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1da177e4 LT |
1 | /* |
2 | =============================================================================== | |
3 | ||
4 | This C source file is part of the SoftFloat IEC/IEEE Floating-point | |
5 | Arithmetic Package, Release 2. | |
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://HTTP.CS.Berkeley.EDU/~jhauser/ | |
15 | arithmetic/softfloat.html'. | |
16 | ||
17 | THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort | |
18 | has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT | |
19 | TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO | |
20 | PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY | |
21 | AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. | |
22 | ||
23 | Derivative works are acceptable, even for commercial purposes, so long as | |
24 | (1) they include prominent notice that the work is derivative, and (2) they | |
25 | include prominent notice akin to these three paragraphs for those parts of | |
26 | this code that are retained. | |
27 | ||
28 | =============================================================================== | |
29 | */ | |
30 | ||
c1241c4c NP |
31 | #include <asm/div64.h> |
32 | ||
1da177e4 LT |
33 | #include "fpa11.h" |
34 | //#include "milieu.h" | |
35 | //#include "softfloat.h" | |
36 | ||
1da177e4 LT |
37 | /* |
38 | ------------------------------------------------------------------------------- | |
39 | Primitive arithmetic functions, including multi-word arithmetic, and | |
40 | division and square root approximations. (Can be specialized to target if | |
41 | desired.) | |
42 | ------------------------------------------------------------------------------- | |
43 | */ | |
44 | #include "softfloat-macros" | |
45 | ||
46 | /* | |
47 | ------------------------------------------------------------------------------- | |
48 | Functions and definitions to determine: (1) whether tininess for underflow | |
49 | is detected before or after rounding by default, (2) what (if anything) | |
50 | happens when exceptions are raised, (3) how signaling NaNs are distinguished | |
51 | from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs | |
52 | are propagated from function inputs to output. These details are target- | |
53 | specific. | |
54 | ------------------------------------------------------------------------------- | |
55 | */ | |
56 | #include "softfloat-specialize" | |
57 | ||
58 | /* | |
59 | ------------------------------------------------------------------------------- | |
60 | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 | |
61 | and 7, and returns the properly rounded 32-bit integer corresponding to the | |
62 | input. If `zSign' is nonzero, the input is negated before being converted | |
63 | to an integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point | |
64 | input is simply rounded to an integer, with the inexact exception raised if | |
65 | the input cannot be represented exactly as an integer. If the fixed-point | |
66 | input is too large, however, the invalid exception is raised and the largest | |
67 | positive or negative integer is returned. | |
68 | ------------------------------------------------------------------------------- | |
69 | */ | |
f148af25 | 70 | static int32 roundAndPackInt32( struct roundingData *roundData, flag zSign, bits64 absZ ) |
1da177e4 LT |
71 | { |
72 | int8 roundingMode; | |
73 | flag roundNearestEven; | |
74 | int8 roundIncrement, roundBits; | |
75 | int32 z; | |
76 | ||
f148af25 | 77 | roundingMode = roundData->mode; |
1da177e4 LT |
78 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
79 | roundIncrement = 0x40; | |
80 | if ( ! roundNearestEven ) { | |
81 | if ( roundingMode == float_round_to_zero ) { | |
82 | roundIncrement = 0; | |
83 | } | |
84 | else { | |
85 | roundIncrement = 0x7F; | |
86 | if ( zSign ) { | |
87 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
88 | } | |
89 | else { | |
90 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
91 | } | |
92 | } | |
93 | } | |
94 | roundBits = absZ & 0x7F; | |
95 | absZ = ( absZ + roundIncrement )>>7; | |
96 | absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
97 | z = absZ; | |
98 | if ( zSign ) z = - z; | |
99 | if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { | |
f148af25 | 100 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
101 | return zSign ? 0x80000000 : 0x7FFFFFFF; |
102 | } | |
f148af25 | 103 | if ( roundBits ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
104 | return z; |
105 | ||
106 | } | |
107 | ||
108 | /* | |
109 | ------------------------------------------------------------------------------- | |
110 | Returns the fraction bits of the single-precision floating-point value `a'. | |
111 | ------------------------------------------------------------------------------- | |
112 | */ | |
113 | INLINE bits32 extractFloat32Frac( float32 a ) | |
114 | { | |
115 | ||
116 | return a & 0x007FFFFF; | |
117 | ||
118 | } | |
119 | ||
120 | /* | |
121 | ------------------------------------------------------------------------------- | |
122 | Returns the exponent bits of the single-precision floating-point value `a'. | |
123 | ------------------------------------------------------------------------------- | |
124 | */ | |
125 | INLINE int16 extractFloat32Exp( float32 a ) | |
126 | { | |
127 | ||
128 | return ( a>>23 ) & 0xFF; | |
129 | ||
130 | } | |
131 | ||
132 | /* | |
133 | ------------------------------------------------------------------------------- | |
134 | Returns the sign bit of the single-precision floating-point value `a'. | |
135 | ------------------------------------------------------------------------------- | |
136 | */ | |
137 | #if 0 /* in softfloat.h */ | |
138 | INLINE flag extractFloat32Sign( float32 a ) | |
139 | { | |
140 | ||
141 | return a>>31; | |
142 | ||
143 | } | |
144 | #endif | |
145 | ||
146 | /* | |
147 | ------------------------------------------------------------------------------- | |
148 | Normalizes the subnormal single-precision floating-point value represented | |
149 | by the denormalized significand `aSig'. The normalized exponent and | |
150 | significand are stored at the locations pointed to by `zExpPtr' and | |
151 | `zSigPtr', respectively. | |
152 | ------------------------------------------------------------------------------- | |
153 | */ | |
154 | static void | |
155 | normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr ) | |
156 | { | |
157 | int8 shiftCount; | |
158 | ||
159 | shiftCount = countLeadingZeros32( aSig ) - 8; | |
160 | *zSigPtr = aSig<<shiftCount; | |
161 | *zExpPtr = 1 - shiftCount; | |
162 | ||
163 | } | |
164 | ||
165 | /* | |
166 | ------------------------------------------------------------------------------- | |
167 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
168 | single-precision floating-point value, returning the result. After being | |
169 | shifted into the proper positions, the three fields are simply added | |
170 | together to form the result. This means that any integer portion of `zSig' | |
171 | will be added into the exponent. Since a properly normalized significand | |
172 | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
173 | than the desired result exponent whenever `zSig' is a complete, normalized | |
174 | significand. | |
175 | ------------------------------------------------------------------------------- | |
176 | */ | |
177 | INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig ) | |
178 | { | |
179 | #if 0 | |
180 | float32 f; | |
181 | __asm__("@ packFloat32 \n\ | |
182 | mov %0, %1, asl #31 \n\ | |
183 | orr %0, %2, asl #23 \n\ | |
184 | orr %0, %3" | |
185 | : /* no outputs */ | |
186 | : "g" (f), "g" (zSign), "g" (zExp), "g" (zSig) | |
187 | : "cc"); | |
188 | return f; | |
189 | #else | |
190 | return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig; | |
191 | #endif | |
192 | } | |
193 | ||
194 | /* | |
195 | ------------------------------------------------------------------------------- | |
196 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
197 | and significand `zSig', and returns the proper single-precision floating- | |
198 | point value corresponding to the abstract input. Ordinarily, the abstract | |
199 | value is simply rounded and packed into the single-precision format, with | |
200 | the inexact exception raised if the abstract input cannot be represented | |
201 | exactly. If the abstract value is too large, however, the overflow and | |
202 | inexact exceptions are raised and an infinity or maximal finite value is | |
203 | returned. If the abstract value is too small, the input value is rounded to | |
204 | a subnormal number, and the underflow and inexact exceptions are raised if | |
205 | the abstract input cannot be represented exactly as a subnormal single- | |
206 | precision floating-point number. | |
207 | The input significand `zSig' has its binary point between bits 30 | |
208 | and 29, which is 7 bits to the left of the usual location. This shifted | |
209 | significand must be normalized or smaller. If `zSig' is not normalized, | |
210 | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
211 | and it must not require rounding. In the usual case that `zSig' is | |
212 | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
213 | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
214 | Binary Floating-point Arithmetic. | |
215 | ------------------------------------------------------------------------------- | |
216 | */ | |
f148af25 | 217 | static float32 roundAndPackFloat32( struct roundingData *roundData, flag zSign, int16 zExp, bits32 zSig ) |
1da177e4 LT |
218 | { |
219 | int8 roundingMode; | |
220 | flag roundNearestEven; | |
221 | int8 roundIncrement, roundBits; | |
222 | flag isTiny; | |
223 | ||
f148af25 | 224 | roundingMode = roundData->mode; |
1da177e4 LT |
225 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
226 | roundIncrement = 0x40; | |
227 | if ( ! roundNearestEven ) { | |
228 | if ( roundingMode == float_round_to_zero ) { | |
229 | roundIncrement = 0; | |
230 | } | |
231 | else { | |
232 | roundIncrement = 0x7F; | |
233 | if ( zSign ) { | |
234 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
235 | } | |
236 | else { | |
237 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
238 | } | |
239 | } | |
240 | } | |
241 | roundBits = zSig & 0x7F; | |
242 | if ( 0xFD <= (bits16) zExp ) { | |
243 | if ( ( 0xFD < zExp ) | |
244 | || ( ( zExp == 0xFD ) | |
245 | && ( (sbits32) ( zSig + roundIncrement ) < 0 ) ) | |
246 | ) { | |
f148af25 | 247 | roundData->exception |= float_flag_overflow | float_flag_inexact; |
1da177e4 LT |
248 | return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 ); |
249 | } | |
250 | if ( zExp < 0 ) { | |
251 | isTiny = | |
252 | ( float_detect_tininess == float_tininess_before_rounding ) | |
253 | || ( zExp < -1 ) | |
254 | || ( zSig + roundIncrement < 0x80000000 ); | |
255 | shift32RightJamming( zSig, - zExp, &zSig ); | |
256 | zExp = 0; | |
257 | roundBits = zSig & 0x7F; | |
f148af25 | 258 | if ( isTiny && roundBits ) roundData->exception |= float_flag_underflow; |
1da177e4 LT |
259 | } |
260 | } | |
f148af25 | 261 | if ( roundBits ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
262 | zSig = ( zSig + roundIncrement )>>7; |
263 | zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); | |
264 | if ( zSig == 0 ) zExp = 0; | |
265 | return packFloat32( zSign, zExp, zSig ); | |
266 | ||
267 | } | |
268 | ||
269 | /* | |
270 | ------------------------------------------------------------------------------- | |
271 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
272 | and significand `zSig', and returns the proper single-precision floating- | |
273 | point value corresponding to the abstract input. This routine is just like | |
274 | `roundAndPackFloat32' except that `zSig' does not have to be normalized in | |
275 | any way. In all cases, `zExp' must be 1 less than the ``true'' floating- | |
276 | point exponent. | |
277 | ------------------------------------------------------------------------------- | |
278 | */ | |
279 | static float32 | |
f148af25 | 280 | normalizeRoundAndPackFloat32( struct roundingData *roundData, flag zSign, int16 zExp, bits32 zSig ) |
1da177e4 LT |
281 | { |
282 | int8 shiftCount; | |
283 | ||
284 | shiftCount = countLeadingZeros32( zSig ) - 1; | |
f148af25 | 285 | return roundAndPackFloat32( roundData, zSign, zExp - shiftCount, zSig<<shiftCount ); |
1da177e4 LT |
286 | |
287 | } | |
288 | ||
289 | /* | |
290 | ------------------------------------------------------------------------------- | |
291 | Returns the fraction bits of the double-precision floating-point value `a'. | |
292 | ------------------------------------------------------------------------------- | |
293 | */ | |
294 | INLINE bits64 extractFloat64Frac( float64 a ) | |
295 | { | |
296 | ||
297 | return a & LIT64( 0x000FFFFFFFFFFFFF ); | |
298 | ||
299 | } | |
300 | ||
301 | /* | |
302 | ------------------------------------------------------------------------------- | |
303 | Returns the exponent bits of the double-precision floating-point value `a'. | |
304 | ------------------------------------------------------------------------------- | |
305 | */ | |
306 | INLINE int16 extractFloat64Exp( float64 a ) | |
307 | { | |
308 | ||
309 | return ( a>>52 ) & 0x7FF; | |
310 | ||
311 | } | |
312 | ||
313 | /* | |
314 | ------------------------------------------------------------------------------- | |
315 | Returns the sign bit of the double-precision floating-point value `a'. | |
316 | ------------------------------------------------------------------------------- | |
317 | */ | |
318 | #if 0 /* in softfloat.h */ | |
319 | INLINE flag extractFloat64Sign( float64 a ) | |
320 | { | |
321 | ||
322 | return a>>63; | |
323 | ||
324 | } | |
325 | #endif | |
326 | ||
327 | /* | |
328 | ------------------------------------------------------------------------------- | |
329 | Normalizes the subnormal double-precision floating-point value represented | |
330 | by the denormalized significand `aSig'. The normalized exponent and | |
331 | significand are stored at the locations pointed to by `zExpPtr' and | |
332 | `zSigPtr', respectively. | |
333 | ------------------------------------------------------------------------------- | |
334 | */ | |
335 | static void | |
336 | normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr ) | |
337 | { | |
338 | int8 shiftCount; | |
339 | ||
340 | shiftCount = countLeadingZeros64( aSig ) - 11; | |
341 | *zSigPtr = aSig<<shiftCount; | |
342 | *zExpPtr = 1 - shiftCount; | |
343 | ||
344 | } | |
345 | ||
346 | /* | |
347 | ------------------------------------------------------------------------------- | |
348 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a | |
349 | double-precision floating-point value, returning the result. After being | |
350 | shifted into the proper positions, the three fields are simply added | |
351 | together to form the result. This means that any integer portion of `zSig' | |
352 | will be added into the exponent. Since a properly normalized significand | |
353 | will have an integer portion equal to 1, the `zExp' input should be 1 less | |
354 | than the desired result exponent whenever `zSig' is a complete, normalized | |
355 | significand. | |
356 | ------------------------------------------------------------------------------- | |
357 | */ | |
358 | INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig ) | |
359 | { | |
360 | ||
361 | return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig; | |
362 | ||
363 | } | |
364 | ||
365 | /* | |
366 | ------------------------------------------------------------------------------- | |
367 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
368 | and significand `zSig', and returns the proper double-precision floating- | |
369 | point value corresponding to the abstract input. Ordinarily, the abstract | |
370 | value is simply rounded and packed into the double-precision format, with | |
371 | the inexact exception raised if the abstract input cannot be represented | |
372 | exactly. If the abstract value is too large, however, the overflow and | |
373 | inexact exceptions are raised and an infinity or maximal finite value is | |
374 | returned. If the abstract value is too small, the input value is rounded to | |
375 | a subnormal number, and the underflow and inexact exceptions are raised if | |
376 | the abstract input cannot be represented exactly as a subnormal double- | |
377 | precision floating-point number. | |
378 | The input significand `zSig' has its binary point between bits 62 | |
379 | and 61, which is 10 bits to the left of the usual location. This shifted | |
380 | significand must be normalized or smaller. If `zSig' is not normalized, | |
381 | `zExp' must be 0; in that case, the result returned is a subnormal number, | |
382 | and it must not require rounding. In the usual case that `zSig' is | |
383 | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. | |
384 | The handling of underflow and overflow follows the IEC/IEEE Standard for | |
385 | Binary Floating-point Arithmetic. | |
386 | ------------------------------------------------------------------------------- | |
387 | */ | |
f148af25 | 388 | static float64 roundAndPackFloat64( struct roundingData *roundData, flag zSign, int16 zExp, bits64 zSig ) |
1da177e4 LT |
389 | { |
390 | int8 roundingMode; | |
391 | flag roundNearestEven; | |
392 | int16 roundIncrement, roundBits; | |
393 | flag isTiny; | |
394 | ||
