| blob | 9c1c5e35f2de427e7fee90619a7ff9c27896e67a |
1 /* Software floating-point emulation. Common operations.
2 Copyright (C) 1997-2015 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Richard Henderson (rth@cygnus.com),
5 Jakub Jelinek (jj@ultra.linux.cz),
6 David S. Miller (davem@redhat.com) and
7 Peter Maydell (pmaydell@chiark.greenend.org.uk).
9 The GNU C Library is free software; you can redistribute it and/or
10 modify it under the terms of the GNU Lesser General Public
11 License as published by the Free Software Foundation; either
12 version 2.1 of the License, or (at your option) any later version.
14 In addition to the permissions in the GNU Lesser General Public
15 License, the Free Software Foundation gives you unlimited
16 permission to link the compiled version of this file into
17 combinations with other programs, and to distribute those
18 combinations without any restriction coming from the use of this
19 file. (The Lesser General Public License restrictions do apply in
20 other respects; for example, they cover modification of the file,
21 and distribution when not linked into a combine executable.)
23 The GNU C Library is distributed in the hope that it will be useful,
24 but WITHOUT ANY WARRANTY; without even the implied warranty of
25 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
26 Lesser General Public License for more details.
28 You should have received a copy of the GNU Lesser General Public
29 License along with the GNU C Library; if not, see
30 <http://www.gnu.org/licenses/>. */
32 #ifndef SOFT_FP_OP_COMMON_H
33 #define SOFT_FP_OP_COMMON_H 1
35 #define _FP_DECL(wc, X) \
36 _FP_I_TYPE X##_c __attribute__ ((unused)) _FP_ZERO_INIT; \
37 _FP_I_TYPE X##_s __attribute__ ((unused)) _FP_ZERO_INIT; \
38 _FP_I_TYPE X##_e __attribute__ ((unused)) _FP_ZERO_INIT; \
39 _FP_FRAC_DECL_##wc (X)
41 /* Test whether the qNaN bit denotes a signaling NaN. */
42 #define _FP_FRAC_SNANP(fs, X) \
43 ((_FP_QNANNEGATEDP) \
44 ? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \
45 : !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs))
46 #define _FP_FRAC_SNANP_SEMIRAW(fs, X) \
47 ((_FP_QNANNEGATEDP) \
48 ? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \
49 : !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs))
51 /* Finish truly unpacking a native fp value by classifying the kind
52 of fp value and normalizing both the exponent and the fraction. */
54 #define _FP_UNPACK_CANONICAL(fs, wc, X) \
55 do \
56 { \
57 switch (X##_e) \
58 { \
59 default: \
60 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
61 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
62 X##_e -= _FP_EXPBIAS_##fs; \
63 X##_c = FP_CLS_NORMAL; \
64 break; \
65 \
66 case 0: \
67 if (_FP_FRAC_ZEROP_##wc (X)) \
68 X##_c = FP_CLS_ZERO; \
69 else if (FP_DENORM_ZERO) \
70 { \
71 X##_c = FP_CLS_ZERO; \
72 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
73 FP_SET_EXCEPTION (FP_EX_DENORM); \
74 } \
75 else \
76 { \
78 _FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \
79 _FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \
80 X); \
81 _FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \
82 _FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \
83 + _FP_WORKBITS)); \
84 X##_e -= (_FP_EXPBIAS_##fs - 1 \
85 + _FP_UNPACK_CANONICAL_shift); \
86 X##_c = FP_CLS_NORMAL; \
87 FP_SET_EXCEPTION (FP_EX_DENORM); \
88 } \
89 break; \
90 \
91 case _FP_EXPMAX_##fs: \
92 if (_FP_FRAC_ZEROP_##wc (X)) \
93 X##_c = FP_CLS_INF; \
94 else \
95 { \
96 X##_c = FP_CLS_NAN; \
98 if (_FP_FRAC_SNANP (fs, X)) \
99 FP_SET_EXCEPTION (FP_EX_INVALID \
100 | FP_EX_INVALID_SNAN); \
101 } \
102 break; \
103 } \
104 } \
105 while (0)
107 /* Finish unpacking an fp value in semi-raw mode: the mantissa is
108 shifted by _FP_WORKBITS but the implicit MSB is not inserted and
109 other classification is not done. */
110 #define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc (X, _FP_WORKBITS)
112 /* Check whether a raw or semi-raw input value should be flushed to
113 zero, and flush it to zero if so. */
114 #define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \
115 do \
116 { \
117 if (FP_DENORM_ZERO \
118 && X##_e == 0 \
119 && !_FP_FRAC_ZEROP_##wc (X)) \
120 { \
121 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
122 FP_SET_EXCEPTION (FP_EX_DENORM); \
123 } \
124 } \
125 while (0)
127 /* A semi-raw value has overflowed to infinity. Adjust the mantissa
128 and exponent appropriately. */
129 #define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \
130 do \
131 { \
132 if (FP_ROUNDMODE == FP_RND_NEAREST \
133 || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \
134 || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \
135 { \
136 X##_e = _FP_EXPMAX_##fs; \
137 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
138 } \
139 else \
140 { \
141 X##_e = _FP_EXPMAX_##fs - 1; \
142 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
143 } \
144 FP_SET_EXCEPTION (FP_EX_INEXACT); \
145 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
146 } \
147 while (0)
149 /* Check for a semi-raw value being a signaling NaN and raise the
150 invalid exception if so. */
151 #define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \
152 do \
153 { \
154 if (X##_e == _FP_EXPMAX_##fs \
155 && !_FP_FRAC_ZEROP_##wc (X) \
156 && _FP_FRAC_SNANP_SEMIRAW (fs, X)) \
157 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
158 } \
159 while (0)
161 /* Choose a NaN result from an operation on two semi-raw NaN
162 values. */
163 #define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \
164 do \
165 { \
167 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
168 _FP_FRAC_SRL_##wc (Y, _FP_WORKBITS); \
