| blob | 86b096827cb86b3a43ea8e703c9d63c8e60b3ee6 |
1 /* Software floating-point emulation. Common operations.
2 Copyright (C) 1997-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
10 In addition to the permissions in the GNU Lesser General Public
11 License, the Free Software Foundation gives you unlimited
12 permission to link the compiled version of this file into
13 combinations with other programs, and to distribute those
14 combinations without any restriction coming from the use of this
15 file. (The Lesser General Public License restrictions do apply in
16 other respects; for example, they cover modification of the file,
17 and distribution when not linked into a combine executable.)
19 The GNU C Library is distributed in the hope that it will be useful,
20 but WITHOUT ANY WARRANTY; without even the implied warranty of
21 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
22 Lesser General Public License for more details.
24 You should have received a copy of the GNU Lesser General Public
25 License along with the GNU C Library; if not, see
26 <https://www.gnu.org/licenses/>. */
28 #ifndef SOFT_FP_OP_COMMON_H
29 #define SOFT_FP_OP_COMMON_H 1
31 #define _FP_DECL(wc, X) \
32 _FP_I_TYPE X##_c __attribute__ ((unused)) _FP_ZERO_INIT; \
33 _FP_I_TYPE X##_s __attribute__ ((unused)) _FP_ZERO_INIT; \
34 _FP_I_TYPE X##_e __attribute__ ((unused)) _FP_ZERO_INIT; \
35 _FP_FRAC_DECL_##wc (X)
37 /* Test whether the qNaN bit denotes a signaling NaN. */
38 #define _FP_FRAC_SNANP(fs, X) \
39 ((_FP_QNANNEGATEDP) \
40 ? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \
41 : !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs))
42 #define _FP_FRAC_SNANP_SEMIRAW(fs, X) \
43 ((_FP_QNANNEGATEDP) \
44 ? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \
45 : !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs))
47 /* Finish truly unpacking a native fp value by classifying the kind
48 of fp value and normalizing both the exponent and the fraction. */
50 #define _FP_UNPACK_CANONICAL(fs, wc, X) \
51 do \
52 { \
53 switch (X##_e) \
54 { \
55 default: \
56 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
57 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
58 X##_e -= _FP_EXPBIAS_##fs; \
59 X##_c = FP_CLS_NORMAL; \
60 break; \
61 \
62 case 0: \
63 if (_FP_FRAC_ZEROP_##wc (X)) \
64 X##_c = FP_CLS_ZERO; \
65 else if (FP_DENORM_ZERO) \
66 { \
67 X##_c = FP_CLS_ZERO; \
68 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
69 FP_SET_EXCEPTION (FP_EX_DENORM); \
70 } \
71 else \
72 { \
74 _FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \
75 _FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \
76 X); \
77 _FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \
78 _FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \
79 + _FP_WORKBITS)); \
80 X##_e -= (_FP_EXPBIAS_##fs - 1 \
81 + _FP_UNPACK_CANONICAL_shift); \
82 X##_c = FP_CLS_NORMAL; \
83 FP_SET_EXCEPTION (FP_EX_DENORM); \
84 } \
85 break; \
86 \
87 case _FP_EXPMAX_##fs: \
88 if (_FP_FRAC_ZEROP_##wc (X)) \
89 X##_c = FP_CLS_INF; \
90 else \
91 { \
92 X##_c = FP_CLS_NAN; \
94 if (_FP_FRAC_SNANP (fs, X)) \
95 FP_SET_EXCEPTION (FP_EX_INVALID \
96 | FP_EX_INVALID_SNAN); \
97 } \
98 break; \
99 } \
100 } \
101 while (0)
103 /* Finish unpacking an fp value in semi-raw mode: the mantissa is
104 shifted by _FP_WORKBITS but the implicit MSB is not inserted and
105 other classification is not done. */
106 #define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc (X, _FP_WORKBITS)
108 /* Check whether a raw or semi-raw input value should be flushed to
109 zero, and flush it to zero if so. */
110 #define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \
111 do \
112 { \
113 if (FP_DENORM_ZERO \
114 && X##_e == 0 \
115 && !_FP_FRAC_ZEROP_##wc (X)) \
116 { \
117 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
118 FP_SET_EXCEPTION (FP_EX_DENORM); \
119 } \
120 } \
121 while (0)
123 /* A semi-raw value has overflowed to infinity. Adjust the mantissa
124 and exponent appropriately. */
125 #define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \
126 do \
127 { \
128 if (FP_ROUNDMODE == FP_RND_NEAREST \
129 || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \
130 || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \
131 { \
132 X##_e = _FP_EXPMAX_##fs; \
133 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
134 } \
135 else \
136 { \
137 X##_e = _FP_EXPMAX_##fs - 1; \
138 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
139 } \
140 FP_SET_EXCEPTION (FP_EX_INEXACT); \
141 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
142 } \
143 while (0)
145 /* Check for a semi-raw value being a signaling NaN and raise the
146 invalid exception if so. */
147 #define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \
148 do \
149 { \
150 if (X##_e == _FP_EXPMAX_##fs \
151 && !_FP_FRAC_ZEROP_##wc (X) \
152 && _FP_FRAC_SNANP_SEMIRAW (fs, X)) \
153 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
154 } \
155 while (0)
157 /* Choose a NaN result from an operation on two semi-raw NaN
158 values. */
159 #define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \
160 do \
161 { \
163 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
164 _FP_FRAC_SRL_##wc (Y, _FP_WORKBITS); \
165 _FP_CHOOSENAN (fs, wc, R, X, Y, OP); \
166 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
167 } \
168 while (0)
170 /* Make the fractional part a quiet NaN, preserving the payload
171 if possible, otherwise make it the canonical quiet NaN and set
172 the sign bit accordingly. */
173 #define _FP_SETQNAN(fs, wc, X) \
174 do \
175 { \
176 if (_FP_QNANNEGATEDP) \
177 { \
178 _FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \
179 if (_FP_FRAC_ZEROP_##wc (X)) \
180 { \
181 X##_s = _FP_NANSIGN_##fs; \
182 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
183 } \
184 } \
185 else \
186 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \
187 } \
188 while (0)
189 #define _FP_SETQNAN_SEMIRAW(fs, wc, X) \
190 do \
191 { \
192 if (_FP_QNANNEGATEDP) \
193 { \
194 _FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \
195 if (_FP_FRAC_ZEROP_##wc (X)) \
196 { \
197 X##_s = _FP_NANSIGN_##fs; \
198 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
199 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
200 } \
201 } \
202 else \
203 _FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \
204 } \
205 while (0)
207 /* Test whether a biased exponent is normal (not zero or maximum). */
208 #define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1)
210 /* Prepare to pack an fp value in semi-raw mode: the mantissa is
211 rounded and shifted right, with the rounding possibly increasing
212 the exponent (including changing a finite value to infinity). */
213 #define _FP_PACK_SEMIRAW(fs, wc, X) \
214 do \
215 { \
216 int _FP_PACK_SEMIRAW_is_tiny \
217 = X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \
218 if (_FP_TININESS_AFTER_ROUNDING \
219 && _FP_PACK_SEMIRAW_is_tiny) \
220 { \
221 FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \
222 _FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \
223 _FP_PACK_SEMIRAW_T##_s = X##_s; \
224 _FP_PACK_SEMIRAW_T##_e = X##_e; \
225 _FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \
226 _FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \
227 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \
228 _FP_PACK_SEMIRAW_is_tiny = 0; \
229 } \
230 _FP_ROUND (wc, X); \
231 if (_FP_PACK_SEMIRAW_is_tiny) \
232 { \
233 if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
234 || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
235 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
236 } \
237 if (_FP_FRAC_HIGH_##fs (X) \
238 & (_FP_OVERFLOW_##fs >> 1)) \
239 { \
240 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_OVERFLOW_##fs >> 1); \
241 X##_e++; \
242 if (X##_e == _FP_EXPMAX_##fs) \
243 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \
244 } \
245 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
246 if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
247 { \
248 if (!_FP_KEEPNANFRACP) \
249 { \