f148af25 | 395 | roundingMode = roundData->mode; |
1da177e4 LT |
396 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
397 | roundIncrement = 0x200; | |
398 | if ( ! roundNearestEven ) { | |
399 | if ( roundingMode == float_round_to_zero ) { | |
400 | roundIncrement = 0; | |
401 | } | |
402 | else { | |
403 | roundIncrement = 0x3FF; | |
404 | if ( zSign ) { | |
405 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
406 | } | |
407 | else { | |
408 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
409 | } | |
410 | } | |
411 | } | |
412 | roundBits = zSig & 0x3FF; | |
413 | if ( 0x7FD <= (bits16) zExp ) { | |
414 | if ( ( 0x7FD < zExp ) | |
415 | || ( ( zExp == 0x7FD ) | |
416 | && ( (sbits64) ( zSig + roundIncrement ) < 0 ) ) | |
417 | ) { | |
418 | //register int lr = __builtin_return_address(0); | |
419 | //printk("roundAndPackFloat64 called from 0x%08x\n",lr); | |
f148af25 | 420 | roundData->exception |= float_flag_overflow | float_flag_inexact; |
1da177e4 LT |
421 | return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 ); |
422 | } | |
423 | if ( zExp < 0 ) { | |
424 | isTiny = | |
425 | ( float_detect_tininess == float_tininess_before_rounding ) | |
426 | || ( zExp < -1 ) | |
427 | || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); | |
428 | shift64RightJamming( zSig, - zExp, &zSig ); | |
429 | zExp = 0; | |
430 | roundBits = zSig & 0x3FF; | |
f148af25 | 431 | if ( isTiny && roundBits ) roundData->exception |= float_flag_underflow; |
1da177e4 LT |
432 | } |
433 | } | |
f148af25 | 434 | if ( roundBits ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
435 | zSig = ( zSig + roundIncrement )>>10; |
436 | zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); | |
437 | if ( zSig == 0 ) zExp = 0; | |
438 | return packFloat64( zSign, zExp, zSig ); | |
439 | ||
440 | } | |
441 | ||
442 | /* | |
443 | ------------------------------------------------------------------------------- | |
444 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
445 | and significand `zSig', and returns the proper double-precision floating- | |
446 | point value corresponding to the abstract input. This routine is just like | |
447 | `roundAndPackFloat64' except that `zSig' does not have to be normalized in | |
448 | any way. In all cases, `zExp' must be 1 less than the ``true'' floating- | |
449 | point exponent. | |
450 | ------------------------------------------------------------------------------- | |
451 | */ | |
452 | static float64 | |
f148af25 | 453 | normalizeRoundAndPackFloat64( struct roundingData *roundData, flag zSign, int16 zExp, bits64 zSig ) |
1da177e4 LT |
454 | { |
455 | int8 shiftCount; | |
456 | ||
457 | shiftCount = countLeadingZeros64( zSig ) - 1; | |
f148af25 | 458 | return roundAndPackFloat64( roundData, zSign, zExp - shiftCount, zSig<<shiftCount ); |
1da177e4 LT |
459 | |
460 | } | |
461 | ||
462 | #ifdef FLOATX80 | |
463 | ||
464 | /* | |
465 | ------------------------------------------------------------------------------- | |
466 | Returns the fraction bits of the extended double-precision floating-point | |
467 | value `a'. | |
468 | ------------------------------------------------------------------------------- | |
469 | */ | |
470 | INLINE bits64 extractFloatx80Frac( floatx80 a ) | |
471 | { | |
472 | ||
473 | return a.low; | |
474 | ||
475 | } | |
476 | ||
477 | /* | |
478 | ------------------------------------------------------------------------------- | |
479 | Returns the exponent bits of the extended double-precision floating-point | |
480 | value `a'. | |
481 | ------------------------------------------------------------------------------- | |
482 | */ | |
483 | INLINE int32 extractFloatx80Exp( floatx80 a ) | |
484 | { | |
485 | ||
486 | return a.high & 0x7FFF; | |
487 | ||
488 | } | |
489 | ||
490 | /* | |
491 | ------------------------------------------------------------------------------- | |
492 | Returns the sign bit of the extended double-precision floating-point value | |
493 | `a'. | |
494 | ------------------------------------------------------------------------------- | |
495 | */ | |
496 | INLINE flag extractFloatx80Sign( floatx80 a ) | |
497 | { | |
498 | ||
499 | return a.high>>15; | |
500 | ||
501 | } | |
502 | ||
503 | /* | |
504 | ------------------------------------------------------------------------------- | |
505 | Normalizes the subnormal extended double-precision floating-point value | |
506 | represented by the denormalized significand `aSig'. The normalized exponent | |
507 | and significand are stored at the locations pointed to by `zExpPtr' and | |
508 | `zSigPtr', respectively. | |
509 | ------------------------------------------------------------------------------- | |
510 | */ | |
511 | static void | |
512 | normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr ) | |
513 | { | |
514 | int8 shiftCount; | |
515 | ||
516 | shiftCount = countLeadingZeros64( aSig ); | |
517 | *zSigPtr = aSig<<shiftCount; | |
518 | *zExpPtr = 1 - shiftCount; | |
519 | ||
520 | } | |
521 | ||
522 | /* | |
523 | ------------------------------------------------------------------------------- | |
524 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an | |
525 | extended double-precision floating-point value, returning the result. | |
526 | ------------------------------------------------------------------------------- | |
527 | */ | |
528 | INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig ) | |
529 | { | |
530 | floatx80 z; | |
531 | ||
532 | z.low = zSig; | |
533 | z.high = ( ( (bits16) zSign )<<15 ) + zExp; | |
06c03cac | 534 | z.__padding = 0; |
1da177e4 LT |
535 | return z; |
536 | ||
537 | } | |
538 | ||
539 | /* | |
540 | ------------------------------------------------------------------------------- | |
541 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', | |
542 | and extended significand formed by the concatenation of `zSig0' and `zSig1', | |
543 | and returns the proper extended double-precision floating-point value | |
544 | corresponding to the abstract input. Ordinarily, the abstract value is | |
545 | rounded and packed into the extended double-precision format, with the | |
546 | inexact exception raised if the abstract input cannot be represented | |
547 | exactly. If the abstract value is too large, however, the overflow and | |
548 | inexact exceptions are raised and an infinity or maximal finite value is | |
549 | returned. If the abstract value is too small, the input value is rounded to | |
550 | a subnormal number, and the underflow and inexact exceptions are raised if | |
551 | the abstract input cannot be represented exactly as a subnormal extended | |
552 | double-precision floating-point number. | |
553 | If `roundingPrecision' is 32 or 64, the result is rounded to the same | |
554 | number of bits as single or double precision, respectively. Otherwise, the | |
555 | result is rounded to the full precision of the extended double-precision | |
556 | format. | |
557 | The input significand must be normalized or smaller. If the input | |
558 | significand is not normalized, `zExp' must be 0; in that case, the result | |
559 | returned is a subnormal number, and it must not require rounding. The | |
560 | handling of underflow and overflow follows the IEC/IEEE Standard for Binary | |
561 | Floating-point Arithmetic. | |
562 | ------------------------------------------------------------------------------- | |
563 | */ | |
564 | static floatx80 | |
565 | roundAndPackFloatx80( | |
f148af25 | 566 | struct roundingData *roundData, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 |
1da177e4 LT |
567 | ) |
568 | { | |
f148af25 | 569 | int8 roundingMode, roundingPrecision; |
1da177e4 LT |
570 | flag roundNearestEven, increment, isTiny; |
571 | int64 roundIncrement, roundMask, roundBits; | |
572 | ||
f148af25 RP |
573 | roundingMode = roundData->mode; |
574 | roundingPrecision = roundData->precision; | |
1da177e4 LT |
575 | roundNearestEven = ( roundingMode == float_round_nearest_even ); |
576 | if ( roundingPrecision == 80 ) goto precision80; | |
577 | if ( roundingPrecision == 64 ) { | |
578 | roundIncrement = LIT64( 0x0000000000000400 ); | |
579 | roundMask = LIT64( 0x00000000000007FF ); | |
580 | } | |
581 | else if ( roundingPrecision == 32 ) { | |
582 | roundIncrement = LIT64( 0x0000008000000000 ); | |
583 | roundMask = LIT64( 0x000000FFFFFFFFFF ); | |
584 | } | |
585 | else { | |
586 | goto precision80; | |
587 | } | |
588 | zSig0 |= ( zSig1 != 0 ); | |
589 | if ( ! roundNearestEven ) { | |
590 | if ( roundingMode == float_round_to_zero ) { | |
591 | roundIncrement = 0; | |
592 | } | |
593 | else { | |
594 | roundIncrement = roundMask; | |
595 | if ( zSign ) { | |
596 | if ( roundingMode == float_round_up ) roundIncrement = 0; | |
597 | } | |
598 | else { | |
599 | if ( roundingMode == float_round_down ) roundIncrement = 0; | |
600 | } | |
601 | } | |
602 | } | |
603 | roundBits = zSig0 & roundMask; | |
604 | if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { | |
605 | if ( ( 0x7FFE < zExp ) | |
606 | || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) | |
607 | ) { | |
608 | goto overflow; | |
609 | } | |
610 | if ( zExp <= 0 ) { | |
611 | isTiny = | |
612 | ( float_detect_tininess == float_tininess_before_rounding ) | |
613 | || ( zExp < 0 ) | |
614 | || ( zSig0 <= zSig0 + roundIncrement ); | |
615 | shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); | |
616 | zExp = 0; | |
617 | roundBits = zSig0 & roundMask; | |
f148af25 RP |
618 | if ( isTiny && roundBits ) roundData->exception |= float_flag_underflow; |
619 | if ( roundBits ) roundData->exception |= float_flag_inexact; | |
1da177e4 LT |
620 | zSig0 += roundIncrement; |
621 | if ( (sbits64) zSig0 < 0 ) zExp = 1; | |
622 | roundIncrement = roundMask + 1; | |
623 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
624 | roundMask |= roundIncrement; | |
625 | } | |
626 | zSig0 &= ~ roundMask; | |
627 | return packFloatx80( zSign, zExp, zSig0 ); | |
628 | } | |
629 | } | |
f148af25 | 630 | if ( roundBits ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
631 | zSig0 += roundIncrement; |
632 | if ( zSig0 < roundIncrement ) { | |
633 | ++zExp; | |
634 | zSig0 = LIT64( 0x8000000000000000 ); | |
635 | } | |
636 | roundIncrement = roundMask + 1; | |
637 | if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { | |
638 | roundMask |= roundIncrement; | |
639 | } | |
640 | zSig0 &= ~ roundMask; | |
641 | if ( zSig0 == 0 ) zExp = 0; | |
642 | return packFloatx80( zSign, zExp, zSig0 ); | |
643 | precision80: | |
644 | increment = ( (sbits64) zSig1 < 0 ); | |
645 | if ( ! roundNearestEven ) { | |
646 | if ( roundingMode == float_round_to_zero ) { | |
647 | increment = 0; | |
648 | } | |
649 | else { | |
650 | if ( zSign ) { | |
651 | increment = ( roundingMode == float_round_down ) && zSig1; | |
652 | } | |
653 | else { | |
654 | increment = ( roundingMode == float_round_up ) && zSig1; | |
655 | } | |
656 | } | |
657 | } | |
658 | if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { | |
659 | if ( ( 0x7FFE < zExp ) | |
660 | || ( ( zExp == 0x7FFE ) | |
661 | && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) | |
662 | && increment | |
663 | ) | |
664 | ) { | |
665 | roundMask = 0; | |
666 | overflow: | |
f148af25 | 667 | roundData->exception |= float_flag_overflow | float_flag_inexact; |
1da177e4 LT |
668 | if ( ( roundingMode == float_round_to_zero ) |
669 | || ( zSign && ( roundingMode == float_round_up ) ) | |
670 | || ( ! zSign && ( roundingMode == float_round_down ) ) | |
671 | ) { | |
672 | return packFloatx80( zSign, 0x7FFE, ~ roundMask ); | |
673 | } | |
674 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
675 | } | |
676 | if ( zExp <= 0 ) { | |
677 | isTiny = | |
678 | ( float_detect_tininess == float_tininess_before_rounding ) | |
679 | || ( zExp < 0 ) | |
680 | || ! increment | |
681 | || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); | |
682 | shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); | |
683 | zExp = 0; | |
f148af25 RP |
684 | if ( isTiny && zSig1 ) roundData->exception |= float_flag_underflow; |
685 | if ( zSig1 ) roundData->exception |= float_flag_inexact; | |
1da177e4 LT |
686 | if ( roundNearestEven ) { |
687 | increment = ( (sbits64) zSig1 < 0 ); | |
688 | } | |
689 | else { | |
690 | if ( zSign ) { | |
691 | increment = ( roundingMode == float_round_down ) && zSig1; | |
692 | } | |
693 | else { | |
694 | increment = ( roundingMode == float_round_up ) && zSig1; | |
695 | } | |
696 | } | |
697 | if ( increment ) { | |
698 | ++zSig0; | |
699 | zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven ); | |
700 | if ( (sbits64) zSig0 < 0 ) zExp = 1; | |
701 | } | |
702 | return packFloatx80( zSign, zExp, zSig0 ); | |
703 | } | |
704 | } | |
f148af25 | 705 | if ( zSig1 ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
706 | if ( increment ) { |
707 | ++zSig0; | |
708 | if ( zSig0 == 0 ) { | |
709 | ++zExp; | |
710 | zSig0 = LIT64( 0x8000000000000000 ); | |
711 | } | |
712 | else { | |
713 | zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven ); | |
714 | } | |
715 | } | |
716 | else { | |
717 | if ( zSig0 == 0 ) zExp = 0; | |
718 | } | |
719 | ||
720 | return packFloatx80( zSign, zExp, zSig0 ); | |
721 | } | |
722 | ||
723 | /* | |
724 | ------------------------------------------------------------------------------- | |
725 | Takes an abstract floating-point value having sign `zSign', exponent | |
726 | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', | |
727 | and returns the proper extended double-precision floating-point value | |
728 | corresponding to the abstract input. This routine is just like | |
729 | `roundAndPackFloatx80' except that the input significand does not have to be | |
730 | normalized. | |
731 | ------------------------------------------------------------------------------- | |
732 | */ | |
733 | static floatx80 | |
734 | normalizeRoundAndPackFloatx80( | |
f148af25 | 735 | struct roundingData *roundData, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 |
1da177e4 LT |
736 | ) |
737 | { | |
738 | int8 shiftCount; | |
739 | ||
740 | if ( zSig0 == 0 ) { | |
741 | zSig0 = zSig1; | |
742 | zSig1 = 0; | |
743 | zExp -= 64; | |
744 | } | |
745 | shiftCount = countLeadingZeros64( zSig0 ); | |
746 | shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); | |
747 | zExp -= shiftCount; | |
748 | return | |
f148af25 | 749 | roundAndPackFloatx80( roundData, zSign, zExp, zSig0, zSig1 ); |
1da177e4 LT |
750 | |
751 | } | |
752 | ||
753 | #endif | |
754 | ||
755 | /* | |
756 | ------------------------------------------------------------------------------- | |
757 | Returns the result of converting the 32-bit two's complement integer `a' to | |
758 | the single-precision floating-point format. The conversion is performed | |
759 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
760 | ------------------------------------------------------------------------------- | |
761 | */ | |
f148af25 | 762 | float32 int32_to_float32(struct roundingData *roundData, int32 a) |
1da177e4 LT |
763 | { |
764 | flag zSign; | |
765 | ||
766 | if ( a == 0 ) return 0; | |
767 | if ( a == 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); | |
768 | zSign = ( a < 0 ); | |
f148af25 | 769 | return normalizeRoundAndPackFloat32( roundData, zSign, 0x9C, zSign ? - a : a ); |
1da177e4 LT |
770 | |
771 | } | |
772 | ||
773 | /* | |
774 | ------------------------------------------------------------------------------- | |
775 | Returns the result of converting the 32-bit two's complement integer `a' to | |
776 | the double-precision floating-point format. The conversion is performed | |
777 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
778 | ------------------------------------------------------------------------------- | |
779 | */ | |
780 | float64 int32_to_float64( int32 a ) | |
781 | { | |
782 | flag aSign; | |
783 | uint32 absA; | |
784 | int8 shiftCount; | |
785 | bits64 zSig; | |
786 | ||
787 | if ( a == 0 ) return 0; | |
788 | aSign = ( a < 0 ); | |
789 | absA = aSign ? - a : a; | |
790 | shiftCount = countLeadingZeros32( absA ) + 21; | |
791 | zSig = absA; | |
792 | return packFloat64( aSign, 0x432 - shiftCount, zSig<<shiftCount ); | |
793 | ||
794 | } | |
795 | ||
796 | #ifdef FLOATX80 | |
797 | ||
798 | /* | |
799 | ------------------------------------------------------------------------------- | |
800 | Returns the result of converting the 32-bit two's complement integer `a' | |
801 | to the extended double-precision floating-point format. The conversion | |
802 | is performed according to the IEC/IEEE Standard for Binary Floating-point | |
803 | Arithmetic. | |
804 | ------------------------------------------------------------------------------- | |
805 | */ | |
806 | floatx80 int32_to_floatx80( int32 a ) | |
807 | { | |
808 | flag zSign; | |
809 | uint32 absA; | |
810 | int8 shiftCount; | |
811 | bits64 zSig; | |
812 | ||
813 | if ( a == 0 ) return packFloatx80( 0, 0, 0 ); | |
814 | zSign = ( a < 0 ); | |
815 | absA = zSign ? - a : a; | |
816 | shiftCount = countLeadingZeros32( absA ) + 32; | |
817 | zSig = absA; | |
818 | return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); | |
819 | ||
820 | } | |
821 | ||
822 | #endif | |
823 | ||
824 | /* | |
825 | ------------------------------------------------------------------------------- | |
826 | Returns the result of converting the single-precision floating-point value | |
827 | `a' to the 32-bit two's complement integer format. The conversion is | |
828 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