169 _FP_CHOOSENAN (fs, wc, R, X, Y, OP); \
170 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
171 } \
172 while (0)
174 /* Make the fractional part a quiet NaN, preserving the payload
175 if possible, otherwise make it the canonical quiet NaN and set
176 the sign bit accordingly. */
177 #define _FP_SETQNAN(fs, wc, X) \
178 do \
179 { \
180 if (_FP_QNANNEGATEDP) \
181 { \
182 _FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \
183 if (_FP_FRAC_ZEROP_##wc (X)) \
184 { \
185 X##_s = _FP_NANSIGN_##fs; \
186 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
187 } \
188 } \
189 else \
190 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_QNANBIT_##fs; \
191 } \
192 while (0)
193 #define _FP_SETQNAN_SEMIRAW(fs, wc, X) \
194 do \
195 { \
196 if (_FP_QNANNEGATEDP) \
197 { \
198 _FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \
199 if (_FP_FRAC_ZEROP_##wc (X)) \
200 { \
201 X##_s = _FP_NANSIGN_##fs; \
202 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
203 _FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
204 } \
205 } \
206 else \
207 _FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \
208 } \
209 while (0)
211 /* Test whether a biased exponent is normal (not zero or maximum). */
212 #define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1)
214 /* Prepare to pack an fp value in semi-raw mode: the mantissa is
215 rounded and shifted right, with the rounding possibly increasing
216 the exponent (including changing a finite value to infinity). */
217 #define _FP_PACK_SEMIRAW(fs, wc, X) \
218 do \
219 { \
220 int _FP_PACK_SEMIRAW_is_tiny \
221 = X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \
222 if (_FP_TININESS_AFTER_ROUNDING \
223 && _FP_PACK_SEMIRAW_is_tiny) \
224 { \
225 FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \
226 _FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \
227 _FP_PACK_SEMIRAW_T##_s = X##_s; \
228 _FP_PACK_SEMIRAW_T##_e = X##_e; \
229 _FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \
230 _FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \
231 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \
232 _FP_PACK_SEMIRAW_is_tiny = 0; \
233 } \
234 _FP_ROUND (wc, X); \
235 if (_FP_PACK_SEMIRAW_is_tiny) \
236 { \
237 if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
238 || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
239 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
240 } \
241 if (_FP_FRAC_HIGH_##fs (X) \
242 & (_FP_OVERFLOW_##fs >> 1)) \
243 { \
244 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_OVERFLOW_##fs >> 1); \
245 X##_e++; \
246 if (X##_e == _FP_EXPMAX_##fs) \
247 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \
248 } \
249 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
250 if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
251 { \
252 if (!_FP_KEEPNANFRACP) \
253 { \
254 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
255 X##_s = _FP_NANSIGN_##fs; \
256 } \
257 else \
258 _FP_SETQNAN (fs, wc, X); \
259 } \
260 } \
261 while (0)
263 /* Before packing the bits back into the native fp result, take care
264 of such mundane things as rounding and overflow. Also, for some
265 kinds of fp values, the original parts may not have been fully
266 extracted -- but that is ok, we can regenerate them now. */
268 #define _FP_PACK_CANONICAL(fs, wc, X) \
269 do \
270 { \
271 switch (X##_c) \
272 { \
273 case FP_CLS_NORMAL: \
274 X##_e += _FP_EXPBIAS_##fs; \
275 if (X##_e > 0) \
276 { \
277 _FP_ROUND (wc, X); \
278 if (_FP_FRAC_OVERP_##wc (fs, X)) \
279 { \
280 _FP_FRAC_CLEAR_OVERP_##wc (fs, X); \
281 X##_e++; \
282 } \
283 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
284 if (X##_e >= _FP_EXPMAX_##fs) \
285 { \
287 switch (FP_ROUNDMODE) \
288 { \
289 case FP_RND_NEAREST: \
290 X##_c = FP_CLS_INF; \
291 break; \
292 case FP_RND_PINF: \
293 if (!X##_s) \
294 X##_c = FP_CLS_INF; \
295 break; \
296 case FP_RND_MINF: \
297 if (X##_s) \
298 X##_c = FP_CLS_INF; \
299 break; \
300 } \
301 if (X##_c == FP_CLS_INF) \
302 { \
304 X##_e = _FP_EXPMAX_##fs; \
305 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
306 } \
307 else \
308 { \
310 X##_e = _FP_EXPMAX_##fs - 1; \
311 _FP_FRAC_SET_##wc (X, _FP_MAXFRAC_##wc); \
312 } \
313 FP_SET_EXCEPTION (FP_EX_OVERFLOW); \
314 FP_SET_EXCEPTION (FP_EX_INEXACT); \
315 } \
316 } \
317 else \
318 { \
320 int _FP_PACK_CANONICAL_is_tiny = 1; \
321 if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \
322 { \
323 FP_DECL_##fs (_FP_PACK_CANONICAL_T); \
324 _FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \
325 _FP_PACK_CANONICAL_T##_s = X##_s; \
326 _FP_PACK_CANONICAL_T##_e = X##_e; \
327 _FP_ROUND (wc, _FP_PACK_CANONICAL_T); \
328 if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \
329 _FP_PACK_CANONICAL_is_tiny = 0; \
330 } \
331 X##_e = -X##_e + 1; \
332 if (X##_e <= _FP_WFRACBITS_##fs) \
333 { \
334 _FP_FRAC_SRS_##wc (X, X##_e, _FP_WFRACBITS_##fs); \
335 _FP_ROUND (wc, X); \
336 if (_FP_FRAC_HIGH_##fs (X) \
337 & (_FP_OVERFLOW_##fs >> 1)) \
338 { \
339 X##_e = 1; \
340 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
341 FP_SET_EXCEPTION (FP_EX_INEXACT); \
342 } \
343 else \
344 { \
345 X##_e = 0; \
346 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
347 } \
348 if (_FP_PACK_CANONICAL_is_tiny \
349 && ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
350 || (FP_TRAPPING_EXCEPTIONS \
351 & FP_EX_UNDERFLOW))) \
352 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
353 } \
354 else \
355 { \
357 X##_e = 0; \
358 if (!_FP_FRAC_ZEROP_##wc (X)) \
359 { \
360 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
361 _FP_ROUND (wc, X); \