250 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
251 X##_s = _FP_NANSIGN_##fs; \
252 } \
253 else \
254 _FP_SETQNAN (fs, wc, X); \
255 } \
256 } \
257 while (0)
259 /* Before packing the bits back into the native fp result, take care
260 of such mundane things as rounding and overflow. Also, for some
261 kinds of fp values, the original parts may not have been fully
262 extracted -- but that is ok, we can regenerate them now. */
264 #define _FP_PACK_CANONICAL(fs, wc, X) \
265 do \
266 { \
267 switch (X##_c) \
268 { \
269 case FP_CLS_NORMAL: \
270 X##_e += _FP_EXPBIAS_##fs; \
271 if (X##_e > 0) \
272 { \
273 _FP_ROUND (wc, X); \
274 if (_FP_FRAC_OVERP_##wc (fs, X)) \
275 { \
276 _FP_FRAC_CLEAR_OVERP_##wc (fs, X); \
277 X##_e++; \
278 } \
279 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
280 if (X##_e >= _FP_EXPMAX_##fs) \
281 { \
283 switch (FP_ROUNDMODE) \
284 { \
285 case FP_RND_NEAREST: \
286 X##_c = FP_CLS_INF; \
287 break; \
288 case FP_RND_PINF: \
289 if (!X##_s) \
290 X##_c = FP_CLS_INF; \
291 break; \
292 case FP_RND_MINF: \
293 if (X##_s) \
294 X##_c = FP_CLS_INF; \
295 break; \
296 } \
297 if (X##_c == FP_CLS_INF) \
298 { \
300 X##_e = _FP_EXPMAX_##fs; \
301 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
302 } \
303 else \
304 { \
306 X##_e = _FP_EXPMAX_##fs - 1; \
307 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
308 } \
309 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
310 FP_SET_EXCEPTION (FP_EX_INEXACT); \
311 } \
312 } \
313 else \
314 { \
316 int _FP_PACK_CANONICAL_is_tiny = 1; \
317 if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \
318 { \
319 FP_DECL_##fs (_FP_PACK_CANONICAL_T); \
320 _FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \
321 _FP_PACK_CANONICAL_T##_s = X##_s; \
322 _FP_PACK_CANONICAL_T##_e = X##_e; \
323 _FP_ROUND (wc, _FP_PACK_CANONICAL_T); \
324 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \
325 _FP_PACK_CANONICAL_is_tiny = 0; \
326 } \
327 X##_e = -X##_e + 1; \
328 if (X##_e <= _FP_WFRACBITS_##fs) \
329 { \
330 _FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \
331 _FP_ROUND (wc, X); \
332 if (_FP_FRAC_HIGH_##fs (X) \
333 & (_FP_OVERFLOW_##fs >> 1)) \
334 { \
335 X##_e = 1; \
336 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
337 FP_SET_EXCEPTION (FP_EX_INEXACT); \
338 } \
339 else \
340 { \
341 X##_e = 0; \
342 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
343 } \
344 if (_FP_PACK_CANONICAL_is_tiny \
345 && ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
346 || (FP_TRAPPING_EXCEPTIONS \
347 & FP_EX_UNDERFLOW))) \
348 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
349 } \
350 else \
351 { \
353 X##_e = 0; \
354 if (!_FP_FRAC_ZEROP_##wc (X)) \
355 { \
356 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
357 _FP_ROUND (wc, X); \
358 _FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \
359 } \
360 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
361 } \
362 } \
363 break; \
364 \
365 case FP_CLS_ZERO: \
366 X##_e = 0; \
367 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
368 break; \
369 \
370 case FP_CLS_INF: \
371 X##_e = _FP_EXPMAX_##fs; \
372 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
373 break; \
374 \
375 case FP_CLS_NAN: \
376 X##_e = _FP_EXPMAX_##fs; \
377 if (!_FP_KEEPNANFRACP) \
378 { \
379 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
380 X##_s = _FP_NANSIGN_##fs; \
381 } \
382 else \
383 _FP_SETQNAN (fs, wc, X); \
384 break; \
385 } \
386 } \
387 while (0)
389 /* This one accepts raw argument and not cooked, returns
390 1 if X is a signaling NaN. */
391 #define _FP_ISSIGNAN(fs, wc, X) \
392 ({ \
393 int _FP_ISSIGNAN_ret = 0; \
394 if (X##_e == _FP_EXPMAX_##fs) \
395 { \
396 if (!_FP_FRAC_ZEROP_##wc (X) \
397 && _FP_FRAC_SNANP (fs, X)) \
398 _FP_ISSIGNAN_ret = 1; \
399 } \
400 _FP_ISSIGNAN_ret; \
401 })
407 /* Addition on semi-raw values. */
408 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
409 do \
410 { \
411 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
412 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
413 if (X##_s == Y##_s) \
414 { \
416 __label__ add1, add2, add3, add_done; \
417 R##_s = X##_s; \
418 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
419 if (_FP_ADD_INTERNAL_ediff > 0) \
420 { \
421 R##_e = X##_e; \
422 if (Y##_e == 0) \
423 { \
425 if (_FP_FRAC_ZEROP_##wc (Y)) \
426 { \
427 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
428 _FP_FRAC_COPY_##wc (R, X); \
429 goto add_done; \
430 } \
431 else \
432 { \
433 FP_SET_EXCEPTION (FP_EX_DENORM); \
434 _FP_ADD_INTERNAL_ediff--; \
435 if (_FP_ADD_INTERNAL_ediff == 0) \
436 { \
437 _FP_FRAC_ADD_##wc (R, X, Y); \
438 goto add3; \
439 } \
440 if (X##_e == _FP_EXPMAX_##fs) \
441 { \
442 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
443 _FP_FRAC_COPY_##wc (R, X); \
444 goto add_done; \
445 } \
446 goto add1; \
447 } \
448 } \
449 else if (X##_e == _FP_EXPMAX_##fs) \
450 { \
452 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
453 _FP_FRAC_COPY_##wc (R, X); \
454 goto add_done; \
455 } \
456 \
458 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
459 \
460 add1: \
461 /* Shift the mantissa of Y to the right \
462 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
464 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
465 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \
466 _FP_WFRACBITS_##fs); \
467 else if (!_FP_FRAC_ZEROP_##wc (Y)) \
468 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
469 _FP_FRAC_ADD_##wc (R, X, Y); \
470 } \
471 else if (_FP_ADD_INTERNAL_ediff < 0) \
472 { \
473 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \
474 R##_e = Y##_e; \
475 if (X##_e == 0) \
476 { \
478 if (_FP_FRAC_ZEROP_##wc (X)) \
479 { \
480 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
481 _FP_FRAC_COPY_##wc (R, Y); \
482 goto add_done; \
483 } \
484 else \
485 { \
486 FP_SET_EXCEPTION (FP_EX_DENORM); \
487 _FP_ADD_INTERNAL_ediff--; \
488 if (_FP_ADD_INTERNAL_ediff == 0) \
489 { \
490 _FP_FRAC_ADD_##wc (R, Y, X); \
491 goto add3; \
492 } \
493 if (Y##_e == _FP_EXPMAX_##fs) \
494 { \
495 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
496 _FP_FRAC_COPY_##wc (R, Y); \
497 goto add_done; \
498 } \
499 goto add2; \
500 } \
501 } \
502 else if (Y##_e == _FP_EXPMAX_##fs) \
503 { \
505 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
506 _FP_FRAC_COPY_##wc (R, Y); \
507 goto add_done; \
508 } \
509 \
511 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
512 \
513 add2: \
514 /* Shift the mantissa of X to the right \
515 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
517 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
518 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \
519 _FP_WFRACBITS_##fs); \
520 else if (!_FP_FRAC_ZEROP_##wc (X)) \
521 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
522 _FP_FRAC_ADD_##wc (R, Y, X); \
523 } \
524 else \
525 { \
527 if (!_FP_EXP_NORMAL (fs, wc, X)) \
528 { \
529 if (X##_e == 0) \
530 { \
532 R##_e = 0; \
533 if (_FP_FRAC_ZEROP_##wc (X)) \
534 { \
535 if (!_FP_FRAC_ZEROP_##wc (Y)) \
536 FP_SET_EXCEPTION (FP_EX_DENORM); \
537 _FP_FRAC_COPY_##wc (R, Y); \
538 goto add_done; \
539 } \
540 else if (_FP_FRAC_ZEROP_##wc (Y)) \
541 { \
542 FP_SET_EXCEPTION (FP_EX_DENORM); \
543 _FP_FRAC_COPY_##wc (R, X); \
544 goto add_done; \
545 } \
546 else \
547 { \
548 FP_SET_EXCEPTION (FP_EX_DENORM); \
549 _FP_FRAC_ADD_##wc (R, X, Y); \
550 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
551 { \
553 _FP_FRAC_HIGH_##fs (R) \
554 &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
555 R##_e = 1; \
556 } \
557 goto add_done; \
558 } \
559 } \
560 else \
561 { \
563 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
564 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
565 R##_e = _FP_EXPMAX_##fs; \
566 if (_FP_FRAC_ZEROP_##wc (X)) \
567 _FP_FRAC_COPY_##wc (R, Y); \
568 else if (_FP_FRAC_ZEROP_##wc (Y)) \
569 _FP_FRAC_COPY_##wc (R, X); \
570 else \
571 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
572 goto add_done; \
573 } \
574 } \
575 /* The exponents of X and Y, both normal, are equal. The \