829 | Arithmetic---which means in particular that the conversion is rounded | |
830 | according to the current rounding mode. If `a' is a NaN, the largest | |
831 | positive integer is returned. Otherwise, if the conversion overflows, the | |
832 | largest integer with the same sign as `a' is returned. | |
833 | ------------------------------------------------------------------------------- | |
834 | */ | |
f148af25 | 835 | int32 float32_to_int32( struct roundingData *roundData, float32 a ) |
1da177e4 LT |
836 | { |
837 | flag aSign; | |
838 | int16 aExp, shiftCount; | |
839 | bits32 aSig; | |
840 | bits64 zSig; | |
841 | ||
842 | aSig = extractFloat32Frac( a ); | |
843 | aExp = extractFloat32Exp( a ); | |
844 | aSign = extractFloat32Sign( a ); | |
845 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
846 | if ( aExp ) aSig |= 0x00800000; | |
847 | shiftCount = 0xAF - aExp; | |
848 | zSig = aSig; | |
849 | zSig <<= 32; | |
850 | if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig ); | |
f148af25 | 851 | return roundAndPackInt32( roundData, aSign, zSig ); |
1da177e4 LT |
852 | |
853 | } | |
854 | ||
855 | /* | |
856 | ------------------------------------------------------------------------------- | |
857 | Returns the result of converting the single-precision floating-point value | |
858 | `a' to the 32-bit two's complement integer format. The conversion is | |
859 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
860 | Arithmetic, except that the conversion is always rounded toward zero. If | |
861 | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
862 | conversion overflows, the largest integer with the same sign as `a' is | |
863 | returned. | |
864 | ------------------------------------------------------------------------------- | |
865 | */ | |
866 | int32 float32_to_int32_round_to_zero( float32 a ) | |
867 | { | |
868 | flag aSign; | |
869 | int16 aExp, shiftCount; | |
870 | bits32 aSig; | |
871 | int32 z; | |
872 | ||
873 | aSig = extractFloat32Frac( a ); | |
874 | aExp = extractFloat32Exp( a ); | |
875 | aSign = extractFloat32Sign( a ); | |
876 | shiftCount = aExp - 0x9E; | |
877 | if ( 0 <= shiftCount ) { | |
878 | if ( a == 0xCF000000 ) return 0x80000000; | |
879 | float_raise( float_flag_invalid ); | |
880 | if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; | |
881 | return 0x80000000; | |
882 | } | |
883 | else if ( aExp <= 0x7E ) { | |
f148af25 | 884 | if ( aExp | aSig ) float_raise( float_flag_inexact ); |
1da177e4 LT |
885 | return 0; |
886 | } | |
887 | aSig = ( aSig | 0x00800000 )<<8; | |
888 | z = aSig>>( - shiftCount ); | |
889 | if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) { | |
f148af25 | 890 | float_raise( float_flag_inexact ); |
1da177e4 LT |
891 | } |
892 | return aSign ? - z : z; | |
893 | ||
894 | } | |
895 | ||
896 | /* | |
897 | ------------------------------------------------------------------------------- | |
898 | Returns the result of converting the single-precision floating-point value | |
899 | `a' to the double-precision floating-point format. The conversion is | |
900 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
901 | Arithmetic. | |
902 | ------------------------------------------------------------------------------- | |
903 | */ | |
904 | float64 float32_to_float64( float32 a ) | |
905 | { | |
906 | flag aSign; | |
907 | int16 aExp; | |
908 | bits32 aSig; | |
909 | ||
910 | aSig = extractFloat32Frac( a ); | |
911 | aExp = extractFloat32Exp( a ); | |
912 | aSign = extractFloat32Sign( a ); | |
913 | if ( aExp == 0xFF ) { | |
914 | if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) ); | |
915 | return packFloat64( aSign, 0x7FF, 0 ); | |
916 | } | |
917 | if ( aExp == 0 ) { | |
918 | if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); | |
919 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
920 | --aExp; | |
921 | } | |
922 | return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 ); | |
923 | ||
924 | } | |
925 | ||
926 | #ifdef FLOATX80 | |
927 | ||
928 | /* | |
929 | ------------------------------------------------------------------------------- | |
930 | Returns the result of converting the single-precision floating-point value | |
931 | `a' to the extended double-precision floating-point format. The conversion | |
932 | is performed according to the IEC/IEEE Standard for Binary Floating-point | |
933 | Arithmetic. | |
934 | ------------------------------------------------------------------------------- | |
935 | */ | |
936 | floatx80 float32_to_floatx80( float32 a ) | |
937 | { | |
938 | flag aSign; | |
939 | int16 aExp; | |
940 | bits32 aSig; | |
941 | ||
942 | aSig = extractFloat32Frac( a ); | |
943 | aExp = extractFloat32Exp( a ); | |
944 | aSign = extractFloat32Sign( a ); | |
945 | if ( aExp == 0xFF ) { | |
946 | if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) ); | |
947 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
948 | } | |
949 | if ( aExp == 0 ) { | |
950 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
951 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
952 | } | |
953 | aSig |= 0x00800000; | |
954 | return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 ); | |
955 | ||
956 | } | |
957 | ||
958 | #endif | |
959 | ||
960 | /* | |
961 | ------------------------------------------------------------------------------- | |
962 | Rounds the single-precision floating-point value `a' to an integer, and | |
963 | returns the result as a single-precision floating-point value. The | |
964 | operation is performed according to the IEC/IEEE Standard for Binary | |
965 | Floating-point Arithmetic. | |
966 | ------------------------------------------------------------------------------- | |
967 | */ | |
f148af25 | 968 | float32 float32_round_to_int( struct roundingData *roundData, float32 a ) |
1da177e4 LT |
969 | { |
970 | flag aSign; | |
971 | int16 aExp; | |
972 | bits32 lastBitMask, roundBitsMask; | |
973 | int8 roundingMode; | |
974 | float32 z; | |
975 | ||
976 | aExp = extractFloat32Exp( a ); | |
977 | if ( 0x96 <= aExp ) { | |
978 | if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { | |
979 | return propagateFloat32NaN( a, a ); | |
980 | } | |
981 | return a; | |
982 | } | |
f148af25 | 983 | roundingMode = roundData->mode; |
1da177e4 LT |
984 | if ( aExp <= 0x7E ) { |
985 | if ( (bits32) ( a<<1 ) == 0 ) return a; | |
f148af25 | 986 | roundData->exception |= float_flag_inexact; |
1da177e4 | 987 | aSign = extractFloat32Sign( a ); |
f148af25 | 988 | switch ( roundingMode ) { |
1da177e4 LT |
989 | case float_round_nearest_even: |
990 | if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { | |
991 | return packFloat32( aSign, 0x7F, 0 ); | |
992 | } | |
993 | break; | |
994 | case float_round_down: | |
995 | return aSign ? 0xBF800000 : 0; | |
996 | case float_round_up: | |
997 | return aSign ? 0x80000000 : 0x3F800000; | |
998 | } | |
999 | return packFloat32( aSign, 0, 0 ); | |
1000 | } | |
1001 | lastBitMask = 1; | |
1002 | lastBitMask <<= 0x96 - aExp; | |
1003 | roundBitsMask = lastBitMask - 1; | |
1004 | z = a; | |
1da177e4 LT |
1005 | if ( roundingMode == float_round_nearest_even ) { |
1006 | z += lastBitMask>>1; | |
1007 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
1008 | } | |
1009 | else if ( roundingMode != float_round_to_zero ) { | |
1010 | if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
1011 | z += roundBitsMask; | |
1012 | } | |
1013 | } | |
1014 | z &= ~ roundBitsMask; | |
f148af25 | 1015 | if ( z != a ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
1016 | return z; |
1017 | ||
1018 | } | |
1019 | ||
1020 | /* | |
1021 | ------------------------------------------------------------------------------- | |
1022 | Returns the result of adding the absolute values of the single-precision | |
1023 | floating-point values `a' and `b'. If `zSign' is true, the sum is negated | |
1024 | before being returned. `zSign' is ignored if the result is a NaN. The | |
1025 | addition is performed according to the IEC/IEEE Standard for Binary | |
1026 | Floating-point Arithmetic. | |
1027 | ------------------------------------------------------------------------------- | |
1028 | */ | |
f148af25 | 1029 | static float32 addFloat32Sigs( struct roundingData *roundData, float32 a, float32 b, flag zSign ) |
1da177e4 LT |
1030 | { |
1031 | int16 aExp, bExp, zExp; | |
1032 | bits32 aSig, bSig, zSig; | |
1033 | int16 expDiff; | |
1034 | ||
1035 | aSig = extractFloat32Frac( a ); | |
1036 | aExp = extractFloat32Exp( a ); | |
1037 | bSig = extractFloat32Frac( b ); | |
1038 | bExp = extractFloat32Exp( b ); | |
1039 | expDiff = aExp - bExp; | |
1040 | aSig <<= 6; | |
1041 | bSig <<= 6; | |
1042 | if ( 0 < expDiff ) { | |
1043 | if ( aExp == 0xFF ) { | |
1044 | if ( aSig ) return propagateFloat32NaN( a, b ); | |
1045 | return a; | |
1046 | } | |
1047 | if ( bExp == 0 ) { | |
1048 | --expDiff; | |
1049 | } | |
1050 | else { | |
1051 | bSig |= 0x20000000; | |
1052 | } | |
1053 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1054 | zExp = aExp; | |
1055 | } | |
1056 | else if ( expDiff < 0 ) { | |
1057 | if ( bExp == 0xFF ) { | |
1058 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
1059 | return packFloat32( zSign, 0xFF, 0 ); | |
1060 | } | |
1061 | if ( aExp == 0 ) { | |
1062 | ++expDiff; | |
1063 | } | |
1064 | else { | |
1065 | aSig |= 0x20000000; | |
1066 | } | |
1067 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1068 | zExp = bExp; | |
1069 | } | |
1070 | else { | |
1071 | if ( aExp == 0xFF ) { | |
1072 | if ( aSig | bSig ) return propagateFloat32NaN( a, b ); | |
1073 | return a; | |
1074 | } | |
1075 | if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); | |
1076 | zSig = 0x40000000 + aSig + bSig; | |
1077 | zExp = aExp; | |
1078 | goto roundAndPack; | |
1079 | } | |
1080 | aSig |= 0x20000000; | |
1081 | zSig = ( aSig + bSig )<<1; | |
1082 | --zExp; | |
1083 | if ( (sbits32) zSig < 0 ) { | |
1084 | zSig = aSig + bSig; | |
1085 | ++zExp; | |
1086 | } | |
1087 | roundAndPack: | |
f148af25 | 1088 | return roundAndPackFloat32( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
1089 | |
1090 | } | |
1091 | ||
1092 | /* | |
1093 | ------------------------------------------------------------------------------- | |
1094 | Returns the result of subtracting the absolute values of the single- | |
1095 | precision floating-point values `a' and `b'. If `zSign' is true, the | |
1096 | difference is negated before being returned. `zSign' is ignored if the | |
1097 | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
1098 | Standard for Binary Floating-point Arithmetic. | |
1099 | ------------------------------------------------------------------------------- | |
1100 | */ | |
f148af25 | 1101 | static float32 subFloat32Sigs( struct roundingData *roundData, float32 a, float32 b, flag zSign ) |
1da177e4 LT |
1102 | { |
1103 | int16 aExp, bExp, zExp; | |
1104 | bits32 aSig, bSig, zSig; | |
1105 | int16 expDiff; | |
1106 | ||
1107 | aSig = extractFloat32Frac( a ); | |
1108 | aExp = extractFloat32Exp( a ); | |
1109 | bSig = extractFloat32Frac( b ); | |
1110 | bExp = extractFloat32Exp( b ); | |
1111 | expDiff = aExp - bExp; | |
1112 | aSig <<= 7; | |
1113 | bSig <<= 7; | |
1114 | if ( 0 < expDiff ) goto aExpBigger; | |
1115 | if ( expDiff < 0 ) goto bExpBigger; | |
1116 | if ( aExp == 0xFF ) { | |
1117 | if ( aSig | bSig ) return propagateFloat32NaN( a, b ); | |
f148af25 | 1118 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1119 | return float32_default_nan; |
1120 | } | |
1121 | if ( aExp == 0 ) { | |
1122 | aExp = 1; | |
1123 | bExp = 1; | |
1124 | } | |
1125 | if ( bSig < aSig ) goto aBigger; | |
1126 | if ( aSig < bSig ) goto bBigger; | |
f148af25 | 1127 | return packFloat32( roundData->mode == float_round_down, 0, 0 ); |
1da177e4 LT |
1128 | bExpBigger: |
1129 | if ( bExp == 0xFF ) { | |
1130 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
1131 | return packFloat32( zSign ^ 1, 0xFF, 0 ); | |
1132 | } | |
1133 | if ( aExp == 0 ) { | |
1134 | ++expDiff; | |
1135 | } | |
1136 | else { | |
1137 | aSig |= 0x40000000; | |
1138 | } | |
1139 | shift32RightJamming( aSig, - expDiff, &aSig ); | |
1140 | bSig |= 0x40000000; | |
1141 | bBigger: | |
1142 | zSig = bSig - aSig; | |
1143 | zExp = bExp; | |
1144 | zSign ^= 1; | |
1145 | goto normalizeRoundAndPack; | |
1146 | aExpBigger: | |
1147 | if ( aExp == 0xFF ) { | |
1148 | if ( aSig ) return propagateFloat32NaN( a, b ); | |
1149 | return a; | |
1150 | } | |
1151 | if ( bExp == 0 ) { | |
1152 | --expDiff; | |
1153 | } | |
1154 | else { | |
1155 | bSig |= 0x40000000; | |
1156 | } | |
1157 | shift32RightJamming( bSig, expDiff, &bSig ); | |
1158 | aSig |= 0x40000000; | |
1159 | aBigger: | |
1160 | zSig = aSig - bSig; | |
1161 | zExp = aExp; | |
1162 | normalizeRoundAndPack: | |
1163 | --zExp; | |
f148af25 | 1164 | return normalizeRoundAndPackFloat32( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
1165 | |
1166 | } | |
1167 | ||
1168 | /* | |
1169 | ------------------------------------------------------------------------------- | |
1170 | Returns the result of adding the single-precision floating-point values `a' | |
1171 | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
1172 | Binary Floating-point Arithmetic. | |
1173 | ------------------------------------------------------------------------------- | |
1174 | */ | |
f148af25 | 1175 | float32 float32_add( struct roundingData *roundData, float32 a, float32 b ) |
1da177e4 LT |
1176 | { |
1177 | flag aSign, bSign; | |
1178 | ||
1179 | aSign = extractFloat32Sign( a ); | |
1180 | bSign = extractFloat32Sign( b ); | |
1181 | if ( aSign == bSign ) { | |
f148af25 | 1182 | return addFloat32Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
1183 | } |
1184 | else { | |
f148af25 | 1185 | return subFloat32Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
1186 | } |
1187 | ||
1188 | } | |
1189 | ||
1190 | /* | |
1191 | ------------------------------------------------------------------------------- | |
1192 | Returns the result of subtracting the single-precision floating-point values | |
1193 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1194 | for Binary Floating-point Arithmetic. | |
1195 | ------------------------------------------------------------------------------- | |
1196 | */ | |
f148af25 | 1197 | float32 float32_sub( struct roundingData *roundData, float32 a, float32 b ) |
1da177e4 LT |
1198 | { |
1199 | flag aSign, bSign; | |
1200 | ||
1201 | aSign = extractFloat32Sign( a ); | |
1202 | bSign = extractFloat32Sign( b ); | |
1203 | if ( aSign == bSign ) { | |
f148af25 | 1204 | return subFloat32Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
1205 | } |
1206 | else { | |
f148af25 | 1207 | return addFloat32Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
1208 | } |
1209 | ||
1210 | } | |
1211 | ||
1212 | /* | |
1213 | ------------------------------------------------------------------------------- | |
1214 | Returns the result of multiplying the single-precision floating-point values | |
1215 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
1216 | for Binary Floating-point Arithmetic. | |
1217 | ------------------------------------------------------------------------------- | |
1218 | */ | |
f148af25 | 1219 | float32 float32_mul( struct roundingData *roundData, float32 a, float32 b ) |
1da177e4 LT |
1220 | { |
1221 | flag aSign, bSign, zSign; | |
1222 | int16 aExp, bExp, zExp; | |
1223 | bits32 aSig, bSig; | |
1224 | bits64 zSig64; | |
1225 | bits32 zSig; | |
1226 | ||
1227 | aSig = extractFloat32Frac( a ); | |
1228 | aExp = extractFloat32Exp( a ); | |
1229 | aSign = extractFloat32Sign( a ); | |
1230 | bSig = extractFloat32Frac( b ); | |
1231 | bExp = extractFloat32Exp( b ); | |
1232 | bSign = extractFloat32Sign( b ); | |
1233 | zSign = aSign ^ bSign; | |
1234 | if ( aExp == 0xFF ) { | |
1235 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
1236 | return propagateFloat32NaN( a, b ); | |
1237 | } | |
1238 | if ( ( bExp | bSig ) == 0 ) { | |
f148af25 | 1239 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1240 | return float32_default_nan; |
1241 | } | |
1242 | return packFloat32( zSign, 0xFF, 0 ); | |
1243 | } | |
1244 | if ( bExp == 0xFF ) { | |
1245 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
1246 | if ( ( aExp | aSig ) == 0 ) { | |
f148af25 | 1247 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1248 | return float32_default_nan; |
1249 | } | |
1250 | return packFloat32( zSign, 0xFF, 0 ); | |
1251 | } | |
1252 | if ( aExp == 0 ) { | |
1253 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1254 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1255 | } | |
1256 | if ( bExp == 0 ) { | |
1257 | if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1258 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1259 | } | |
1260 | zExp = aExp + bExp - 0x7F; | |
1261 | aSig = ( aSig | 0x00800000 )<<7; | |
1262 | bSig = ( bSig | 0x00800000 )<<8; | |
1263 | shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 ); | |
1264 | zSig = zSig64; | |
1265 | if ( 0 <= (sbits32) ( zSig<<1 ) ) { | |
1266 | zSig <<= 1; | |
1267 | --zExp; | |
1268 | } | |
f148af25 | 1269 | return roundAndPackFloat32( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
1270 | |
1271 | } | |
1272 | ||
1273 | /* | |
1274 | ------------------------------------------------------------------------------- | |
1275 | Returns the result of dividing the single-precision floating-point value `a' | |
1276 | by the corresponding value `b'. The operation is performed according to the | |
