 aExp; | |
2366 | bits64 aSig; | |
2367 | bits32 zSig; | |
2368 | ||
2369 | aSig = extractFloat64Frac( a ); | |
2370 | aExp = extractFloat64Exp( a ); | |
2371 | aSign = extractFloat64Sign( a ); | |
2372 | if ( aExp == 0x7FF ) { | |
2373 | if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) ); | |
2374 | return packFloat32( aSign, 0xFF, 0 ); | |
2375 | } | |
2376 | shift64RightJamming( aSig, 22, &aSig ); | |
2377 | zSig = aSig; | |
2378 | if ( aExp || zSig ) { | |
2379 | zSig |= 0x40000000; | |
2380 | aExp -= 0x381; | |
2381 | } | |
2382 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); | |
2383 | ||
2384 | } | |
2385 | ||
2386 | #ifdef FLOATX80 | |
2387 | ||
2388 | /*---------------------------------------------------------------------------- | |
2389 | | Returns the result of converting the double-precision floating-point value | |
2390 | | `a' to the extended double-precision floating-point format. The conversion | |
2391 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2392 | | Arithmetic. | |
2393 | *----------------------------------------------------------------------------*/ | |
2394 | ||
2395 | floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) | |
2396 | { | |
2397 | flag aSign; | |
2398 | int16 aExp; | |
2399 | bits64 aSig; | |
2400 | ||
2401 | aSig = extractFloat64Frac( a ); | |
2402 | aExp = extractFloat64Exp( a ); | |
2403 | aSign = extractFloat64Sign( a ); | |
2404 | if ( aExp == 0x7FF ) { | |
2405 | if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) ); | |
2406 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
2407 | } | |
2408 | if ( aExp == 0 ) { | |
2409 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
2410 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2411 | } | |
2412 | return | |
2413 | packFloatx80( | |
2414 | aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); | |
2415 | ||
2416 | } | |
2417 | ||
2418 | #endif | |
2419 | ||
2420 | #ifdef FLOAT128 | |
2421 | ||
2422 | /*---------------------------------------------------------------------------- | |
2423 | | Returns the result of converting the double-precision floating-point value | |
2424 | | `a' to the quadruple-precision floating-point format. The conversion is | |
2425 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
2426 | | Arithmetic. | |
2427 | *----------------------------------------------------------------------------*/ | |
2428 | ||
2429 | float128 float64_to_float128( float64 a STATUS_PARAM ) | |
2430 | { | |
2431 | flag aSign; | |
2432 | int16 aExp; | |
2433 | bits64 aSig, zSig0, zSig1; | |
2434 | ||
2435 | aSig = extractFloat64Frac( a ); | |
2436 | aExp = extractFloat64Exp( a ); | |
2437 | aSign = extractFloat64Sign( a ); | |
2438 | if ( aExp == 0x7FF ) { | |
2439 | if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) ); | |
2440 | return packFloat128( aSign, 0x7FFF, 0, 0 ); | |
2441 | } | |
2442 | if ( aExp == 0 ) { | |
2443 | if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); | |
2444 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2445 | --aExp; | |
2446 | } | |
2447 | shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); | |
2448 | return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); | |
2449 | ||
2450 | } | |
2451 | ||
2452 | #endif | |
2453 | ||
2454 | /*---------------------------------------------------------------------------- | |
2455 | | Rounds the double-precision floating-point value `a' to an integer, and | |
2456 | | returns the result as a double-precision floating-point value. The | |
2457 | | operation is performed according to the IEC/IEEE Standard for Binary | |
2458 | | Floating-Point Arithmetic. | |
2459 | *----------------------------------------------------------------------------*/ | |
2460 | ||
2461 | float64 float64_round_to_int( float64 a STATUS_PARAM ) | |
2462 | { | |
2463 | flag aSign; | |
2464 | int16 aExp; | |
2465 | bits64 lastBitMask, roundBitsMask; | |
2466 | int8 roundingMode; | |
2467 | float64 z; | |
2468 | ||
2469 | aExp = extractFloat64Exp( a ); | |
2470 | if ( 0x433 <= aExp ) { | |
2471 | if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { | |
2472 | return propagateFloat64NaN( a, a STATUS_VAR ); | |
2473 | } | |
2474 | return a; | |
2475 | } | |
2476 | if ( aExp < 0x3FF ) { | |
2477 | if ( (bits64) ( a<<1 ) == 0 ) return a; | |
2478 | STATUS(float_exception_flags) |= float_flag_inexact; | |
2479 | aSign = extractFloat64Sign( a ); | |
2480 | switch ( STATUS(float_rounding_mode) ) { | |
2481 | case float_round_nearest_even: | |
2482 | if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { | |
2483 | return packFloat64( aSign, 0x3FF, 0 ); | |
2484 | } | |
2485 | break; | |
2486 | case float_round_down: | |
2487 | return aSign ? LIT64( 0xBFF0000000000000 ) : 0; | |
2488 | case float_round_up: | |
2489 | return | |
2490 | aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ); | |
2491 | } | |
2492 | return packFloat64( aSign, 0, 0 ); | |
2493 | } | |
2494 | lastBitMask = 1; | |
2495 | lastBitMask <<= 0x433 - aExp; | |
2496 | roundBitsMask = lastBitMask - 1; | |
2497 | z = a; | |
2498 | roundingMode = STATUS(float_rounding_mode); | |
2499 | if ( roundingMode == float_round_nearest_even ) { | |
2500 | z += lastBitMask>>1; | |
2501 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
2502 | } | |
2503 | else if ( roundingMode != float_round_to_zero ) { | |
2504 | if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
2505 | z += roundBitsMask; | |
2506 | } | |
2507 | } | |
2508 | z &= ~ roundBitsMask; | |
2509 | if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact; | |
2510 | return z; | |
2511 | ||
2512 | } | |
2513 | ||
e6e5906b PB |
2514 | float64 float64_trunc_to_int( float64 a STATUS_PARAM) |
2515 | { | |
2516 | int oldmode; | |
2517 | float64 res; | |
2518 | oldmode = STATUS(float_rounding_mode); | |
2519 | STATUS(float_rounding_mode) = float_round_to_zero; | |
2520 | res = float64_round_to_int(a STATUS_VAR); | |
2521 | STATUS(float_rounding_mode) = oldmode; | |
2522 | return res; | |
2523 | } | |
2524 | ||
158142c2 FB |
2525 | /*---------------------------------------------------------------------------- |
2526 | | Returns the result of adding the absolute values of the double-precision | |
2527 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
2528 | | before being returned. `zSign' is ignored if the result is a NaN. | |
2529 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
2530 | | Floating-Point Arithmetic. | |
2531 | *----------------------------------------------------------------------------*/ | |
2532 | ||
2533 | static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) | |
2534 | { | |
2535 | int16 aExp, bExp, zExp; | |
2536 | bits64 aSig, bSig, zSig; | |
2537 | int16 expDiff; | |
2538 | ||
2539 | aSig = extractFloat64Frac( a ); | |
2540 | aExp = extractFloat64Exp( a ); | |
2541 | bSig = extractFloat64Frac( b ); | |
2542 | bExp = extractFloat64Exp( b ); | |
2543 | expDiff = aExp - bExp; | |
2544 | aSig <<= 9; | |
2545 | bSig <<= 9; | |
2546 | if ( 0 < expDiff ) { | |
2547 | if ( aExp == 0x7FF ) { | |
2548 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2549 | return a; | |
2550 | } | |
2551 | if ( bExp == 0 ) { | |
2552 | --expDiff; | |
2553 | } | |
2554 | else { | |
2555 | bSig |= LIT64( 0x2000000000000000 ); | |
2556 | } | |
2557 | shift64RightJamming( bSig, expDiff, &bSig ); | |
2558 | zExp = aExp; | |
2559 | } | |
2560 | else if ( expDiff < 0 ) { | |
2561 | if ( bExp == 0x7FF ) { | |
2562 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2563 | return packFloat64( zSign, 0x7FF, 0 ); | |
2564 | } | |
2565 | if ( aExp == 0 ) { | |
2566 | ++expDiff; | |
2567 | } | |
2568 | else { | |
2569 | aSig |= LIT64( 0x2000000000000000 ); | |
2570 | } | |
2571 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
2572 | zExp = bExp; | |
2573 | } | |
2574 | else { | |
2575 | if ( aExp == 0x7FF ) { | |
2576 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2577 | return a; | |
2578 | } | |
2579 | if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); | |
2580 | zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; | |
2581 | zExp = aExp; | |
2582 | goto roundAndPack; | |
2583 | } | |
2584 | aSig |= LIT64( 0x2000000000000000 ); | |
2585 | zSig = ( aSig + bSig )<<1; | |
2586 | --zExp; | |
2587 | if ( (sbits64) zSig < 0 ) { | |
2588 | zSig = aSig + bSig; | |
2589 | ++zExp; | |
2590 | } | |
2591 | roundAndPack: | |
2592 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
2593 | ||
2594 | } | |
2595 | ||
2596 | /*---------------------------------------------------------------------------- | |
2597 | | Returns the result of subtracting the absolute values of the double- | |
2598 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
2599 | | difference is negated before being returned. `zSign' is ignored if the | |
2600 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
2601 | | Standard for Binary Floating-Point Arithmetic. | |
2602 | *----------------------------------------------------------------------------*/ | |
2603 | ||
2604 | static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) | |
2605 | { | |
2606 | int16 aExp, bExp, zExp; | |
2607 | bits64 aSig, bSig, zSig; | |
2608 | int16 expDiff; | |
2609 | ||
2610 | aSig = extractFloat64Frac( a ); | |
2611 | aExp = extractFloat64Exp( a ); | |
2612 | bSig = extractFloat64Frac( b ); | |
2613 | bExp = extractFloat64Exp( b ); | |
2614 | expDiff = aExp - bExp; | |
2615 | aSig <<= 10; | |
2616 | bSig <<= 10; | |
2617 | if ( 0 < expDiff ) goto aExpBigger; | |
2618 | if ( expDiff < 0 ) goto bExpBigger; | |
2619 | if ( aExp == 0x7FF ) { | |
2620 | if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2621 | float_raise( float_flag_invalid STATUS_VAR); | |
2622 | return float64_default_nan; | |
2623 | } | |
2624 | if ( aExp == 0 ) { | |
2625 | aExp = 1; | |
2626 | bExp = 1; | |
2627 | } | |
2628 | if ( bSig < aSig ) goto aBigger; | |
2629 | if ( aSig < bSig ) goto bBigger; | |
2630 | return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
2631 | bExpBigger: | |
2632 | if ( bExp == 0x7FF ) { | |
2633 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2634 | return packFloat64( zSign ^ 1, 0x7FF, 0 ); | |
2635 | } | |
2636 | if ( aExp == 0 ) { | |
2637 | ++expDiff; | |
2638 | } | |
2639 | else { | |
2640 | aSig |= LIT64( 0x4000000000000000 ); | |
2641 | } | |
2642 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
2643 | bSig |= LIT64( 0x4000000000000000 ); | |
2644 | bBigger: | |
2645 | zSig = bSig - aSig; | |
2646 | zExp = bExp; | |
2647 | zSign ^= 1; | |
2648 | goto normalizeRoundAndPack; | |
2649 | aExpBigger: | |
2650 | if ( aExp == 0x7FF ) { | |
2651 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2652 | return a; | |
2653 | } | |
2654 | if ( bExp == 0 ) { | |
2655 | --expDiff; | |
2656 | } | |
2657 | else { | |
2658 | bSig |= LIT64( 0x4000000000000000 ); | |
2659 | } | |
2660 | shift64RightJamming( bSig, expDiff, &bSig ); | |
2661 | aSig |= LIT64( 0x4000000000000000 ); | |
2662 | aBigger: | |
2663 | zSig = aSig - bSig; | |
2664 | zExp = aExp; | |
2665 | normalizeRoundAndPack: | |
2666 | --zExp; | |
2667 | return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
2668 | ||
2669 | } | |
2670 | ||
2671 | /*---------------------------------------------------------------------------- | |
2672 | | Returns the result of adding the double-precision floating-point values `a' | |
2673 | | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
2674 | | Binary Floating-Point Arithmetic. | |
2675 | *----------------------------------------------------------------------------*/ | |
2676 | ||
2677 | float64 float64_add( float64 a, float64 b STATUS_PARAM ) | |
2678 | { | |
2679 | flag aSign, bSign; | |
2680 | ||
2681 | aSign = extractFloat64Sign( a ); | |
2682 | bSign = extractFloat64Sign( b ); | |
2683 | if ( aSign == bSign ) { | |
2684 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); | |
2685 | } | |
2686 | else { | |
2687 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); | |
2688 | } | |
2689 | ||
2690 | } | |
2691 | ||
2692 | /*---------------------------------------------------------------------------- | |
2693 | | Returns the result of subtracting the double-precision floating-point values | |
2694 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
2695 | | for Binary Floating-Point Arithmetic. | |
2696 | *----------------------------------------------------------------------------*/ | |
2697 | ||
2698 | float64 float64_sub( float64 a, float64 b STATUS_PARAM ) | |
2699 | { | |
2700 | flag aSign, bSign; | |
2701 | ||
2702 | aSign = extractFloat64Sign( a ); | |
2703 | bSign = extractFloat64Sign( b ); | |
2704 | if ( aSign == bSign ) { | |
2705 | return subFloat64Sigs( a, b, aSign STATUS_VAR ); | |
2706 | } | |
2707 | else { | |
2708 | return addFloat64Sigs( a, b, aSign STATUS_VAR ); | |
2709 | } | |
2710 | ||
2711 | } | |
2712 | ||
2713 | /*---------------------------------------------------------------------------- | |
2714 | | Returns the result of multiplying the double-precision floating-point values | |
2715 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
2716 | | for Binary Floating-Point Arithmetic. | |
2717 | *----------------------------------------------------------------------------*/ | |
2718 | ||
2719 | float64 float64_mul( float64 a, float64 b STATUS_PARAM ) | |
2720 | { | |
2721 | flag aSign, bSign, zSign; | |
2722 | int16 aExp, bExp, zExp; | |
2723 | bits64 aSig, bSig, zSig0, zSig1; | |
2724 | ||
2725 | aSig = extractFloat64Frac( a ); | |
2726 | aExp = extractFloat64Exp( a ); | |
2727 | aSign = extractFloat64Sign( a ); | |
2728 | bSig = extractFloat64Frac( b ); | |
2729 | bExp = extractFloat64Exp( b ); | |
2730 | bSign = extractFloat64Sign( b ); | |
2731 | zSign = aSign ^ bSign; | |
2732 | if ( aExp == 0x7FF ) { | |
2733 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
2734 | return propagateFloat64NaN( a, b STATUS_VAR ); | |
2735 | } | |
2736 | if ( ( bExp | bSig ) == 0 ) { | |
2737 | float_raise( float_flag_invalid STATUS_VAR); | |
2738 | return float64_default_nan; | |
2739 | } | |
2740 | return packFloat64( zSign, 0x7FF, 0 ); | |
2741 | } | |
2742 | if ( bExp == 0x7FF ) { | |
2743 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2744 | if ( ( aExp | aSig ) == 0 ) { | |
2745 | float_raise( float_flag_invalid STATUS_VAR); | |
2746 | return float64_default_nan; | |
2747 | } | |
2748 | return packFloat64( zSign, 0x7FF, 0 ); | |
2749 | } | |
2750 | if ( aExp == 0 ) { | |
2751 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2752 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2753 | } | |
2754 | if ( bExp == 0 ) { | |
2755 | if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2756 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2757 | } | |
2758 | zExp = aExp + bExp - 0x3FF; | |
2759 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
2760 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2761 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
2762 | zSig0 |= ( zSig1 != 0 ); | |
2763 | if ( 0 <= (sbits64) ( zSig0<<1 ) ) { | |
2764 | zSig0 <<= 1; | |