576 implicit MSBs will always add to increase the \
578 _FP_FRAC_ADD_##wc (R, X, Y); \
579 R##_e = X##_e + 1; \
580 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
581 if (R##_e == _FP_EXPMAX_##fs) \
583 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \
584 goto add_done; \
585 } \
586 add3: \
587 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
588 { \
590 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
591 R##_e++; \
592 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
593 if (R##_e == _FP_EXPMAX_##fs) \
595 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \
596 } \
597 add_done: ; \
598 } \
599 else \
600 { \
602 __label__ sub1, sub2, sub3, norm, sub_done; \
603 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
604 if (_FP_ADD_INTERNAL_ediff > 0) \
605 { \
606 R##_e = X##_e; \
607 R##_s = X##_s; \
608 if (Y##_e == 0) \
609 { \
611 if (_FP_FRAC_ZEROP_##wc (Y)) \
612 { \
613 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
614 _FP_FRAC_COPY_##wc (R, X); \
615 goto sub_done; \
616 } \
617 else \
618 { \
619 FP_SET_EXCEPTION (FP_EX_DENORM); \
620 _FP_ADD_INTERNAL_ediff--; \
621 if (_FP_ADD_INTERNAL_ediff == 0) \
622 { \
623 _FP_FRAC_SUB_##wc (R, X, Y); \
624 goto sub3; \
625 } \
626 if (X##_e == _FP_EXPMAX_##fs) \
627 { \
628 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
629 _FP_FRAC_COPY_##wc (R, X); \
630 goto sub_done; \
631 } \
632 goto sub1; \
633 } \
634 } \
635 else if (X##_e == _FP_EXPMAX_##fs) \
636 { \
638 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
639 _FP_FRAC_COPY_##wc (R, X); \
640 goto sub_done; \
641 } \
642 \
644 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
645 \
646 sub1: \
647 /* Shift the mantissa of Y to the right \
648 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
650 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
651 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \
652 _FP_WFRACBITS_##fs); \
653 else if (!_FP_FRAC_ZEROP_##wc (Y)) \
654 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
655 _FP_FRAC_SUB_##wc (R, X, Y); \
656 } \
657 else if (_FP_ADD_INTERNAL_ediff < 0) \
658 { \
659 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \
660 R##_e = Y##_e; \
661 R##_s = Y##_s; \
662 if (X##_e == 0) \
663 { \
665 if (_FP_FRAC_ZEROP_##wc (X)) \
666 { \
667 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
668 _FP_FRAC_COPY_##wc (R, Y); \
669 goto sub_done; \
670 } \
671 else \
672 { \
673 FP_SET_EXCEPTION (FP_EX_DENORM); \
674 _FP_ADD_INTERNAL_ediff--; \
675 if (_FP_ADD_INTERNAL_ediff == 0) \
676 { \
677 _FP_FRAC_SUB_##wc (R, Y, X); \
678 goto sub3; \
679 } \
680 if (Y##_e == _FP_EXPMAX_##fs) \
681 { \
682 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
683 _FP_FRAC_COPY_##wc (R, Y); \
684 goto sub_done; \
685 } \
686 goto sub2; \
687 } \
688 } \
689 else if (Y##_e == _FP_EXPMAX_##fs) \
690 { \
692 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
693 _FP_FRAC_COPY_##wc (R, Y); \
694 goto sub_done; \
695 } \
696 \
698 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
699 \
700 sub2: \
701 /* Shift the mantissa of X to the right \
702 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
704 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
705 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \
706 _FP_WFRACBITS_##fs); \
707 else if (!_FP_FRAC_ZEROP_##wc (X)) \
708 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
709 _FP_FRAC_SUB_##wc (R, Y, X); \
710 } \
711 else \
712 { \
714 if (!_FP_EXP_NORMAL (fs, wc, X)) \
715 { \
716 if (X##_e == 0) \
717 { \
719 R##_e = 0; \
720 if (_FP_FRAC_ZEROP_##wc (X)) \
721 { \
722 _FP_FRAC_COPY_##wc (R, Y); \
723 if (_FP_FRAC_ZEROP_##wc (Y)) \
724 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
725 else \
726 { \
727 FP_SET_EXCEPTION (FP_EX_DENORM); \
728 R##_s = Y##_s; \
729 } \
730 goto sub_done; \
731 } \
732 else if (_FP_FRAC_ZEROP_##wc (Y)) \
733 { \
734 FP_SET_EXCEPTION (FP_EX_DENORM); \
735 _FP_FRAC_COPY_##wc (R, X); \
736 R##_s = X##_s; \
737 goto sub_done; \
738 } \
739 else \
740 { \
741 FP_SET_EXCEPTION (FP_EX_DENORM); \
742 _FP_FRAC_SUB_##wc (R, X, Y); \
743 R##_s = X##_s; \
744 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
745 { \
747 _FP_FRAC_SUB_##wc (R, Y, X); \
748 R##_s = Y##_s; \
749 } \
750 else if (_FP_FRAC_ZEROP_##wc (R)) \
751 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
752 goto sub_done; \
753 } \
754 } \
755 else \
756 { \
758 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
759 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
760 R##_e = _FP_EXPMAX_##fs; \
761 if (_FP_FRAC_ZEROP_##wc (X)) \
762 { \
763 if (_FP_FRAC_ZEROP_##wc (Y)) \
764 { \
766 R##_s = _FP_NANSIGN_##fs; \
767 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
768 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
769 FP_SET_EXCEPTION (FP_EX_INVALID \
770 | FP_EX_INVALID_ISI); \
771 } \
772 else \
773 { \
775 R##_s = Y##_s; \
776 _FP_FRAC_COPY_##wc (R, Y); \
777 } \
778 } \
779 else \
780 { \
781 if (_FP_FRAC_ZEROP_##wc (Y)) \
782 { \
784 R##_s = X##_s; \
785 _FP_FRAC_COPY_##wc (R, X); \
786 } \
787 else \
788 { \
790 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
791 } \
792 } \
793 goto sub_done; \
794 } \
795 } \
796 /* The exponents of X and Y, both normal, are equal. The \
798 R##_e = X##_e; \
799 _FP_FRAC_SUB_##wc (R, X, Y); \
800 R##_s = X##_s; \
801 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
802 { \
804 _FP_FRAC_SUB_##wc (R, Y, X); \
805 R##_s = Y##_s; \
806 } \
807 else if (_FP_FRAC_ZEROP_##wc (R)) \
808 { \
809 R##_e = 0; \
810 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
811 goto sub_done; \
812 } \
813 goto norm; \
814 } \
815 sub3: \
816 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
817 { \
818 int _FP_ADD_INTERNAL_diff; \
819 /* Carry into most significant bit of larger one of X and Y, \
821 _FP_FRAC_HIGH_##fs (R) &= _FP_IMPLBIT_SH_##fs - 1; \
822 norm: \
823 _FP_FRAC_CLZ_##wc (_FP_ADD_INTERNAL_diff, R); \
824 _FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \
825 _FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \
826 if (R##_e <= _FP_ADD_INTERNAL_diff) \
827 { \
829 _FP_ADD_INTERNAL_diff \
830 = _FP_ADD_INTERNAL_diff - R##_e + 1; \
831 _FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \
832 _FP_WFRACBITS_##fs); \
833 R##_e = 0; \
834 } \
835 else \
836 { \
837 R##_e -= _FP_ADD_INTERNAL_diff; \
838 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
839 } \
840 } \
841 sub_done: ; \
842 } \
843 } \
844 while (0)
847 #define _FP_SUB(fs, wc, R, X, Y) \
848 do \
849 { \
850 if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
851 Y##_s ^= 1; \
853 } \
854 while (0)
857 /* Main negation routine. The input value is raw. */
859 #define _FP_NEG(fs, wc, R, X) \
860 do \
861 { \
862 _FP_FRAC_COPY_##wc (R, X); \
863 R##_e = X##_e; \
864 R##_s = 1 ^ X##_s; \
865 } \
866 while (0)
869 /* Main multiplication routine. The input values should be cooked. */
871 #define _FP_MUL(fs, wc, R, X, Y) \
872 do \
873 { \
874 R##_s = X##_s ^ Y##_s; \
875 R##_e = X##_e + Y##_e + 1; \
876 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
877 { \
878 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
879 R##_c = FP_CLS_NORMAL; \
880 \
881 _FP_MUL_MEAT_##fs (R, X, Y); \
882 \
883 if (_FP_FRAC_OVERP_##wc (fs, R)) \
884 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
885 else \
886 R##_e--; \
887 break; \
888 \
889 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
891 break; \
892 \
893 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
894 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
895 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
896 R##_s = X##_s; \
898 \
899 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
900 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
901 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
902 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
903 _FP_FRAC_COPY_##wc (R, X); \
904 R##_c = X##_c; \
905 break; \
906 \
907 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
908 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