1277 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1278 | ------------------------------------------------------------------------------- | |
1279 | */ | |
f148af25 | 1280 | float32 float32_div( struct roundingData *roundData, float32 a, float32 b ) |
1da177e4 LT |
1281 | { |
1282 | flag aSign, bSign, zSign; | |
1283 | int16 aExp, bExp, zExp; | |
1284 | bits32 aSig, bSig, zSig; | |
1285 | ||
1286 | aSig = extractFloat32Frac( a ); | |
1287 | aExp = extractFloat32Exp( a ); | |
1288 | aSign = extractFloat32Sign( a ); | |
1289 | bSig = extractFloat32Frac( b ); | |
1290 | bExp = extractFloat32Exp( b ); | |
1291 | bSign = extractFloat32Sign( b ); | |
1292 | zSign = aSign ^ bSign; | |
1293 | if ( aExp == 0xFF ) { | |
1294 | if ( aSig ) return propagateFloat32NaN( a, b ); | |
1295 | if ( bExp == 0xFF ) { | |
1296 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
f148af25 | 1297 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1298 | return float32_default_nan; |
1299 | } | |
1300 | return packFloat32( zSign, 0xFF, 0 ); | |
1301 | } | |
1302 | if ( bExp == 0xFF ) { | |
1303 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
1304 | return packFloat32( zSign, 0, 0 ); | |
1305 | } | |
1306 | if ( bExp == 0 ) { | |
1307 | if ( bSig == 0 ) { | |
1308 | if ( ( aExp | aSig ) == 0 ) { | |
f148af25 | 1309 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1310 | return float32_default_nan; |
1311 | } | |
f148af25 | 1312 | roundData->exception |= float_flag_divbyzero; |
1da177e4 LT |
1313 | return packFloat32( zSign, 0xFF, 0 ); |
1314 | } | |
1315 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1316 | } | |
1317 | if ( aExp == 0 ) { | |
1318 | if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); | |
1319 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1320 | } | |
1321 | zExp = aExp - bExp + 0x7D; | |
1322 | aSig = ( aSig | 0x00800000 )<<7; | |
1323 | bSig = ( bSig | 0x00800000 )<<8; | |
1324 | if ( bSig <= ( aSig + aSig ) ) { | |
1325 | aSig >>= 1; | |
1326 | ++zExp; | |
1327 | } | |
c1241c4c NP |
1328 | { |
1329 | bits64 tmp = ( (bits64) aSig )<<32; | |
1330 | do_div( tmp, bSig ); | |
1331 | zSig = tmp; | |
1332 | } | |
1da177e4 LT |
1333 | if ( ( zSig & 0x3F ) == 0 ) { |
1334 | zSig |= ( ( (bits64) bSig ) * zSig != ( (bits64) aSig )<<32 ); | |
1335 | } | |
f148af25 | 1336 | return roundAndPackFloat32( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
1337 | |
1338 | } | |
1339 | ||
1340 | /* | |
1341 | ------------------------------------------------------------------------------- | |
1342 | Returns the remainder of the single-precision floating-point value `a' | |
1343 | with respect to the corresponding value `b'. The operation is performed | |
1344 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1345 | ------------------------------------------------------------------------------- | |
1346 | */ | |
f148af25 | 1347 | float32 float32_rem( struct roundingData *roundData, float32 a, float32 b ) |
1da177e4 LT |
1348 | { |
1349 | flag aSign, bSign, zSign; | |
1350 | int16 aExp, bExp, expDiff; | |
1351 | bits32 aSig, bSig; | |
1352 | bits32 q; | |
1353 | bits64 aSig64, bSig64, q64; | |
1354 | bits32 alternateASig; | |
1355 | sbits32 sigMean; | |
1356 | ||
1357 | aSig = extractFloat32Frac( a ); | |
1358 | aExp = extractFloat32Exp( a ); | |
1359 | aSign = extractFloat32Sign( a ); | |
1360 | bSig = extractFloat32Frac( b ); | |
1361 | bExp = extractFloat32Exp( b ); | |
1362 | bSign = extractFloat32Sign( b ); | |
1363 | if ( aExp == 0xFF ) { | |
1364 | if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { | |
1365 | return propagateFloat32NaN( a, b ); | |
1366 | } | |
f148af25 | 1367 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1368 | return float32_default_nan; |
1369 | } | |
1370 | if ( bExp == 0xFF ) { | |
1371 | if ( bSig ) return propagateFloat32NaN( a, b ); | |
1372 | return a; | |
1373 | } | |
1374 | if ( bExp == 0 ) { | |
1375 | if ( bSig == 0 ) { | |
f148af25 | 1376 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1377 | return float32_default_nan; |
1378 | } | |
1379 | normalizeFloat32Subnormal( bSig, &bExp, &bSig ); | |
1380 | } | |
1381 | if ( aExp == 0 ) { | |
1382 | if ( aSig == 0 ) return a; | |
1383 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1384 | } | |
1385 | expDiff = aExp - bExp; | |
1386 | aSig |= 0x00800000; | |
1387 | bSig |= 0x00800000; | |
1388 | if ( expDiff < 32 ) { | |
1389 | aSig <<= 8; | |
1390 | bSig <<= 8; | |
1391 | if ( expDiff < 0 ) { | |
1392 | if ( expDiff < -1 ) return a; | |
1393 | aSig >>= 1; | |
1394 | } | |
1395 | q = ( bSig <= aSig ); | |
1396 | if ( q ) aSig -= bSig; | |
1397 | if ( 0 < expDiff ) { | |
c1241c4c NP |
1398 | bits64 tmp = ( (bits64) aSig )<<32; |
1399 | do_div( tmp, bSig ); | |
1400 | q = tmp; | |
1da177e4 LT |
1401 | q >>= 32 - expDiff; |
1402 | bSig >>= 2; | |
1403 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
1404 | } | |
1405 | else { | |
1406 | aSig >>= 2; | |
1407 | bSig >>= 2; | |
1408 | } | |
1409 | } | |
1410 | else { | |
1411 | if ( bSig <= aSig ) aSig -= bSig; | |
1412 | aSig64 = ( (bits64) aSig )<<40; | |
1413 | bSig64 = ( (bits64) bSig )<<40; | |
1414 | expDiff -= 64; | |
1415 | while ( 0 < expDiff ) { | |
1416 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
1417 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
1418 | aSig64 = - ( ( bSig * q64 )<<38 ); | |
1419 | expDiff -= 62; | |
1420 | } | |
1421 | expDiff += 64; | |
1422 | q64 = estimateDiv128To64( aSig64, 0, bSig64 ); | |
1423 | q64 = ( 2 < q64 ) ? q64 - 2 : 0; | |
1424 | q = q64>>( 64 - expDiff ); | |
1425 | bSig <<= 6; | |
1426 | aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; | |
1427 | } | |
1428 | do { | |
1429 | alternateASig = aSig; | |
1430 | ++q; | |
1431 | aSig -= bSig; | |
1432 | } while ( 0 <= (sbits32) aSig ); | |
1433 | sigMean = aSig + alternateASig; | |
1434 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
1435 | aSig = alternateASig; | |
1436 | } | |
1437 | zSign = ( (sbits32) aSig < 0 ); | |
1438 | if ( zSign ) aSig = - aSig; | |
f148af25 | 1439 | return normalizeRoundAndPackFloat32( roundData, aSign ^ zSign, bExp, aSig ); |
1da177e4 LT |
1440 | |
1441 | } | |
1442 | ||
1443 | /* | |
1444 | ------------------------------------------------------------------------------- | |
1445 | Returns the square root of the single-precision floating-point value `a'. | |
1446 | The operation is performed according to the IEC/IEEE Standard for Binary | |
1447 | Floating-point Arithmetic. | |
1448 | ------------------------------------------------------------------------------- | |
1449 | */ | |
f148af25 | 1450 | float32 float32_sqrt( struct roundingData *roundData, float32 a ) |
1da177e4 LT |
1451 | { |
1452 | flag aSign; | |
1453 | int16 aExp, zExp; | |
1454 | bits32 aSig, zSig; | |
1455 | bits64 rem, term; | |
1456 | ||
1457 | aSig = extractFloat32Frac( a ); | |
1458 | aExp = extractFloat32Exp( a ); | |
1459 | aSign = extractFloat32Sign( a ); | |
1460 | if ( aExp == 0xFF ) { | |
1461 | if ( aSig ) return propagateFloat32NaN( a, 0 ); | |
1462 | if ( ! aSign ) return a; | |
f148af25 | 1463 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1464 | return float32_default_nan; |
1465 | } | |
1466 | if ( aSign ) { | |
1467 | if ( ( aExp | aSig ) == 0 ) return a; | |
f148af25 | 1468 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
1469 | return float32_default_nan; |
1470 | } | |
1471 | if ( aExp == 0 ) { | |
1472 | if ( aSig == 0 ) return 0; | |
1473 | normalizeFloat32Subnormal( aSig, &aExp, &aSig ); | |
1474 | } | |
1475 | zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; | |
1476 | aSig = ( aSig | 0x00800000 )<<8; | |
1477 | zSig = estimateSqrt32( aExp, aSig ) + 2; | |
1478 | if ( ( zSig & 0x7F ) <= 5 ) { | |
1479 | if ( zSig < 2 ) { | |
1480 | zSig = 0xFFFFFFFF; | |
1481 | } | |
1482 | else { | |
1483 | aSig >>= aExp & 1; | |
1484 | term = ( (bits64) zSig ) * zSig; | |
1485 | rem = ( ( (bits64) aSig )<<32 ) - term; | |
1486 | while ( (sbits64) rem < 0 ) { | |
1487 | --zSig; | |
1488 | rem += ( ( (bits64) zSig )<<1 ) | 1; | |
1489 | } | |
1490 | zSig |= ( rem != 0 ); | |
1491 | } | |
1492 | } | |
1493 | shift32RightJamming( zSig, 1, &zSig ); | |
f148af25 | 1494 | return roundAndPackFloat32( roundData, 0, zExp, zSig ); |
1da177e4 LT |
1495 | |
1496 | } | |
1497 | ||
1498 | /* | |
1499 | ------------------------------------------------------------------------------- | |
1500 | Returns 1 if the single-precision floating-point value `a' is equal to the | |
1501 | corresponding value `b', and 0 otherwise. The comparison is performed | |
1502 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1503 | ------------------------------------------------------------------------------- | |
1504 | */ | |
1505 | flag float32_eq( float32 a, float32 b ) | |
1506 | { | |
1507 | ||
1508 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1509 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1510 | ) { | |
1511 | if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { | |
1512 | float_raise( float_flag_invalid ); | |
1513 | } | |
1514 | return 0; | |
1515 | } | |
1516 | return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
1517 | ||
1518 | } | |
1519 | ||
1520 | /* | |
1521 | ------------------------------------------------------------------------------- | |
1522 | Returns 1 if the single-precision floating-point value `a' is less than or | |
1523 | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
1524 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
1525 | Arithmetic. | |
1526 | ------------------------------------------------------------------------------- | |
1527 | */ | |
1528 | flag float32_le( float32 a, float32 b ) | |
1529 | { | |
1530 | flag aSign, bSign; | |
1531 | ||
1532 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1533 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1534 | ) { | |
1535 | float_raise( float_flag_invalid ); | |
1536 | return 0; | |
1537 | } | |
1538 | aSign = extractFloat32Sign( a ); | |
1539 | bSign = extractFloat32Sign( b ); | |
1540 | if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
1541 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
1542 | ||
1543 | } | |
1544 | ||
1545 | /* | |
1546 | ------------------------------------------------------------------------------- | |
1547 | Returns 1 if the single-precision floating-point value `a' is less than | |
1548 | the corresponding value `b', and 0 otherwise. The comparison is performed | |
1549 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1550 | ------------------------------------------------------------------------------- | |
1551 | */ | |
1552 | flag float32_lt( float32 a, float32 b ) | |
1553 | { | |
1554 | flag aSign, bSign; | |
1555 | ||
1556 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1557 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1558 | ) { | |
1559 | float_raise( float_flag_invalid ); | |
1560 | return 0; | |
1561 | } | |
1562 | aSign = extractFloat32Sign( a ); | |
1563 | bSign = extractFloat32Sign( b ); | |
1564 | if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); | |
1565 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
1566 | ||
1567 | } | |
1568 | ||
1569 | /* | |
1570 | ------------------------------------------------------------------------------- | |
1571 | Returns 1 if the single-precision floating-point value `a' is equal to the | |
1572 | corresponding value `b', and 0 otherwise. The invalid exception is raised | |
1573 | if either operand is a NaN. Otherwise, the comparison is performed | |
1574 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1575 | ------------------------------------------------------------------------------- | |
1576 | */ | |
1577 | flag float32_eq_signaling( float32 a, float32 b ) | |
1578 | { | |
1579 | ||
1580 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1581 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1582 | ) { | |
1583 | float_raise( float_flag_invalid ); | |
1584 | return 0; | |
1585 | } | |
1586 | return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
1587 | ||
1588 | } | |
1589 | ||
1590 | /* | |
1591 | ------------------------------------------------------------------------------- | |
1592 | Returns 1 if the single-precision floating-point value `a' is less than or | |
1593 | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
1594 | cause an exception. Otherwise, the comparison is performed according to the | |
1595 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
1596 | ------------------------------------------------------------------------------- | |
1597 | */ | |
1598 | flag float32_le_quiet( float32 a, float32 b ) | |
1599 | { | |
1600 | flag aSign, bSign; | |
1601 | //int16 aExp, bExp; | |
1602 | ||
1603 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1604 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1605 | ) { | |
54738e82 | 1606 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
1607 | return 0; |
1608 | } | |
1609 | aSign = extractFloat32Sign( a ); | |
1610 | bSign = extractFloat32Sign( b ); | |
1611 | if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); | |
1612 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
1613 | ||
1614 | } | |
1615 | ||
1616 | /* | |
1617 | ------------------------------------------------------------------------------- | |
1618 | Returns 1 if the single-precision floating-point value `a' is less than | |
1619 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
1620 | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
1621 | Standard for Binary Floating-point Arithmetic. | |
1622 | ------------------------------------------------------------------------------- | |
1623 | */ | |
1624 | flag float32_lt_quiet( float32 a, float32 b ) | |
1625 | { | |
1626 | flag aSign, bSign; | |
1627 | ||
1628 | if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) | |
1629 | || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) | |
1630 | ) { | |
54738e82 | 1631 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
1632 | return 0; |
1633 | } | |
1634 | aSign = extractFloat32Sign( a ); | |
1635 | bSign = extractFloat32Sign( b ); | |
1636 | if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); | |
1637 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
1638 | ||
1639 | } | |
1640 | ||
1641 | /* | |
1642 | ------------------------------------------------------------------------------- | |
1643 | Returns the result of converting the double-precision floating-point value | |
1644 | `a' to the 32-bit two's complement integer format. The conversion is | |
1645 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
1646 | Arithmetic---which means in particular that the conversion is rounded | |
1647 | according to the current rounding mode. If `a' is a NaN, the largest | |
1648 | positive integer is returned. Otherwise, if the conversion overflows, the | |
1649 | largest integer with the same sign as `a' is returned. | |
1650 | ------------------------------------------------------------------------------- | |
1651 | */ | |
f148af25 | 1652 | int32 float64_to_int32( struct roundingData *roundData, float64 a ) |
1da177e4 LT |
1653 | { |
1654 | flag aSign; | |
1655 | int16 aExp, shiftCount; | |
1656 | bits64 aSig; | |
1657 | ||
1658 | aSig = extractFloat64Frac( a ); | |
1659 | aExp = extractFloat64Exp( a ); | |
1660 | aSign = extractFloat64Sign( a ); | |
1661 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
1662 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
1663 | shiftCount = 0x42C - aExp; | |
1664 | if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); | |
f148af25 | 1665 | return roundAndPackInt32( roundData, aSign, aSig ); |
1da177e4 LT |
1666 | |
1667 | } | |
1668 | ||
1669 | /* | |
1670 | ------------------------------------------------------------------------------- | |
1671 | Returns the result of converting the double-precision floating-point value | |
1672 | `a' to the 32-bit two's complement integer format. The conversion is | |
1673 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
1674 | Arithmetic, except that the conversion is always rounded toward zero. If | |
1675 | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
1676 | conversion overflows, the largest integer with the same sign as `a' is | |
1677 | returned. | |
1678 | ------------------------------------------------------------------------------- | |
1679 | */ | |
1680 | int32 float64_to_int32_round_to_zero( float64 a ) | |
1681 | { | |
1682 | flag aSign; | |
1683 | int16 aExp, shiftCount; | |
1684 | bits64 aSig, savedASig; | |
1685 | int32 z; | |
1686 | ||
1687 | aSig = extractFloat64Frac( a ); | |
1688 | aExp = extractFloat64Exp( a ); | |
1689 | aSign = extractFloat64Sign( a ); | |
1690 | shiftCount = 0x433 - aExp; | |
1691 | if ( shiftCount < 21 ) { | |
1692 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
1693 | goto invalid; | |
1694 | } | |
1695 | else if ( 52 < shiftCount ) { | |
f148af25 | 1696 | if ( aExp || aSig ) float_raise( float_flag_inexact ); |
1da177e4 LT |
1697 | return 0; |
1698 | } | |
1699 | aSig |= LIT64( 0x0010000000000000 ); | |
1700 | savedASig = aSig; | |
1701 | aSig >>= shiftCount; | |
1702 | z = aSig; | |
1703 | if ( aSign ) z = - z; | |
1704 | if ( ( z < 0 ) ^ aSign ) { | |
1705 | invalid: | |
f148af25 | 1706 | float_raise( float_flag_invalid ); |
1da177e4 LT |
1707 | return aSign ? 0x80000000 : 0x7FFFFFFF; |
1708 | } | |
1709 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
f148af25 | 1710 | float_raise( float_flag_inexact ); |
1da177e4 LT |
1711 | } |
1712 | return z; | |
1713 | ||
1714 | } | |
1715 | ||
1716 | /* | |