2765 | --zExp; | |
2766 | } | |
2767 | return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR ); | |
2768 | ||
2769 | } | |
2770 | ||
2771 | /*---------------------------------------------------------------------------- | |
2772 | | Returns the result of dividing the double-precision floating-point value `a' | |
2773 | | by the corresponding value `b'. The operation is performed according to | |
2774 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2775 | *----------------------------------------------------------------------------*/ | |
2776 | ||
2777 | float64 float64_div( float64 a, float64 b STATUS_PARAM ) | |
2778 | { | |
2779 | flag aSign, bSign, zSign; | |
2780 | int16 aExp, bExp, zExp; | |
2781 | bits64 aSig, bSig, zSig; | |
2782 | bits64 rem0, rem1; | |
2783 | bits64 term0, term1; | |
2784 | ||
2785 | aSig = extractFloat64Frac( a ); | |
2786 | aExp = extractFloat64Exp( a ); | |
2787 | aSign = extractFloat64Sign( a ); | |
2788 | bSig = extractFloat64Frac( b ); | |
2789 | bExp = extractFloat64Exp( b ); | |
2790 | bSign = extractFloat64Sign( b ); | |
2791 | zSign = aSign ^ bSign; | |
2792 | if ( aExp == 0x7FF ) { | |
2793 | if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2794 | if ( bExp == 0x7FF ) { | |
2795 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2796 | float_raise( float_flag_invalid STATUS_VAR); | |
2797 | return float64_default_nan; | |
2798 | } | |
2799 | return packFloat64( zSign, 0x7FF, 0 ); | |
2800 | } | |
2801 | if ( bExp == 0x7FF ) { | |
2802 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2803 | return packFloat64( zSign, 0, 0 ); | |
2804 | } | |
2805 | if ( bExp == 0 ) { | |
2806 | if ( bSig == 0 ) { | |
2807 | if ( ( aExp | aSig ) == 0 ) { | |
2808 | float_raise( float_flag_invalid STATUS_VAR); | |
2809 | return float64_default_nan; | |
2810 | } | |
2811 | float_raise( float_flag_divbyzero STATUS_VAR); | |
2812 | return packFloat64( zSign, 0x7FF, 0 ); | |
2813 | } | |
2814 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2815 | } | |
2816 | if ( aExp == 0 ) { | |
2817 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2818 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2819 | } | |
2820 | zExp = aExp - bExp + 0x3FD; | |
2821 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
2822 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2823 | if ( bSig <= ( aSig + aSig ) ) { | |
2824 | aSig >>= 1; | |
2825 | ++zExp; | |
2826 | } | |
2827 | zSig = estimateDiv128To64( aSig, 0, bSig ); | |
2828 | if ( ( zSig & 0x1FF ) <= 2 ) { | |
2829 | mul64To128( bSig, zSig, &term0, &term1 ); | |
2830 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
2831 | while ( (sbits64) rem0 < 0 ) { | |
2832 | --zSig; | |
2833 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
2834 | } | |
2835 | zSig |= ( rem1 != 0 ); | |
2836 | } | |
2837 | return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); | |
2838 | ||
2839 | } | |
2840 | ||
2841 | /*---------------------------------------------------------------------------- | |
2842 | | Returns the remainder of the double-precision floating-point value `a' | |
2843 | | with respect to the corresponding value `b'. The operation is performed | |
2844 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2845 | *----------------------------------------------------------------------------*/ | |
2846 | ||
2847 | float64 float64_rem( float64 a, float64 b STATUS_PARAM ) | |
2848 | { | |
2849 | flag aSign, bSign, zSign; | |
2850 | int16 aExp, bExp, expDiff; | |
2851 | bits64 aSig, bSig; | |
2852 | bits64 q, alternateASig; | |
2853 | sbits64 sigMean; | |
2854 | ||
2855 | aSig = extractFloat64Frac( a ); | |
2856 | aExp = extractFloat64Exp( a ); | |
2857 | aSign = extractFloat64Sign( a ); | |
2858 | bSig = extractFloat64Frac( b ); | |
2859 | bExp = extractFloat64Exp( b ); | |
2860 | bSign = extractFloat64Sign( b ); | |
2861 | if ( aExp == 0x7FF ) { | |
2862 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
2863 | return propagateFloat64NaN( a, b STATUS_VAR ); | |
2864 | } | |
2865 | float_raise( float_flag_invalid STATUS_VAR); | |
2866 | return float64_default_nan; | |
2867 | } | |
2868 | if ( bExp == 0x7FF ) { | |
2869 | if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); | |
2870 | return a; | |
2871 | } | |
2872 | if ( bExp == 0 ) { | |
2873 | if ( bSig == 0 ) { | |
2874 | float_raise( float_flag_invalid STATUS_VAR); | |
2875 | return float64_default_nan; | |
2876 | } | |
2877 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2878 | } | |
2879 | if ( aExp == 0 ) { | |
2880 | if ( aSig == 0 ) return a; | |
2881 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2882 | } | |
2883 | expDiff = aExp - bExp; | |
2884 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; | |
2885 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2886 | if ( expDiff < 0 ) { | |
2887 | if ( expDiff < -1 ) return a; | |
2888 | aSig >>= 1; | |
2889 | } | |
2890 | q = ( bSig <= aSig ); | |
2891 | if ( q ) aSig -= bSig; | |
2892 | expDiff -= 64; | |
2893 | while ( 0 < expDiff ) { | |
2894 | q = estimateDiv128To64( aSig, 0, bSig ); | |
2895 | q = ( 2 < q ) ? q - 2 : 0; | |
2896 | aSig = - ( ( bSig>>2 ) * q ); | |
2897 | expDiff -= 62; | |
2898 | } | |
2899 | expDiff += 64; | |
2900 | if ( 0 < expDiff ) { | |
2901 | q = estimateDiv128To64( aSig, 0, bSig ); | |
2902 | q = ( 2 < q ) ? q - 2 : 0; | |
2903 | q >>= 64 - expDiff; | |
2904 | bSig >>= 2; | |
2905 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
2906 | } | |
2907 | else { | |
2908 | aSig >>= 2; | |
2909 | bSig >>= 2; | |
2910 | } | |
2911 | do { | |
2912 | alternateASig = aSig; | |
2913 | ++q; | |
2914 | aSig -= bSig; | |
2915 | } while ( 0 <= (sbits64) aSig ); | |
2916 | sigMean = aSig + alternateASig; | |
2917 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
2918 | aSig = alternateASig; | |
2919 | } | |
2920 | zSign = ( (sbits64) aSig < 0 ); | |
2921 | if ( zSign ) aSig = - aSig; | |
2922 | return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR ); | |
2923 | ||
2924 | } | |
2925 | ||
2926 | /*---------------------------------------------------------------------------- | |
2927 | | Returns the square root of the double-precision floating-point value `a'. | |
2928 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
2929 | | Floating-Point Arithmetic. | |
2930 | *----------------------------------------------------------------------------*/ | |
2931 | ||
2932 | float64 float64_sqrt( float64 a STATUS_PARAM ) | |
2933 | { | |
2934 | flag aSign; | |
2935 | int16 aExp, zExp; | |
2936 | bits64 aSig, zSig, doubleZSig; | |
2937 | bits64 rem0, rem1, term0, term1; | |
2938 | ||
2939 | aSig = extractFloat64Frac( a ); | |
2940 | aExp = extractFloat64Exp( a ); | |
2941 | aSign = extractFloat64Sign( a ); | |
2942 | if ( aExp == 0x7FF ) { | |
2943 | if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); | |
2944 | if ( ! aSign ) return a; | |
2945 | float_raise( float_flag_invalid STATUS_VAR); | |
2946 | return float64_default_nan; | |
2947 | } | |
2948 | if ( aSign ) { | |
2949 | if ( ( aExp | aSig ) == 0 ) return a; | |
2950 | float_raise( float_flag_invalid STATUS_VAR); | |
2951 | return float64_default_nan; | |
2952 | } | |
2953 | if ( aExp == 0 ) { | |
2954 | if ( aSig == 0 ) return 0; | |
2955 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2956 | } | |
2957 | zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; | |
2958 | aSig |= LIT64( 0x0010000000000000 ); | |
2959 | zSig = estimateSqrt32( aExp, aSig>>21 ); | |
2960 | aSig <<= 9 - ( aExp & 1 ); | |
2961 | zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); | |
2962 | if ( ( zSig & 0x1FF ) <= 5 ) { | |
2963 | doubleZSig = zSig<<1; | |
2964 | mul64To128( zSig, zSig, &term0, &term1 ); | |
2965 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
2966 | while ( (sbits64) rem0 < 0 ) { | |
2967 | --zSig; | |
2968 | doubleZSig -= 2; | |
2969 | add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); | |
2970 | } | |
2971 | zSig |= ( ( rem0 | rem1 ) != 0 ); | |
2972 | } | |
2973 | return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); | |
2974 | ||
2975 | } | |
2976 | ||
2977 | /*---------------------------------------------------------------------------- | |
2978 | | Returns 1 if the double-precision floating-point value `a' is equal to the | |
2979 | | corresponding value `b', and 0 otherwise. The comparison is performed | |
2980 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
2981 | *----------------------------------------------------------------------------*/ | |
2982 | ||
750afe93 | 2983 | int float64_eq( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
2984 | { |
2985 | ||
2986 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2987 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2988 | ) { | |
2989 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
2990 | float_raise( float_flag_invalid STATUS_VAR); | |
2991 | } | |
2992 | return 0; | |
2993 | } | |
2994 | return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
2995 | ||
2996 | } | |
2997 | ||
2998 | /*---------------------------------------------------------------------------- | |
2999 | | Returns 1 if the double-precision floating-point value `a' is less than or | |
3000 | | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
3001 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
3002 | | Arithmetic. | |
3003 | *----------------------------------------------------------------------------*/ | |
3004 | ||
750afe93 | 3005 | int float64_le( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3006 | { |
3007 | flag aSign, bSign; | |
3008 | ||
3009 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3010 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3011 | ) { | |
3012 | float_raise( float_flag_invalid STATUS_VAR); | |
3013 | return 0; | |
3014 | } | |
3015 | aSign = extractFloat64Sign( a ); | |
3016 | bSign = extractFloat64Sign( b ); | |
3017 | if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
3018 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
3019 | ||
3020 | } | |
3021 | ||
3022 | /*---------------------------------------------------------------------------- | |
3023 | | Returns 1 if the double-precision floating-point value `a' is less than | |
3024 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
3025 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3026 | *----------------------------------------------------------------------------*/ | |
3027 | ||
750afe93 | 3028 | int float64_lt( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3029 | { |
3030 | flag aSign, bSign; | |
3031 | ||
3032 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3033 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3034 | ) { | |
3035 | float_raise( float_flag_invalid STATUS_VAR); | |
3036 | return 0; | |
3037 | } | |
3038 | aSign = extractFloat64Sign( a ); | |
3039 | bSign = extractFloat64Sign( b ); | |
3040 | if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); | |
3041 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
3042 | ||
3043 | } | |
3044 | ||
3045 | /*---------------------------------------------------------------------------- | |
3046 | | Returns 1 if the double-precision floating-point value `a' is equal to the | |
3047 | | corresponding value `b', and 0 otherwise. The invalid exception is raised | |
3048 | | if either operand is a NaN. Otherwise, the comparison is performed | |
3049 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3050 | *----------------------------------------------------------------------------*/ | |
3051 | ||
750afe93 | 3052 | int float64_eq_signaling( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3053 | { |
3054 | ||
3055 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3056 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3057 | ) { | |
3058 | float_raise( float_flag_invalid STATUS_VAR); | |
3059 | return 0; | |
3060 | } | |
3061 | return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
3062 | ||
3063 | } | |
3064 | ||
3065 | /*---------------------------------------------------------------------------- | |
3066 | | Returns 1 if the double-precision floating-point value `a' is less than or | |
3067 | | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
3068 | | cause an exception. Otherwise, the comparison is performed according to the | |
3069 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3070 | *----------------------------------------------------------------------------*/ | |
3071 | ||
750afe93 | 3072 | int float64_le_quiet( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3073 | { |
3074 | flag aSign, bSign; | |
3075 | ||
3076 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3077 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3078 | ) { | |
3079 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
3080 | float_raise( float_flag_invalid STATUS_VAR); | |
3081 | } | |
3082 | return 0; | |
3083 | } | |
3084 | aSign = extractFloat64Sign( a ); | |
3085 | bSign = extractFloat64Sign( b ); | |
3086 | if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
3087 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
3088 | ||
3089 | } | |
3090 | ||
3091 | /*---------------------------------------------------------------------------- | |
3092 | | Returns 1 if the double-precision floating-point value `a' is less than | |
3093 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
3094 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
3095 | | Standard for Binary Floating-Point Arithmetic. | |
3096 | *----------------------------------------------------------------------------*/ | |
3097 | ||
750afe93 | 3098 | int float64_lt_quiet( float64 a, float64 b STATUS_PARAM ) |
158142c2 FB |
3099 | { |
3100 | flag aSign, bSign; | |
3101 | ||
3102 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
3103 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
3104 | ) { | |
3105 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
3106 | float_raise( float_flag_invalid STATUS_VAR); | |
3107 | } | |
3108 | return 0; | |
3109 | } | |
3110 | aSign = extractFloat64Sign( a ); | |
3111 | bSign = extractFloat64Sign( b ); | |
3112 | if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); | |
3113 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
3114 | ||
3115 | } | |
3116 | ||
3117 | #ifdef FLOATX80 | |
3118 | ||
3119 | /*---------------------------------------------------------------------------- | |
3120 | | Returns the result of converting the extended double-precision floating- | |
3121 | | point value `a' to the 32-bit two's complement integer format. The | |
3122 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3123 | | Floating-Point Arithmetic---which means in particular that the conversion | |
3124 | | is rounded according to the current rounding mode. If `a' is a NaN, the | |
3125 | | largest positive integer is returned. Otherwise, if the conversion | |
3126 | | overflows, the largest integer with the same sign as `a' is returned. | |
3127 | *----------------------------------------------------------------------------*/ | |