909 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
910 R##_s = Y##_s; \
912 \
913 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
914 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
915 _FP_FRAC_COPY_##wc (R, Y); \
916 R##_c = Y##_c; \
917 break; \
918 \
919 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
920 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
921 R##_s = _FP_NANSIGN_##fs; \
922 R##_c = FP_CLS_NAN; \
923 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
924 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ); \
925 break; \
926 \
927 default: \
928 _FP_UNREACHABLE; \
929 } \
930 } \
931 while (0)
934 /* Fused multiply-add. The input values should be cooked. */
936 #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
937 do \
938 { \
939 __label__ done_fma; \
940 FP_DECL_##fs (_FP_FMA_T); \
941 _FP_FMA_T##_s = X##_s ^ Y##_s; \
942 _FP_FMA_T##_e = X##_e + Y##_e + 1; \
943 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
944 { \
945 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
946 switch (Z##_c) \
947 { \
948 case FP_CLS_INF: \
949 case FP_CLS_NAN: \
950 R##_s = Z##_s; \
951 _FP_FRAC_COPY_##wc (R, Z); \
952 R##_c = Z##_c; \
953 break; \
954 \
955 case FP_CLS_ZERO: \
956 R##_c = FP_CLS_NORMAL; \
957 R##_s = _FP_FMA_T##_s; \
958 R##_e = _FP_FMA_T##_e; \
959 \
960 _FP_MUL_MEAT_##fs (R, X, Y); \
961 \
962 if (_FP_FRAC_OVERP_##wc (fs, R)) \
963 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
964 else \
965 R##_e--; \
966 break; \
967 \
968 case FP_CLS_NORMAL:; \
969 _FP_FRAC_DECL_##dwc (_FP_FMA_TD); \
970 _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \
971 _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \
972 _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \
973 R##_e = _FP_FMA_T##_e; \
974 int _FP_FMA_tsh \
975 = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \
976 _FP_FMA_T##_e -= _FP_FMA_tsh; \
977 int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \
978 if (_FP_FMA_ediff >= 0) \
979 { \
980 int _FP_FMA_shift \
981 = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \
982 if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \
983 _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \
984 else \
985 { \
986 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
987 if (_FP_FMA_shift < 0) \
988 _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \
989 _FP_WFRACBITS_DW_##fs); \
990 else if (_FP_FMA_shift > 0) \
991 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \
992 } \
993 R##_s = _FP_FMA_T##_s; \
994 if (_FP_FMA_T##_s == Z##_s) \
995 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
996 _FP_FMA_ZD); \
997 else \
998 { \
999 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
1000 _FP_FMA_ZD); \
1001 if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \
1002 { \
1003 R##_s = Z##_s; \
1004 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1005 _FP_FMA_TD); \
1006 } \
1007 } \
1008 } \
1009 else \
1010 { \
1011 R##_e = Z##_e; \
1012 R##_s = Z##_s; \
1013 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
1014 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \
1015 int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \
1016 if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \
1017 _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \
1018 else if (_FP_FMA_shift > 0) \
1019 _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \
1020 _FP_WFRACBITS_DW_##fs); \
1021 if (Z##_s == _FP_FMA_T##_s) \
1022 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1023 _FP_FMA_TD); \
1024 else \
1025 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1026 _FP_FMA_TD); \
1027 } \
1028 if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \
1029 { \
1030 if (_FP_FMA_T##_s == Z##_s) \
1031 R##_s = Z##_s; \
1032 else \
1033 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1034 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1035 R##_c = FP_CLS_ZERO; \
1036 } \
1037 else \
1038 { \
1039 int _FP_FMA_rlz; \
1040 _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \
1041 _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \
1042 R##_e -= _FP_FMA_rlz; \
1043 int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \
1044 if (_FP_FMA_shift > 0) \
1045 _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \
1046 _FP_WFRACBITS_DW_##fs); \
1047 else if (_FP_FMA_shift < 0) \
1048 _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \
1049 _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \
1050 R##_c = FP_CLS_NORMAL; \
1051 } \
1052 break; \
1053 } \
1054 goto done_fma; \
1055 \
1056 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1058 break; \
1059 \
1060 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1061 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1062 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1063 _FP_FMA_T##_s = X##_s; \
1065 \
1066 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1067 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1068 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1069 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1070 _FP_FRAC_COPY_##wc (_FP_FMA_T, X); \
1071 _FP_FMA_T##_c = X##_c; \
1072 break; \
1073 \
1074 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
1075 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1076 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1077 _FP_FMA_T##_s = Y##_s; \
1079 \
1080 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
1081 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
1082 _FP_FRAC_COPY_##wc (_FP_FMA_T, Y); \
1083 _FP_FMA_T##_c = Y##_c; \
1084 break; \
1085 \
1086 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1087 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1088 _FP_FMA_T##_s = _FP_NANSIGN_##fs; \
1089 _FP_FMA_T##_c = FP_CLS_NAN; \
1090 _FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \
1091 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \
1092 break; \
1093 \
1094 default: \
1095 _FP_UNREACHABLE; \
1096 } \
1097 \
1099 switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \
1100 { \
1101 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1103 break; \
1104 \
1105 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1106 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1107 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1108 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1109 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1110 R##_s = _FP_FMA_T##_s; \
1111 _FP_FRAC_COPY_##wc (R, _FP_FMA_T); \
1112 R##_c = _FP_FMA_T##_c; \
1113 break; \
1114 \
1115 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1116 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1117 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1118 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1119 R##_s = Z##_s; \
1120 _FP_FRAC_COPY_##wc (R, Z); \
1121 R##_c = Z##_c; \
1122 R##_e = Z##_e; \
1123 break; \
1124 \
1125 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1126 if (_FP_FMA_T##_s == Z##_s) \
1127 { \
1128 R##_s = Z##_s; \
1129 _FP_FRAC_COPY_##wc (R, Z); \
1130 R##_c = Z##_c; \
1131 } \
1132 else \
1133 { \
1134 R##_s = _FP_NANSIGN_##fs; \
1135 R##_c = FP_CLS_NAN; \
1136 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1137 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_ISI); \
1138 } \
1139 break; \
1140 \
1141 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1142 if (_FP_FMA_T##_s == Z##_s) \
1143 R##_s = Z##_s; \
1144 else \
1145 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1146 _FP_FRAC_COPY_##wc (R, Z); \
1147 R##_c = Z##_c; \
1148 break; \
1149 \
1150 default: \
1151 _FP_UNREACHABLE; \
1152 } \
1153 done_fma: ; \
1154 } \
1155 while (0)
1158 /* Main division routine. The input values should be cooked. */
1160 #define _FP_DIV(fs, wc, R, X, Y) \
1161 do \
1162 { \
1163 R##_s = X##_s ^ Y##_s; \
1164 R##_e = X##_e - Y##_e; \
1165 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
1166 { \
1167 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
1168 R##_c = FP_CLS_NORMAL; \
1169 \