362 _FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \
363 } \
364 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
365 } \
366 } \
367 break; \
368 \
369 case FP_CLS_ZERO: \
370 X##_e = 0; \
371 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
372 break; \
373 \
374 case FP_CLS_INF: \
375 X##_e = _FP_EXPMAX_##fs; \
376 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
377 break; \
378 \
379 case FP_CLS_NAN: \
380 X##_e = _FP_EXPMAX_##fs; \
381 if (!_FP_KEEPNANFRACP) \
382 { \
383 _FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
384 X##_s = _FP_NANSIGN_##fs; \
385 } \
386 else \
387 _FP_SETQNAN (fs, wc, X); \
388 break; \
389 } \
390 } \
391 while (0)
393 /* This one accepts raw argument and not cooked, returns
394 1 if X is a signaling NaN. */
395 #define _FP_ISSIGNAN(fs, wc, X) \
396 ({ \
397 int _FP_ISSIGNAN_ret = 0; \
398 if (X##_e == _FP_EXPMAX_##fs) \
399 { \
400 if (!_FP_FRAC_ZEROP_##wc (X) \
401 && _FP_FRAC_SNANP (fs, X)) \
402 _FP_ISSIGNAN_ret = 1; \
403 } \
404 _FP_ISSIGNAN_ret; \
405 })
411 /* Addition on semi-raw values. */
412 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
413 do \
414 { \
415 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
416 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
417 if (X##_s == Y##_s) \
418 { \
420 __label__ add1, add2, add3, add_done; \
421 R##_s = X##_s; \
422 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
423 if (_FP_ADD_INTERNAL_ediff > 0) \
424 { \
425 R##_e = X##_e; \
426 if (Y##_e == 0) \
427 { \
429 if (_FP_FRAC_ZEROP_##wc (Y)) \
430 { \
431 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
432 _FP_FRAC_COPY_##wc (R, X); \
433 goto add_done; \
434 } \
435 else \
436 { \
437 FP_SET_EXCEPTION (FP_EX_DENORM); \
438 _FP_ADD_INTERNAL_ediff--; \
439 if (_FP_ADD_INTERNAL_ediff == 0) \
440 { \
441 _FP_FRAC_ADD_##wc (R, X, Y); \
442 goto add3; \
443 } \
444 if (X##_e == _FP_EXPMAX_##fs) \
445 { \
446 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
447 _FP_FRAC_COPY_##wc (R, X); \
448 goto add_done; \
449 } \
450 goto add1; \
451 } \
452 } \
453 else if (X##_e == _FP_EXPMAX_##fs) \
454 { \
456 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
457 _FP_FRAC_COPY_##wc (R, X); \
458 goto add_done; \
459 } \
460 \
462 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
463 \
464 add1: \
465 /* Shift the mantissa of Y to the right \
466 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
468 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
469 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \
470 _FP_WFRACBITS_##fs); \
471 else if (!_FP_FRAC_ZEROP_##wc (Y)) \
472 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
473 _FP_FRAC_ADD_##wc (R, X, Y); \
474 } \
475 else if (_FP_ADD_INTERNAL_ediff < 0) \
476 { \
477 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \
478 R##_e = Y##_e; \
479 if (X##_e == 0) \
480 { \
482 if (_FP_FRAC_ZEROP_##wc (X)) \
483 { \
484 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
485 _FP_FRAC_COPY_##wc (R, Y); \
486 goto add_done; \
487 } \
488 else \
489 { \
490 FP_SET_EXCEPTION (FP_EX_DENORM); \
491 _FP_ADD_INTERNAL_ediff--; \
492 if (_FP_ADD_INTERNAL_ediff == 0) \
493 { \
494 _FP_FRAC_ADD_##wc (R, Y, X); \
495 goto add3; \
496 } \
497 if (Y##_e == _FP_EXPMAX_##fs) \
498 { \
499 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
500 _FP_FRAC_COPY_##wc (R, Y); \
501 goto add_done; \
502 } \
503 goto add2; \
504 } \
505 } \
506 else if (Y##_e == _FP_EXPMAX_##fs) \
507 { \
509 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
510 _FP_FRAC_COPY_##wc (R, Y); \
511 goto add_done; \
512 } \
513 \
515 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
516 \
517 add2: \
518 /* Shift the mantissa of X to the right \
519 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
521 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
522 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \
523 _FP_WFRACBITS_##fs); \
524 else if (!_FP_FRAC_ZEROP_##wc (X)) \
525 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
526 _FP_FRAC_ADD_##wc (R, Y, X); \
527 } \
528 else \
529 { \
531 if (!_FP_EXP_NORMAL (fs, wc, X)) \
532 { \
533 if (X##_e == 0) \
534 { \
536 R##_e = 0; \
537 if (_FP_FRAC_ZEROP_##wc (X)) \
538 { \
539 if (!_FP_FRAC_ZEROP_##wc (Y)) \
540 FP_SET_EXCEPTION (FP_EX_DENORM); \
541 _FP_FRAC_COPY_##wc (R, Y); \
542 goto add_done; \
543 } \
544 else if (_FP_FRAC_ZEROP_##wc (Y)) \
545 { \
546 FP_SET_EXCEPTION (FP_EX_DENORM); \
547 _FP_FRAC_COPY_##wc (R, X); \
548 goto add_done; \
549 } \
550 else \
551 { \
552 FP_SET_EXCEPTION (FP_EX_DENORM); \
553 _FP_FRAC_ADD_##wc (R, X, Y); \
554 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
555 { \
557 _FP_FRAC_HIGH_##fs (R) \
558 &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
559 R##_e = 1; \
560 } \
561 goto add_done; \
562 } \
563 } \
564 else \
565 { \
567 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
568 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
569 R##_e = _FP_EXPMAX_##fs; \
570 if (_FP_FRAC_ZEROP_##wc (X)) \
571 _FP_FRAC_COPY_##wc (R, Y); \
572 else if (_FP_FRAC_ZEROP_##wc (Y)) \
573 _FP_FRAC_COPY_##wc (R, X); \
574 else \
575 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
576 goto add_done; \
577 } \
578 } \
579 /* The exponents of X and Y, both normal, are equal. The \
580 implicit MSBs will always add to increase the \
582 _FP_FRAC_ADD_##wc (R, X, Y); \
583 R##_e = X##_e + 1; \
584 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
585 if (R##_e == _FP_EXPMAX_##fs) \
587 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \
588 goto add_done; \
589 } \
590 add3: \
591 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
592 { \