3128 | ||
3129 | int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) | |
3130 | { | |
3131 | flag aSign; | |
3132 | int32 aExp, shiftCount; | |
3133 | bits64 aSig; | |
3134 | ||
3135 | aSig = extractFloatx80Frac( a ); | |
3136 | aExp = extractFloatx80Exp( a ); | |
3137 | aSign = extractFloatx80Sign( a ); | |
3138 | if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; | |
3139 | shiftCount = 0x4037 - aExp; | |
3140 | if ( shiftCount <= 0 ) shiftCount = 1; | |
3141 | shift64RightJamming( aSig, shiftCount, &aSig ); | |
3142 | return roundAndPackInt32( aSign, aSig STATUS_VAR ); | |
3143 | ||
3144 | } | |
3145 | ||
3146 | /*---------------------------------------------------------------------------- | |
3147 | | Returns the result of converting the extended double-precision floating- | |
3148 | | point value `a' to the 32-bit two's complement integer format. The | |
3149 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3150 | | Floating-Point Arithmetic, except that the conversion is always rounded | |
3151 | | toward zero. If `a' is a NaN, the largest positive integer is returned. | |
3152 | | Otherwise, if the conversion overflows, the largest integer with the same | |
3153 | | sign as `a' is returned. | |
3154 | *----------------------------------------------------------------------------*/ | |
3155 | ||
3156 | int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) | |
3157 | { | |
3158 | flag aSign; | |
3159 | int32 aExp, shiftCount; | |
3160 | bits64 aSig, savedASig; | |
3161 | int32 z; | |
3162 | ||
3163 | aSig = extractFloatx80Frac( a ); | |
3164 | aExp = extractFloatx80Exp( a ); | |
3165 | aSign = extractFloatx80Sign( a ); | |
3166 | if ( 0x401E < aExp ) { | |
3167 | if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; | |
3168 | goto invalid; | |
3169 | } | |
3170 | else if ( aExp < 0x3FFF ) { | |
3171 | if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
3172 | return 0; | |
3173 | } | |
3174 | shiftCount = 0x403E - aExp; | |
3175 | savedASig = aSig; | |
3176 | aSig >>= shiftCount; | |
3177 | z = aSig; | |
3178 | if ( aSign ) z = - z; | |
3179 | if ( ( z < 0 ) ^ aSign ) { | |
3180 | invalid: | |
3181 | float_raise( float_flag_invalid STATUS_VAR); | |
3182 | return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; | |
3183 | } | |
3184 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
3185 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3186 | } | |
3187 | return z; | |
3188 | ||
3189 | } | |
3190 | ||
3191 | /*---------------------------------------------------------------------------- | |
3192 | | Returns the result of converting the extended double-precision floating- | |
3193 | | point value `a' to the 64-bit two's complement integer format. The | |
3194 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3195 | | Floating-Point Arithmetic---which means in particular that the conversion | |
3196 | | is rounded according to the current rounding mode. If `a' is a NaN, | |
3197 | | the largest positive integer is returned. Otherwise, if the conversion | |
3198 | | overflows, the largest integer with the same sign as `a' is returned. | |
3199 | *----------------------------------------------------------------------------*/ | |
3200 | ||
3201 | int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) | |
3202 | { | |
3203 | flag aSign; | |
3204 | int32 aExp, shiftCount; | |
3205 | bits64 aSig, aSigExtra; | |
3206 | ||
3207 | aSig = extractFloatx80Frac( a ); | |
3208 | aExp = extractFloatx80Exp( a ); | |
3209 | aSign = extractFloatx80Sign( a ); | |
3210 | shiftCount = 0x403E - aExp; | |
3211 | if ( shiftCount <= 0 ) { | |
3212 | if ( shiftCount ) { | |
3213 | float_raise( float_flag_invalid STATUS_VAR); | |
3214 | if ( ! aSign | |
3215 | || ( ( aExp == 0x7FFF ) | |
3216 | && ( aSig != LIT64( 0x8000000000000000 ) ) ) | |
3217 | ) { | |
3218 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3219 | } | |
3220 | return (sbits64) LIT64( 0x8000000000000000 ); | |
3221 | } | |
3222 | aSigExtra = 0; | |
3223 | } | |
3224 | else { | |
3225 | shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); | |
3226 | } | |
3227 | return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); | |
3228 | ||
3229 | } | |
3230 | ||
3231 | /*---------------------------------------------------------------------------- | |
3232 | | Returns the result of converting the extended double-precision floating- | |
3233 | | point value `a' to the 64-bit two's complement integer format. The | |
3234 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3235 | | Floating-Point Arithmetic, except that the conversion is always rounded | |
3236 | | toward zero. If `a' is a NaN, the largest positive integer is returned. | |
3237 | | Otherwise, if the conversion overflows, the largest integer with the same | |
3238 | | sign as `a' is returned. | |
3239 | *----------------------------------------------------------------------------*/ | |
3240 | ||
3241 | int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) | |
3242 | { | |
3243 | flag aSign; | |
3244 | int32 aExp, shiftCount; | |
3245 | bits64 aSig; | |
3246 | int64 z; | |
3247 | ||
3248 | aSig = extractFloatx80Frac( a ); | |
3249 | aExp = extractFloatx80Exp( a ); | |
3250 | aSign = extractFloatx80Sign( a ); | |
3251 | shiftCount = aExp - 0x403E; | |
3252 | if ( 0 <= shiftCount ) { | |
3253 | aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3254 | if ( ( a.high != 0xC03E ) || aSig ) { | |
3255 | float_raise( float_flag_invalid STATUS_VAR); | |
3256 | if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { | |
3257 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
3258 | } | |
3259 | } | |
3260 | return (sbits64) LIT64( 0x8000000000000000 ); | |
3261 | } | |
3262 | else if ( aExp < 0x3FFF ) { | |
3263 | if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; | |
3264 | return 0; | |
3265 | } | |
3266 | z = aSig>>( - shiftCount ); | |
3267 | if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { | |
3268 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3269 | } | |
3270 | if ( aSign ) z = - z; | |
3271 | return z; | |
3272 | ||
3273 | } | |
3274 | ||
3275 | /*---------------------------------------------------------------------------- | |
3276 | | Returns the result of converting the extended double-precision floating- | |
3277 | | point value `a' to the single-precision floating-point format. The | |
3278 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3279 | | Floating-Point Arithmetic. | |
3280 | *----------------------------------------------------------------------------*/ | |
3281 | ||
3282 | float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) | |
3283 | { | |
3284 | flag aSign; | |
3285 | int32 aExp; | |
3286 | bits64 aSig; | |
3287 | ||
3288 | aSig = extractFloatx80Frac( a ); | |
3289 | aExp = extractFloatx80Exp( a ); | |
3290 | aSign = extractFloatx80Sign( a ); | |
3291 | if ( aExp == 0x7FFF ) { | |
3292 | if ( (bits64) ( aSig<<1 ) ) { | |
3293 | return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) ); | |
3294 | } | |
3295 | return packFloat32( aSign, 0xFF, 0 ); | |
3296 | } | |
3297 | shift64RightJamming( aSig, 33, &aSig ); | |
3298 | if ( aExp || aSig ) aExp -= 0x3F81; | |
3299 | return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); | |
3300 | ||
3301 | } | |
3302 | ||
3303 | /*---------------------------------------------------------------------------- | |
3304 | | Returns the result of converting the extended double-precision floating- | |
3305 | | point value `a' to the double-precision floating-point format. The | |
3306 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3307 | | Floating-Point Arithmetic. | |
3308 | *----------------------------------------------------------------------------*/ | |
3309 | ||
3310 | float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) | |
3311 | { | |
3312 | flag aSign; | |
3313 | int32 aExp; | |
3314 | bits64 aSig, zSig; | |
3315 | ||
3316 | aSig = extractFloatx80Frac( a ); | |
3317 | aExp = extractFloatx80Exp( a ); | |
3318 | aSign = extractFloatx80Sign( a ); | |
3319 | if ( aExp == 0x7FFF ) { | |
3320 | if ( (bits64) ( aSig<<1 ) ) { | |
3321 | return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) ); | |
3322 | } | |
3323 | return packFloat64( aSign, 0x7FF, 0 ); | |
3324 | } | |
3325 | shift64RightJamming( aSig, 1, &zSig ); | |
3326 | if ( aExp || aSig ) aExp -= 0x3C01; | |
3327 | return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR ); | |
3328 | ||
3329 | } | |
3330 | ||
3331 | #ifdef FLOAT128 | |
3332 | ||
3333 | /*---------------------------------------------------------------------------- | |
3334 | | Returns the result of converting the extended double-precision floating- | |
3335 | | point value `a' to the quadruple-precision floating-point format. The | |
3336 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
3337 | | Floating-Point Arithmetic. | |
3338 | *----------------------------------------------------------------------------*/ | |
3339 | ||
3340 | float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) | |
3341 | { | |
3342 | flag aSign; | |
3343 | int16 aExp; | |
3344 | bits64 aSig, zSig0, zSig1; | |
3345 | ||
3346 | aSig = extractFloatx80Frac( a ); | |
3347 | aExp = extractFloatx80Exp( a ); | |
3348 | aSign = extractFloatx80Sign( a ); | |
3349 | if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) { | |
3350 | return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) ); | |
3351 | } | |
3352 | shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); | |
3353 | return packFloat128( aSign, aExp, zSig0, zSig1 ); | |
3354 | ||
3355 | } | |
3356 | ||
3357 | #endif | |
3358 | ||
3359 | /*---------------------------------------------------------------------------- | |
3360 | | Rounds the extended double-precision floating-point value `a' to an integer, | |
3361 | | and returns the result as an extended quadruple-precision floating-point | |
3362 | | value. The operation is performed according to the IEC/IEEE Standard for | |
3363 | | Binary Floating-Point Arithmetic. | |
3364 | *----------------------------------------------------------------------------*/ | |
3365 | ||
3366 | floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) | |
3367 | { | |
3368 | flag aSign; | |
3369 | int32 aExp; | |
3370 | bits64 lastBitMask, roundBitsMask; | |
3371 | int8 roundingMode; | |
3372 | floatx80 z; | |
3373 | ||
3374 | aExp = extractFloatx80Exp( a ); | |
3375 | if ( 0x403E <= aExp ) { | |
3376 | if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) { | |
3377 | return propagateFloatx80NaN( a, a STATUS_VAR ); | |
3378 | } | |
3379 | return a; | |
3380 | } | |
3381 | if ( aExp < 0x3FFF ) { | |
3382 | if ( ( aExp == 0 ) | |
3383 | && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { | |
3384 | return a; | |
3385 | } | |
3386 | STATUS(float_exception_flags) |= float_flag_inexact; | |
3387 | aSign = extractFloatx80Sign( a ); | |
3388 | switch ( STATUS(float_rounding_mode) ) { | |
3389 | case float_round_nearest_even: | |
3390 | if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 ) | |
3391 | ) { | |
3392 | return | |
3393 | packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
3394 | } | |
3395 | break; | |
3396 | case float_round_down: | |
3397 | return | |
3398 | aSign ? | |
3399 | packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) | |
3400 | : packFloatx80( 0, 0, 0 ); | |
3401 | case float_round_up: | |
3402 | return | |
3403 | aSign ? packFloatx80( 1, 0, 0 ) | |
3404 | : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
3405 | } | |
3406 | return packFloatx80( aSign, 0, 0 ); | |
3407 | } | |
3408 | lastBitMask = 1; | |
3409 | lastBitMask <<= 0x403E - aExp; | |
3410 | roundBitsMask = lastBitMask - 1; | |
3411 | z = a; | |
3412 | roundingMode = STATUS(float_rounding_mode); | |
3413 | if ( roundingMode == float_round_nearest_even ) { | |
3414 | z.low += lastBitMask>>1; | |
3415 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; | |
3416 | } | |
3417 | else if ( roundingMode != float_round_to_zero ) { | |
3418 | if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
3419 | z.low += roundBitsMask; | |
3420 | } | |
3421 | } | |
3422 | z.low &= ~ roundBitsMask; | |
3423 | if ( z.low == 0 ) { | |
3424 | ++z.high; | |
3425 | z.low = LIT64( 0x8000000000000000 ); | |
3426 | } | |
3427 | if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact; | |
3428 | return z; | |
3429 | ||
3430 | } | |
3431 | ||
3432 | /*---------------------------------------------------------------------------- | |
3433 | | Returns the result of adding the absolute values of the extended double- | |
3434 | | precision floating-point values `a' and `b'. If `zSign' is 1, the sum is | |
3435 | | negated before being returned. `zSign' is ignored if the result is a NaN. | |
3436 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
3437 | | Floating-Point Arithmetic. | |
3438 | *----------------------------------------------------------------------------*/ | |
3439 | ||
3440 | static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM) | |
3441 | { | |
3442 | int32 aExp, bExp, zExp; | |
3443 | bits64 aSig, bSig, zSig0, zSig1; | |
3444 | int32 expDiff; | |
3445 | ||
3446 | aSig = extractFloatx80Frac( a ); | |
3447 | aExp = extractFloatx80Exp( a ); | |
3448 | bSig = extractFloatx80Frac( b ); | |
3449 | bExp = extractFloatx80Exp( b ); | |
3450 | expDiff = aExp - bExp; | |
3451 | if ( 0 < expDiff ) { | |
3452 | if ( aExp == 0x7FFF ) { | |
3453 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3454 | return a; | |
3455 | } | |
3456 | if ( bExp == 0 ) --expDiff; | |
3457 | shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
3458 | zExp = aExp; | |
3459 | } | |
3460 | else if ( expDiff < 0 ) { | |
3461 | if ( bExp == 0x7FFF ) { | |
3462 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3463 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3464 | } | |
3465 | if ( aExp == 0 ) ++expDiff; | |
3466 | shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
3467 | zExp = bExp; | |
3468 | } | |
3469 | else { | |
3470 | if ( aExp == 0x7FFF ) { | |
3471 | if ( (bits64) ( ( aSig | bSig )<<1 ) ) { | |
3472 | return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3473 | } | |
3474 | return a; | |
3475 | } | |
3476 | zSig1 = 0; | |
3477 | zSig0 = aSig + bSig; | |
3478 | if ( aExp == 0 ) { | |
3479 | normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); | |
3480 | goto roundAndPack; | |
3481 | } | |
3482 | zExp = aExp; | |
3483 | goto shiftRight1; | |
3484 | } | |
3485 | zSig0 = aSig + bSig; | |
3486 | if ( (sbits64) zSig0 < 0 ) goto roundAndPack; | |
3487 | shiftRight1: | |
3488 | shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); | |
3489 | zSig0 |= LIT64( 0x8000000000000000 ); | |
3490 | ++zExp; | |
3491 | roundAndPack: | |
3492 | return | |
3493 | roundAndPackFloatx80( | |
3494 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
3495 | ||
3496 | } | |
3497 | ||
3498 | /*---------------------------------------------------------------------------- | |
3499 | | Returns the result of subtracting the absolute values of the extended | |