1170 _FP_DIV_MEAT_##fs (R, X, Y); \
1171 break; \
1172 \
1173 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1175 break; \
1176 \
1177 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1178 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1179 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1180 R##_s = X##_s; \
1181 _FP_FRAC_COPY_##wc (R, X); \
1182 R##_c = X##_c; \
1183 break; \
1184 \
1185 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
1186 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1187 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1188 R##_s = Y##_s; \
1189 _FP_FRAC_COPY_##wc (R, Y); \
1190 R##_c = Y##_c; \
1191 break; \
1192 \
1193 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
1194 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1195 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1196 R##_c = FP_CLS_ZERO; \
1197 break; \
1198 \
1199 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
1200 FP_SET_EXCEPTION (FP_EX_DIVZERO); \
1202 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1203 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1204 R##_c = FP_CLS_INF; \
1205 break; \
1206 \
1207 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1208 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1209 R##_s = _FP_NANSIGN_##fs; \
1210 R##_c = FP_CLS_NAN; \
1211 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1212 FP_SET_EXCEPTION (FP_EX_INVALID \
1213 | (X##_c == FP_CLS_INF \
1214 ? FP_EX_INVALID_IDI \
1215 : FP_EX_INVALID_ZDZ)); \
1216 break; \
1217 \
1218 default: \
1219 _FP_UNREACHABLE; \
1220 } \
1221 } \
1222 while (0)
1225 /* Helper for comparisons. EX is 0 not to raise exceptions, 1 to
1226 raise exceptions for signaling NaN operands, 2 to raise exceptions
1227 for all NaN operands. Conditionals are organized to allow the
1228 compiler to optimize away code based on the value of EX. */
1230 #define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \
1231 do \
1232 { \
1233 /* The arguments are unordered, which may or may not result in \
1235 if (ex) \
1236 { \
1237 /* At least some cases of unordered arguments result in \
1239 if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \
1240 { \
1241 /* Check separately for each case of "invalid" \
1243 if ((ex) == 2) \
1244 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \
1245 if (_FP_ISSIGNAN (fs, wc, X) \
1246 || _FP_ISSIGNAN (fs, wc, Y)) \
1247 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
1248 } \
1249 /* Otherwise, we only need to check whether to raise an \
1251 else if ((ex) == 2 \
1252 || _FP_ISSIGNAN (fs, wc, X) \
1253 || _FP_ISSIGNAN (fs, wc, Y)) \
1254 FP_SET_EXCEPTION (FP_EX_INVALID); \
1255 } \
1256 } \
1257 while (0)
1259 /* Helper for comparisons. If denormal operands would raise an
1260 exception, check for them, and flush to zero as appropriate
1261 (otherwise, we need only check and flush to zero if it might affect
1262 the result, which is done later with _FP_CMP_CHECK_FLUSH_ZERO). */
1263 #define _FP_CMP_CHECK_DENORM(fs, wc, X, Y) \
1264 do \
1265 { \
1266 if (FP_EX_DENORM != 0) \
1267 { \
1268 /* We must ensure the correct exceptions are raised for \
1269 denormal operands, even though this may not affect the \
1271 if (FP_DENORM_ZERO) \
1272 { \
1273 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1274 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1275 } \
1276 else \
1277 { \
1278 if ((X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X)) \
1279 || (Y##_e == 0 && !_FP_FRAC_ZEROP_##wc (Y))) \
1280 FP_SET_EXCEPTION (FP_EX_DENORM); \
1281 } \
1282 } \
1283 } \
1284 while (0)
1286 /* Helper for comparisons. Check for flushing denormals for zero if
1287 we didn't need to check earlier for any denormal operands. */
1288 #define _FP_CMP_CHECK_FLUSH_ZERO(fs, wc, X, Y) \
1289 do \
1290 { \
1291 if (FP_EX_DENORM == 0) \
1292 { \
1293 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1294 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1295 } \
1296 } \
1297 while (0)
1299 /* Main differential comparison routine. The inputs should be raw not
1300 cooked. The return is -1, 0, 1 for normal values, UN
1301 otherwise. */
1303 #define _FP_CMP(fs, wc, ret, X, Y, un, ex) \
1304 do \
1305 { \
1306 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1308 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1309 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1310 { \
1311 (ret) = (un); \
1312 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1313 } \
1314 else \
1315 { \
1316 int _FP_CMP_is_zero_x; \
1317 int _FP_CMP_is_zero_y; \
1318 \
1319 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1320 \
1321 _FP_CMP_is_zero_x \
1322 = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
1323 _FP_CMP_is_zero_y \
1324 = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
1325 \
1326 if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \
1327 (ret) = 0; \
1328 else if (_FP_CMP_is_zero_x) \
1329 (ret) = Y##_s ? 1 : -1; \
1330 else if (_FP_CMP_is_zero_y) \
1331 (ret) = X##_s ? -1 : 1; \
1332 else if (X##_s != Y##_s) \
1333 (ret) = X##_s ? -1 : 1; \
1334 else if (X##_e > Y##_e) \
1335 (ret) = X##_s ? -1 : 1; \
1336 else if (X##_e < Y##_e) \
1337 (ret) = X##_s ? 1 : -1; \
1338 else if (_FP_FRAC_GT_##wc (X, Y)) \
1339 (ret) = X##_s ? -1 : 1; \
1340 else if (_FP_FRAC_GT_##wc (Y, X)) \
1341 (ret) = X##_s ? 1 : -1; \
1342 else \
1343 (ret) = 0; \
1344 } \
1345 } \
1346 while (0)
1349 /* Simplification for strict equality. */
1351 #define _FP_CMP_EQ(fs, wc, ret, X, Y, ex) \
1352 do \
1353 { \
1354 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1356 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1357 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1358 { \
1359 (ret) = 1; \
1360 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1361 } \
1362 else \
1363 { \
1364 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1365 \
1366 (ret) = !(X##_e == Y##_e \
1367 && _FP_FRAC_EQ_##wc (X, Y) \
1368 && (X##_s == Y##_s \
1369 || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \
1370 } \
1371 } \
1372 while (0)
1374 /* Version to test unordered. */
1376 #define _FP_CMP_UNORD(fs, wc, ret, X, Y, ex) \
1377 do \
1378 { \
1379 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1380 (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1381 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
1382 if (ret) \
1383 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1384 } \
1385 while (0)
1387 /* Main square root routine. The input value should be cooked. */
1389 #define _FP_SQRT(fs, wc, R, X) \
1390 do \
1391 { \
1392 _FP_FRAC_DECL_##wc (_FP_SQRT_T); \
1393 _FP_FRAC_DECL_##wc (_FP_SQRT_S); \
1394 _FP_W_TYPE _FP_SQRT_q; \
1395 switch (X##_c) \
1396 { \
1397 case FP_CLS_NAN: \
1398 _FP_FRAC_COPY_##wc (R, X); \
1399 R##_s = X##_s; \
1400 R##_c = FP_CLS_NAN; \
1401 break; \
1402 case FP_CLS_INF: \
1403 if (X##_s) \
1404 { \
1405 R##_s = _FP_NANSIGN_##fs; \
1407 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1408 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1409 } \
1410 else \
1411 { \
1412 R##_s = 0; \
1414 } \
1415 break; \
1416 case FP_CLS_ZERO: \
1417 R##_s = X##_s; \
1419 break; \
1420 case FP_CLS_NORMAL: \
1421 R##_s = 0; \
1422 if (X##_s) \
1423 { \
1425 R##_s = _FP_NANSIGN_##fs; \
1426 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1427 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1428 break; \
1429 } \
1430 R##_c = FP_CLS_NORMAL; \
1431 if (X##_e & 1) \
1432 _FP_FRAC_SLL_##wc (X, 1); \
1433 R##_e = X##_e >> 1; \
1434 _FP_FRAC_SET_##wc (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \
1435 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1436 _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \
1437 _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \
1438 _FP_SQRT_q); \
1439 } \
1440 } \
1441 while (0)
1443 /* Convert from FP to integer. Input is raw. */
1445 /* RSIGNED can have following values:
1446 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
1447 the result is either 0 or (2^rsize)-1 depending on the sign in such
1448 case.