1717 | ------------------------------------------------------------------------------- | |
1718 | Returns the result of converting the double-precision floating-point value | |
1719 | `a' to the 32-bit two's complement unsigned integer format. The conversion | |
1720 | is performed according to the IEC/IEEE Standard for Binary Floating-point | |
1721 | Arithmetic---which means in particular that the conversion is rounded | |
1722 | according to the current rounding mode. If `a' is a NaN, the largest | |
1723 | positive integer is returned. Otherwise, if the conversion overflows, the | |
1724 | largest positive integer is returned. | |
1725 | ------------------------------------------------------------------------------- | |
1726 | */ | |
f148af25 | 1727 | int32 float64_to_uint32( struct roundingData *roundData, float64 a ) |
1da177e4 LT |
1728 | { |
1729 | flag aSign; | |
1730 | int16 aExp, shiftCount; | |
1731 | bits64 aSig; | |
1732 | ||
1733 | aSig = extractFloat64Frac( a ); | |
1734 | aExp = extractFloat64Exp( a ); | |
1735 | aSign = 0; //extractFloat64Sign( a ); | |
1736 | //if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
1737 | if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); | |
1738 | shiftCount = 0x42C - aExp; | |
1739 | if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); | |
f148af25 | 1740 | return roundAndPackInt32( roundData, aSign, aSig ); |
1da177e4 LT |
1741 | } |
1742 | ||
1743 | /* | |
1744 | ------------------------------------------------------------------------------- | |
1745 | Returns the result of converting the double-precision floating-point value | |
1746 | `a' to the 32-bit two's complement integer format. The conversion is | |
1747 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
1748 | Arithmetic, except that the conversion is always rounded toward zero. If | |
1749 | `a' is a NaN, the largest positive integer is returned. Otherwise, if the | |
1750 | conversion overflows, the largest positive integer is returned. | |
1751 | ------------------------------------------------------------------------------- | |
1752 | */ | |
1753 | int32 float64_to_uint32_round_to_zero( float64 a ) | |
1754 | { | |
1755 | flag aSign; | |
1756 | int16 aExp, shiftCount; | |
1757 | bits64 aSig, savedASig; | |
1758 | int32 z; | |
1759 | ||
1760 | aSig = extractFloat64Frac( a ); | |
1761 | aExp = extractFloat64Exp( a ); | |
1762 | aSign = extractFloat64Sign( a ); | |
1763 | shiftCount = 0x433 - aExp; | |
1764 | if ( shiftCount < 21 ) { | |
1765 | if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; | |
1766 | goto invalid; | |
1767 | } | |
1768 | else if ( 52 < shiftCount ) { | |
f148af25 | 1769 | if ( aExp || aSig ) float_raise( float_flag_inexact ); |
1da177e4 LT |
1770 | return 0; |
1771 | } | |
1772 | aSig |= LIT64( 0x0010000000000000 ); | |
1773 | savedASig = aSig; | |
1774 | aSig >>= shiftCount; | |
1775 | z = aSig; | |
1776 | if ( aSign ) z = - z; | |
1777 | if ( ( z < 0 ) ^ aSign ) { | |
1778 | invalid: | |
f148af25 | 1779 | float_raise( float_flag_invalid ); |
1da177e4 LT |
1780 | return aSign ? 0x80000000 : 0x7FFFFFFF; |
1781 | } | |
1782 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
f148af25 | 1783 | float_raise( float_flag_inexact ); |
1da177e4 LT |
1784 | } |
1785 | return z; | |
1786 | } | |
1787 | ||
1788 | /* | |
1789 | ------------------------------------------------------------------------------- | |
1790 | Returns the result of converting the double-precision floating-point value | |
1791 | `a' to the single-precision floating-point format. The conversion is | |
1792 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
1793 | Arithmetic. | |
1794 | ------------------------------------------------------------------------------- | |
1795 | */ | |
f148af25 | 1796 | float32 float64_to_float32( struct roundingData *roundData, float64 a ) |
1da177e4 LT |
1797 | { |
1798 | flag aSign; | |
1799 | int16 aExp; | |
1800 | bits64 aSig; | |
1801 | bits32 zSig; | |
1802 | ||
1803 | aSig = extractFloat64Frac( a ); | |
1804 | aExp = extractFloat64Exp( a ); | |
1805 | aSign = extractFloat64Sign( a ); | |
1806 | if ( aExp == 0x7FF ) { | |
1807 | if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a ) ); | |
1808 | return packFloat32( aSign, 0xFF, 0 ); | |
1809 | } | |
1810 | shift64RightJamming( aSig, 22, &aSig ); | |
1811 | zSig = aSig; | |
1812 | if ( aExp || zSig ) { | |
1813 | zSig |= 0x40000000; | |
1814 | aExp -= 0x381; | |
1815 | } | |
f148af25 | 1816 | return roundAndPackFloat32( roundData, aSign, aExp, zSig ); |
1da177e4 LT |
1817 | |
1818 | } | |
1819 | ||
1820 | #ifdef FLOATX80 | |
1821 | ||
1822 | /* | |
1823 | ------------------------------------------------------------------------------- | |
1824 | Returns the result of converting the double-precision floating-point value | |
1825 | `a' to the extended double-precision floating-point format. The conversion | |
1826 | is performed according to the IEC/IEEE Standard for Binary Floating-point | |
1827 | Arithmetic. | |
1828 | ------------------------------------------------------------------------------- | |
1829 | */ | |
1830 | floatx80 float64_to_floatx80( float64 a ) | |
1831 | { | |
1832 | flag aSign; | |
1833 | int16 aExp; | |
1834 | bits64 aSig; | |
1835 | ||
1836 | aSig = extractFloat64Frac( a ); | |
1837 | aExp = extractFloat64Exp( a ); | |
1838 | aSign = extractFloat64Sign( a ); | |
1839 | if ( aExp == 0x7FF ) { | |
1840 | if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) ); | |
1841 | return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
1842 | } | |
1843 | if ( aExp == 0 ) { | |
1844 | if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); | |
1845 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
1846 | } | |
1847 | return | |
1848 | packFloatx80( | |
1849 | aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); | |
1850 | ||
1851 | } | |
1852 | ||
1853 | #endif | |
1854 | ||
1855 | /* | |
1856 | ------------------------------------------------------------------------------- | |
1857 | Rounds the double-precision floating-point value `a' to an integer, and | |
1858 | returns the result as a double-precision floating-point value. The | |
1859 | operation is performed according to the IEC/IEEE Standard for Binary | |
1860 | Floating-point Arithmetic. | |
1861 | ------------------------------------------------------------------------------- | |
1862 | */ | |
f148af25 | 1863 | float64 float64_round_to_int( struct roundingData *roundData, float64 a ) |
1da177e4 LT |
1864 | { |
1865 | flag aSign; | |
1866 | int16 aExp; | |
1867 | bits64 lastBitMask, roundBitsMask; | |
1868 | int8 roundingMode; | |
1869 | float64 z; | |
1870 | ||
1871 | aExp = extractFloat64Exp( a ); | |
1872 | if ( 0x433 <= aExp ) { | |
1873 | if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { | |
1874 | return propagateFloat64NaN( a, a ); | |
1875 | } | |
1876 | return a; | |
1877 | } | |
1878 | if ( aExp <= 0x3FE ) { | |
1879 | if ( (bits64) ( a<<1 ) == 0 ) return a; | |
f148af25 | 1880 | roundData->exception |= float_flag_inexact; |
1da177e4 | 1881 | aSign = extractFloat64Sign( a ); |
f148af25 | 1882 | switch ( roundData->mode ) { |
1da177e4 LT |
1883 | case float_round_nearest_even: |
1884 | if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { | |
1885 | return packFloat64( aSign, 0x3FF, 0 ); | |
1886 | } | |
1887 | break; | |
1888 | case float_round_down: | |
1889 | return aSign ? LIT64( 0xBFF0000000000000 ) : 0; | |
1890 | case float_round_up: | |
1891 | return | |
1892 | aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ); | |
1893 | } | |
1894 | return packFloat64( aSign, 0, 0 ); | |
1895 | } | |
1896 | lastBitMask = 1; | |
1897 | lastBitMask <<= 0x433 - aExp; | |
1898 | roundBitsMask = lastBitMask - 1; | |
1899 | z = a; | |
f148af25 | 1900 | roundingMode = roundData->mode; |
1da177e4 LT |
1901 | if ( roundingMode == float_round_nearest_even ) { |
1902 | z += lastBitMask>>1; | |
1903 | if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; | |
1904 | } | |
1905 | else if ( roundingMode != float_round_to_zero ) { | |
1906 | if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
1907 | z += roundBitsMask; | |
1908 | } | |
1909 | } | |
1910 | z &= ~ roundBitsMask; | |
f148af25 | 1911 | if ( z != a ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
1912 | return z; |
1913 | ||
1914 | } | |
1915 | ||
1916 | /* | |
1917 | ------------------------------------------------------------------------------- | |
1918 | Returns the result of adding the absolute values of the double-precision | |
1919 | floating-point values `a' and `b'. If `zSign' is true, the sum is negated | |
1920 | before being returned. `zSign' is ignored if the result is a NaN. The | |
1921 | addition is performed according to the IEC/IEEE Standard for Binary | |
1922 | Floating-point Arithmetic. | |
1923 | ------------------------------------------------------------------------------- | |
1924 | */ | |
f148af25 | 1925 | static float64 addFloat64Sigs( struct roundingData *roundData, float64 a, float64 b, flag zSign ) |
1da177e4 LT |
1926 | { |
1927 | int16 aExp, bExp, zExp; | |
1928 | bits64 aSig, bSig, zSig; | |
1929 | int16 expDiff; | |
1930 | ||
1931 | aSig = extractFloat64Frac( a ); | |
1932 | aExp = extractFloat64Exp( a ); | |
1933 | bSig = extractFloat64Frac( b ); | |
1934 | bExp = extractFloat64Exp( b ); | |
1935 | expDiff = aExp - bExp; | |
1936 | aSig <<= 9; | |
1937 | bSig <<= 9; | |
1938 | if ( 0 < expDiff ) { | |
1939 | if ( aExp == 0x7FF ) { | |
1940 | if ( aSig ) return propagateFloat64NaN( a, b ); | |
1941 | return a; | |
1942 | } | |
1943 | if ( bExp == 0 ) { | |
1944 | --expDiff; | |
1945 | } | |
1946 | else { | |
1947 | bSig |= LIT64( 0x2000000000000000 ); | |
1948 | } | |
1949 | shift64RightJamming( bSig, expDiff, &bSig ); | |
1950 | zExp = aExp; | |
1951 | } | |
1952 | else if ( expDiff < 0 ) { | |
1953 | if ( bExp == 0x7FF ) { | |
1954 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
1955 | return packFloat64( zSign, 0x7FF, 0 ); | |
1956 | } | |
1957 | if ( aExp == 0 ) { | |
1958 | ++expDiff; | |
1959 | } | |
1960 | else { | |
1961 | aSig |= LIT64( 0x2000000000000000 ); | |
1962 | } | |
1963 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
1964 | zExp = bExp; | |
1965 | } | |
1966 | else { | |
1967 | if ( aExp == 0x7FF ) { | |
1968 | if ( aSig | bSig ) return propagateFloat64NaN( a, b ); | |
1969 | return a; | |
1970 | } | |
1971 | if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); | |
1972 | zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; | |
1973 | zExp = aExp; | |
1974 | goto roundAndPack; | |
1975 | } | |
1976 | aSig |= LIT64( 0x2000000000000000 ); | |
1977 | zSig = ( aSig + bSig )<<1; | |
1978 | --zExp; | |
1979 | if ( (sbits64) zSig < 0 ) { | |
1980 | zSig = aSig + bSig; | |
1981 | ++zExp; | |
1982 | } | |
1983 | roundAndPack: | |
f148af25 | 1984 | return roundAndPackFloat64( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
1985 | |
1986 | } | |
1987 | ||
1988 | /* | |
1989 | ------------------------------------------------------------------------------- | |
1990 | Returns the result of subtracting the absolute values of the double- | |
1991 | precision floating-point values `a' and `b'. If `zSign' is true, the | |
1992 | difference is negated before being returned. `zSign' is ignored if the | |
1993 | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
1994 | Standard for Binary Floating-point Arithmetic. | |
1995 | ------------------------------------------------------------------------------- | |
1996 | */ | |
f148af25 | 1997 | static float64 subFloat64Sigs( struct roundingData *roundData, float64 a, float64 b, flag zSign ) |
1da177e4 LT |
1998 | { |
1999 | int16 aExp, bExp, zExp; | |
2000 | bits64 aSig, bSig, zSig; | |
2001 | int16 expDiff; | |
2002 | ||
2003 | aSig = extractFloat64Frac( a ); | |
2004 | aExp = extractFloat64Exp( a ); | |
2005 | bSig = extractFloat64Frac( b ); | |
2006 | bExp = extractFloat64Exp( b ); | |
2007 | expDiff = aExp - bExp; | |
2008 | aSig <<= 10; | |
2009 | bSig <<= 10; | |
2010 | if ( 0 < expDiff ) goto aExpBigger; | |
2011 | if ( expDiff < 0 ) goto bExpBigger; | |
2012 | if ( aExp == 0x7FF ) { | |
2013 | if ( aSig | bSig ) return propagateFloat64NaN( a, b ); | |
f148af25 | 2014 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2015 | return float64_default_nan; |
2016 | } | |
2017 | if ( aExp == 0 ) { | |
2018 | aExp = 1; | |
2019 | bExp = 1; | |
2020 | } | |
2021 | if ( bSig < aSig ) goto aBigger; | |
2022 | if ( aSig < bSig ) goto bBigger; | |
f148af25 | 2023 | return packFloat64( roundData->mode == float_round_down, 0, 0 ); |
1da177e4 LT |
2024 | bExpBigger: |
2025 | if ( bExp == 0x7FF ) { | |
2026 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
2027 | return packFloat64( zSign ^ 1, 0x7FF, 0 ); | |
2028 | } | |
2029 | if ( aExp == 0 ) { | |
2030 | ++expDiff; | |
2031 | } | |
2032 | else { | |
2033 | aSig |= LIT64( 0x4000000000000000 ); | |
2034 | } | |
2035 | shift64RightJamming( aSig, - expDiff, &aSig ); | |
2036 | bSig |= LIT64( 0x4000000000000000 ); | |
2037 | bBigger: | |
2038 | zSig = bSig - aSig; | |
2039 | zExp = bExp; | |
2040 | zSign ^= 1; | |
2041 | goto normalizeRoundAndPack; | |
2042 | aExpBigger: | |
2043 | if ( aExp == 0x7FF ) { | |
2044 | if ( aSig ) return propagateFloat64NaN( a, b ); | |
2045 | return a; | |
2046 | } | |
2047 | if ( bExp == 0 ) { | |
2048 | --expDiff; | |
2049 | } | |
2050 | else { | |
2051 | bSig |= LIT64( 0x4000000000000000 ); | |
2052 | } | |
2053 | shift64RightJamming( bSig, expDiff, &bSig ); | |
2054 | aSig |= LIT64( 0x4000000000000000 ); | |
2055 | aBigger: | |
2056 | zSig = aSig - bSig; | |
2057 | zExp = aExp; | |
2058 | normalizeRoundAndPack: | |
2059 | --zExp; | |
f148af25 | 2060 | return normalizeRoundAndPackFloat64( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
2061 | |
2062 | } | |
2063 | ||
2064 | /* | |
2065 | ------------------------------------------------------------------------------- | |
2066 | Returns the result of adding the double-precision floating-point values `a' | |
2067 | and `b'. The operation is performed according to the IEC/IEEE Standard for | |
2068 | Binary Floating-point Arithmetic. | |
2069 | ------------------------------------------------------------------------------- | |
2070 | */ | |
f148af25 | 2071 | float64 float64_add( struct roundingData *roundData, float64 a, float64 b ) |
1da177e4 LT |
2072 | { |
2073 | flag aSign, bSign; | |
2074 | ||
2075 | aSign = extractFloat64Sign( a ); | |
2076 | bSign = extractFloat64Sign( b ); | |
2077 | if ( aSign == bSign ) { | |
f148af25 | 2078 | return addFloat64Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2079 | } |
2080 | else { | |
f148af25 | 2081 | return subFloat64Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2082 | } |
2083 | ||
2084 | } | |
2085 | ||
2086 | /* | |
2087 | ------------------------------------------------------------------------------- | |
2088 | Returns the result of subtracting the double-precision floating-point values | |
2089 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
2090 | for Binary Floating-point Arithmetic. | |
2091 | ------------------------------------------------------------------------------- | |
2092 | */ | |
f148af25 | 2093 | float64 float64_sub( struct roundingData *roundData, float64 a, float64 b ) |
1da177e4 LT |
2094 | { |
2095 | flag aSign, bSign; | |
2096 | ||
2097 | aSign = extractFloat64Sign( a ); | |
2098 | bSign = extractFloat64Sign( b ); | |
2099 | if ( aSign == bSign ) { | |
f148af25 | 2100 | return subFloat64Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2101 | } |
2102 | else { | |
f148af25 | 2103 | return addFloat64Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2104 | } |
2105 | ||
2106 | } | |
2107 | ||
2108 | /* | |
2109 | ------------------------------------------------------------------------------- | |
2110 | Returns the result of multiplying the double-precision floating-point values | |
2111 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard | |
2112 | for Binary Floating-point Arithmetic. | |
2113 | ------------------------------------------------------------------------------- | |
2114 | */ | |
f148af25 | 2115 | float64 float64_mul( struct roundingData *roundData, float64 a, float64 b ) |
1da177e4 LT |
2116 | { |
2117 | flag aSign, bSign, zSign; | |
2118 | int16 aExp, bExp, zExp; | |
2119 | bits64 aSig, bSig, zSig0, zSig1; | |
2120 | ||
2121 | aSig = extractFloat64Frac( a ); | |
2122 | aExp = extractFloat64Exp( a ); | |
2123 | aSign = extractFloat64Sign( a ); | |
2124 | bSig = extractFloat64Frac( b ); | |
2125 | bExp = extractFloat64Exp( b ); | |
2126 | bSign = extractFloat64Sign( b ); | |
2127 | zSign = aSign ^ bSign; | |
2128 | if ( aExp == 0x7FF ) { | |
2129 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
2130 | return propagateFloat64NaN( a, b ); | |
2131 | } | |
2132 | if ( ( bExp | bSig ) == 0 ) { | |
f148af25 | 2133 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2134 | return float64_default_nan; |
2135 | } | |
2136 | return packFloat64( zSign, 0x7FF, 0 ); | |
2137 | } | |
2138 | if ( bExp == 0x7FF ) { | |
2139 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
2140 | if ( ( aExp | aSig ) == 0 ) { | |
f148af25 | 2141 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2142 | return float64_default_nan; |
2143 | } | |
2144 | return packFloat64( zSign, 0x7FF, 0 ); | |
2145 | } | |
2146 | if ( aExp == 0 ) { | |
2147 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2148 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2149 | } | |
2150 | if ( bExp == 0 ) { | |