3500 | | double-precision floating-point values `a' and `b'. If `zSign' is 1, the | |
3501 | | difference is negated before being returned. `zSign' is ignored if the | |
3502 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
3503 | | Standard for Binary Floating-Point Arithmetic. | |
3504 | *----------------------------------------------------------------------------*/ | |
3505 | ||
3506 | static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM ) | |
3507 | { | |
3508 | int32 aExp, bExp, zExp; | |
3509 | bits64 aSig, bSig, zSig0, zSig1; | |
3510 | int32 expDiff; | |
3511 | floatx80 z; | |
3512 | ||
3513 | aSig = extractFloatx80Frac( a ); | |
3514 | aExp = extractFloatx80Exp( a ); | |
3515 | bSig = extractFloatx80Frac( b ); | |
3516 | bExp = extractFloatx80Exp( b ); | |
3517 | expDiff = aExp - bExp; | |
3518 | if ( 0 < expDiff ) goto aExpBigger; | |
3519 | if ( expDiff < 0 ) goto bExpBigger; | |
3520 | if ( aExp == 0x7FFF ) { | |
3521 | if ( (bits64) ( ( aSig | bSig )<<1 ) ) { | |
3522 | return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3523 | } | |
3524 | float_raise( float_flag_invalid STATUS_VAR); | |
3525 | z.low = floatx80_default_nan_low; | |
3526 | z.high = floatx80_default_nan_high; | |
3527 | return z; | |
3528 | } | |
3529 | if ( aExp == 0 ) { | |
3530 | aExp = 1; | |
3531 | bExp = 1; | |
3532 | } | |
3533 | zSig1 = 0; | |
3534 | if ( bSig < aSig ) goto aBigger; | |
3535 | if ( aSig < bSig ) goto bBigger; | |
3536 | return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); | |
3537 | bExpBigger: | |
3538 | if ( bExp == 0x7FFF ) { | |
3539 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3540 | return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3541 | } | |
3542 | if ( aExp == 0 ) ++expDiff; | |
3543 | shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
3544 | bBigger: | |
3545 | sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); | |
3546 | zExp = bExp; | |
3547 | zSign ^= 1; | |
3548 | goto normalizeRoundAndPack; | |
3549 | aExpBigger: | |
3550 | if ( aExp == 0x7FFF ) { | |
3551 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3552 | return a; | |
3553 | } | |
3554 | if ( bExp == 0 ) --expDiff; | |
3555 | shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
3556 | aBigger: | |
3557 | sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); | |
3558 | zExp = aExp; | |
3559 | normalizeRoundAndPack: | |
3560 | return | |
3561 | normalizeRoundAndPackFloatx80( | |
3562 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
3563 | ||
3564 | } | |
3565 | ||
3566 | /*---------------------------------------------------------------------------- | |
3567 | | Returns the result of adding the extended double-precision floating-point | |
3568 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
3569 | | Standard for Binary Floating-Point Arithmetic. | |
3570 | *----------------------------------------------------------------------------*/ | |
3571 | ||
3572 | floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) | |
3573 | { | |
3574 | flag aSign, bSign; | |
3575 | ||
3576 | aSign = extractFloatx80Sign( a ); | |
3577 | bSign = extractFloatx80Sign( b ); | |
3578 | if ( aSign == bSign ) { | |
3579 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
3580 | } | |
3581 | else { | |
3582 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
3583 | } | |
3584 | ||
3585 | } | |
3586 | ||
3587 | /*---------------------------------------------------------------------------- | |
3588 | | Returns the result of subtracting the extended double-precision floating- | |
3589 | | point values `a' and `b'. The operation is performed according to the | |
3590 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3591 | *----------------------------------------------------------------------------*/ | |
3592 | ||
3593 | floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) | |
3594 | { | |
3595 | flag aSign, bSign; | |
3596 | ||
3597 | aSign = extractFloatx80Sign( a ); | |
3598 | bSign = extractFloatx80Sign( b ); | |
3599 | if ( aSign == bSign ) { | |
3600 | return subFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
3601 | } | |
3602 | else { | |
3603 | return addFloatx80Sigs( a, b, aSign STATUS_VAR ); | |
3604 | } | |
3605 | ||
3606 | } | |
3607 | ||
3608 | /*---------------------------------------------------------------------------- | |
3609 | | Returns the result of multiplying the extended double-precision floating- | |
3610 | | point values `a' and `b'. The operation is performed according to the | |
3611 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3612 | *----------------------------------------------------------------------------*/ | |
3613 | ||
3614 | floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) | |
3615 | { | |
3616 | flag aSign, bSign, zSign; | |
3617 | int32 aExp, bExp, zExp; | |
3618 | bits64 aSig, bSig, zSig0, zSig1; | |
3619 | floatx80 z; | |
3620 | ||
3621 | aSig = extractFloatx80Frac( a ); | |
3622 | aExp = extractFloatx80Exp( a ); | |
3623 | aSign = extractFloatx80Sign( a ); | |
3624 | bSig = extractFloatx80Frac( b ); | |
3625 | bExp = extractFloatx80Exp( b ); | |
3626 | bSign = extractFloatx80Sign( b ); | |
3627 | zSign = aSign ^ bSign; | |
3628 | if ( aExp == 0x7FFF ) { | |
3629 | if ( (bits64) ( aSig<<1 ) | |
3630 | || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { | |
3631 | return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3632 | } | |
3633 | if ( ( bExp | bSig ) == 0 ) goto invalid; | |
3634 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3635 | } | |
3636 | if ( bExp == 0x7FFF ) { | |
3637 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3638 | if ( ( aExp | aSig ) == 0 ) { | |
3639 | invalid: | |
3640 | float_raise( float_flag_invalid STATUS_VAR); | |
3641 | z.low = floatx80_default_nan_low; | |
3642 | z.high = floatx80_default_nan_high; | |
3643 | return z; | |
3644 | } | |
3645 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3646 | } | |
3647 | if ( aExp == 0 ) { | |
3648 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
3649 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
3650 | } | |
3651 | if ( bExp == 0 ) { | |
3652 | if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
3653 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
3654 | } | |
3655 | zExp = aExp + bExp - 0x3FFE; | |
3656 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
3657 | if ( 0 < (sbits64) zSig0 ) { | |
3658 | shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); | |
3659 | --zExp; | |
3660 | } | |
3661 | return | |
3662 | roundAndPackFloatx80( | |
3663 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
3664 | ||
3665 | } | |
3666 | ||
3667 | /*---------------------------------------------------------------------------- | |
3668 | | Returns the result of dividing the extended double-precision floating-point | |
3669 | | value `a' by the corresponding value `b'. The operation is performed | |
3670 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3671 | *----------------------------------------------------------------------------*/ | |
3672 | ||
3673 | floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) | |
3674 | { | |
3675 | flag aSign, bSign, zSign; | |
3676 | int32 aExp, bExp, zExp; | |
3677 | bits64 aSig, bSig, zSig0, zSig1; | |
3678 | bits64 rem0, rem1, rem2, term0, term1, term2; | |
3679 | floatx80 z; | |
3680 | ||
3681 | aSig = extractFloatx80Frac( a ); | |
3682 | aExp = extractFloatx80Exp( a ); | |
3683 | aSign = extractFloatx80Sign( a ); | |
3684 | bSig = extractFloatx80Frac( b ); | |
3685 | bExp = extractFloatx80Exp( b ); | |
3686 | bSign = extractFloatx80Sign( b ); | |
3687 | zSign = aSign ^ bSign; | |
3688 | if ( aExp == 0x7FFF ) { | |
3689 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3690 | if ( bExp == 0x7FFF ) { | |
3691 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3692 | goto invalid; | |
3693 | } | |
3694 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3695 | } | |
3696 | if ( bExp == 0x7FFF ) { | |
3697 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3698 | return packFloatx80( zSign, 0, 0 ); | |
3699 | } | |
3700 | if ( bExp == 0 ) { | |
3701 | if ( bSig == 0 ) { | |
3702 | if ( ( aExp | aSig ) == 0 ) { | |
3703 | invalid: | |
3704 | float_raise( float_flag_invalid STATUS_VAR); | |
3705 | z.low = floatx80_default_nan_low; | |
3706 | z.high = floatx80_default_nan_high; | |
3707 | return z; | |
3708 | } | |
3709 | float_raise( float_flag_divbyzero STATUS_VAR); | |
3710 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3711 | } | |
3712 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
3713 | } | |
3714 | if ( aExp == 0 ) { | |
3715 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
3716 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
3717 | } | |
3718 | zExp = aExp - bExp + 0x3FFE; | |
3719 | rem1 = 0; | |
3720 | if ( bSig <= aSig ) { | |
3721 | shift128Right( aSig, 0, 1, &aSig, &rem1 ); | |
3722 | ++zExp; | |
3723 | } | |
3724 | zSig0 = estimateDiv128To64( aSig, rem1, bSig ); | |
3725 | mul64To128( bSig, zSig0, &term0, &term1 ); | |
3726 | sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); | |
3727 | while ( (sbits64) rem0 < 0 ) { | |
3728 | --zSig0; | |
3729 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
3730 | } | |
3731 | zSig1 = estimateDiv128To64( rem1, 0, bSig ); | |
3732 | if ( (bits64) ( zSig1<<1 ) <= 8 ) { | |
3733 | mul64To128( bSig, zSig1, &term1, &term2 ); | |
3734 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
3735 | while ( (sbits64) rem1 < 0 ) { | |
3736 | --zSig1; | |
3737 | add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); | |
3738 | } | |
3739 | zSig1 |= ( ( rem1 | rem2 ) != 0 ); | |
3740 | } | |
3741 | return | |
3742 | roundAndPackFloatx80( | |
3743 | STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); | |
3744 | ||
3745 | } | |
3746 | ||
3747 | /*---------------------------------------------------------------------------- | |
3748 | | Returns the remainder of the extended double-precision floating-point value | |
3749 | | `a' with respect to the corresponding value `b'. The operation is performed | |
3750 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
3751 | *----------------------------------------------------------------------------*/ | |
3752 | ||
3753 | floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) | |
3754 | { | |
3755 | flag aSign, bSign, zSign; | |
3756 | int32 aExp, bExp, expDiff; | |
3757 | bits64 aSig0, aSig1, bSig; | |
3758 | bits64 q, term0, term1, alternateASig0, alternateASig1; | |
3759 | floatx80 z; | |
3760 | ||
3761 | aSig0 = extractFloatx80Frac( a ); | |
3762 | aExp = extractFloatx80Exp( a ); | |
3763 | aSign = extractFloatx80Sign( a ); | |
3764 | bSig = extractFloatx80Frac( b ); | |
3765 | bExp = extractFloatx80Exp( b ); | |
3766 | bSign = extractFloatx80Sign( b ); | |
3767 | if ( aExp == 0x7FFF ) { | |
3768 | if ( (bits64) ( aSig0<<1 ) | |
3769 | || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { | |
3770 | return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3771 | } | |
3772 | goto invalid; | |
3773 | } | |
3774 | if ( bExp == 0x7FFF ) { | |
3775 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); | |
3776 | return a; | |
3777 | } | |
3778 | if ( bExp == 0 ) { | |
3779 | if ( bSig == 0 ) { | |
3780 | invalid: | |
3781 | float_raise( float_flag_invalid STATUS_VAR); | |
3782 | z.low = floatx80_default_nan_low; | |
3783 | z.high = floatx80_default_nan_high; | |
3784 | return z; | |
3785 | } | |
3786 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
3787 | } | |
3788 | if ( aExp == 0 ) { | |
3789 | if ( (bits64) ( aSig0<<1 ) == 0 ) return a; | |
3790 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); | |
3791 | } | |
3792 | bSig |= LIT64( 0x8000000000000000 ); | |
3793 | zSign = aSign; | |
3794 | expDiff = aExp - bExp; | |
3795 | aSig1 = 0; | |
3796 | if ( expDiff < 0 ) { | |
3797 | if ( expDiff < -1 ) return a; | |
3798 | shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); | |
3799 | expDiff = 0; | |
3800 | } | |
3801 | q = ( bSig <= aSig0 ); | |
3802 | if ( q ) aSig0 -= bSig; | |
3803 | expDiff -= 64; | |
3804 | while ( 0 < expDiff ) { | |
3805 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
3806 | q = ( 2 < q ) ? q - 2 : 0; | |
3807 | mul64To128( bSig, q, &term0, &term1 ); | |
3808 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3809 | shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); | |
3810 | expDiff -= 62; | |
3811 | } | |
3812 | expDiff += 64; | |
3813 | if ( 0 < expDiff ) { | |
3814 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
3815 | q = ( 2 < q ) ? q - 2 : 0; | |
3816 | q >>= 64 - expDiff; | |
3817 | mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); | |
3818 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3819 | shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); | |
3820 | while ( le128( term0, term1, aSig0, aSig1 ) ) { | |
3821 | ++q; | |
3822 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3823 | } | |
3824 | } | |
3825 | else { | |
3826 | term1 = 0; | |
3827 | term0 = bSig; | |
3828 | } | |
3829 | sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); | |
3830 | if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
3831 | || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
3832 | && ( q & 1 ) ) | |
3833 | ) { | |
3834 | aSig0 = alternateASig0; | |
3835 | aSig1 = alternateASig1; | |
3836 | zSign = ! zSign; | |
3837 | } | |
3838 | return | |
3839 | normalizeRoundAndPackFloatx80( | |
3840 | 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR ); | |
3841 | ||
3842 | } | |
3843 | ||
3844 | /*---------------------------------------------------------------------------- | |
3845 | | Returns the square root of the extended double-precision floating-point | |
3846 | | value `a'. The operation is performed according to the IEC/IEEE Standard | |
3847 | | for Binary Floating-Point Arithmetic. | |
3848 | *----------------------------------------------------------------------------*/ | |
3849 | ||
3850 | floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) | |
3851 | { | |
3852 | flag aSign; | |
3853 | int32 aExp, zExp; | |
3854 | bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0; | |
3855 | bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
3856 | floatx80 z; | |
3857 | ||
3858 | aSig0 = extractFloatx80Frac( a ); | |
3859 | aExp = extractFloatx80Exp( a ); | |
3860 | aSign = extractFloatx80Sign( a ); | |
3861 | if ( aExp == 0x7FFF ) { | |
3862 | if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); | |
3863 | if ( ! aSign ) return a; | |
3864 | goto invalid; | |
3865 | } | |
3866 | if ( aSign ) { | |
3867 | if ( ( aExp | aSig0 ) == 0 ) return a; | |
3868 | invalid: | |
3869 | float_raise( float_flag_invalid STATUS_VAR); | |
3870 | z.low = floatx80_default_nan_low; | |
3871 | z.high = floatx80_default_nan_high; | |
3872 | return z; | |
3873 | } | |
3874 | if ( aExp == 0 ) { | |
3875 | if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); | |
3876 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); | |
3877 | } | |