1449 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1450 NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1451 depending on the sign in such case.
1452 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1453 NV is set plus the result is reduced modulo 2^rsize.
1454 -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
1455 set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1456 depending on the sign in such case. */
1457 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
1458 do \
1459 { \
1460 if (X##_e < _FP_EXPBIAS_##fs) \
1461 { \
1462 (r) = 0; \
1463 if (X##_e == 0) \
1464 { \
1465 if (!_FP_FRAC_ZEROP_##wc (X)) \
1466 { \
1467 if (!FP_DENORM_ZERO) \
1468 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1469 FP_SET_EXCEPTION (FP_EX_DENORM); \
1470 } \
1471 } \
1472 else \
1473 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1474 } \
1475 else if ((rsigned) == 2 \
1476 && (X##_e \
1477 >= ((_FP_EXPMAX_##fs \
1478 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1479 ? _FP_EXPMAX_##fs \
1480 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1481 { \
1483 (r) = 0; \
1484 FP_SET_EXCEPTION (FP_EX_INVALID \
1485 | FP_EX_INVALID_CVI \
1486 | ((FP_EX_INVALID_SNAN \
1487 && _FP_ISSIGNAN (fs, wc, X)) \
1488 ? FP_EX_INVALID_SNAN \
1489 : 0)); \
1490 } \
1491 else if ((rsigned) != 2 \
1492 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1493 ? _FP_EXPMAX_##fs \
1494 : (_FP_EXPBIAS_##fs + (rsize) \
1495 - ((rsigned) > 0 || X##_s))) \
1496 || (!(rsigned) && X##_s))) \
1497 { \
1499 if (rsigned) \
1500 { \
1501 (r) = 1; \
1502 (r) <<= (rsize) - 1; \
1503 (r) -= 1 - X##_s; \
1504 } \
1505 else \
1506 { \
1507 (r) = 0; \
1508 if (!X##_s) \
1509 (r) = ~(r); \
1510 } \
1511 \
1512 if (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \
1513 && (rsigned) \
1514 && X##_s \
1515 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \
1516 { \
1517 /* Possibly converting to most negative integer; check the \
1519 int _FP_TO_INT_inexact = 0; \
1520 (void) ((_FP_FRACBITS_##fs > (rsize)) \
1521 ? ({ \
1522 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1523 _FP_FRACBITS_##fs - (rsize), \
1524 _FP_FRACBITS_##fs); \
1525 0; \
1526 }) \
1527 : 0); \
1528 if (!_FP_FRAC_ZEROP_##wc (X)) \
1529 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1530 else if (_FP_TO_INT_inexact) \
1531 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1532 } \
1533 else \
1534 FP_SET_EXCEPTION (FP_EX_INVALID \
1535 | FP_EX_INVALID_CVI \
1536 | ((FP_EX_INVALID_SNAN \
1537 && _FP_ISSIGNAN (fs, wc, X)) \
1538 ? FP_EX_INVALID_SNAN \
1539 : 0)); \
1540 } \
1541 else \
1542 { \
1543 int _FP_TO_INT_inexact = 0; \
1544 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1545 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1546 { \
1547 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1548 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1549 } \
1550 else \
1551 { \
1552 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1553 (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
1554 - X##_e), \
1555 _FP_FRACBITS_##fs); \
1556 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1557 } \
1558 if ((rsigned) && X##_s) \
1559 (r) = -(r); \
1560 if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \
1561 { \
1563 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1564 || !X##_s \
1565 || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \
1566 { \
1567 _FP_TO_INT_inexact = 0; \
1568 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1569 } \
1570 } \
1571 if (_FP_TO_INT_inexact) \
1572 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1573 } \
1574 } \
1575 while (0)
1577 /* Convert from floating point to integer, rounding according to the
1578 current rounding direction. Input is raw. RSIGNED is as for
1579 _FP_TO_INT. */
1580 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \
1581 do \
1582 { \
1583 __label__ _FP_TO_INT_ROUND_done; \
1584 if (X##_e < _FP_EXPBIAS_##fs) \
1585 { \
1586 int _FP_TO_INT_ROUND_rounds_away = 0; \
1587 if (X##_e == 0) \
1588 { \
1589 if (_FP_FRAC_ZEROP_##wc (X)) \
1590 { \
1591 (r) = 0; \
1592 goto _FP_TO_INT_ROUND_done; \
1593 } \
1594 else \
1595 { \
1596 FP_SET_EXCEPTION (FP_EX_DENORM); \
1597 if (FP_DENORM_ZERO) \
1598 { \
1599 (r) = 0; \
1600 goto _FP_TO_INT_ROUND_done; \
1601 } \
1602 } \
1603 } \
1604 /* The result is 0, 1 or -1 depending on the rounding mode; \
1606 switch (FP_ROUNDMODE) \
1607 { \
1608 case FP_RND_NEAREST: \
1609 _FP_TO_INT_ROUND_rounds_away \
1610 = (X##_e == _FP_EXPBIAS_##fs - 1 \
1611 && !_FP_FRAC_ZEROP_##wc (X)); \
1612 break; \
1613 case FP_RND_ZERO: \
1615 break; \
1616 case FP_RND_PINF: \
1617 _FP_TO_INT_ROUND_rounds_away = !X##_s; \
1618 break; \
1619 case FP_RND_MINF: \
1620 _FP_TO_INT_ROUND_rounds_away = X##_s; \
1621 break; \
1622 } \
1623 if ((rsigned) == 0 && _FP_TO_INT_ROUND_rounds_away && X##_s) \
1624 { \
1626 (r) = 0; \
1627 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1628 } \
1629 else if ((rsize) == 1 && (rsigned) > 0 \
1630 && _FP_TO_INT_ROUND_rounds_away && !X##_s) \
1631 { \
1632 /* Converting to a 1-bit signed bit-field, which cannot \
1634 (r) = ((rsigned) == 2 ? -1 : 0); \
1635 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1636 } \
1637 else \
1638 { \
1639 (r) = (_FP_TO_INT_ROUND_rounds_away \
1640 ? (X##_s ? -1 : 1) \
1641 : 0); \
1642 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1643 } \
1644 } \
1645 else if ((rsigned) == 2 \
1646 && (X##_e \
1647 >= ((_FP_EXPMAX_##fs \
1648 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1649 ? _FP_EXPMAX_##fs \
1650 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1651 { \
1653 (r) = 0; \
1654 FP_SET_EXCEPTION (FP_EX_INVALID \
1655 | FP_EX_INVALID_CVI \
1656 | ((FP_EX_INVALID_SNAN \
1657 && _FP_ISSIGNAN (fs, wc, X)) \
1658 ? FP_EX_INVALID_SNAN \
1659 : 0)); \
1660 } \
1661 else if ((rsigned) != 2 \
1662 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1663 ? _FP_EXPMAX_##fs \
1664 : (_FP_EXPBIAS_##fs + (rsize) \
1665 - ((rsigned) > 0 && !X##_s))) \
1666 || ((rsigned) == 0 && X##_s))) \
1667 { \
1669 if ((rsigned) != 0) \
1670 { \
1671 (r) = 1; \
1672 (r) <<= (rsize) - 1; \
1673 (r) -= 1 - X##_s; \
1674 } \
1675 else \
1676 { \
1677 (r) = 0; \
1678 if (!X##_s) \
1679 (r) = ~(r); \
1680 } \
1681 \
1682 FP_SET_EXCEPTION (FP_EX_INVALID \
1683 | FP_EX_INVALID_CVI \
1684 | ((FP_EX_INVALID_SNAN \
1685 && _FP_ISSIGNAN (fs, wc, X)) \
1686 ? FP_EX_INVALID_SNAN \
1687 : 0)); \
1688 } \
1689 else \
1690 { \
1691 /* The value is finite, with magnitude at least 1. If \
1692 the conversion is unsigned, the value is positive. \
1693 If RSIGNED is not 2, the value does not definitely \
1694 overflow by virtue of its exponent, but may still turn \
1695 out to overflow after rounding; if RSIGNED is 2, the \
1696 exponent may be such that the value definitely overflows, \
1698 int _FP_TO_INT_ROUND_inexact = 0; \
1699 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1700 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1701 { \
1703 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1704 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1705 } \
1706 else \
1707 { \
1708 /* May need to shift in order to round (unless there \
1710 int _FP_TO_INT_ROUND_rshift \
1711 = (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs \
1712 - 1 - _FP_WORKBITS - X##_e); \
1713 if (_FP_TO_INT_ROUND_rshift > 0) \
1714 _FP_FRAC_SRS_##wc (X, _FP_TO_INT_ROUND_rshift, \
1715 _FP_WFRACBITS_##fs); \
1716 else if (_FP_TO_INT_ROUND_rshift < 0) \
1717 _FP_FRAC_SLL_##wc (X, -_FP_TO_INT_ROUND_rshift); \
1718 /* Round like _FP_ROUND, but setting \
1719 _FP_TO_INT_ROUND_inexact instead of directly setting \
1720 the "inexact" exception, since it may turn out we \
1722 if (_FP_FRAC_LOW_##wc (X) & 7) \
1723 { \
1724 _FP_TO_INT_ROUND_inexact = 1; \
1725 switch (FP_ROUNDMODE) \
1726 { \
1727 case FP_RND_NEAREST: \
1728 _FP_ROUND_NEAREST (wc, X); \
1729 break; \
1730 case FP_RND_ZERO: \
1731 _FP_ROUND_ZERO (wc, X); \
1732 break; \
1733 case FP_RND_PINF: \
1734 _FP_ROUND_PINF (wc, X); \
1735 break; \
1736 case FP_RND_MINF: \
1737 _FP_ROUND_MINF (wc, X); \
1738 break; \
1739 } \
1740 } \
1741 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
1742 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1743 } \
1744 if ((rsigned) != 0 && X##_s) \
1745 (r) = -(r); \
1746 /* An exponent of RSIZE - 1 always needs testing for \
1747 overflow (either directly overflowing, or overflowing \
1748 when rounding up results in 2^RSIZE). An exponent of \
1749 RSIZE - 2 can overflow for positive values when rounding \
1750 up to 2^(RSIZE-1), but cannot overflow for negative \
1752 if (X##_e >= (_FP_EXPBIAS_##fs + (rsize) - 1 \
1753 - ((rsigned) > 0 && !X##_s))) \
1754 { \
1755 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1756 || (X##_e == _FP_EXPBIAS_##fs + (rsize) - 1 \
1757 && (X##_s \
1758 ? (r) != (((typeof (r)) 1) << ((rsize) - 1)) \
1759 : ((rsigned) > 0 || (r) == 0))) \
1760 || ((rsigned) > 0 \
1761 && !X##_s \
1762 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 2 \
1763 && (r) == (((typeof (r)) 1) << ((rsize) - 1)))) \
1764 { \
1765 if ((rsigned) != 2) \
1766 { \
1767 if ((rsigned) != 0) \
1768 { \
1769 (r) = 1; \
1770 (r) <<= (rsize) - 1; \
1771 (r) -= 1 - X##_s; \
1772 } \
1773 else \
1774 { \
1775 (r) = 0; \
1776 (r) = ~(r); \
1777 } \
1778 } \
1779 _FP_TO_INT_ROUND_inexact = 0; \
1780 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1781 } \
1782 } \
1783 if (_FP_TO_INT_ROUND_inexact) \
1784 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1785 } \
1786 _FP_TO_INT_ROUND_done: ; \
1787 } \
1788 while (0)
1790 /* Convert integer to fp. Output is raw. RTYPE is unsigned even if
1791 input is signed. */
1792 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
1793 do \
1794 { \
1795 __label__ pack_semiraw; \
1796 if (r) \
1797 { \
1798 rtype _FP_FROM_INT_ur = (r); \
1799 \
1800 if ((X##_s = ((r) < 0))) \
1801 _FP_FROM_INT_ur = -_FP_FROM_INT_ur; \
1802 \
1803 _FP_STATIC_ASSERT ((rsize) <= 2 * _FP_W_TYPE_SIZE, \
1805 (void) (((rsize) <= _FP_W_TYPE_SIZE) \
1806 ? ({ \
1807 int _FP_FROM_INT_lz; \
1808 __FP_CLZ (_FP_FROM_INT_lz, \
1809 (_FP_W_TYPE) _FP_FROM_INT_ur); \
1810 X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \
1811 - _FP_FROM_INT_lz); \
1812 }) \
1813 : ({ \
1814 int _FP_FROM_INT_lz; \
1815 __FP_CLZ_2 (_FP_FROM_INT_lz, \
1816 (_FP_W_TYPE) (_FP_FROM_INT_ur \
1817 >> _FP_W_TYPE_SIZE), \
1818 (_FP_W_TYPE) _FP_FROM_INT_ur); \
1819 X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
1820 - _FP_FROM_INT_lz); \
1821 })); \
1822 \
1823 if ((rsize) - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
1824 && X##_e >= _FP_EXPMAX_##fs) \
1825 { \
1826 /* Exponent too big; overflow to infinity. (May also \
1828 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \
1829 goto pack_semiraw; \
1830 } \
1831 \
1832 if ((rsize) <= _FP_FRACBITS_##fs \
1833 || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
1834 { \
1836 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \
1837 if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \
1838 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
1839 + _FP_FRACBITS_##fs - 1 - X##_e)); \
1840 } \
1841 else \
1842 { \
1843 /* More bits in integer than in floating type; need to \
1845 if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
1846 _FP_FROM_INT_ur \
1847 = ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \
1848 - _FP_WFRACBITS_##fs + 1)) \
1849 | ((_FP_FROM_INT_ur \
1850 << ((rsize) - (X##_e - _FP_EXPBIAS_##fs \
1851 - _FP_WFRACBITS_##fs + 1))) \
1852 != 0)); \
1853 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \
1854 if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
1855 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
1856 + _FP_WFRACBITS_##fs - 1 - X##_e)); \
1857 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
1858 pack_semiraw: \
1859 _FP_PACK_SEMIRAW (fs, wc, X); \
1860 } \
1861 } \
1862 else \
1863 { \
1864 X##_s = 0; \
1865 X##_e = 0; \
1866 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
1867 } \
1868 } \
1869 while (0)
1872 /* Extend from a narrower floating-point format to a wider one. Input
1873 and output are raw. If CHECK_NAN, then signaling NaNs are
1874 converted to quiet with the "invalid" exception raised; otherwise
1875 signaling NaNs remain signaling with no exception. */
1876 #define _FP_EXTEND_CNAN(dfs, sfs, dwc, swc, D, S, check_nan) \
1877 do \
1878 { \
1879 _FP_STATIC_ASSERT (_FP_FRACBITS_##dfs >= _FP_FRACBITS_##sfs, \
1881 _FP_STATIC_ASSERT ((_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
1882 >= _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs), \
1885 _FP_STATIC_ASSERT (((_FP_EXPBIAS_##dfs \
1886 >= (_FP_EXPBIAS_##sfs \
1887 + _FP_FRACBITS_##sfs - 1)) \
1888 || (_FP_EXPBIAS_##dfs == _FP_EXPBIAS_##sfs)), \
1891 D##_s = S##_s; \
1892 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
1893 if (_FP_EXP_NORMAL (sfs, swc, S)) \
1894 { \
1895 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1896 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
1897 } \
1898 else \
1899 { \
1900 if (S##_e == 0) \
1901 { \
1902 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
1903 if (_FP_FRAC_ZEROP_##swc (S)) \
1904 D##_e = 0; \
1905 else if (_FP_EXPBIAS_##dfs \
1906 < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
1907 { \
1908 FP_SET_EXCEPTION (FP_EX_DENORM); \
1909 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
1910 - _FP_FRACBITS_##sfs)); \
1911 D##_e = 0; \
1912 if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \
1913 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
1914 } \
1915 else \
1916 { \
1917 int FP_EXTEND_lz; \
1918 FP_SET_EXCEPTION (FP_EX_DENORM); \
1919 _FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \
1920 _FP_FRAC_SLL_##dwc (D, \
1921 FP_EXTEND_lz + _FP_FRACBITS_##dfs \
1922 - _FP_FRACTBITS_##sfs); \
1923 D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
1924 + _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \
1925 } \
1926 } \
1927 else \
1928 { \
1929 D##_e = _FP_EXPMAX_##dfs; \
1930 if (!_FP_FRAC_ZEROP_##swc (S)) \
1931 { \
1932 if (check_nan && _FP_FRAC_SNANP (sfs, S)) \
1933 FP_SET_EXCEPTION (FP_EX_INVALID \
1934 | FP_EX_INVALID_SNAN); \
1935 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
1936 - _FP_FRACBITS_##sfs)); \
1937 if (check_nan) \
1938 _FP_SETQNAN (dfs, dwc, D); \
1939 } \
1940 } \
1941 } \
1942 } \
1943 while (0)
1945 #define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \
1946 _FP_EXTEND_CNAN (dfs, sfs, dwc, swc, D, S, 1)
1948 /* Truncate from a wider floating-point format to a narrower one.