594 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
595 R##_e++; \
596 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
597 if (R##_e == _FP_EXPMAX_##fs) \
599 _FP_OVERFLOW_SEMIRAW (fs, wc, R); \
600 } \
601 add_done: ; \
602 } \
603 else \
604 { \
606 __label__ sub1, sub2, sub3, norm, sub_done; \
607 int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
608 if (_FP_ADD_INTERNAL_ediff > 0) \
609 { \
610 R##_e = X##_e; \
611 R##_s = X##_s; \
612 if (Y##_e == 0) \
613 { \
615 if (_FP_FRAC_ZEROP_##wc (Y)) \
616 { \
617 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
618 _FP_FRAC_COPY_##wc (R, X); \
619 goto sub_done; \
620 } \
621 else \
622 { \
623 FP_SET_EXCEPTION (FP_EX_DENORM); \
624 _FP_ADD_INTERNAL_ediff--; \
625 if (_FP_ADD_INTERNAL_ediff == 0) \
626 { \
627 _FP_FRAC_SUB_##wc (R, X, Y); \
628 goto sub3; \
629 } \
630 if (X##_e == _FP_EXPMAX_##fs) \
631 { \
632 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
633 _FP_FRAC_COPY_##wc (R, X); \
634 goto sub_done; \
635 } \
636 goto sub1; \
637 } \
638 } \
639 else if (X##_e == _FP_EXPMAX_##fs) \
640 { \
642 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
643 _FP_FRAC_COPY_##wc (R, X); \
644 goto sub_done; \
645 } \
646 \
648 _FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
649 \
650 sub1: \
651 /* Shift the mantissa of Y to the right \
652 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
654 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
655 _FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_ediff, \
656 _FP_WFRACBITS_##fs); \
657 else if (!_FP_FRAC_ZEROP_##wc (Y)) \
658 _FP_FRAC_SET_##wc (Y, _FP_MINFRAC_##wc); \
659 _FP_FRAC_SUB_##wc (R, X, Y); \
660 } \
661 else if (_FP_ADD_INTERNAL_ediff < 0) \
662 { \
663 _FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_ediff; \
664 R##_e = Y##_e; \
665 R##_s = Y##_s; \
666 if (X##_e == 0) \
667 { \
669 if (_FP_FRAC_ZEROP_##wc (X)) \
670 { \
671 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
672 _FP_FRAC_COPY_##wc (R, Y); \
673 goto sub_done; \
674 } \
675 else \
676 { \
677 FP_SET_EXCEPTION (FP_EX_DENORM); \
678 _FP_ADD_INTERNAL_ediff--; \
679 if (_FP_ADD_INTERNAL_ediff == 0) \
680 { \
681 _FP_FRAC_SUB_##wc (R, Y, X); \
682 goto sub3; \
683 } \
684 if (Y##_e == _FP_EXPMAX_##fs) \
685 { \
686 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
687 _FP_FRAC_COPY_##wc (R, Y); \
688 goto sub_done; \
689 } \
690 goto sub2; \
691 } \
692 } \
693 else if (Y##_e == _FP_EXPMAX_##fs) \
694 { \
696 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
697 _FP_FRAC_COPY_##wc (R, Y); \
698 goto sub_done; \
699 } \
700 \
702 _FP_FRAC_HIGH_##fs (X) |= _FP_IMPLBIT_SH_##fs; \
703 \
704 sub2: \
705 /* Shift the mantissa of X to the right \
706 _FP_ADD_INTERNAL_EDIFF steps; remember to account \
708 if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
709 _FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_ediff, \
710 _FP_WFRACBITS_##fs); \
711 else if (!_FP_FRAC_ZEROP_##wc (X)) \
712 _FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
713 _FP_FRAC_SUB_##wc (R, Y, X); \
714 } \
715 else \
716 { \
718 if (!_FP_EXP_NORMAL (fs, wc, X)) \
719 { \
720 if (X##_e == 0) \
721 { \
723 R##_e = 0; \
724 if (_FP_FRAC_ZEROP_##wc (X)) \
725 { \
726 _FP_FRAC_COPY_##wc (R, Y); \
727 if (_FP_FRAC_ZEROP_##wc (Y)) \
728 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
729 else \
730 { \
731 FP_SET_EXCEPTION (FP_EX_DENORM); \
732 R##_s = Y##_s; \
733 } \
734 goto sub_done; \
735 } \
736 else if (_FP_FRAC_ZEROP_##wc (Y)) \
737 { \
738 FP_SET_EXCEPTION (FP_EX_DENORM); \
739 _FP_FRAC_COPY_##wc (R, X); \
740 R##_s = X##_s; \
741 goto sub_done; \
742 } \
743 else \
744 { \
745 FP_SET_EXCEPTION (FP_EX_DENORM); \
746 _FP_FRAC_SUB_##wc (R, X, Y); \
747 R##_s = X##_s; \
748 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
749 { \
751 _FP_FRAC_SUB_##wc (R, Y, X); \
752 R##_s = Y##_s; \
753 } \
754 else if (_FP_FRAC_ZEROP_##wc (R)) \
755 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
756 goto sub_done; \
757 } \
758 } \
759 else \
760 { \
762 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
763 _FP_CHECK_SIGNAN_SEMIRAW (fs, wc, Y); \
764 R##_e = _FP_EXPMAX_##fs; \
765 if (_FP_FRAC_ZEROP_##wc (X)) \
766 { \
767 if (_FP_FRAC_ZEROP_##wc (Y)) \
768 { \
770 R##_s = _FP_NANSIGN_##fs; \
771 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
772 _FP_FRAC_SLL_##wc (R, _FP_WORKBITS); \
773 FP_SET_EXCEPTION (FP_EX_INVALID \
774 | FP_EX_INVALID_ISI); \
775 } \
776 else \
777 { \
779 R##_s = Y##_s; \
780 _FP_FRAC_COPY_##wc (R, Y); \
781 } \
782 } \
783 else \
784 { \
785 if (_FP_FRAC_ZEROP_##wc (Y)) \
786 { \
788 R##_s = X##_s; \
789 _FP_FRAC_COPY_##wc (R, X); \
790 } \
791 else \
792 { \
794 _FP_CHOOSENAN_SEMIRAW (fs, wc, R, X, Y, OP); \
795 } \
796 } \
797 goto sub_done; \
798 } \
799 } \
800 /* The exponents of X and Y, both normal, are equal. The \
802 R##_e = X##_e; \
803 _FP_FRAC_SUB_##wc (R, X, Y); \
804 R##_s = X##_s; \
805 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
806 { \
808 _FP_FRAC_SUB_##wc (R, Y, X); \
809 R##_s = Y##_s; \
810 } \
811 else if (_FP_FRAC_ZEROP_##wc (R)) \
812 { \
813 R##_e = 0; \
814 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
815 goto sub_done; \
816 } \
817 goto norm; \
818 } \
819 sub3: \
820 if (_FP_FRAC_HIGH_##fs (R) & _FP_IMPLBIT_SH_##fs) \
821 { \
822 int _FP_ADD_INTERNAL_diff; \
823 /* Carry into most significant bit of larger one of X and Y, \
825 _FP_FRAC_HIGH_##fs (R) &= _FP_IMPLBIT_SH_##fs - 1; \
826 norm: \
827 _FP_FRAC_CLZ_##wc (_FP_ADD_INTERNAL_diff, R); \
828 _FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \
829 _FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \
830 if (R##_e <= _FP_ADD_INTERNAL_diff) \
831 { \
833 _FP_ADD_INTERNAL_diff \
834 = _FP_ADD_INTERNAL_diff - R##_e + 1; \
835 _FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \
836 _FP_WFRACBITS_##fs); \
837 R##_e = 0; \
838 } \
839 else \
840 { \
841 R##_e -= _FP_ADD_INTERNAL_diff; \
842 _FP_FRAC_HIGH_##fs (R) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
843 } \
844 } \
845 sub_done: ; \
846 } \
847 } \
848 while (0)
851 #define _FP_SUB(fs, wc, R, X, Y) \
852 do \
853 { \
854 if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
855 Y##_s ^= 1; \
857 } \
858 while (0)
861 /* Main negation routine. The input value is raw. */
863 #define _FP_NEG(fs, wc, R, X) \
864 do \
865 { \
866 _FP_FRAC_COPY_##wc (R, X); \
867 R##_e = X##_e; \
868 R##_s = 1 ^ X##_s; \
869 } \
870 while (0)
873 /* Main multiplication routine. The input values should be cooked. */
875 #define _FP_MUL(fs, wc, R, X, Y) \
876 do \
877 { \
878 R##_s = X##_s ^ Y##_s; \
879 R##_e = X##_e + Y##_e + 1; \
880 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
881 { \
882 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
883 R##_c = FP_CLS_NORMAL; \
884 \
885 _FP_MUL_MEAT_##fs (R, X, Y); \
886 \
887 if (_FP_FRAC_OVERP_##wc (fs, R)) \
888 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
889 else \
890 R##_e--; \
891 break; \
892 \
893 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
895 break; \
896 \
897 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
898 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
899 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
900 R##_s = X##_s; \
901 \
902 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
903 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
904 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
905 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
906 _FP_FRAC_COPY_##wc (R, X); \
907 R##_c = X##_c; \
908 break; \
909 \
910 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
911 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
912 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
913 R##_s = Y##_s; \
914 \
915 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
916 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
917 _FP_FRAC_COPY_##wc (R, Y); \
918 R##_c = Y##_c; \
919 break; \
920 \
921 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
922 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
923 R##_s = _FP_NANSIGN_##fs; \
924 R##_c = FP_CLS_NAN; \
925 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
926 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ); \
927 break; \
928 \
929 default: \
930 _FP_UNREACHABLE; \
931 } \
932 } \
933 while (0)
936 /* Fused multiply-add. The input values should be cooked. */
938 #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
939 do \
940 { \
941 __label__ done_fma; \
942 FP_DECL_##fs (_FP_FMA_T); \
943 _FP_FMA_T##_s = X##_s ^ Y##_s; \
944 _FP_FMA_T##_e = X##_e + Y##_e + 1; \
945 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
946 { \
947 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
948 switch (Z##_c) \
949 { \
950 case FP_CLS_INF: \
951 case FP_CLS_NAN: \
952 R##_s = Z##_s; \
953 _FP_FRAC_COPY_##wc (R, Z); \
954 R##_c = Z##_c; \
955 break; \
956 \
957 case FP_CLS_ZERO: \
958 R##_c = FP_CLS_NORMAL; \
959 R##_s = _FP_FMA_T##_s; \
960 R##_e = _FP_FMA_T##_e; \
961 \
962 _FP_MUL_MEAT_##fs (R, X, Y); \
963 \
964 if (_FP_FRAC_OVERP_##wc (fs, R)) \
965 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
966 else \
967 R##_e--; \
968 break; \
969 \
970 case FP_CLS_NORMAL:; \
971 _FP_FRAC_DECL_##dwc (_FP_FMA_TD); \
972 _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \
973 _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \
974 _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \
975 R##_e = _FP_FMA_T##_e; \
976 int _FP_FMA_tsh \
977 = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \
978 _FP_FMA_T##_e -= _FP_FMA_tsh; \
979 int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \
980 if (_FP_FMA_ediff >= 0) \
981 { \
982 int _FP_FMA_shift \
983 = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \
984 if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \
985 _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \
986 else \
987 { \
988 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
989 if (_FP_FMA_shift < 0) \
990 _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \
991 _FP_WFRACBITS_DW_##fs); \
992 else if (_FP_FMA_shift > 0) \
993 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \
994 } \
995 R##_s = _FP_FMA_T##_s; \
996 if (_FP_FMA_T##_s == Z##_s) \
997 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
998 _FP_FMA_ZD); \
999 else \
1000 { \
1001 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
1002 _FP_FMA_ZD); \
1003 if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \
1004 { \
1005 R##_s = Z##_s; \
1006 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1007 _FP_FMA_TD); \
1008 } \
1009 } \
1010 } \
1011 else \
1012 { \
1013 R##_e = Z##_e; \
1014 R##_s = Z##_s; \
1015 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
1016 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \
1017 int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \
1018 if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \
1019 _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \
1020 else if (_FP_FMA_shift > 0) \
1021 _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \
1022 _FP_WFRACBITS_DW_##fs); \
1023 if (Z##_s == _FP_FMA_T##_s) \
1024 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1025 _FP_FMA_TD); \
1026 else \
1027 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1028 _FP_FMA_TD); \