3878 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; | |
3879 | zSig0 = estimateSqrt32( aExp, aSig0>>32 ); | |
3880 | shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); | |
3881 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); | |
3882 | doubleZSig0 = zSig0<<1; | |
3883 | mul64To128( zSig0, zSig0, &term0, &term1 ); | |
3884 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); | |
3885 | while ( (sbits64) rem0 < 0 ) { | |
3886 | --zSig0; | |
3887 | doubleZSig0 -= 2; | |
3888 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); | |
3889 | } | |
3890 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); | |
3891 | if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { | |
3892 | if ( zSig1 == 0 ) zSig1 = 1; | |
3893 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); | |
3894 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
3895 | mul64To128( zSig1, zSig1, &term2, &term3 ); | |
3896 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
3897 | while ( (sbits64) rem1 < 0 ) { | |
3898 | --zSig1; | |
3899 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); | |
3900 | term3 |= 1; | |
3901 | term2 |= doubleZSig0; | |
3902 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
3903 | } | |
3904 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
3905 | } | |
3906 | shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); | |
3907 | zSig0 |= doubleZSig0; | |
3908 | return | |
3909 | roundAndPackFloatx80( | |
3910 | STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR ); | |
3911 | ||
3912 | } | |
3913 | ||
3914 | /*---------------------------------------------------------------------------- | |
3915 | | Returns 1 if the extended double-precision floating-point value `a' is | |
3916 | | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
3917 | | performed according to the IEC/IEEE Standard for Binary Floating-Point | |
3918 | | Arithmetic. | |
3919 | *----------------------------------------------------------------------------*/ | |
3920 | ||
750afe93 | 3921 | int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
3922 | { |
3923 | ||
3924 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3925 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3926 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3927 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3928 | ) { | |
3929 | if ( floatx80_is_signaling_nan( a ) | |
3930 | || floatx80_is_signaling_nan( b ) ) { | |
3931 | float_raise( float_flag_invalid STATUS_VAR); | |
3932 | } | |
3933 | return 0; | |
3934 | } | |
3935 | return | |
3936 | ( a.low == b.low ) | |
3937 | && ( ( a.high == b.high ) | |
3938 | || ( ( a.low == 0 ) | |
3939 | && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
3940 | ); | |
3941 | ||
3942 | } | |
3943 | ||
3944 | /*---------------------------------------------------------------------------- | |
3945 | | Returns 1 if the extended double-precision floating-point value `a' is | |
3946 | | less than or equal to the corresponding value `b', and 0 otherwise. The | |
3947 | | comparison is performed according to the IEC/IEEE Standard for Binary | |
3948 | | Floating-Point Arithmetic. | |
3949 | *----------------------------------------------------------------------------*/ | |
3950 | ||
750afe93 | 3951 | int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
3952 | { |
3953 | flag aSign, bSign; | |
3954 | ||
3955 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3956 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3957 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3958 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3959 | ) { | |
3960 | float_raise( float_flag_invalid STATUS_VAR); | |
3961 | return 0; | |
3962 | } | |
3963 | aSign = extractFloatx80Sign( a ); | |
3964 | bSign = extractFloatx80Sign( b ); | |
3965 | if ( aSign != bSign ) { | |
3966 | return | |
3967 | aSign | |
3968 | || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
3969 | == 0 ); | |
3970 | } | |
3971 | return | |
3972 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
3973 | : le128( a.high, a.low, b.high, b.low ); | |
3974 | ||
3975 | } | |
3976 | ||
3977 | /*---------------------------------------------------------------------------- | |
3978 | | Returns 1 if the extended double-precision floating-point value `a' is | |
3979 | | less than the corresponding value `b', and 0 otherwise. The comparison | |
3980 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
3981 | | Arithmetic. | |
3982 | *----------------------------------------------------------------------------*/ | |
3983 | ||
750afe93 | 3984 | int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
3985 | { |
3986 | flag aSign, bSign; | |
3987 | ||
3988 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3989 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3990 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3991 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3992 | ) { | |
3993 | float_raise( float_flag_invalid STATUS_VAR); | |
3994 | return 0; | |
3995 | } | |
3996 | aSign = extractFloatx80Sign( a ); | |
3997 | bSign = extractFloatx80Sign( b ); | |
3998 | if ( aSign != bSign ) { | |
3999 | return | |
4000 | aSign | |
4001 | && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
4002 | != 0 ); | |
4003 | } | |
4004 | return | |
4005 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
4006 | : lt128( a.high, a.low, b.high, b.low ); | |
4007 | ||
4008 | } | |
4009 | ||
4010 | /*---------------------------------------------------------------------------- | |
4011 | | Returns 1 if the extended double-precision floating-point value `a' is equal | |
4012 | | to the corresponding value `b', and 0 otherwise. The invalid exception is | |
4013 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
4014 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4015 | *----------------------------------------------------------------------------*/ | |
4016 | ||
750afe93 | 4017 | int floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4018 | { |
4019 | ||
4020 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
4021 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
4022 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
4023 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
4024 | ) { | |
4025 | float_raise( float_flag_invalid STATUS_VAR); | |
4026 | return 0; | |
4027 | } | |
4028 | return | |
4029 | ( a.low == b.low ) | |
4030 | && ( ( a.high == b.high ) | |
4031 | || ( ( a.low == 0 ) | |
4032 | && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
4033 | ); | |
4034 | ||
4035 | } | |
4036 | ||
4037 | /*---------------------------------------------------------------------------- | |
4038 | | Returns 1 if the extended double-precision floating-point value `a' is less | |
4039 | | than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs | |
4040 | | do not cause an exception. Otherwise, the comparison is performed according | |
4041 | | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4042 | *----------------------------------------------------------------------------*/ | |
4043 | ||
750afe93 | 4044 | int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4045 | { |
4046 | flag aSign, bSign; | |
4047 | ||
4048 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
4049 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
4050 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
4051 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
4052 | ) { | |
4053 | if ( floatx80_is_signaling_nan( a ) | |
4054 | || floatx80_is_signaling_nan( b ) ) { | |
4055 | float_raise( float_flag_invalid STATUS_VAR); | |
4056 | } | |
4057 | return 0; | |
4058 | } | |
4059 | aSign = extractFloatx80Sign( a ); | |
4060 | bSign = extractFloatx80Sign( b ); | |
4061 | if ( aSign != bSign ) { | |
4062 | return | |
4063 | aSign | |
4064 | || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
4065 | == 0 ); | |
4066 | } | |
4067 | return | |
4068 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
4069 | : le128( a.high, a.low, b.high, b.low ); | |
4070 | ||
4071 | } | |
4072 | ||
4073 | /*---------------------------------------------------------------------------- | |
4074 | | Returns 1 if the extended double-precision floating-point value `a' is less | |
4075 | | than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause | |
4076 | | an exception. Otherwise, the comparison is performed according to the | |
4077 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4078 | *----------------------------------------------------------------------------*/ | |
4079 | ||
750afe93 | 4080 | int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM ) |
158142c2 FB |
4081 | { |
4082 | flag aSign, bSign; | |
4083 | ||
4084 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
4085 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
4086 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
4087 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
4088 | ) { | |
4089 | if ( floatx80_is_signaling_nan( a ) | |
4090 | || floatx80_is_signaling_nan( b ) ) { | |
4091 | float_raise( float_flag_invalid STATUS_VAR); | |
4092 | } | |
4093 | return 0; | |
4094 | } | |
4095 | aSign = extractFloatx80Sign( a ); | |
4096 | bSign = extractFloatx80Sign( b ); | |
4097 | if ( aSign != bSign ) { | |
4098 | return | |
4099 | aSign | |
4100 | && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
4101 | != 0 ); | |
4102 | } | |
4103 | return | |
4104 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
4105 | : lt128( a.high, a.low, b.high, b.low ); | |
4106 | ||
4107 | } | |
4108 | ||
4109 | #endif | |
4110 | ||
4111 | #ifdef FLOAT128 | |
4112 | ||
4113 | /*---------------------------------------------------------------------------- | |
4114 | | Returns the result of converting the quadruple-precision floating-point | |
4115 | | value `a' to the 32-bit two's complement integer format. The conversion | |
4116 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4117 | | Arithmetic---which means in particular that the conversion is rounded | |
4118 | | according to the current rounding mode. If `a' is a NaN, the largest | |
4119 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
4120 | | largest integer with the same sign as `a' is returned. | |
4121 | *----------------------------------------------------------------------------*/ | |
4122 | ||
4123 | int32 float128_to_int32( float128 a STATUS_PARAM ) | |
4124 | { | |
4125 | flag aSign; | |
4126 | int32 aExp, shiftCount; | |
4127 | bits64 aSig0, aSig1; | |
4128 | ||
4129 | aSig1 = extractFloat128Frac1( a ); | |
4130 | aSig0 = extractFloat128Frac0( a ); | |
4131 | aExp = extractFloat128Exp( a ); | |
4132 | aSign = extractFloat128Sign( a ); | |
4133 | if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; | |
4134 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4135 | aSig0 |= ( aSig1 != 0 ); | |
4136 | shiftCount = 0x4028 - aExp; | |
4137 | if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); | |
4138 | return roundAndPackInt32( aSign, aSig0 STATUS_VAR ); | |
4139 | ||
4140 | } | |
4141 | ||
4142 | /*---------------------------------------------------------------------------- | |
4143 | | Returns the result of converting the quadruple-precision floating-point | |
4144 | | value `a' to the 32-bit two's complement integer format. The conversion | |
4145 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4146 | | Arithmetic, except that the conversion is always rounded toward zero. If | |
4147 | | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
4148 | | conversion overflows, the largest integer with the same sign as `a' is | |
4149 | | returned. | |
4150 | *----------------------------------------------------------------------------*/ | |
4151 | ||
4152 | int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) | |
4153 | { | |
4154 | flag aSign; | |
4155 | int32 aExp, shiftCount; | |
4156 | bits64 aSig0, aSig1, savedASig; | |
4157 | int32 z; | |
4158 | ||
4159 | aSig1 = extractFloat128Frac1( a ); | |
4160 | aSig0 = extractFloat128Frac0( a ); | |
4161 | aExp = extractFloat128Exp( a ); | |
4162 | aSign = extractFloat128Sign( a ); | |
4163 | aSig0 |= ( aSig1 != 0 ); | |
4164 | if ( 0x401E < aExp ) { | |
4165 | if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; | |
4166 | goto invalid; | |
4167 | } | |
4168 | else if ( aExp < 0x3FFF ) { | |
4169 | if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
4170 | return 0; | |
4171 | } | |
4172 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4173 | shiftCount = 0x402F - aExp; | |
4174 | savedASig = aSig0; | |
4175 | aSig0 >>= shiftCount; | |
4176 | z = aSig0; | |
4177 | if ( aSign ) z = - z; | |
4178 | if ( ( z < 0 ) ^ aSign ) { | |
4179 | invalid: | |
4180 | float_raise( float_flag_invalid STATUS_VAR); | |
4181 | return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; | |
4182 | } | |
4183 | if ( ( aSig0<<shiftCount ) != savedASig ) { | |
4184 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4185 | } | |
4186 | return z; | |
4187 | ||
4188 | } | |
4189 | ||
4190 | /*---------------------------------------------------------------------------- | |
4191 | | Returns the result of converting the quadruple-precision floating-point | |
4192 | | value `a' to the 64-bit two's complement integer format. The conversion | |
4193 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4194 | | Arithmetic---which means in particular that the conversion is rounded | |
4195 | | according to the current rounding mode. If `a' is a NaN, the largest | |
4196 | | positive integer is returned. Otherwise, if the conversion overflows, the | |
4197 | | largest integer with the same sign as `a' is returned. | |
4198 | *----------------------------------------------------------------------------*/ | |
4199 | ||
4200 | int64 float128_to_int64( float128 a STATUS_PARAM ) | |
4201 | { | |
4202 | flag aSign; | |
4203 | int32 aExp, shiftCount; | |
4204 | bits64 aSig0, aSig1; | |
4205 | ||
4206 | aSig1 = extractFloat128Frac1( a ); | |
4207 | aSig0 = extractFloat128Frac0( a ); | |
4208 | aExp = extractFloat128Exp( a ); | |
4209 | aSign = extractFloat128Sign( a ); | |
4210 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4211 | shiftCount = 0x402F - aExp; | |
4212 | if ( shiftCount <= 0 ) { | |
4213 | if ( 0x403E < aExp ) { | |
4214 | float_raise( float_flag_invalid STATUS_VAR); | |
4215 | if ( ! aSign | |
4216 | || ( ( aExp == 0x7FFF ) | |
4217 | && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) | |
4218 | ) | |
4219 | ) { | |
4220 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
4221 | } | |
4222 | return (sbits64) LIT64( 0x8000000000000000 ); | |
4223 | } | |
4224 | shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); | |
4225 | } | |
4226 | else { | |
4227 | shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); | |
4228 | } | |
4229 | return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR ); | |
4230 | ||
4231 | } | |
4232 | ||
4233 | /*---------------------------------------------------------------------------- | |