1949 Input and output are semi-raw. */
1950 #define FP_TRUNC(dfs, sfs, dwc, swc, D, S) \
1951 do \
1952 { \
1953 _FP_STATIC_ASSERT (_FP_FRACBITS_##sfs >= _FP_FRACBITS_##dfs, \
1955 _FP_STATIC_ASSERT (((_FP_EXPBIAS_##sfs \
1956 >= (_FP_EXPBIAS_##dfs \
1957 + _FP_FRACBITS_##dfs - 1)) \
1958 || _FP_EXPBIAS_##sfs == _FP_EXPBIAS_##dfs), \
1961 D##_s = S##_s; \
1962 if (_FP_EXP_NORMAL (sfs, swc, S)) \
1963 { \
1964 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1965 if (D##_e >= _FP_EXPMAX_##dfs) \
1966 _FP_OVERFLOW_SEMIRAW (dfs, dwc, D); \
1967 else \
1968 { \
1969 if (D##_e <= 0) \
1970 { \
1971 if (D##_e < 1 - _FP_FRACBITS_##dfs) \
1972 { \
1973 _FP_FRAC_SET_##swc (S, _FP_ZEROFRAC_##swc); \
1974 _FP_FRAC_LOW_##swc (S) |= 1; \
1975 } \
1976 else \
1977 { \
1978 _FP_FRAC_HIGH_##sfs (S) |= _FP_IMPLBIT_SH_##sfs; \
1979 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
1980 - _FP_WFRACBITS_##dfs \
1981 + 1 - D##_e), \
1982 _FP_WFRACBITS_##sfs); \
1983 } \
1984 D##_e = 0; \
1985 } \
1986 else \
1987 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
1988 - _FP_WFRACBITS_##dfs), \
1989 _FP_WFRACBITS_##sfs); \
1990 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
1991 } \
1992 } \
1993 else \
1994 { \
1995 if (S##_e == 0) \
1996 { \
1997 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
1998 D##_e = 0; \
1999 if (_FP_FRAC_ZEROP_##swc (S)) \
2000 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2001 else \
2002 { \
2003 FP_SET_EXCEPTION (FP_EX_DENORM); \
2004 if (_FP_EXPBIAS_##sfs \
2005 < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
2006 { \
2007 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
2008 - _FP_WFRACBITS_##dfs), \
2009 _FP_WFRACBITS_##sfs); \
2010 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
2011 } \
2012 else \
2013 { \
2014 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2015 _FP_FRAC_LOW_##dwc (D) |= 1; \
2016 } \
2017 } \
2018 } \
2019 else \
2020 { \
2021 D##_e = _FP_EXPMAX_##dfs; \
2022 if (_FP_FRAC_ZEROP_##swc (S)) \
2023 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2024 else \
2025 { \
2026 _FP_CHECK_SIGNAN_SEMIRAW (sfs, swc, S); \
2027 _FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \
2028 - _FP_WFRACBITS_##dfs)); \
2029 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
2031 _FP_FRAC_LOW_##dwc (D) \
2032 &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
2033 _FP_SETQNAN_SEMIRAW (dfs, dwc, D); \
2034 } \
2035 } \
2036 } \
2037 } \
2038 while (0)
2040 /* Truncate from a wider floating-point format to a narrower one.
2041 Input and output are cooked. */
2042 #define FP_TRUNC_COOKED(dfs, sfs, dwc, swc, D, S) \
2043 do \
2044 { \
2045 _FP_STATIC_ASSERT (_FP_FRACBITS_##sfs >= _FP_FRACBITS_##dfs, \
2047 if (S##_c == FP_CLS_NAN) \
2048 _FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \
2049 - _FP_WFRACBITS_##dfs)); \
2050 else \
2051 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
2052 - _FP_WFRACBITS_##dfs), \
2053 _FP_WFRACBITS_##sfs); \
2054 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
2055 D##_e = S##_e; \
2056 D##_c = S##_c; \
2057 D##_s = S##_s; \
2058 } \
2059 while (0)
2061 /* Helper primitives. */
2063 /* Count leading zeros in a word. */
2065 #ifndef __FP_CLZ
2066 /* GCC 3.4 and later provide the builtins for us. */
2067 # define __FP_CLZ(r, x) \
2068 do \
2069 { \
2070 _FP_STATIC_ASSERT ((sizeof (_FP_W_TYPE) == sizeof (unsigned int) \
2071 || (sizeof (_FP_W_TYPE) \
2072 == sizeof (unsigned long)) \
2073 || (sizeof (_FP_W_TYPE) \
2074 == sizeof (unsigned long long))), \
2076 if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
2077 (r) = __builtin_clz (x); \
2078 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
2079 (r) = __builtin_clzl (x); \
2081 (r) = __builtin_clzll (x); \
2082 } \
2083 while (0)
2086 #define _FP_DIV_HELP_imm(q, r, n, d) \
2087 do \
2088 { \
2089 (q) = (n) / (d), (r) = (n) % (d); \
2090 } \
2091 while (0)
2094 /* A restoring bit-by-bit division primitive. */
2096 #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
2097 do \
2098 { \
2099 int _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \
2100 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \
2101 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \
2102 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \
2103 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \
2104 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
2106 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \
2107 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_v, _FP_WFRACXBITS_##fs); \
2108 /* First round. Since the operands are normalized, either the \
2109 first or second bit will be set in the fraction. Produce a \
2110 normalized result by checking which and adjusting the loop \
2112 if (_FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \
2113 { \
2114 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2115 _FP_DIV_MEAT_N_loop_u, \
2116 _FP_DIV_MEAT_N_loop_v); \
2117 _FP_FRAC_LOW_##wc (R) |= 1; \
2118 _FP_DIV_MEAT_N_loop_count--; \
2119 } \
2120 else \
2121 R##_e--; \
2123 do \
2124 { \
2125 int _FP_DIV_MEAT_N_loop_msb \
2126 = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \
2127 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \
2128 _FP_FRAC_SLL_##wc (R, 1); \
2129 if (_FP_DIV_MEAT_N_loop_msb \
2130 || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \
2131 _FP_DIV_MEAT_N_loop_v)) \
2132 { \
2133 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2134 _FP_DIV_MEAT_N_loop_u, \
2135 _FP_DIV_MEAT_N_loop_v); \
2136 _FP_FRAC_LOW_##wc (R) |= 1; \
2137 } \
2138 } \
2139 while (--_FP_DIV_MEAT_N_loop_count > 0); \
2140 /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \
2142 _FP_FRAC_LOW_##wc (R) \
2143 |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \
2144 } \
2145 while (0)
2147 #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
2148 #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
2149 #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)