1029 } \
1030 if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \
1031 { \
1032 if (_FP_FMA_T##_s == Z##_s) \
1033 R##_s = Z##_s; \
1034 else \
1035 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1036 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1037 R##_c = FP_CLS_ZERO; \
1038 } \
1039 else \
1040 { \
1041 int _FP_FMA_rlz; \
1042 _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \
1043 _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \
1044 R##_e -= _FP_FMA_rlz; \
1045 int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \
1046 if (_FP_FMA_shift > 0) \
1047 _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \
1048 _FP_WFRACBITS_DW_##fs); \
1049 else if (_FP_FMA_shift < 0) \
1050 _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \
1051 _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \
1052 R##_c = FP_CLS_NORMAL; \
1053 } \
1054 break; \
1055 } \
1056 goto done_fma; \
1057 \
1058 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1060 break; \
1061 \
1062 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1063 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1064 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1065 _FP_FMA_T##_s = X##_s; \
1066 \
1067 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1068 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1069 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1070 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1071 _FP_FRAC_COPY_##wc (_FP_FMA_T, X); \
1072 _FP_FMA_T##_c = X##_c; \
1073 break; \
1074 \
1075 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
1076 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1077 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1078 _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); \
1201 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1202 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1203 R##_c = FP_CLS_INF; \
1204 break; \
1205 \
1206 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1207 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1208 R##_s = _FP_NANSIGN_##fs; \
1209 R##_c = FP_CLS_NAN; \
1210 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1211 FP_SET_EXCEPTION (FP_EX_INVALID \
1212 | (X##_c == FP_CLS_INF \
1213 ? FP_EX_INVALID_IDI \
1214 : FP_EX_INVALID_ZDZ)); \
1215 break; \
1216 \
1217 default: \
1218 _FP_UNREACHABLE; \
1219 } \
1220 } \
1221 while (0)
1224 /* Helper for comparisons. EX is 0 not to raise exceptions, 1 to
1225 raise exceptions for signaling NaN operands, 2 to raise exceptions
1226 for all NaN operands. Conditionals are organized to allow the
1227 compiler to optimize away code based on the value of EX. */
1229 #define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \
1230 do \
1231 { \
1232 /* The arguments are unordered, which may or may not result in \
1234 if (ex) \
1235 { \
1236 /* At least some cases of unordered arguments result in \
1238 if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \
1239 { \
1240 /* Check separately for each case of "invalid" \
1242 if ((ex) == 2) \
1243 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \
1244 if (_FP_ISSIGNAN (fs, wc, X) \
1245 || _FP_ISSIGNAN (fs, wc, Y)) \
1246 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
1247 } \
1248 /* Otherwise, we only need to check whether to raise an \
1250 else if ((ex) == 2 \
1251 || _FP_ISSIGNAN (fs, wc, X) \
1252 || _FP_ISSIGNAN (fs, wc, Y)) \
1253 FP_SET_EXCEPTION (FP_EX_INVALID); \
1254 } \
1255 } \
1256 while (0)
1258 /* Helper for comparisons. If denormal operands would raise an
1259 exception, check for them, and flush to zero as appropriate
1260 (otherwise, we need only check and flush to zero if it might affect
1261 the result, which is done later with _FP_CMP_CHECK_FLUSH_ZERO). */
1262 #define _FP_CMP_CHECK_DENORM(fs, wc, X, Y) \
1263 do \
1264 { \
1265 if (FP_EX_DENORM != 0) \
1266 { \
1267 /* We must ensure the correct exceptions are raised for \
1268 denormal operands, even though this may not affect the \
1270 if (FP_DENORM_ZERO) \
1271 { \
1272 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1273 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1274 } \
1275 else \
1276 { \
1277 if ((X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X)) \
1278 || (Y##_e == 0 && !_FP_FRAC_ZEROP_##wc (Y))) \
1279 FP_SET_EXCEPTION (FP_EX_DENORM); \
1280 } \
1281 } \
1282 } \
1283 while (0)
1285 /* Helper for comparisons. Check for flushing denormals for zero if
1286 we didn't need to check earlier for any denormal operands. */
1287 #define _FP_CMP_CHECK_FLUSH_ZERO(fs, wc, X, Y) \
1288 do \
1289 { \
1290 if (FP_EX_DENORM == 0) \
1291 { \
1292 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1293 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1294 } \
1295 } \
1296 while (0)
1298 /* Main differential comparison routine. The inputs should be raw not
1299 cooked. The return is -1, 0, 1 for normal values, UN
1300 otherwise. */
1302 #define _FP_CMP(fs, wc, ret, X, Y, un, ex) \
1303 do \
1304 { \
1305 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1307 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1308 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1309 { \
1310 (ret) = (un); \
1311 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1312 } \
1313 else \
1314 { \
1315 int _FP_CMP_is_zero_x; \
1316 int _FP_CMP_is_zero_y; \
1317 \
1318 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1319 \
1320 _FP_CMP_is_zero_x \
1321 = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
1322 _FP_CMP_is_zero_y \
1323 = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
1324 \
1325 if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \
1326 (ret) = 0; \
1327 else if (_FP_CMP_is_zero_x) \
1328 (ret) = Y##_s ? 1 : -1; \
1329 else if (_FP_CMP_is_zero_y) \
1330 (ret) = X##_s ? -1 : 1; \
1331 else if (X##_s != Y##_s) \
1332 (ret) = X##_s ? -1 : 1; \
1333 else if (X##_e > Y##_e) \
1334 (ret) = X##_s ? -1 : 1; \
1335 else if (X##_e < Y##_e) \
1336 (ret) = X##_s ? 1 : -1; \
1337 else if (_FP_FRAC_GT_##wc (X, Y)) \
1338 (ret) = X##_s ? -1 : 1; \
1339 else if (_FP_FRAC_GT_##wc (Y, X)) \
1340 (ret) = X##_s ? 1 : -1; \
1341 else \
1342 (ret) = 0; \
1343 } \
1344 } \
1345 while (0)
1348 /* Simplification for strict equality. */
1350 #define _FP_CMP_EQ(fs, wc, ret, X, Y, ex) \
1351 do \
1352 { \
1353 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1355 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1356 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1357 { \
1358 (ret) = 1; \
1359 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1360 } \
1361 else \
1362 { \
1363 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1364 \
1365 (ret) = !(X##_e == Y##_e \
1366 && _FP_FRAC_EQ_##wc (X, Y) \
1367 && (X##_s == Y##_s \
1368 || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \
1369 } \
1370 } \
1371 while (0)
1373 /* Version to test unordered. */
1375 #define _FP_CMP_UNORD(fs, wc, ret, X, Y, ex) \
1376 do \
1377 { \
1378 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1379 (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1380 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
1381 if (ret) \
1382 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1383 } \
1384 while (0)
1386 /* Main square root routine. The input value should be cooked. */
1388 #define _FP_SQRT(fs, wc, R, X) \
1389 do \
1390 { \
1391 _FP_FRAC_DECL_##wc (_FP_SQRT_T); \
1392 _FP_FRAC_DECL_##wc (_FP_SQRT_S); \
1393 _FP_W_TYPE _FP_SQRT_q; \
1394 switch (X##_c) \
1395 { \
1396 case FP_CLS_NAN: \
1397 _FP_FRAC_COPY_##wc (R, X); \
1398 R##_s = X##_s; \
1399 R##_c = FP_CLS_NAN; \
1400 break; \
1401 case FP_CLS_INF: \
1402 if (X##_s) \
1403 { \
1404 R##_s = _FP_NANSIGN_##fs; \
1406 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1407 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1408 } \
1409 else \
1410 { \
1411 R##_s = 0; \
1413 } \
1414 break; \
1415 case FP_CLS_ZERO: \
1416 R##_s = X##_s; \
1418 break; \
1419 case FP_CLS_NORMAL: \
1420 R##_s = 0; \
1421 if (X##_s) \
1422 { \
1424 R##_s = _FP_NANSIGN_##fs; \
1425 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1426 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1427 break; \
1428 } \
1429 R##_c = FP_CLS_NORMAL; \
1430 if (X##_e & 1) \
1431 _FP_FRAC_SLL_##wc (X, 1); \
1432 R##_e = X##_e >> 1; \
1433 _FP_FRAC_SET_##wc (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \
1434 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1435 _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \
1436 _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \
1437 _FP_SQRT_q); \
1438 } \
1439 } \
1440 while (0)
1442 /* Convert from FP to integer. Input is raw. */
1444 /* RSIGNED can have following values:
1445 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
1446 the result is either 0 or (2^rsize)-1 depending on the sign in such
1447 case.
1448 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1449 NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1450 depending on the sign in such case.
1451 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1452 NV is set plus the result is reduced modulo 2^rsize.
1453 -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
1454 set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1455 depending on the sign in such case. */
1456 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
1457 do \
1458 { \
1459 if (X##_e < _FP_EXPBIAS_##fs) \
1460 { \
1461 (r) = 0; \
1462 if (X##_e == 0) \
1463 { \
1464 if (!_FP_FRAC_ZEROP_##wc (X)) \
1465 { \
1466 if (!FP_DENORM_ZERO) \
1467 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1468 FP_SET_EXCEPTION (FP_EX_DENORM); \
1469 } \
1470 } \
1471 else \
1472 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1473 } \
1474 else if ((rsigned) == 2 \
1475 && (X##_e \
1476 >= ((_FP_EXPMAX_##fs \
1477 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1478 ? _FP_EXPMAX_##fs \
1479 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1480 { \
1482 (r) = 0; \
1483 FP_SET_EXCEPTION (FP_EX_INVALID \
1484 | FP_EX_INVALID_CVI \
1485 | ((FP_EX_INVALID_SNAN \
1486 && _FP_ISSIGNAN (fs, wc, X)) \
1487 ? FP_EX_INVALID_SNAN \
1488 : 0)); \
1489 } \
1490 else if ((rsigned) != 2 \
1491 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1492 ? _FP_EXPMAX_##fs \
1493 : (_FP_EXPBIAS_##fs + (rsize) \
1494 - ((rsigned) > 0 || X##_s))) \
1495 || (!(rsigned) && X##_s))) \
1496 { \
1498 if (rsigned) \
1499 { \
1500 (r) = 1; \
1501 (r) <<= (rsize) - 1; \
1502 (r) -= 1 - X##_s; \
1503 } \
1504 else \
1505 { \
1506 (r) = 0; \
1507 if (!X##_s) \
1508 (r) = ~(r); \
1509 } \
1510 \
1511 if (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \
1512 && (rsigned) \
1513 && X##_s \
1514 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \
1515 { \
1516 /* Possibly converting to most negative integer; check the \
1518 int _FP_TO_INT_inexact = 0; \
1519 (void) ((_FP_FRACBITS_##fs > (rsize)) \
1520 ? ({ \
1521 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1522 _FP_FRACBITS_##fs - (rsize), \
1523 _FP_FRACBITS_##fs); \
1524 0; \
1525 }) \
1526 : 0); \
1527 if (!_FP_FRAC_ZEROP_##wc (X)) \
1528 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1529 else if (_FP_TO_INT_inexact) \
1530 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1531 } \
1532 else \