4234 | | Returns the result of converting the quadruple-precision floating-point | |
4235 | | value `a' to the 64-bit two's complement integer format. The conversion | |
4236 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4237 | | Arithmetic, except that the conversion is always rounded toward zero. | |
4238 | | If `a' is a NaN, the largest positive integer is returned. Otherwise, if | |
4239 | | the conversion overflows, the largest integer with the same sign as `a' is | |
4240 | | returned. | |
4241 | *----------------------------------------------------------------------------*/ | |
4242 | ||
4243 | int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) | |
4244 | { | |
4245 | flag aSign; | |
4246 | int32 aExp, shiftCount; | |
4247 | bits64 aSig0, aSig1; | |
4248 | int64 z; | |
4249 | ||
4250 | aSig1 = extractFloat128Frac1( a ); | |
4251 | aSig0 = extractFloat128Frac0( a ); | |
4252 | aExp = extractFloat128Exp( a ); | |
4253 | aSign = extractFloat128Sign( a ); | |
4254 | if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); | |
4255 | shiftCount = aExp - 0x402F; | |
4256 | if ( 0 < shiftCount ) { | |
4257 | if ( 0x403E <= aExp ) { | |
4258 | aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); | |
4259 | if ( ( a.high == LIT64( 0xC03E000000000000 ) ) | |
4260 | && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { | |
4261 | if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; | |
4262 | } | |
4263 | else { | |
4264 | float_raise( float_flag_invalid STATUS_VAR); | |
4265 | if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { | |
4266 | return LIT64( 0x7FFFFFFFFFFFFFFF ); | |
4267 | } | |
4268 | } | |
4269 | return (sbits64) LIT64( 0x8000000000000000 ); | |
4270 | } | |
4271 | z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); | |
4272 | if ( (bits64) ( aSig1<<shiftCount ) ) { | |
4273 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4274 | } | |
4275 | } | |
4276 | else { | |
4277 | if ( aExp < 0x3FFF ) { | |
4278 | if ( aExp | aSig0 | aSig1 ) { | |
4279 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4280 | } | |
4281 | return 0; | |
4282 | } | |
4283 | z = aSig0>>( - shiftCount ); | |
4284 | if ( aSig1 | |
4285 | || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) { | |
4286 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4287 | } | |
4288 | } | |
4289 | if ( aSign ) z = - z; | |
4290 | return z; | |
4291 | ||
4292 | } | |
4293 | ||
4294 | /*---------------------------------------------------------------------------- | |
4295 | | Returns the result of converting the quadruple-precision floating-point | |
4296 | | value `a' to the single-precision floating-point format. The conversion | |
4297 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4298 | | Arithmetic. | |
4299 | *----------------------------------------------------------------------------*/ | |
4300 | ||
4301 | float32 float128_to_float32( float128 a STATUS_PARAM ) | |
4302 | { | |
4303 | flag aSign; | |
4304 | int32 aExp; | |
4305 | bits64 aSig0, aSig1; | |
4306 | bits32 zSig; | |
4307 | ||
4308 | aSig1 = extractFloat128Frac1( a ); | |
4309 | aSig0 = extractFloat128Frac0( a ); | |
4310 | aExp = extractFloat128Exp( a ); | |
4311 | aSign = extractFloat128Sign( a ); | |
4312 | if ( aExp == 0x7FFF ) { | |
4313 | if ( aSig0 | aSig1 ) { | |
4314 | return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) ); | |
4315 | } | |
4316 | return packFloat32( aSign, 0xFF, 0 ); | |
4317 | } | |
4318 | aSig0 |= ( aSig1 != 0 ); | |
4319 | shift64RightJamming( aSig0, 18, &aSig0 ); | |
4320 | zSig = aSig0; | |
4321 | if ( aExp || zSig ) { | |
4322 | zSig |= 0x40000000; | |
4323 | aExp -= 0x3F81; | |
4324 | } | |
4325 | return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); | |
4326 | ||
4327 | } | |
4328 | ||
4329 | /*---------------------------------------------------------------------------- | |
4330 | | Returns the result of converting the quadruple-precision floating-point | |
4331 | | value `a' to the double-precision floating-point format. The conversion | |
4332 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
4333 | | Arithmetic. | |
4334 | *----------------------------------------------------------------------------*/ | |
4335 | ||
4336 | float64 float128_to_float64( float128 a STATUS_PARAM ) | |
4337 | { | |
4338 | flag aSign; | |
4339 | int32 aExp; | |
4340 | bits64 aSig0, aSig1; | |
4341 | ||
4342 | aSig1 = extractFloat128Frac1( a ); | |
4343 | aSig0 = extractFloat128Frac0( a ); | |
4344 | aExp = extractFloat128Exp( a ); | |
4345 | aSign = extractFloat128Sign( a ); | |
4346 | if ( aExp == 0x7FFF ) { | |
4347 | if ( aSig0 | aSig1 ) { | |
4348 | return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) ); | |
4349 | } | |
4350 | return packFloat64( aSign, 0x7FF, 0 ); | |
4351 | } | |
4352 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); | |
4353 | aSig0 |= ( aSig1 != 0 ); | |
4354 | if ( aExp || aSig0 ) { | |
4355 | aSig0 |= LIT64( 0x4000000000000000 ); | |
4356 | aExp -= 0x3C01; | |
4357 | } | |
4358 | return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR ); | |
4359 | ||
4360 | } | |
4361 | ||
4362 | #ifdef FLOATX80 | |
4363 | ||
4364 | /*---------------------------------------------------------------------------- | |
4365 | | Returns the result of converting the quadruple-precision floating-point | |
4366 | | value `a' to the extended double-precision floating-point format. The | |
4367 | | conversion is performed according to the IEC/IEEE Standard for Binary | |
4368 | | Floating-Point Arithmetic. | |
4369 | *----------------------------------------------------------------------------*/ | |
4370 | ||
4371 | floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) | |
4372 | { | |
4373 | flag aSign; | |
4374 | int32 aExp; | |
4375 | bits64 aSig0, aSig1; | |
4376 | ||
4377 | aSig1 = extractFloat128Frac1( a ); | |
4378 | aSig0 = extractFloat128Frac0( a ); | |
4379 | aExp = extractFloat128Exp( a ); | |
4380 | aSign = extractFloat128Sign( a ); | |
4381 | if ( aExp == 0x7FFF ) { | |
4382 | if ( aSig0 | aSig1 ) { | |
4383 | return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) ); | |
4384 | } | |
4385 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
4386 | } | |
4387 | if ( aExp == 0 ) { | |
4388 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); | |
4389 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
4390 | } | |
4391 | else { | |
4392 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4393 | } | |
4394 | shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); | |
4395 | return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); | |
4396 | ||
4397 | } | |
4398 | ||
4399 | #endif | |
4400 | ||
4401 | /*---------------------------------------------------------------------------- | |
4402 | | Rounds the quadruple-precision floating-point value `a' to an integer, and | |
4403 | | returns the result as a quadruple-precision floating-point value. The | |
4404 | | operation is performed according to the IEC/IEEE Standard for Binary | |
4405 | | Floating-Point Arithmetic. | |
4406 | *----------------------------------------------------------------------------*/ | |
4407 | ||
4408 | float128 float128_round_to_int( float128 a STATUS_PARAM ) | |
4409 | { | |
4410 | flag aSign; | |
4411 | int32 aExp; | |
4412 | bits64 lastBitMask, roundBitsMask; | |
4413 | int8 roundingMode; | |
4414 | float128 z; | |
4415 | ||
4416 | aExp = extractFloat128Exp( a ); | |
4417 | if ( 0x402F <= aExp ) { | |
4418 | if ( 0x406F <= aExp ) { | |
4419 | if ( ( aExp == 0x7FFF ) | |
4420 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) | |
4421 | ) { | |
4422 | return propagateFloat128NaN( a, a STATUS_VAR ); | |
4423 | } | |
4424 | return a; | |
4425 | } | |
4426 | lastBitMask = 1; | |
4427 | lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; | |
4428 | roundBitsMask = lastBitMask - 1; | |
4429 | z = a; | |
4430 | roundingMode = STATUS(float_rounding_mode); | |
4431 | if ( roundingMode == float_round_nearest_even ) { | |
4432 | if ( lastBitMask ) { | |
4433 | add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); | |
4434 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; | |
4435 | } | |
4436 | else { | |
4437 | if ( (sbits64) z.low < 0 ) { | |
4438 | ++z.high; | |
4439 | if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1; | |
4440 | } | |
4441 | } | |
4442 | } | |
4443 | else if ( roundingMode != float_round_to_zero ) { | |
4444 | if ( extractFloat128Sign( z ) | |
4445 | ^ ( roundingMode == float_round_up ) ) { | |
4446 | add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); | |
4447 | } | |
4448 | } | |
4449 | z.low &= ~ roundBitsMask; | |
4450 | } | |
4451 | else { | |
4452 | if ( aExp < 0x3FFF ) { | |
4453 | if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a; | |
4454 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4455 | aSign = extractFloat128Sign( a ); | |
4456 | switch ( STATUS(float_rounding_mode) ) { | |
4457 | case float_round_nearest_even: | |
4458 | if ( ( aExp == 0x3FFE ) | |
4459 | && ( extractFloat128Frac0( a ) | |
4460 | | extractFloat128Frac1( a ) ) | |
4461 | ) { | |
4462 | return packFloat128( aSign, 0x3FFF, 0, 0 ); | |
4463 | } | |
4464 | break; | |
4465 | case float_round_down: | |
4466 | return | |
4467 | aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) | |
4468 | : packFloat128( 0, 0, 0, 0 ); | |
4469 | case float_round_up: | |
4470 | return | |
4471 | aSign ? packFloat128( 1, 0, 0, 0 ) | |
4472 | : packFloat128( 0, 0x3FFF, 0, 0 ); | |
4473 | } | |
4474 | return packFloat128( aSign, 0, 0, 0 ); | |
4475 | } | |
4476 | lastBitMask = 1; | |
4477 | lastBitMask <<= 0x402F - aExp; | |
4478 | roundBitsMask = lastBitMask - 1; | |
4479 | z.low = 0; | |
4480 | z.high = a.high; | |
4481 | roundingMode = STATUS(float_rounding_mode); | |
4482 | if ( roundingMode == float_round_nearest_even ) { | |
4483 | z.high += lastBitMask>>1; | |
4484 | if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { | |
4485 | z.high &= ~ lastBitMask; | |
4486 | } | |
4487 | } | |
4488 | else if ( roundingMode != float_round_to_zero ) { | |
4489 | if ( extractFloat128Sign( z ) | |
4490 | ^ ( roundingMode == float_round_up ) ) { | |
4491 | z.high |= ( a.low != 0 ); | |
4492 | z.high += roundBitsMask; | |
4493 | } | |
4494 | } | |
4495 | z.high &= ~ roundBitsMask; | |
4496 | } | |
4497 | if ( ( z.low != a.low ) || ( z.high != a.high ) ) { | |
4498 | STATUS(float_exception_flags) |= float_flag_inexact; | |
4499 | } | |
4500 | return z; | |
4501 | ||
4502 | } | |
4503 | ||
4504 | /*---------------------------------------------------------------------------- | |
4505 | | Returns the result of adding the absolute values of the quadruple-precision | |
4506 | | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated | |
4507 | | before being returned. `zSign' is ignored if the result is a NaN. | |
4508 | | The addition is performed according to the IEC/IEEE Standard for Binary | |
4509 | | Floating-Point Arithmetic. | |
4510 | *----------------------------------------------------------------------------*/ | |
4511 | ||
4512 | static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) | |
4513 | { | |
4514 | int32 aExp, bExp, zExp; | |
4515 | bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; | |
4516 | int32 expDiff; | |
4517 | ||
4518 | aSig1 = extractFloat128Frac1( a ); | |
4519 | aSig0 = extractFloat128Frac0( a ); | |
4520 | aExp = extractFloat128Exp( a ); | |
4521 | bSig1 = extractFloat128Frac1( b ); | |
4522 | bSig0 = extractFloat128Frac0( b ); | |
4523 | bExp = extractFloat128Exp( b ); | |
4524 | expDiff = aExp - bExp; | |
4525 | if ( 0 < expDiff ) { | |
4526 | if ( aExp == 0x7FFF ) { | |
4527 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4528 | return a; | |
4529 | } | |
4530 | if ( bExp == 0 ) { | |
4531 | --expDiff; | |
4532 | } | |
4533 | else { | |
4534 | bSig0 |= LIT64( 0x0001000000000000 ); | |
4535 | } | |
4536 | shift128ExtraRightJamming( | |
4537 | bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); | |
4538 | zExp = aExp; | |
4539 | } | |
4540 | else if ( expDiff < 0 ) { | |
4541 | if ( bExp == 0x7FFF ) { | |
4542 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4543 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
4544 | } | |
4545 | if ( aExp == 0 ) { | |
4546 | ++expDiff; | |
4547 | } | |
4548 | else { | |
4549 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4550 | } | |
4551 | shift128ExtraRightJamming( | |
4552 | aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); | |
4553 | zExp = bExp; | |
4554 | } | |
4555 | else { | |
4556 | if ( aExp == 0x7FFF ) { | |
4557 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { | |
4558 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
4559 | } | |
4560 | return a; | |
4561 | } | |
4562 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
4563 | if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 ); | |
4564 | zSig2 = 0; | |
4565 | zSig0 |= LIT64( 0x0002000000000000 ); | |
4566 | zExp = aExp; | |
4567 | goto shiftRight1; | |
4568 | } | |
4569 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4570 | add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
4571 | --zExp; | |
4572 | if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; | |
4573 | ++zExp; | |
4574 | shiftRight1: | |
4575 | shift128ExtraRightJamming( | |
4576 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); | |
4577 | roundAndPack: | |
4578 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
4579 | ||
4580 | } | |
4581 | ||
4582 | /*---------------------------------------------------------------------------- | |
4583 | | Returns the result of subtracting the absolute values of the quadruple- | |
4584 | | precision floating-point values `a' and `b'. If `zSign' is 1, the | |
4585 | | difference is negated before being returned. `zSign' is ignored if the | |
4586 | | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
4587 | | Standard for Binary Floating-Point Arithmetic. | |
4588 | *----------------------------------------------------------------------------*/ | |
4589 | ||
4590 | static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) | |
4591 | { | |
4592 | int32 aExp, bExp, zExp; | |
4593 | bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; | |
4594 | int32 expDiff; | |
4595 | float128 z; | |
4596 | ||
4597 | aSig1 = extractFloat128Frac1( a ); | |
4598 | aSig0 = extractFloat128Frac0( a ); | |
4599 | aExp = extractFloat128Exp( a ); | |
4600 | bSig1 = extractFloat128Frac1( b ); | |
4601 | bSig0 = extractFloat128Frac0( b ); | |
4602 | bExp = extractFloat128Exp( b ); | |
4603 | expDiff = aExp - bExp; | |
4604 | shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); | |
4605 | shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); | |
4606 | if ( 0 < expDiff ) goto aExpBigger; | |
4607 | if ( expDiff < 0 ) goto bExpBigger; | |
4608 | if ( aExp == 0x7FFF ) { | |
4609 | if ( aSig0 | aSig1 | bSig0 | bSig1 ) { | |
4610 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
4611 | } | |
4612 | float_raise( float_flag_invalid STATUS_VAR); | |
4613 | z.low = float128_default_nan_low; | |