2151 | if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2152 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2153 | } | |
2154 | zExp = aExp + bExp - 0x3FF; | |
2155 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
2156 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2157 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
2158 | zSig0 |= ( zSig1 != 0 ); | |
2159 | if ( 0 <= (sbits64) ( zSig0<<1 ) ) { | |
2160 | zSig0 <<= 1; | |
2161 | --zExp; | |
2162 | } | |
f148af25 | 2163 | return roundAndPackFloat64( roundData, zSign, zExp, zSig0 ); |
1da177e4 LT |
2164 | |
2165 | } | |
2166 | ||
2167 | /* | |
2168 | ------------------------------------------------------------------------------- | |
2169 | Returns the result of dividing the double-precision floating-point value `a' | |
2170 | by the corresponding value `b'. The operation is performed according to | |
2171 | the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2172 | ------------------------------------------------------------------------------- | |
2173 | */ | |
f148af25 | 2174 | float64 float64_div( struct roundingData *roundData, float64 a, float64 b ) |
1da177e4 LT |
2175 | { |
2176 | flag aSign, bSign, zSign; | |
2177 | int16 aExp, bExp, zExp; | |
2178 | bits64 aSig, bSig, zSig; | |
2179 | bits64 rem0, rem1; | |
2180 | bits64 term0, term1; | |
2181 | ||
2182 | aSig = extractFloat64Frac( a ); | |
2183 | aExp = extractFloat64Exp( a ); | |
2184 | aSign = extractFloat64Sign( a ); | |
2185 | bSig = extractFloat64Frac( b ); | |
2186 | bExp = extractFloat64Exp( b ); | |
2187 | bSign = extractFloat64Sign( b ); | |
2188 | zSign = aSign ^ bSign; | |
2189 | if ( aExp == 0x7FF ) { | |
2190 | if ( aSig ) return propagateFloat64NaN( a, b ); | |
2191 | if ( bExp == 0x7FF ) { | |
2192 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
f148af25 | 2193 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2194 | return float64_default_nan; |
2195 | } | |
2196 | return packFloat64( zSign, 0x7FF, 0 ); | |
2197 | } | |
2198 | if ( bExp == 0x7FF ) { | |
2199 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
2200 | return packFloat64( zSign, 0, 0 ); | |
2201 | } | |
2202 | if ( bExp == 0 ) { | |
2203 | if ( bSig == 0 ) { | |
2204 | if ( ( aExp | aSig ) == 0 ) { | |
f148af25 | 2205 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2206 | return float64_default_nan; |
2207 | } | |
f148af25 | 2208 | roundData->exception |= float_flag_divbyzero; |
1da177e4 LT |
2209 | return packFloat64( zSign, 0x7FF, 0 ); |
2210 | } | |
2211 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2212 | } | |
2213 | if ( aExp == 0 ) { | |
2214 | if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); | |
2215 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2216 | } | |
2217 | zExp = aExp - bExp + 0x3FD; | |
2218 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; | |
2219 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2220 | if ( bSig <= ( aSig + aSig ) ) { | |
2221 | aSig >>= 1; | |
2222 | ++zExp; | |
2223 | } | |
2224 | zSig = estimateDiv128To64( aSig, 0, bSig ); | |
2225 | if ( ( zSig & 0x1FF ) <= 2 ) { | |
2226 | mul64To128( bSig, zSig, &term0, &term1 ); | |
2227 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
2228 | while ( (sbits64) rem0 < 0 ) { | |
2229 | --zSig; | |
2230 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
2231 | } | |
2232 | zSig |= ( rem1 != 0 ); | |
2233 | } | |
f148af25 | 2234 | return roundAndPackFloat64( roundData, zSign, zExp, zSig ); |
1da177e4 LT |
2235 | |
2236 | } | |
2237 | ||
2238 | /* | |
2239 | ------------------------------------------------------------------------------- | |
2240 | Returns the remainder of the double-precision floating-point value `a' | |
2241 | with respect to the corresponding value `b'. The operation is performed | |
2242 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2243 | ------------------------------------------------------------------------------- | |
2244 | */ | |
f148af25 | 2245 | float64 float64_rem( struct roundingData *roundData, float64 a, float64 b ) |
1da177e4 LT |
2246 | { |
2247 | flag aSign, bSign, zSign; | |
2248 | int16 aExp, bExp, expDiff; | |
2249 | bits64 aSig, bSig; | |
2250 | bits64 q, alternateASig; | |
2251 | sbits64 sigMean; | |
2252 | ||
2253 | aSig = extractFloat64Frac( a ); | |
2254 | aExp = extractFloat64Exp( a ); | |
2255 | aSign = extractFloat64Sign( a ); | |
2256 | bSig = extractFloat64Frac( b ); | |
2257 | bExp = extractFloat64Exp( b ); | |
2258 | bSign = extractFloat64Sign( b ); | |
2259 | if ( aExp == 0x7FF ) { | |
2260 | if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { | |
2261 | return propagateFloat64NaN( a, b ); | |
2262 | } | |
f148af25 | 2263 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2264 | return float64_default_nan; |
2265 | } | |
2266 | if ( bExp == 0x7FF ) { | |
2267 | if ( bSig ) return propagateFloat64NaN( a, b ); | |
2268 | return a; | |
2269 | } | |
2270 | if ( bExp == 0 ) { | |
2271 | if ( bSig == 0 ) { | |
f148af25 | 2272 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2273 | return float64_default_nan; |
2274 | } | |
2275 | normalizeFloat64Subnormal( bSig, &bExp, &bSig ); | |
2276 | } | |
2277 | if ( aExp == 0 ) { | |
2278 | if ( aSig == 0 ) return a; | |
2279 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2280 | } | |
2281 | expDiff = aExp - bExp; | |
2282 | aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; | |
2283 | bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; | |
2284 | if ( expDiff < 0 ) { | |
2285 | if ( expDiff < -1 ) return a; | |
2286 | aSig >>= 1; | |
2287 | } | |
2288 | q = ( bSig <= aSig ); | |
2289 | if ( q ) aSig -= bSig; | |
2290 | expDiff -= 64; | |
2291 | while ( 0 < expDiff ) { | |
2292 | q = estimateDiv128To64( aSig, 0, bSig ); | |
2293 | q = ( 2 < q ) ? q - 2 : 0; | |
2294 | aSig = - ( ( bSig>>2 ) * q ); | |
2295 | expDiff -= 62; | |
2296 | } | |
2297 | expDiff += 64; | |
2298 | if ( 0 < expDiff ) { | |
2299 | q = estimateDiv128To64( aSig, 0, bSig ); | |
2300 | q = ( 2 < q ) ? q - 2 : 0; | |
2301 | q >>= 64 - expDiff; | |
2302 | bSig >>= 2; | |
2303 | aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; | |
2304 | } | |
2305 | else { | |
2306 | aSig >>= 2; | |
2307 | bSig >>= 2; | |
2308 | } | |
2309 | do { | |
2310 | alternateASig = aSig; | |
2311 | ++q; | |
2312 | aSig -= bSig; | |
2313 | } while ( 0 <= (sbits64) aSig ); | |
2314 | sigMean = aSig + alternateASig; | |
2315 | if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { | |
2316 | aSig = alternateASig; | |
2317 | } | |
2318 | zSign = ( (sbits64) aSig < 0 ); | |
2319 | if ( zSign ) aSig = - aSig; | |
f148af25 | 2320 | return normalizeRoundAndPackFloat64( roundData, aSign ^ zSign, bExp, aSig ); |
1da177e4 LT |
2321 | |
2322 | } | |
2323 | ||
2324 | /* | |
2325 | ------------------------------------------------------------------------------- | |
2326 | Returns the square root of the double-precision floating-point value `a'. | |
2327 | The operation is performed according to the IEC/IEEE Standard for Binary | |
2328 | Floating-point Arithmetic. | |
2329 | ------------------------------------------------------------------------------- | |
2330 | */ | |
f148af25 | 2331 | float64 float64_sqrt( struct roundingData *roundData, float64 a ) |
1da177e4 LT |
2332 | { |
2333 | flag aSign; | |
2334 | int16 aExp, zExp; | |
2335 | bits64 aSig, zSig; | |
2336 | bits64 rem0, rem1, term0, term1; //, shiftedRem; | |
2337 | //float64 z; | |
2338 | ||
2339 | aSig = extractFloat64Frac( a ); | |
2340 | aExp = extractFloat64Exp( a ); | |
2341 | aSign = extractFloat64Sign( a ); | |
2342 | if ( aExp == 0x7FF ) { | |
2343 | if ( aSig ) return propagateFloat64NaN( a, a ); | |
2344 | if ( ! aSign ) return a; | |
f148af25 | 2345 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2346 | return float64_default_nan; |
2347 | } | |
2348 | if ( aSign ) { | |
2349 | if ( ( aExp | aSig ) == 0 ) return a; | |
f148af25 | 2350 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2351 | return float64_default_nan; |
2352 | } | |
2353 | if ( aExp == 0 ) { | |
2354 | if ( aSig == 0 ) return 0; | |
2355 | normalizeFloat64Subnormal( aSig, &aExp, &aSig ); | |
2356 | } | |
2357 | zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; | |
2358 | aSig |= LIT64( 0x0010000000000000 ); | |
2359 | zSig = estimateSqrt32( aExp, aSig>>21 ); | |
2360 | zSig <<= 31; | |
2361 | aSig <<= 9 - ( aExp & 1 ); | |
2362 | zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2; | |
2363 | if ( ( zSig & 0x3FF ) <= 5 ) { | |
2364 | if ( zSig < 2 ) { | |
2365 | zSig = LIT64( 0xFFFFFFFFFFFFFFFF ); | |
2366 | } | |
2367 | else { | |
2368 | aSig <<= 2; | |
2369 | mul64To128( zSig, zSig, &term0, &term1 ); | |
2370 | sub128( aSig, 0, term0, term1, &rem0, &rem1 ); | |
2371 | while ( (sbits64) rem0 < 0 ) { | |
2372 | --zSig; | |
2373 | shortShift128Left( 0, zSig, 1, &term0, &term1 ); | |
2374 | term1 |= 1; | |
2375 | add128( rem0, rem1, term0, term1, &rem0, &rem1 ); | |
2376 | } | |
2377 | zSig |= ( ( rem0 | rem1 ) != 0 ); | |
2378 | } | |
2379 | } | |
2380 | shift64RightJamming( zSig, 1, &zSig ); | |
f148af25 | 2381 | return roundAndPackFloat64( roundData, 0, zExp, zSig ); |
1da177e4 LT |
2382 | |
2383 | } | |
2384 | ||
2385 | /* | |
2386 | ------------------------------------------------------------------------------- | |
2387 | Returns 1 if the double-precision floating-point value `a' is equal to the | |
2388 | corresponding value `b', and 0 otherwise. The comparison is performed | |
2389 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2390 | ------------------------------------------------------------------------------- | |
2391 | */ | |
2392 | flag float64_eq( float64 a, float64 b ) | |
2393 | { | |
2394 | ||
2395 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2396 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2397 | ) { | |
2398 | if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { | |
2399 | float_raise( float_flag_invalid ); | |
2400 | } | |
2401 | return 0; | |
2402 | } | |
2403 | return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
2404 | ||
2405 | } | |
2406 | ||
2407 | /* | |
2408 | ------------------------------------------------------------------------------- | |
2409 | Returns 1 if the double-precision floating-point value `a' is less than or | |
2410 | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
2411 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
2412 | Arithmetic. | |
2413 | ------------------------------------------------------------------------------- | |
2414 | */ | |
2415 | flag float64_le( float64 a, float64 b ) | |
2416 | { | |
2417 | flag aSign, bSign; | |
2418 | ||
2419 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2420 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2421 | ) { | |
2422 | float_raise( float_flag_invalid ); | |
2423 | return 0; | |
2424 | } | |
2425 | aSign = extractFloat64Sign( a ); | |
2426 | bSign = extractFloat64Sign( b ); | |
2427 | if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
2428 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
2429 | ||
2430 | } | |
2431 | ||
2432 | /* | |
2433 | ------------------------------------------------------------------------------- | |
2434 | Returns 1 if the double-precision floating-point value `a' is less than | |
2435 | the corresponding value `b', and 0 otherwise. The comparison is performed | |
2436 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2437 | ------------------------------------------------------------------------------- | |
2438 | */ | |
2439 | flag float64_lt( float64 a, float64 b ) | |
2440 | { | |
2441 | flag aSign, bSign; | |
2442 | ||
2443 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2444 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2445 | ) { | |
2446 | float_raise( float_flag_invalid ); | |
2447 | return 0; | |
2448 | } | |
2449 | aSign = extractFloat64Sign( a ); | |
2450 | bSign = extractFloat64Sign( b ); | |
2451 | if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); | |
2452 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
2453 | ||
2454 | } | |
2455 | ||
2456 | /* | |
2457 | ------------------------------------------------------------------------------- | |
2458 | Returns 1 if the double-precision floating-point value `a' is equal to the | |
2459 | corresponding value `b', and 0 otherwise. The invalid exception is raised | |
2460 | if either operand is a NaN. Otherwise, the comparison is performed | |
2461 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2462 | ------------------------------------------------------------------------------- | |
2463 | */ | |
2464 | flag float64_eq_signaling( float64 a, float64 b ) | |
2465 | { | |
2466 | ||
2467 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2468 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2469 | ) { | |
2470 | float_raise( float_flag_invalid ); | |
2471 | return 0; | |
2472 | } | |
2473 | return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
2474 | ||
2475 | } | |
2476 | ||
2477 | /* | |
2478 | ------------------------------------------------------------------------------- | |
2479 | Returns 1 if the double-precision floating-point value `a' is less than or | |
2480 | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not | |
2481 | cause an exception. Otherwise, the comparison is performed according to the | |
2482 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2483 | ------------------------------------------------------------------------------- | |
2484 | */ | |
2485 | flag float64_le_quiet( float64 a, float64 b ) | |
2486 | { | |
2487 | flag aSign, bSign; | |
2488 | //int16 aExp, bExp; | |
2489 | ||
2490 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2491 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2492 | ) { | |
54738e82 | 2493 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
2494 | return 0; |
2495 | } | |
2496 | aSign = extractFloat64Sign( a ); | |
2497 | bSign = extractFloat64Sign( b ); | |
2498 | if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); | |
2499 | return ( a == b ) || ( aSign ^ ( a < b ) ); | |
2500 | ||
2501 | } | |
2502 | ||
2503 | /* | |
2504 | ------------------------------------------------------------------------------- | |
2505 | Returns 1 if the double-precision floating-point value `a' is less than | |
2506 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an | |
2507 | exception. Otherwise, the comparison is performed according to the IEC/IEEE | |
2508 | Standard for Binary Floating-point Arithmetic. | |
2509 | ------------------------------------------------------------------------------- | |
2510 | */ | |
2511 | flag float64_lt_quiet( float64 a, float64 b ) | |
2512 | { | |
2513 | flag aSign, bSign; | |
2514 | ||
2515 | if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) | |
2516 | || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) | |
2517 | ) { | |
54738e82 | 2518 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
2519 | return 0; |
2520 | } | |
2521 | aSign = extractFloat64Sign( a ); | |
2522 | bSign = extractFloat64Sign( b ); | |
2523 | if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); | |
2524 | return ( a != b ) && ( aSign ^ ( a < b ) ); | |
2525 | ||
2526 | } | |
2527 | ||
2528 | #ifdef FLOATX80 | |
2529 | ||
2530 | /* | |
2531 | ------------------------------------------------------------------------------- | |
2532 | Returns the result of converting the extended double-precision floating- | |
2533 | point value `a' to the 32-bit two's complement integer format. The | |
2534 | conversion is performed according to the IEC/IEEE Standard for Binary | |
2535 | Floating-point Arithmetic---which means in particular that the conversion | |
2536 | is rounded according to the current rounding mode. If `a' is a NaN, the | |
2537 | largest positive integer is returned. Otherwise, if the conversion | |
2538 | overflows, the largest integer with the same sign as `a' is returned. | |
2539 | ------------------------------------------------------------------------------- | |
2540 | */ | |
f148af25 | 2541 | int32 floatx80_to_int32( struct roundingData *roundData, floatx80 a ) |
1da177e4 LT |
2542 | { |
2543 | flag aSign; | |
2544 | int32 aExp, shiftCount; | |
2545 | bits64 aSig; | |
2546 | ||
2547 | aSig = extractFloatx80Frac( a ); | |
2548 | aExp = extractFloatx80Exp( a ); | |
2549 | aSign = extractFloatx80Sign( a ); | |
2550 | if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; | |
2551 | shiftCount = 0x4037 - aExp; | |
2552 | if ( shiftCount <= 0 ) shiftCount = 1; | |
2553 | shift64RightJamming( aSig, shiftCount, &aSig ); | |
f148af25 | 2554 | return roundAndPackInt32( roundData, aSign, aSig ); |
1da177e4 LT |
2555 | |
2556 | } | |
2557 | ||
2558 | /* | |
2559 | ------------------------------------------------------------------------------- | |
2560 | Returns the result of converting the extended double-precision floating- | |
2561 | point value `a' to the 32-bit two's complement integer format. The | |
2562 | conversion is performed according to the IEC/IEEE Standard for Binary | |
2563 | Floating-point Arithmetic, except that the conversion is always rounded | |
2564 | toward zero. If `a' is a NaN, the largest positive integer is returned. | |
2565 | Otherwise, if the conversion overflows, the largest integer with the same | |
2566 | sign as `a' is returned. | |
2567 | ------------------------------------------------------------------------------- | |
2568 | */ | |
2569 | int32 floatx80_to_int32_round_to_zero( floatx80 a ) | |
2570 | { | |
2571 | flag aSign; | |