4614 | z.high = float128_default_nan_high; | |
4615 | return z; | |
4616 | } | |
4617 | if ( aExp == 0 ) { | |
4618 | aExp = 1; | |
4619 | bExp = 1; | |
4620 | } | |
4621 | if ( bSig0 < aSig0 ) goto aBigger; | |
4622 | if ( aSig0 < bSig0 ) goto bBigger; | |
4623 | if ( bSig1 < aSig1 ) goto aBigger; | |
4624 | if ( aSig1 < bSig1 ) goto bBigger; | |
4625 | return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); | |
4626 | bExpBigger: | |
4627 | if ( bExp == 0x7FFF ) { | |
4628 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4629 | return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); | |
4630 | } | |
4631 | if ( aExp == 0 ) { | |
4632 | ++expDiff; | |
4633 | } | |
4634 | else { | |
4635 | aSig0 |= LIT64( 0x4000000000000000 ); | |
4636 | } | |
4637 | shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); | |
4638 | bSig0 |= LIT64( 0x4000000000000000 ); | |
4639 | bBigger: | |
4640 | sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); | |
4641 | zExp = bExp; | |
4642 | zSign ^= 1; | |
4643 | goto normalizeRoundAndPack; | |
4644 | aExpBigger: | |
4645 | if ( aExp == 0x7FFF ) { | |
4646 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4647 | return a; | |
4648 | } | |
4649 | if ( bExp == 0 ) { | |
4650 | --expDiff; | |
4651 | } | |
4652 | else { | |
4653 | bSig0 |= LIT64( 0x4000000000000000 ); | |
4654 | } | |
4655 | shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); | |
4656 | aSig0 |= LIT64( 0x4000000000000000 ); | |
4657 | aBigger: | |
4658 | sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); | |
4659 | zExp = aExp; | |
4660 | normalizeRoundAndPack: | |
4661 | --zExp; | |
4662 | return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); | |
4663 | ||
4664 | } | |
4665 | ||
4666 | /*---------------------------------------------------------------------------- | |
4667 | | Returns the result of adding the quadruple-precision floating-point values | |
4668 | | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
4669 | | for Binary Floating-Point Arithmetic. | |
4670 | *----------------------------------------------------------------------------*/ | |
4671 | ||
4672 | float128 float128_add( float128 a, float128 b STATUS_PARAM ) | |
4673 | { | |
4674 | flag aSign, bSign; | |
4675 | ||
4676 | aSign = extractFloat128Sign( a ); | |
4677 | bSign = extractFloat128Sign( b ); | |
4678 | if ( aSign == bSign ) { | |
4679 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); | |
4680 | } | |
4681 | else { | |
4682 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); | |
4683 | } | |
4684 | ||
4685 | } | |
4686 | ||
4687 | /*---------------------------------------------------------------------------- | |
4688 | | Returns the result of subtracting the quadruple-precision floating-point | |
4689 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
4690 | | Standard for Binary Floating-Point Arithmetic. | |
4691 | *----------------------------------------------------------------------------*/ | |
4692 | ||
4693 | float128 float128_sub( float128 a, float128 b STATUS_PARAM ) | |
4694 | { | |
4695 | flag aSign, bSign; | |
4696 | ||
4697 | aSign = extractFloat128Sign( a ); | |
4698 | bSign = extractFloat128Sign( b ); | |
4699 | if ( aSign == bSign ) { | |
4700 | return subFloat128Sigs( a, b, aSign STATUS_VAR ); | |
4701 | } | |
4702 | else { | |
4703 | return addFloat128Sigs( a, b, aSign STATUS_VAR ); | |
4704 | } | |
4705 | ||
4706 | } | |
4707 | ||
4708 | /*---------------------------------------------------------------------------- | |
4709 | | Returns the result of multiplying the quadruple-precision floating-point | |
4710 | | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
4711 | | Standard for Binary Floating-Point Arithmetic. | |
4712 | *----------------------------------------------------------------------------*/ | |
4713 | ||
4714 | float128 float128_mul( float128 a, float128 b STATUS_PARAM ) | |
4715 | { | |
4716 | flag aSign, bSign, zSign; | |
4717 | int32 aExp, bExp, zExp; | |
4718 | bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; | |
4719 | float128 z; | |
4720 | ||
4721 | aSig1 = extractFloat128Frac1( a ); | |
4722 | aSig0 = extractFloat128Frac0( a ); | |
4723 | aExp = extractFloat128Exp( a ); | |
4724 | aSign = extractFloat128Sign( a ); | |
4725 | bSig1 = extractFloat128Frac1( b ); | |
4726 | bSig0 = extractFloat128Frac0( b ); | |
4727 | bExp = extractFloat128Exp( b ); | |
4728 | bSign = extractFloat128Sign( b ); | |
4729 | zSign = aSign ^ bSign; | |
4730 | if ( aExp == 0x7FFF ) { | |
4731 | if ( ( aSig0 | aSig1 ) | |
4732 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { | |
4733 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
4734 | } | |
4735 | if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; | |
4736 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
4737 | } | |
4738 | if ( bExp == 0x7FFF ) { | |
4739 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4740 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { | |
4741 | invalid: | |
4742 | float_raise( float_flag_invalid STATUS_VAR); | |
4743 | z.low = float128_default_nan_low; | |
4744 | z.high = float128_default_nan_high; | |
4745 | return z; | |
4746 | } | |
4747 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
4748 | } | |
4749 | if ( aExp == 0 ) { | |
4750 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
4751 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
4752 | } | |
4753 | if ( bExp == 0 ) { | |
4754 | if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
4755 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
4756 | } | |
4757 | zExp = aExp + bExp - 0x4000; | |
4758 | aSig0 |= LIT64( 0x0001000000000000 ); | |
4759 | shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); | |
4760 | mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); | |
4761 | add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); | |
4762 | zSig2 |= ( zSig3 != 0 ); | |
4763 | if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { | |
4764 | shift128ExtraRightJamming( | |
4765 | zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); | |
4766 | ++zExp; | |
4767 | } | |
4768 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
4769 | ||
4770 | } | |
4771 | ||
4772 | /*---------------------------------------------------------------------------- | |
4773 | | Returns the result of dividing the quadruple-precision floating-point value | |
4774 | | `a' by the corresponding value `b'. The operation is performed according to | |
4775 | | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4776 | *----------------------------------------------------------------------------*/ | |
4777 | ||
4778 | float128 float128_div( float128 a, float128 b STATUS_PARAM ) | |
4779 | { | |
4780 | flag aSign, bSign, zSign; | |
4781 | int32 aExp, bExp, zExp; | |
4782 | bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; | |
4783 | bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
4784 | float128 z; | |
4785 | ||
4786 | aSig1 = extractFloat128Frac1( a ); | |
4787 | aSig0 = extractFloat128Frac0( a ); | |
4788 | aExp = extractFloat128Exp( a ); | |
4789 | aSign = extractFloat128Sign( a ); | |
4790 | bSig1 = extractFloat128Frac1( b ); | |
4791 | bSig0 = extractFloat128Frac0( b ); | |
4792 | bExp = extractFloat128Exp( b ); | |
4793 | bSign = extractFloat128Sign( b ); | |
4794 | zSign = aSign ^ bSign; | |
4795 | if ( aExp == 0x7FFF ) { | |
4796 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4797 | if ( bExp == 0x7FFF ) { | |
4798 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4799 | goto invalid; | |
4800 | } | |
4801 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
4802 | } | |
4803 | if ( bExp == 0x7FFF ) { | |
4804 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4805 | return packFloat128( zSign, 0, 0, 0 ); | |
4806 | } | |
4807 | if ( bExp == 0 ) { | |
4808 | if ( ( bSig0 | bSig1 ) == 0 ) { | |
4809 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) { | |
4810 | invalid: | |
4811 | float_raise( float_flag_invalid STATUS_VAR); | |
4812 | z.low = float128_default_nan_low; | |
4813 | z.high = float128_default_nan_high; | |
4814 | return z; | |
4815 | } | |
4816 | float_raise( float_flag_divbyzero STATUS_VAR); | |
4817 | return packFloat128( zSign, 0x7FFF, 0, 0 ); | |
4818 | } | |
4819 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
4820 | } | |
4821 | if ( aExp == 0 ) { | |
4822 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); | |
4823 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
4824 | } | |
4825 | zExp = aExp - bExp + 0x3FFD; | |
4826 | shortShift128Left( | |
4827 | aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); | |
4828 | shortShift128Left( | |
4829 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); | |
4830 | if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { | |
4831 | shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); | |
4832 | ++zExp; | |
4833 | } | |
4834 | zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
4835 | mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); | |
4836 | sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); | |
4837 | while ( (sbits64) rem0 < 0 ) { | |
4838 | --zSig0; | |
4839 | add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); | |
4840 | } | |
4841 | zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); | |
4842 | if ( ( zSig1 & 0x3FFF ) <= 4 ) { | |
4843 | mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); | |
4844 | sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); | |
4845 | while ( (sbits64) rem1 < 0 ) { | |
4846 | --zSig1; | |
4847 | add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); | |
4848 | } | |
4849 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
4850 | } | |
4851 | shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); | |
4852 | return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
4853 | ||
4854 | } | |
4855 | ||
4856 | /*---------------------------------------------------------------------------- | |
4857 | | Returns the remainder of the quadruple-precision floating-point value `a' | |
4858 | | with respect to the corresponding value `b'. The operation is performed | |
4859 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
4860 | *----------------------------------------------------------------------------*/ | |
4861 | ||
4862 | float128 float128_rem( float128 a, float128 b STATUS_PARAM ) | |
4863 | { | |
4864 | flag aSign, bSign, zSign; | |
4865 | int32 aExp, bExp, expDiff; | |
4866 | bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; | |
4867 | bits64 allZero, alternateASig0, alternateASig1, sigMean1; | |
4868 | sbits64 sigMean0; | |
4869 | float128 z; | |
4870 | ||
4871 | aSig1 = extractFloat128Frac1( a ); | |
4872 | aSig0 = extractFloat128Frac0( a ); | |
4873 | aExp = extractFloat128Exp( a ); | |
4874 | aSign = extractFloat128Sign( a ); | |
4875 | bSig1 = extractFloat128Frac1( b ); | |
4876 | bSig0 = extractFloat128Frac0( b ); | |
4877 | bExp = extractFloat128Exp( b ); | |
4878 | bSign = extractFloat128Sign( b ); | |
4879 | if ( aExp == 0x7FFF ) { | |
4880 | if ( ( aSig0 | aSig1 ) | |
4881 | || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { | |
4882 | return propagateFloat128NaN( a, b STATUS_VAR ); | |
4883 | } | |
4884 | goto invalid; | |
4885 | } | |
4886 | if ( bExp == 0x7FFF ) { | |
4887 | if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); | |
4888 | return a; | |
4889 | } | |
4890 | if ( bExp == 0 ) { | |
4891 | if ( ( bSig0 | bSig1 ) == 0 ) { | |
4892 | invalid: | |
4893 | float_raise( float_flag_invalid STATUS_VAR); | |
4894 | z.low = float128_default_nan_low; | |
4895 | z.high = float128_default_nan_high; | |
4896 | return z; | |
4897 | } | |
4898 | normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); | |
4899 | } | |
4900 | if ( aExp == 0 ) { | |
4901 | if ( ( aSig0 | aSig1 ) == 0 ) return a; | |
4902 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
4903 | } | |
4904 | expDiff = aExp - bExp; | |
4905 | if ( expDiff < -1 ) return a; | |
4906 | shortShift128Left( | |
4907 | aSig0 | LIT64( 0x0001000000000000 ), | |
4908 | aSig1, | |
4909 | 15 - ( expDiff < 0 ), | |
4910 | &aSig0, | |
4911 | &aSig1 | |
4912 | ); | |
4913 | shortShift128Left( | |
4914 | bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); | |
4915 | q = le128( bSig0, bSig1, aSig0, aSig1 ); | |
4916 | if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); | |
4917 | expDiff -= 64; | |
4918 | while ( 0 < expDiff ) { | |
4919 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
4920 | q = ( 4 < q ) ? q - 4 : 0; | |
4921 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); | |
4922 | shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); | |
4923 | shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); | |
4924 | sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); | |
4925 | expDiff -= 61; | |
4926 | } | |
4927 | if ( -64 < expDiff ) { | |
4928 | q = estimateDiv128To64( aSig0, aSig1, bSig0 ); | |
4929 | q = ( 4 < q ) ? q - 4 : 0; | |
4930 | q >>= - expDiff; | |
4931 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); | |
4932 | expDiff += 52; | |
4933 | if ( expDiff < 0 ) { | |
4934 | shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); | |
4935 | } | |
4936 | else { | |
4937 | shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); | |
4938 | } | |
4939 | mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); | |
4940 | sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); | |
4941 | } | |
4942 | else { | |
4943 | shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); | |
4944 | shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); | |
4945 | } | |
4946 | do { | |
4947 | alternateASig0 = aSig0; | |
4948 | alternateASig1 = aSig1; | |
4949 | ++q; | |
4950 | sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); | |
4951 | } while ( 0 <= (sbits64) aSig0 ); | |
4952 | add128( | |
4953 | aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 ); | |
4954 | if ( ( sigMean0 < 0 ) | |
4955 | || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { | |
4956 | aSig0 = alternateASig0; | |
4957 | aSig1 = alternateASig1; | |
4958 | } | |
4959 | zSign = ( (sbits64) aSig0 < 0 ); | |
4960 | if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); | |
4961 | return | |
4962 | normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR ); | |
4963 | ||
4964 | } | |
4965 | ||
4966 | /*---------------------------------------------------------------------------- | |
4967 | | Returns the square root of the quadruple-precision floating-point value `a'. | |
4968 | | The operation is performed according to the IEC/IEEE Standard for Binary | |
4969 | | Floating-Point Arithmetic. | |
4970 | *----------------------------------------------------------------------------*/ | |
4971 | ||
4972 | float128 float128_sqrt( float128 a STATUS_PARAM ) | |
4973 | { | |
4974 | flag aSign; | |
4975 | int32 aExp, zExp; | |
4976 | bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; | |
4977 | bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
4978 | float128 z; | |
4979 | ||
4980 | aSig1 = extractFloat128Frac1( a ); | |
4981 | aSig0 = extractFloat128Frac0( a ); | |
4982 | aExp = extractFloat128Exp( a ); | |
4983 | aSign = extractFloat128Sign( a ); | |
4984 | if ( aExp == 0x7FFF ) { | |
4985 | if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); | |
4986 | if ( ! aSign ) return a; | |
4987 | goto invalid; | |
4988 | } | |
4989 | if ( aSign ) { | |
4990 | if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; | |
4991 | invalid: | |
4992 | float_raise( float_flag_invalid STATUS_VAR); | |
4993 | z.low = float128_default_nan_low; | |
4994 | z.high = float128_default_nan_high; | |
4995 | return z; | |
4996 | } | |
4997 | if ( aExp == 0 ) { | |
4998 | if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); | |
4999 | normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); | |
5000 | } | |
5001 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; | |
5002 | aSig0 |= LIT64( 0x0001000000000000 ); | |
5003 | zSig0 = estimateSqrt32( aExp, aSig0>>17 ); | |
5004 | shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); | |
5005 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); | |
5006 | doubleZSig0 = zSig0<<1; | |
5007 | mul64To128( zSig0, zSig0, &term0, &term1 ); | |
5008 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); | |
5009 | while ( (sbits64) rem0 < 0 ) { | |
5010 | --zSig0; | |
5011 | doubleZSig0 -= 2; | |
5012 | add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); | |
5013 | } | |
5014 | zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); | |
5015 | if ( ( zSig1 & 0x1FFF ) <= 5 ) { | |
5016 | if ( zSig1 == 0 ) zSig1 = 1; | |
5017 | mul64To128( doubleZSig0, zSig1, &term1, &term2 ); | |
5018 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
5019 | mul64To128( zSig1, zSig1, &term2, &term3 ); | |
5020 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
5021 | while ( (sbits64) rem1 < 0 ) { | |
5022 | --zSig1; | |
5023 | shortShift128Left( 0, zSig1, 1, &term2, &term3 ); | |
5024 | term3 |= 1; | |
5025 | term2 |= doubleZSig0; | |
5026 | add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
5027 | } | |
5028 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
5029 | } | |
5030 | shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); | |
5031 | return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); | |
5032 | ||
5033 | } | |
5034 | ||
5035 | /*---------------------------------------------------------------------------- | |
5036 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to | |
5037 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
5038 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5039 | *----------------------------------------------------------------------------*/ | |
5040 | ||
750afe93 | 5041 | int float128_eq( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5042 | { |
5043 | ||
5044 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5045 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5046 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5047 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5048 | ) { | |
5049 | if ( float128_is_signaling_nan( a ) | |
5050 | || float128_is_signaling_nan( b ) ) { | |
5051 | float_raise( float_flag_invalid STATUS_VAR); | |
5052 | } | |
5053 | return 0; | |
5054 | } | |
5055 | return | |
5056 | ( a.low == b.low ) | |
5057 | && ( ( a.high == b.high ) | |
5058 | || ( ( a.low == 0 ) | |
5059 | && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
5060 | ); | |
5061 | ||
5062 | } | |
5063 | ||
5064 | /*---------------------------------------------------------------------------- | |
5065 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5066 | | or equal to the corresponding value `b', and 0 otherwise. The comparison | |
5067 | | is performed according to the IEC/IEEE Standard for Binary Floating-Point | |
5068 | | Arithmetic. | |
5069 | *----------------------------------------------------------------------------*/ | |
5070 | ||
750afe93 | 5071 | int float128_le( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5072 | { |
5073 | flag aSign, bSign; | |
5074 | ||
5075 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5076 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5077 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5078 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5079 | ) { | |
5080 | float_raise( float_flag_invalid STATUS_VAR); | |
5081 | return 0; | |
5082 | } | |
5083 | aSign = extractFloat128Sign( a ); | |
5084 | bSign = extractFloat128Sign( b ); | |
5085 | if ( aSign != bSign ) { | |
5086 | return | |
5087 | aSign | |
5088 | || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
5089 | == 0 ); | |
5090 | } | |
5091 | return | |
5092 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
5093 | : le128( a.high, a.low, b.high, b.low ); | |
5094 | ||
5095 | } | |
5096 | ||
5097 | /*---------------------------------------------------------------------------- | |
5098 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5099 | | the corresponding value `b', and 0 otherwise. The comparison is performed | |
5100 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5101 | *----------------------------------------------------------------------------*/ | |
5102 | ||
750afe93 | 5103 | int float128_lt( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5104 | { |
5105 | flag aSign, bSign; | |
5106 | ||
5107 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5108 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5109 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5110 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5111 | ) { | |
5112 | float_raise( float_flag_invalid STATUS_VAR); | |
5113 | return 0; | |
5114 | } | |
5115 | aSign = extractFloat128Sign( a ); | |
5116 | bSign = extractFloat128Sign( b ); | |
5117 | if ( aSign != bSign ) { | |
5118 | return | |
5119 | aSign | |
5120 | && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
5121 | != 0 ); | |
5122 | } | |
5123 | return | |
5124 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
5125 | : lt128( a.high, a.low, b.high, b.low ); | |
5126 | ||
5127 | } | |
5128 | ||
5129 | /*---------------------------------------------------------------------------- | |
5130 | | Returns 1 if the quadruple-precision floating-point value `a' is equal to | |
5131 | | the corresponding value `b', and 0 otherwise. The invalid exception is | |
5132 | | raised if either operand is a NaN. Otherwise, the comparison is performed | |
5133 | | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5134 | *----------------------------------------------------------------------------*/ | |
5135 | ||
750afe93 | 5136 | int float128_eq_signaling( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5137 | { |
5138 | ||
5139 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5140 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5141 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5142 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5143 | ) { | |
5144 | float_raise( float_flag_invalid STATUS_VAR); | |
5145 | return 0; | |
5146 | } | |
5147 | return | |
5148 | ( a.low == b.low ) | |
5149 | && ( ( a.high == b.high ) | |
5150 | || ( ( a.low == 0 ) | |
5151 | && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
5152 | ); | |
5153 | ||
5154 | } | |
5155 | ||
5156 | /*---------------------------------------------------------------------------- | |
5157 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5158 | | or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
5159 | | cause an exception. Otherwise, the comparison is performed according to the | |
5160 | | IEC/IEEE Standard for Binary Floating-Point Arithmetic. | |
5161 | *----------------------------------------------------------------------------*/ | |
5162 | ||
750afe93 | 5163 | int float128_le_quiet( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5164 | { |
5165 | flag aSign, bSign; | |
5166 | ||
5167 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5168 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5169 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5170 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5171 | ) { | |
5172 | if ( float128_is_signaling_nan( a ) | |
5173 | || float128_is_signaling_nan( b ) ) { | |
5174 | float_raise( float_flag_invalid STATUS_VAR); | |
5175 | } | |
5176 | return 0; | |
5177 | } | |
5178 | aSign = extractFloat128Sign( a ); | |
5179 | bSign = extractFloat128Sign( b ); | |
5180 | if ( aSign != bSign ) { | |
5181 | return | |
5182 | aSign | |
5183 | || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
5184 | == 0 ); | |
5185 | } | |
5186 | return | |
5187 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
5188 | : le128( a.high, a.low, b.high, b.low ); | |
5189 | ||
5190 | } | |
5191 | ||
5192 | /*---------------------------------------------------------------------------- | |
5193 | | Returns 1 if the quadruple-precision floating-point value `a' is less than | |
5194 | | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
5195 | | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
5196 | | Standard for Binary Floating-Point Arithmetic. | |
5197 | *----------------------------------------------------------------------------*/ | |
5198 | ||
750afe93 | 5199 | int float128_lt_quiet( float128 a, float128 b STATUS_PARAM ) |
158142c2 FB |
5200 | { |
5201 | flag aSign, bSign; | |
5202 | ||
5203 | if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) | |
5204 | && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) | |
5205 | || ( ( extractFloat128Exp( b ) == 0x7FFF ) | |
5206 | && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) | |
5207 | ) { | |
5208 | if ( float128_is_signaling_nan( a ) | |
5209 | || float128_is_signaling_nan( b ) ) { | |
5210 | float_raise( float_flag_invalid STATUS_VAR); | |
5211 | } | |
5212 | return 0; | |
5213 | } | |
5214 | aSign = extractFloat128Sign( a ); | |
5215 | bSign = extractFloat128Sign( b ); | |
5216 | if ( aSign != bSign ) { | |
5217 | return | |
5218 | aSign | |
5219 | && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
5220 | != 0 ); | |
5221 | } | |
5222 | return | |
5223 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
5224 | : lt128( a.high, a.low, b.high, b.low ); | |
5225 | ||
5226 | } | |
5227 | ||
5228 | #endif | |
5229 | ||
1d6bda35 FB |
5230 | /* misc functions */ |
5231 | float32 uint32_to_float32( unsigned int a STATUS_PARAM ) | |
5232 | { | |
5233 | return int64_to_float32(a STATUS_VAR); | |
5234 | } | |
5235 | ||
5236 | float64 uint32_to_float64( unsigned int a STATUS_PARAM ) | |
5237 | { | |
5238 | return int64_to_float64(a STATUS_VAR); | |
5239 | } | |
5240 | ||
5241 | unsigned int float32_to_uint32( float32 a STATUS_PARAM ) | |
5242 | { | |
5243 | int64_t v; | |
5244 | unsigned int res; | |
5245 | ||
5246 | v = float32_to_int64(a STATUS_VAR); | |
5247 | if (v < 0) { | |
5248 | res = 0; | |
5249 | float_raise( float_flag_invalid STATUS_VAR); | |
5250 | } else if (v > 0xffffffff) { | |
5251 | res = 0xffffffff; | |
5252 | float_raise( float_flag_invalid STATUS_VAR); | |
5253 | } else { | |
5254 | res = v; | |
5255 | } | |
5256 | return res; | |
5257 | } | |
5258 | ||
5259 | unsigned int float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) | |
5260 | { | |
5261 | int64_t v; | |
5262 | unsigned int res; | |
5263 | ||
5264 | v = float32_to_int64_round_to_zero(a STATUS_VAR); | |
5265 | if (v < 0) { | |
5266 | res = 0; | |
5267 | float_raise( float_flag_invalid STATUS_VAR); | |
5268 | } else if (v > 0xffffffff) { | |
5269 | res = 0xffffffff; | |
5270 | float_raise( float_flag_invalid STATUS_VAR); | |
5271 | } else { | |
5272 | res = v; | |
5273 | } | |
5274 | return res; | |
5275 | } | |
5276 | ||
5277 | unsigned int float64_to_uint32( float64 a STATUS_PARAM ) | |
5278 | { | |
5279 | int64_t v; | |
5280 | unsigned int res; | |
5281 | ||
5282 | v = float64_to_int64(a STATUS_VAR); | |
5283 | if (v < 0) { | |
5284 | res = 0; | |
5285 | float_raise( float_flag_invalid STATUS_VAR); | |
5286 | } else if (v > 0xffffffff) { | |
5287 | res = 0xffffffff; | |
5288 | float_raise( float_flag_invalid STATUS_VAR); | |
5289 | } else { | |
5290 | res = v; | |
5291 | } | |
5292 | return res; | |
5293 | } | |
5294 | ||
5295 | unsigned int float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) | |
5296 | { | |
5297 | int64_t v; | |
5298 | unsigned int res; | |
5299 | ||
5300 | v = float64_to_int64_round_to_zero(a STATUS_VAR); | |
5301 | if (v < 0) { | |
5302 | res = 0; | |
5303 | float_raise( float_flag_invalid STATUS_VAR); | |
5304 | } else if (v > 0xffffffff) { | |
5305 | res = 0xffffffff; | |
5306 | float_raise( float_flag_invalid STATUS_VAR); | |
5307 | } else { | |
5308 | res = v; | |
5309 | } | |
5310 | return res; | |
5311 | } | |
5312 | ||
75d62a58 JM |
5313 | uint64_t float64_to_uint64 (float64 a STATUS_PARAM) |
5314 | { | |
5315 | int64_t v; | |
5316 | ||
5317 | v = int64_to_float64(INT64_MIN STATUS_VAR); | |
5318 | v = float64_to_int64((a + v) STATUS_VAR); | |
5319 | ||
5320 | return v - INT64_MIN; | |
5321 | } | |
5322 | ||
5323 | uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) | |
5324 | { | |
5325 | int64_t v; | |
5326 | ||
5327 | v = int64_to_float64(INT64_MIN STATUS_VAR); | |
5328 | v = float64_to_int64_round_to_zero((a + v) STATUS_VAR); | |
5329 | ||
5330 | return v - INT64_MIN; | |
5331 | } | |
5332 | ||
1d6bda35 | 5333 | #define COMPARE(s, nan_exp) \ |
750afe93 | 5334 | INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ |
1d6bda35 FB |
5335 | int is_quiet STATUS_PARAM ) \ |
5336 | { \ | |
5337 | flag aSign, bSign; \ | |
5338 | \ | |
5339 | if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ | |
5340 | extractFloat ## s ## Frac( a ) ) || \ | |
5341 | ( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ | |
5342 | extractFloat ## s ## Frac( b ) )) { \ | |
5343 | if (!is_quiet || \ | |
5344 | float ## s ## _is_signaling_nan( a ) || \ | |
5345 | float ## s ## _is_signaling_nan( b ) ) { \ | |
5346 | float_raise( float_flag_invalid STATUS_VAR); \ | |
5347 | } \ | |
5348 | return float_relation_unordered; \ | |
5349 | } \ | |
5350 | aSign = extractFloat ## s ## Sign( a ); \ | |
5351 | bSign = extractFloat ## s ## Sign( b ); \ | |
5352 | if ( aSign != bSign ) { \ | |
5353 | if ( (bits ## s) ( ( a | b )<<1 ) == 0 ) { \ | |
5354 | /* zero case */ \ | |
5355 | return float_relation_equal; \ | |
5356 | } else { \ | |
5357 | return 1 - (2 * aSign); \ | |
5358 | } \ | |
5359 | } else { \ | |
5360 | if (a == b) { \ | |
5361 | return float_relation_equal; \ | |
5362 | } else { \ | |
5363 | return 1 - 2 * (aSign ^ ( a < b )); \ | |
5364 | } \ | |
5365 | } \ | |
5366 | } \ | |
5367 | \ | |
750afe93 | 5368 | int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ |
1d6bda35 FB |
5369 | { \ |
5370 | return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ | |
5371 | } \ | |
5372 | \ | |
750afe93 | 5373 | int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ |
1d6bda35 FB |
5374 | { \ |
5375 | return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ | |
5376 | } | |
5377 | ||
5378 | COMPARE(32, 0xff) | |
5379 | COMPARE(64, 0x7ff) |