2572 | int32 aExp, shiftCount; | |
2573 | bits64 aSig, savedASig; | |
2574 | int32 z; | |
2575 | ||
2576 | aSig = extractFloatx80Frac( a ); | |
2577 | aExp = extractFloatx80Exp( a ); | |
2578 | aSign = extractFloatx80Sign( a ); | |
2579 | shiftCount = 0x403E - aExp; | |
2580 | if ( shiftCount < 32 ) { | |
2581 | if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; | |
2582 | goto invalid; | |
2583 | } | |
2584 | else if ( 63 < shiftCount ) { | |
f148af25 | 2585 | if ( aExp || aSig ) float_raise( float_flag_inexact ); |
1da177e4 LT |
2586 | return 0; |
2587 | } | |
2588 | savedASig = aSig; | |
2589 | aSig >>= shiftCount; | |
2590 | z = aSig; | |
2591 | if ( aSign ) z = - z; | |
2592 | if ( ( z < 0 ) ^ aSign ) { | |
2593 | invalid: | |
f148af25 | 2594 | float_raise( float_flag_invalid ); |
1da177e4 LT |
2595 | return aSign ? 0x80000000 : 0x7FFFFFFF; |
2596 | } | |
2597 | if ( ( aSig<<shiftCount ) != savedASig ) { | |
f148af25 | 2598 | float_raise( float_flag_inexact ); |
1da177e4 LT |
2599 | } |
2600 | return z; | |
2601 | ||
2602 | } | |
2603 | ||
2604 | /* | |
2605 | ------------------------------------------------------------------------------- | |
2606 | Returns the result of converting the extended double-precision floating- | |
2607 | point value `a' to the single-precision floating-point format. The | |
2608 | conversion is performed according to the IEC/IEEE Standard for Binary | |
2609 | Floating-point Arithmetic. | |
2610 | ------------------------------------------------------------------------------- | |
2611 | */ | |
f148af25 | 2612 | float32 floatx80_to_float32( struct roundingData *roundData, floatx80 a ) |
1da177e4 LT |
2613 | { |
2614 | flag aSign; | |
2615 | int32 aExp; | |
2616 | bits64 aSig; | |
2617 | ||
2618 | aSig = extractFloatx80Frac( a ); | |
2619 | aExp = extractFloatx80Exp( a ); | |
2620 | aSign = extractFloatx80Sign( a ); | |
2621 | if ( aExp == 0x7FFF ) { | |
2622 | if ( (bits64) ( aSig<<1 ) ) { | |
2623 | return commonNaNToFloat32( floatx80ToCommonNaN( a ) ); | |
2624 | } | |
2625 | return packFloat32( aSign, 0xFF, 0 ); | |
2626 | } | |
2627 | shift64RightJamming( aSig, 33, &aSig ); | |
2628 | if ( aExp || aSig ) aExp -= 0x3F81; | |
f148af25 | 2629 | return roundAndPackFloat32( roundData, aSign, aExp, aSig ); |
1da177e4 LT |
2630 | |
2631 | } | |
2632 | ||
2633 | /* | |
2634 | ------------------------------------------------------------------------------- | |
2635 | Returns the result of converting the extended double-precision floating- | |
2636 | point value `a' to the double-precision floating-point format. The | |
2637 | conversion is performed according to the IEC/IEEE Standard for Binary | |
2638 | Floating-point Arithmetic. | |
2639 | ------------------------------------------------------------------------------- | |
2640 | */ | |
f148af25 | 2641 | float64 floatx80_to_float64( struct roundingData *roundData, floatx80 a ) |
1da177e4 LT |
2642 | { |
2643 | flag aSign; | |
2644 | int32 aExp; | |
2645 | bits64 aSig, zSig; | |
2646 | ||
2647 | aSig = extractFloatx80Frac( a ); | |
2648 | aExp = extractFloatx80Exp( a ); | |
2649 | aSign = extractFloatx80Sign( a ); | |
2650 | if ( aExp == 0x7FFF ) { | |
2651 | if ( (bits64) ( aSig<<1 ) ) { | |
2652 | return commonNaNToFloat64( floatx80ToCommonNaN( a ) ); | |
2653 | } | |
2654 | return packFloat64( aSign, 0x7FF, 0 ); | |
2655 | } | |
2656 | shift64RightJamming( aSig, 1, &zSig ); | |
2657 | if ( aExp || aSig ) aExp -= 0x3C01; | |
f148af25 | 2658 | return roundAndPackFloat64( roundData, aSign, aExp, zSig ); |
1da177e4 LT |
2659 | |
2660 | } | |
2661 | ||
2662 | /* | |
2663 | ------------------------------------------------------------------------------- | |
2664 | Rounds the extended double-precision floating-point value `a' to an integer, | |
2665 | and returns the result as an extended quadruple-precision floating-point | |
2666 | value. The operation is performed according to the IEC/IEEE Standard for | |
2667 | Binary Floating-point Arithmetic. | |
2668 | ------------------------------------------------------------------------------- | |
2669 | */ | |
f148af25 | 2670 | floatx80 floatx80_round_to_int( struct roundingData *roundData, floatx80 a ) |
1da177e4 LT |
2671 | { |
2672 | flag aSign; | |
2673 | int32 aExp; | |
2674 | bits64 lastBitMask, roundBitsMask; | |
2675 | int8 roundingMode; | |
2676 | floatx80 z; | |
2677 | ||
2678 | aExp = extractFloatx80Exp( a ); | |
2679 | if ( 0x403E <= aExp ) { | |
2680 | if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) { | |
2681 | return propagateFloatx80NaN( a, a ); | |
2682 | } | |
2683 | return a; | |
2684 | } | |
2685 | if ( aExp <= 0x3FFE ) { | |
2686 | if ( ( aExp == 0 ) | |
2687 | && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { | |
2688 | return a; | |
2689 | } | |
f148af25 | 2690 | roundData->exception |= float_flag_inexact; |
1da177e4 | 2691 | aSign = extractFloatx80Sign( a ); |
f148af25 | 2692 | switch ( roundData->mode ) { |
1da177e4 LT |
2693 | case float_round_nearest_even: |
2694 | if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 ) | |
2695 | ) { | |
2696 | return | |
2697 | packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
2698 | } | |
2699 | break; | |
2700 | case float_round_down: | |
2701 | return | |
2702 | aSign ? | |
2703 | packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) | |
2704 | : packFloatx80( 0, 0, 0 ); | |
2705 | case float_round_up: | |
2706 | return | |
2707 | aSign ? packFloatx80( 1, 0, 0 ) | |
2708 | : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); | |
2709 | } | |
2710 | return packFloatx80( aSign, 0, 0 ); | |
2711 | } | |
2712 | lastBitMask = 1; | |
2713 | lastBitMask <<= 0x403E - aExp; | |
2714 | roundBitsMask = lastBitMask - 1; | |
2715 | z = a; | |
f148af25 | 2716 | roundingMode = roundData->mode; |
1da177e4 LT |
2717 | if ( roundingMode == float_round_nearest_even ) { |
2718 | z.low += lastBitMask>>1; | |
2719 | if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; | |
2720 | } | |
2721 | else if ( roundingMode != float_round_to_zero ) { | |
2722 | if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { | |
2723 | z.low += roundBitsMask; | |
2724 | } | |
2725 | } | |
2726 | z.low &= ~ roundBitsMask; | |
2727 | if ( z.low == 0 ) { | |
2728 | ++z.high; | |
2729 | z.low = LIT64( 0x8000000000000000 ); | |
2730 | } | |
f148af25 | 2731 | if ( z.low != a.low ) roundData->exception |= float_flag_inexact; |
1da177e4 LT |
2732 | return z; |
2733 | ||
2734 | } | |
2735 | ||
2736 | /* | |
2737 | ------------------------------------------------------------------------------- | |
2738 | Returns the result of adding the absolute values of the extended double- | |
2739 | precision floating-point values `a' and `b'. If `zSign' is true, the sum is | |
2740 | negated before being returned. `zSign' is ignored if the result is a NaN. | |
2741 | The addition is performed according to the IEC/IEEE Standard for Binary | |
2742 | Floating-point Arithmetic. | |
2743 | ------------------------------------------------------------------------------- | |
2744 | */ | |
f148af25 | 2745 | static floatx80 addFloatx80Sigs( struct roundingData *roundData, floatx80 a, floatx80 b, flag zSign ) |
1da177e4 LT |
2746 | { |
2747 | int32 aExp, bExp, zExp; | |
2748 | bits64 aSig, bSig, zSig0, zSig1; | |
2749 | int32 expDiff; | |
2750 | ||
2751 | aSig = extractFloatx80Frac( a ); | |
2752 | aExp = extractFloatx80Exp( a ); | |
2753 | bSig = extractFloatx80Frac( b ); | |
2754 | bExp = extractFloatx80Exp( b ); | |
2755 | expDiff = aExp - bExp; | |
2756 | if ( 0 < expDiff ) { | |
2757 | if ( aExp == 0x7FFF ) { | |
2758 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
2759 | return a; | |
2760 | } | |
2761 | if ( bExp == 0 ) --expDiff; | |
2762 | shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
2763 | zExp = aExp; | |
2764 | } | |
2765 | else if ( expDiff < 0 ) { | |
2766 | if ( bExp == 0x7FFF ) { | |
2767 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
2768 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
2769 | } | |
2770 | if ( aExp == 0 ) ++expDiff; | |
2771 | shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
2772 | zExp = bExp; | |
2773 | } | |
2774 | else { | |
2775 | if ( aExp == 0x7FFF ) { | |
2776 | if ( (bits64) ( ( aSig | bSig )<<1 ) ) { | |
2777 | return propagateFloatx80NaN( a, b ); | |
2778 | } | |
2779 | return a; | |
2780 | } | |
2781 | zSig1 = 0; | |
2782 | zSig0 = aSig + bSig; | |
2783 | if ( aExp == 0 ) { | |
2784 | normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); | |
2785 | goto roundAndPack; | |
2786 | } | |
2787 | zExp = aExp; | |
2788 | goto shiftRight1; | |
2789 | } | |
2790 | ||
2791 | zSig0 = aSig + bSig; | |
2792 | ||
2793 | if ( (sbits64) zSig0 < 0 ) goto roundAndPack; | |
2794 | shiftRight1: | |
2795 | shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); | |
2796 | zSig0 |= LIT64( 0x8000000000000000 ); | |
2797 | ++zExp; | |
2798 | roundAndPack: | |
2799 | return | |
2800 | roundAndPackFloatx80( | |
f148af25 | 2801 | roundData, zSign, zExp, zSig0, zSig1 ); |
1da177e4 LT |
2802 | |
2803 | } | |
2804 | ||
2805 | /* | |
2806 | ------------------------------------------------------------------------------- | |
2807 | Returns the result of subtracting the absolute values of the extended | |
2808 | double-precision floating-point values `a' and `b'. If `zSign' is true, | |
2809 | the difference is negated before being returned. `zSign' is ignored if the | |
2810 | result is a NaN. The subtraction is performed according to the IEC/IEEE | |
2811 | Standard for Binary Floating-point Arithmetic. | |
2812 | ------------------------------------------------------------------------------- | |
2813 | */ | |
f148af25 | 2814 | static floatx80 subFloatx80Sigs( struct roundingData *roundData, floatx80 a, floatx80 b, flag zSign ) |
1da177e4 LT |
2815 | { |
2816 | int32 aExp, bExp, zExp; | |
2817 | bits64 aSig, bSig, zSig0, zSig1; | |
2818 | int32 expDiff; | |
2819 | floatx80 z; | |
2820 | ||
2821 | aSig = extractFloatx80Frac( a ); | |
2822 | aExp = extractFloatx80Exp( a ); | |
2823 | bSig = extractFloatx80Frac( b ); | |
2824 | bExp = extractFloatx80Exp( b ); | |
2825 | expDiff = aExp - bExp; | |
2826 | if ( 0 < expDiff ) goto aExpBigger; | |
2827 | if ( expDiff < 0 ) goto bExpBigger; | |
2828 | if ( aExp == 0x7FFF ) { | |
2829 | if ( (bits64) ( ( aSig | bSig )<<1 ) ) { | |
2830 | return propagateFloatx80NaN( a, b ); | |
2831 | } | |
f148af25 | 2832 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2833 | z.low = floatx80_default_nan_low; |
2834 | z.high = floatx80_default_nan_high; | |
06c03cac | 2835 | z.__padding = 0; |
1da177e4 LT |
2836 | return z; |
2837 | } | |
2838 | if ( aExp == 0 ) { | |
2839 | aExp = 1; | |
2840 | bExp = 1; | |
2841 | } | |
2842 | zSig1 = 0; | |
2843 | if ( bSig < aSig ) goto aBigger; | |
2844 | if ( aSig < bSig ) goto bBigger; | |
f148af25 | 2845 | return packFloatx80( roundData->mode == float_round_down, 0, 0 ); |
1da177e4 LT |
2846 | bExpBigger: |
2847 | if ( bExp == 0x7FFF ) { | |
2848 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
2849 | return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
2850 | } | |
2851 | if ( aExp == 0 ) ++expDiff; | |
2852 | shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); | |
2853 | bBigger: | |
2854 | sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); | |
2855 | zExp = bExp; | |
2856 | zSign ^= 1; | |
2857 | goto normalizeRoundAndPack; | |
2858 | aExpBigger: | |
2859 | if ( aExp == 0x7FFF ) { | |
2860 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
2861 | return a; | |
2862 | } | |
2863 | if ( bExp == 0 ) --expDiff; | |
2864 | shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); | |
2865 | aBigger: | |
2866 | sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); | |
2867 | zExp = aExp; | |
2868 | normalizeRoundAndPack: | |
2869 | return | |
2870 | normalizeRoundAndPackFloatx80( | |
f148af25 | 2871 | roundData, zSign, zExp, zSig0, zSig1 ); |
1da177e4 LT |
2872 | |
2873 | } | |
2874 | ||
2875 | /* | |
2876 | ------------------------------------------------------------------------------- | |
2877 | Returns the result of adding the extended double-precision floating-point | |
2878 | values `a' and `b'. The operation is performed according to the IEC/IEEE | |
2879 | Standard for Binary Floating-point Arithmetic. | |
2880 | ------------------------------------------------------------------------------- | |
2881 | */ | |
f148af25 | 2882 | floatx80 floatx80_add( struct roundingData *roundData, floatx80 a, floatx80 b ) |
1da177e4 LT |
2883 | { |
2884 | flag aSign, bSign; | |
2885 | ||
2886 | aSign = extractFloatx80Sign( a ); | |
2887 | bSign = extractFloatx80Sign( b ); | |
2888 | if ( aSign == bSign ) { | |
f148af25 | 2889 | return addFloatx80Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2890 | } |
2891 | else { | |
f148af25 | 2892 | return subFloatx80Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2893 | } |
2894 | ||
2895 | } | |
2896 | ||
2897 | /* | |
2898 | ------------------------------------------------------------------------------- | |
2899 | Returns the result of subtracting the extended double-precision floating- | |
2900 | point values `a' and `b'. The operation is performed according to the | |
2901 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2902 | ------------------------------------------------------------------------------- | |
2903 | */ | |
f148af25 | 2904 | floatx80 floatx80_sub( struct roundingData *roundData, floatx80 a, floatx80 b ) |
1da177e4 LT |
2905 | { |
2906 | flag aSign, bSign; | |
2907 | ||
2908 | aSign = extractFloatx80Sign( a ); | |
2909 | bSign = extractFloatx80Sign( b ); | |
2910 | if ( aSign == bSign ) { | |
f148af25 | 2911 | return subFloatx80Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2912 | } |
2913 | else { | |
f148af25 | 2914 | return addFloatx80Sigs( roundData, a, b, aSign ); |
1da177e4 LT |
2915 | } |
2916 | ||
2917 | } | |
2918 | ||
2919 | /* | |
2920 | ------------------------------------------------------------------------------- | |
2921 | Returns the result of multiplying the extended double-precision floating- | |
2922 | point values `a' and `b'. The operation is performed according to the | |
2923 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2924 | ------------------------------------------------------------------------------- | |
2925 | */ | |
f148af25 | 2926 | floatx80 floatx80_mul( struct roundingData *roundData, floatx80 a, floatx80 b ) |
1da177e4 LT |
2927 | { |
2928 | flag aSign, bSign, zSign; | |
2929 | int32 aExp, bExp, zExp; | |
2930 | bits64 aSig, bSig, zSig0, zSig1; | |
2931 | floatx80 z; | |
2932 | ||
2933 | aSig = extractFloatx80Frac( a ); | |
2934 | aExp = extractFloatx80Exp( a ); | |
2935 | aSign = extractFloatx80Sign( a ); | |
2936 | bSig = extractFloatx80Frac( b ); | |
2937 | bExp = extractFloatx80Exp( b ); | |
2938 | bSign = extractFloatx80Sign( b ); | |
2939 | zSign = aSign ^ bSign; | |
2940 | if ( aExp == 0x7FFF ) { | |
2941 | if ( (bits64) ( aSig<<1 ) | |
2942 | || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { | |
2943 | return propagateFloatx80NaN( a, b ); | |
2944 | } | |
2945 | if ( ( bExp | bSig ) == 0 ) goto invalid; | |
2946 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
2947 | } | |
2948 | if ( bExp == 0x7FFF ) { | |
2949 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
2950 | if ( ( aExp | aSig ) == 0 ) { | |
2951 | invalid: | |
f148af25 | 2952 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
2953 | z.low = floatx80_default_nan_low; |
2954 | z.high = floatx80_default_nan_high; | |
06c03cac | 2955 | z.__padding = 0; |
1da177e4 LT |
2956 | return z; |
2957 | } | |
2958 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
2959 | } | |
2960 | if ( aExp == 0 ) { | |
2961 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
2962 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
2963 | } | |
2964 | if ( bExp == 0 ) { | |
2965 | if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
2966 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
2967 | } | |
2968 | zExp = aExp + bExp - 0x3FFE; | |
2969 | mul64To128( aSig, bSig, &zSig0, &zSig1 ); | |
2970 | if ( 0 < (sbits64) zSig0 ) { | |
2971 | shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); | |
2972 | --zExp; | |
2973 | } | |
2974 | return | |
2975 | roundAndPackFloatx80( | |
f148af25 | 2976 | roundData, zSign, zExp, zSig0, zSig1 ); |
1da177e4 LT |
2977 | |
2978 | } | |
2979 | ||
2980 | /* | |
2981 | ------------------------------------------------------------------------------- | |
2982 | Returns the result of dividing the extended double-precision floating-point | |
2983 | value `a' by the corresponding value `b'. The operation is performed | |
2984 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
2985 | ------------------------------------------------------------------------------- | |
2986 | */ | |
f148af25 | 2987 | floatx80 floatx80_div( struct roundingData *roundData, floatx80 a, floatx80 b ) |
1da177e4 LT |
2988 | { |
2989 | flag aSign, bSign, zSign; | |
2990 | int32 aExp, bExp, zExp; | |
2991 | bits64 aSig, bSig, zSig0, zSig1; | |
2992 | bits64 rem0, rem1, rem2, term0, term1, term2; | |
2993 | floatx80 z; | |
2994 | ||
2995 | aSig = extractFloatx80Frac( a ); | |
2996 | aExp = extractFloatx80Exp( a ); | |
2997 | aSign = extractFloatx80Sign( a ); | |
2998 | bSig = extractFloatx80Frac( b ); | |
2999 | bExp = extractFloatx80Exp( b ); | |
3000 | bSign = extractFloatx80Sign( b ); | |
3001 | zSign = aSign ^ bSign; | |
3002 | if ( aExp == 0x7FFF ) { | |
3003 | if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
3004 | if ( bExp == 0x7FFF ) { | |
3005 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
3006 | goto invalid; | |
3007 | } | |
3008 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); | |
3009 | } | |
3010 | if ( bExp == 0x7FFF ) { | |
3011 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
3012 | return packFloatx80( zSign, 0, 0 ); | |
3013 | } | |
3014 | if ( bExp == 0 ) { | |
3015 | if ( bSig == 0 ) { | |
3016 | if ( ( aExp | aSig ) == 0 ) { | |
3017 | invalid: | |
f148af25 | 3018 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
3019 | z.low = floatx80_default_nan_low; |
3020 | z.high = floatx80_default_nan_high; | |
06c03cac | 3021 | z.__padding = 0; |
1da177e4 LT |
3022 | return z; |
3023 | } | |
f148af25 | 3024 | roundData->exception |= float_flag_divbyzero; |
1da177e4 LT |
3025 | return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); |
3026 | } | |
3027 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
3028 | } | |
3029 | if ( aExp == 0 ) { | |
3030 | if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); | |
3031 | normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); | |
3032 | } | |
3033 | zExp = aExp - bExp + 0x3FFE; | |
3034 | rem1 = 0; | |
3035 | if ( bSig <= aSig ) { | |
3036 | shift128Right( aSig, 0, 1, &aSig, &rem1 ); | |
3037 | ++zExp; | |
3038 | } | |
3039 | zSig0 = estimateDiv128To64( aSig, rem1, bSig ); | |
3040 | mul64To128( bSig, zSig0, &term0, &term1 ); | |
3041 | sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); | |
3042 | while ( (sbits64) rem0 < 0 ) { | |
3043 | --zSig0; | |
3044 | add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); | |
3045 | } | |
3046 | zSig1 = estimateDiv128To64( rem1, 0, bSig ); | |
3047 | if ( (bits64) ( zSig1<<1 ) <= 8 ) { | |
3048 | mul64To128( bSig, zSig1, &term1, &term2 ); | |
3049 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
3050 | while ( (sbits64) rem1 < 0 ) { | |
3051 | --zSig1; | |
3052 | add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); | |
3053 | } | |
3054 | zSig1 |= ( ( rem1 | rem2 ) != 0 ); | |
3055 | } | |
3056 | return | |
3057 | roundAndPackFloatx80( | |
f148af25 | 3058 | roundData, zSign, zExp, zSig0, zSig1 ); |
1da177e4 LT |
3059 | |
3060 | } | |
3061 | ||
3062 | /* | |
3063 | ------------------------------------------------------------------------------- | |
3064 | Returns the remainder of the extended double-precision floating-point value | |
3065 | `a' with respect to the corresponding value `b'. The operation is performed | |
3066 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
3067 | ------------------------------------------------------------------------------- | |
3068 | */ | |
f148af25 | 3069 | floatx80 floatx80_rem( struct roundingData *roundData, floatx80 a, floatx80 b ) |
1da177e4 LT |
3070 | { |
3071 | flag aSign, bSign, zSign; | |
3072 | int32 aExp, bExp, expDiff; | |
3073 | bits64 aSig0, aSig1, bSig; | |
3074 | bits64 q, term0, term1, alternateASig0, alternateASig1; | |
3075 | floatx80 z; | |
3076 | ||
3077 | aSig0 = extractFloatx80Frac( a ); | |
3078 | aExp = extractFloatx80Exp( a ); | |
3079 | aSign = extractFloatx80Sign( a ); | |
3080 | bSig = extractFloatx80Frac( b ); | |
3081 | bExp = extractFloatx80Exp( b ); | |
3082 | bSign = extractFloatx80Sign( b ); | |
3083 | if ( aExp == 0x7FFF ) { | |
3084 | if ( (bits64) ( aSig0<<1 ) | |
3085 | || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { | |
3086 | return propagateFloatx80NaN( a, b ); | |
3087 | } | |
3088 | goto invalid; | |
3089 | } | |
3090 | if ( bExp == 0x7FFF ) { | |
3091 | if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b ); | |
3092 | return a; | |
3093 | } | |
3094 | if ( bExp == 0 ) { | |
3095 | if ( bSig == 0 ) { | |
3096 | invalid: | |
f148af25 | 3097 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
3098 | z.low = floatx80_default_nan_low; |
3099 | z.high = floatx80_default_nan_high; | |
06c03cac | 3100 | z.__padding = 0; |
1da177e4 LT |
3101 | return z; |
3102 | } | |
3103 | normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); | |
3104 | } | |
3105 | if ( aExp == 0 ) { | |
3106 | if ( (bits64) ( aSig0<<1 ) == 0 ) return a; | |
3107 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); | |
3108 | } | |
3109 | bSig |= LIT64( 0x8000000000000000 ); | |
3110 | zSign = aSign; | |
3111 | expDiff = aExp - bExp; | |
3112 | aSig1 = 0; | |
3113 | if ( expDiff < 0 ) { | |
3114 | if ( expDiff < -1 ) return a; | |
3115 | shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); | |
3116 | expDiff = 0; | |
3117 | } | |
3118 | q = ( bSig <= aSig0 ); | |
3119 | if ( q ) aSig0 -= bSig; | |
3120 | expDiff -= 64; | |
3121 | while ( 0 < expDiff ) { | |
3122 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
3123 | q = ( 2 < q ) ? q - 2 : 0; | |
3124 | mul64To128( bSig, q, &term0, &term1 ); | |
3125 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3126 | shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); | |
3127 | expDiff -= 62; | |
3128 | } | |
3129 | expDiff += 64; | |
3130 | if ( 0 < expDiff ) { | |
3131 | q = estimateDiv128To64( aSig0, aSig1, bSig ); | |
3132 | q = ( 2 < q ) ? q - 2 : 0; | |
3133 | q >>= 64 - expDiff; | |
3134 | mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); | |
3135 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3136 | shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); | |
3137 | while ( le128( term0, term1, aSig0, aSig1 ) ) { | |
3138 | ++q; | |
3139 | sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); | |
3140 | } | |
3141 | } | |
3142 | else { | |
3143 | term1 = 0; | |
3144 | term0 = bSig; | |
3145 | } | |
3146 | sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); | |
3147 | if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
3148 | || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) | |
3149 | && ( q & 1 ) ) | |
3150 | ) { | |
3151 | aSig0 = alternateASig0; | |
3152 | aSig1 = alternateASig1; | |
3153 | zSign = ! zSign; | |
3154 | } | |
f148af25 | 3155 | |
1da177e4 LT |
3156 | return |
3157 | normalizeRoundAndPackFloatx80( | |
f148af25 | 3158 | roundData, zSign, bExp + expDiff, aSig0, aSig1 ); |
1da177e4 LT |
3159 | |
3160 | } | |
3161 | ||
3162 | /* | |
3163 | ------------------------------------------------------------------------------- | |
3164 | Returns the square root of the extended double-precision floating-point | |
3165 | value `a'. The operation is performed according to the IEC/IEEE Standard | |
3166 | for Binary Floating-point Arithmetic. | |
3167 | ------------------------------------------------------------------------------- | |
3168 | */ | |
f148af25 | 3169 | floatx80 floatx80_sqrt( struct roundingData *roundData, floatx80 a ) |
1da177e4 LT |
3170 | { |
3171 | flag aSign; | |
3172 | int32 aExp, zExp; | |
3173 | bits64 aSig0, aSig1, zSig0, zSig1; | |
3174 | bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; | |
3175 | bits64 shiftedRem0, shiftedRem1; | |
3176 | floatx80 z; | |
3177 | ||
3178 | aSig0 = extractFloatx80Frac( a ); | |
3179 | aExp = extractFloatx80Exp( a ); | |
3180 | aSign = extractFloatx80Sign( a ); | |
3181 | if ( aExp == 0x7FFF ) { | |
3182 | if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a ); | |
3183 | if ( ! aSign ) return a; | |
3184 | goto invalid; | |
3185 | } | |
3186 | if ( aSign ) { | |
3187 | if ( ( aExp | aSig0 ) == 0 ) return a; | |
3188 | invalid: | |
f148af25 | 3189 | roundData->exception |= float_flag_invalid; |
1da177e4 LT |
3190 | z.low = floatx80_default_nan_low; |
3191 | z.high = floatx80_default_nan_high; | |
06c03cac | 3192 | z.__padding = 0; |
1da177e4 LT |
3193 | return z; |
3194 | } | |
3195 | if ( aExp == 0 ) { | |
3196 | if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); | |
3197 | normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); | |
3198 | } | |
3199 | zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; | |
3200 | zSig0 = estimateSqrt32( aExp, aSig0>>32 ); | |
3201 | zSig0 <<= 31; | |
3202 | aSig1 = 0; | |
3203 | shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 ); | |
3204 | zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4; | |
3205 | if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF ); | |
3206 | shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 ); | |
3207 | mul64To128( zSig0, zSig0, &term0, &term1 ); | |
3208 | sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); | |
3209 | while ( (sbits64) rem0 < 0 ) { | |
3210 | --zSig0; | |
3211 | shortShift128Left( 0, zSig0, 1, &term0, &term1 ); | |
3212 | term1 |= 1; | |
3213 | add128( rem0, rem1, term0, term1, &rem0, &rem1 ); | |
3214 | } | |
3215 | shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 ); | |
3216 | zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 ); | |
3217 | if ( (bits64) ( zSig1<<1 ) <= 10 ) { | |
3218 | if ( zSig1 == 0 ) zSig1 = 1; | |
3219 | mul64To128( zSig0, zSig1, &term1, &term2 ); | |
3220 | shortShift128Left( term1, term2, 1, &term1, &term2 ); | |
3221 | sub128( rem1, 0, term1, term2, &rem1, &rem2 ); | |
3222 | mul64To128( zSig1, zSig1, &term2, &term3 ); | |
3223 | sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); | |
3224 | while ( (sbits64) rem1 < 0 ) { | |
3225 | --zSig1; | |
3226 | shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 ); | |
3227 | term3 |= 1; | |
3228 | add192( | |
3229 | rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 ); | |
3230 | } | |
3231 | zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); | |
3232 | } | |
3233 | return | |
3234 | roundAndPackFloatx80( | |
f148af25 | 3235 | roundData, 0, zExp, zSig0, zSig1 ); |
1da177e4 LT |
3236 | |
3237 | } | |
3238 | ||
3239 | /* | |
3240 | ------------------------------------------------------------------------------- | |
3241 | Returns 1 if the extended double-precision floating-point value `a' is | |
3242 | equal to the corresponding value `b', and 0 otherwise. The comparison is | |
3243 | performed according to the IEC/IEEE Standard for Binary Floating-point | |
3244 | Arithmetic. | |
3245 | ------------------------------------------------------------------------------- | |
3246 | */ | |
3247 | flag floatx80_eq( floatx80 a, floatx80 b ) | |
3248 | { | |
3249 | ||
3250 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3251 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3252 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3253 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3254 | ) { | |
3255 | if ( floatx80_is_signaling_nan( a ) | |
3256 | || floatx80_is_signaling_nan( b ) ) { | |
54738e82 | 3257 | float_raise( float_flag_invalid ); |
1da177e4 LT |
3258 | } |
3259 | return 0; | |
3260 | } | |
3261 | return | |
3262 | ( a.low == b.low ) | |
3263 | && ( ( a.high == b.high ) | |
3264 | || ( ( a.low == 0 ) | |
3265 | && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
3266 | ); | |
3267 | ||
3268 | } | |
3269 | ||
3270 | /* | |
3271 | ------------------------------------------------------------------------------- | |
3272 | Returns 1 if the extended double-precision floating-point value `a' is | |
3273 | less than or equal to the corresponding value `b', and 0 otherwise. The | |
3274 | comparison is performed according to the IEC/IEEE Standard for Binary | |
3275 | Floating-point Arithmetic. | |
3276 | ------------------------------------------------------------------------------- | |
3277 | */ | |
3278 | flag floatx80_le( floatx80 a, floatx80 b ) | |
3279 | { | |
3280 | flag aSign, bSign; | |
3281 | ||
3282 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3283 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3284 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3285 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3286 | ) { | |
54738e82 | 3287 | float_raise( float_flag_invalid ); |
1da177e4 LT |
3288 | return 0; |
3289 | } | |
3290 | aSign = extractFloatx80Sign( a ); | |
3291 | bSign = extractFloatx80Sign( b ); | |
3292 | if ( aSign != bSign ) { | |
3293 | return | |
3294 | aSign | |
3295 | || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
3296 | == 0 ); | |
3297 | } | |
3298 | return | |
3299 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
3300 | : le128( a.high, a.low, b.high, b.low ); | |
3301 | ||
3302 | } | |
3303 | ||
3304 | /* | |
3305 | ------------------------------------------------------------------------------- | |
3306 | Returns 1 if the extended double-precision floating-point value `a' is | |
3307 | less than the corresponding value `b', and 0 otherwise. The comparison | |
3308 | is performed according to the IEC/IEEE Standard for Binary Floating-point | |
3309 | Arithmetic. | |
3310 | ------------------------------------------------------------------------------- | |
3311 | */ | |
3312 | flag floatx80_lt( floatx80 a, floatx80 b ) | |
3313 | { | |
3314 | flag aSign, bSign; | |
3315 | ||
3316 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3317 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3318 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3319 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3320 | ) { | |
54738e82 | 3321 | float_raise( float_flag_invalid ); |
1da177e4 LT |
3322 | return 0; |
3323 | } | |
3324 | aSign = extractFloatx80Sign( a ); | |
3325 | bSign = extractFloatx80Sign( b ); | |
3326 | if ( aSign != bSign ) { | |
3327 | return | |
3328 | aSign | |
3329 | && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
3330 | != 0 ); | |
3331 | } | |
3332 | return | |
3333 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
3334 | : lt128( a.high, a.low, b.high, b.low ); | |
3335 | ||
3336 | } | |
3337 | ||
3338 | /* | |
3339 | ------------------------------------------------------------------------------- | |
3340 | Returns 1 if the extended double-precision floating-point value `a' is equal | |
3341 | to the corresponding value `b', and 0 otherwise. The invalid exception is | |
3342 | raised if either operand is a NaN. Otherwise, the comparison is performed | |
3343 | according to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
3344 | ------------------------------------------------------------------------------- | |
3345 | */ | |
3346 | flag floatx80_eq_signaling( floatx80 a, floatx80 b ) | |
3347 | { | |
3348 | ||
3349 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3350 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3351 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3352 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3353 | ) { | |
54738e82 | 3354 | float_raise( float_flag_invalid ); |
1da177e4 LT |
3355 | return 0; |
3356 | } | |
3357 | return | |
3358 | ( a.low == b.low ) | |
3359 | && ( ( a.high == b.high ) | |
3360 | || ( ( a.low == 0 ) | |
3361 | && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) | |
3362 | ); | |
3363 | ||
3364 | } | |
3365 | ||
3366 | /* | |
3367 | ------------------------------------------------------------------------------- | |
3368 | Returns 1 if the extended double-precision floating-point value `a' is less | |
3369 | than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs | |
3370 | do not cause an exception. Otherwise, the comparison is performed according | |
3371 | to the IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
3372 | ------------------------------------------------------------------------------- | |
3373 | */ | |
3374 | flag floatx80_le_quiet( floatx80 a, floatx80 b ) | |
3375 | { | |
3376 | flag aSign, bSign; | |
3377 | ||
3378 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3379 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3380 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3381 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3382 | ) { | |
54738e82 | 3383 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
3384 | return 0; |
3385 | } | |
3386 | aSign = extractFloatx80Sign( a ); | |
3387 | bSign = extractFloatx80Sign( b ); | |
3388 | if ( aSign != bSign ) { | |
3389 | return | |
3390 | aSign | |
3391 | || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
3392 | == 0 ); | |
3393 | } | |
3394 | return | |
3395 | aSign ? le128( b.high, b.low, a.high, a.low ) | |
3396 | : le128( a.high, a.low, b.high, b.low ); | |
3397 | ||
3398 | } | |
3399 | ||
3400 | /* | |
3401 | ------------------------------------------------------------------------------- | |
3402 | Returns 1 if the extended double-precision floating-point value `a' is less | |
3403 | than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause | |
3404 | an exception. Otherwise, the comparison is performed according to the | |
3405 | IEC/IEEE Standard for Binary Floating-point Arithmetic. | |
3406 | ------------------------------------------------------------------------------- | |
3407 | */ | |
3408 | flag floatx80_lt_quiet( floatx80 a, floatx80 b ) | |
3409 | { | |
3410 | flag aSign, bSign; | |
3411 | ||
3412 | if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) | |
3413 | && (bits64) ( extractFloatx80Frac( a )<<1 ) ) | |
3414 | || ( ( extractFloatx80Exp( b ) == 0x7FFF ) | |
3415 | && (bits64) ( extractFloatx80Frac( b )<<1 ) ) | |
3416 | ) { | |
54738e82 | 3417 | /* Do nothing, even if NaN as we're quiet */ |
1da177e4 LT |
3418 | return 0; |
3419 | } | |
3420 | aSign = extractFloatx80Sign( a ); | |
3421 | bSign = extractFloatx80Sign( b ); | |
3422 | if ( aSign != bSign ) { | |
3423 | return | |
3424 | aSign | |
3425 | && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) | |
3426 | != 0 ); | |
3427 | } | |
3428 | return | |
3429 | aSign ? lt128( b.high, b.low, a.high, a.low ) | |
3430 | : lt128( a.high, a.low, b.high, b.low ); | |
3431 | ||
3432 | } | |
3433 | ||
3434 | #endif | |
3435 |