1533 FP_SET_EXCEPTION (FP_EX_INVALID \
1534 | FP_EX_INVALID_CVI \
1535 | ((FP_EX_INVALID_SNAN \
1536 && _FP_ISSIGNAN (fs, wc, X)) \
1537 ? FP_EX_INVALID_SNAN \
1538 : 0)); \
1539 } \
1540 else \
1541 { \
1542 int _FP_TO_INT_inexact = 0; \
1543 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1544 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1545 { \
1546 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1547 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1548 } \
1549 else \
1550 { \
1551 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1552 (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
1553 - X##_e), \
1554 _FP_FRACBITS_##fs); \
1555 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1556 } \
1557 if ((rsigned) && X##_s) \
1558 (r) = -(r); \
1559 if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \
1560 { \
1562 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1563 || !X##_s \
1564 || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \
1565 { \
1566 _FP_TO_INT_inexact = 0; \
1567 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1568 } \
1569 } \
1570 if (_FP_TO_INT_inexact) \
1571 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1572 } \
1573 } \
1574 while (0)
1576 /* Convert from floating point to integer, rounding according to the
1577 current rounding direction. Input is raw. RSIGNED is as for
1578 _FP_TO_INT. */
1579 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \
1580 do \
1581 { \
1582 __label__ _FP_TO_INT_ROUND_done; \
1583 if (X##_e < _FP_EXPBIAS_##fs) \
1584 { \
1585 int _FP_TO_INT_ROUND_rounds_away = 0; \
1586 if (X##_e == 0) \
1587 { \
1588 if (_FP_FRAC_ZEROP_##wc (X)) \
1589 { \
1590 (r) = 0; \
1591 goto _FP_TO_INT_ROUND_done; \
1592 } \
1593 else \
1594 { \
1595 FP_SET_EXCEPTION (FP_EX_DENORM); \
1596 if (FP_DENORM_ZERO) \
1597 { \
1598 (r) = 0; \
1599 goto _FP_TO_INT_ROUND_done; \
1600 } \
1601 } \
1602 } \
1603 /* The result is 0, 1 or -1 depending on the rounding mode; \
1605 switch (FP_ROUNDMODE) \
1606 { \
1607 case FP_RND_NEAREST: \
1608 _FP_TO_INT_ROUND_rounds_away \
1609 = (X##_e == _FP_EXPBIAS_##fs - 1 \
1610 && !_FP_FRAC_ZEROP_##wc (X)); \
1611 break; \
1612 case FP_RND_ZERO: \
1614 break; \
1615 case FP_RND_PINF: \
1616 _FP_TO_INT_ROUND_rounds_away = !X##_s; \
1617 break; \
1618 case FP_RND_MINF: \
1619 _FP_TO_INT_ROUND_rounds_away = X##_s; \
1620 break; \
1621 } \
1622 if ((rsigned) == 0 && _FP_TO_INT_ROUND_rounds_away && X##_s) \
1623 { \
1625 (r) = 0; \
1626 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1627 } \
1628 else if ((rsize) == 1 && (rsigned) > 0 \
1629 && _FP_TO_INT_ROUND_rounds_away && !X##_s) \
1630 { \
1631 /* Converting to a 1-bit signed bit-field, which cannot \
1633 (r) = ((rsigned) == 2 ? -1 : 0); \
1634 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1635 } \
1636 else \
1637 { \
1638 (r) = (_FP_TO_INT_ROUND_rounds_away \
1639 ? (X##_s ? -1 : 1) \
1640 : 0); \
1641 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1642 } \
1643 } \
1644 else if ((rsigned) == 2 \
1645 && (X##_e \
1646 >= ((_FP_EXPMAX_##fs \
1647 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1648 ? _FP_EXPMAX_##fs \
1649 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1650 { \
1652 (r) = 0; \
1653 FP_SET_EXCEPTION (FP_EX_INVALID \
1654 | FP_EX_INVALID_CVI \
1655 | ((FP_EX_INVALID_SNAN \
1656 && _FP_ISSIGNAN (fs, wc, X)) \
1657 ? FP_EX_INVALID_SNAN \
1658 : 0)); \
1659 } \
1660 else if ((rsigned) != 2 \
1661 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1662 ? _FP_EXPMAX_##fs \
1663 : (_FP_EXPBIAS_##fs + (rsize) \
1664 - ((rsigned) > 0 && !X##_s))) \
1665 || ((rsigned) == 0 && X##_s))) \
1666 { \
1668 if ((rsigned) != 0) \
1669 { \
1670 (r) = 1; \
1671 (r) <<= (rsize) - 1; \
1672 (r) -= 1 - X##_s; \
1673 } \
1674 else \
1675 { \
1676 (r) = 0; \
1677 if (!X##_s) \
1678 (r) = ~(r); \
1679 } \
1680 \
1681 FP_SET_EXCEPTION (FP_EX_INVALID \
1682 | FP_EX_INVALID_CVI \
1683 | ((FP_EX_INVALID_SNAN \
1684 && _FP_ISSIGNAN (fs, wc, X)) \
1685 ? FP_EX_INVALID_SNAN \
1686 : 0)); \
1687 } \
1688 else \
1689 { \
1690 /* The value is finite, with magnitude at least 1. If \
1691 the conversion is unsigned, the value is positive. \
1692 If RSIGNED is not 2, the value does not definitely \
1693 overflow by virtue of its exponent, but may still turn \
1694 out to overflow after rounding; if RSIGNED is 2, the \
1695 exponent may be such that the value definitely overflows, \
1697 int _FP_TO_INT_ROUND_inexact = 0; \
1698 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1699 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1700 { \
1702 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1703 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1704 } \
1705 else \
1706 { \
1707 /* May need to shift in order to round (unless there \
1709 int _FP_TO_INT_ROUND_rshift \
1710 = (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs \
1711 - 1 - _FP_WORKBITS - X##_e); \
1712 if (_FP_TO_INT_ROUND_rshift > 0) \
1713 _FP_FRAC_SRS_##wc (X, _FP_TO_INT_ROUND_rshift, \
1714 _FP_WFRACBITS_##fs); \
1715 else if (_FP_TO_INT_ROUND_rshift < 0) \
1716 _FP_FRAC_SLL_##wc (X, -_FP_TO_INT_ROUND_rshift); \
1717 /* Round like _FP_ROUND, but setting \
1718 _FP_TO_INT_ROUND_inexact instead of directly setting \
1719 the "inexact" exception, since it may turn out we \
1721 if (_FP_FRAC_LOW_##wc (X) & 7) \
1722 { \
1723 _FP_TO_INT_ROUND_inexact = 1; \
1724 switch (FP_ROUNDMODE) \
1725 { \
1726 case FP_RND_NEAREST: \
1727 _FP_ROUND_NEAREST (wc, X); \
1728 break; \
1729 case FP_RND_ZERO: \
1730 _FP_ROUND_ZERO (wc, X); \
1731 break; \
1732 case FP_RND_PINF: \
1733 _FP_ROUND_PINF (wc, X); \
1734 break; \
1735 case FP_RND_MINF: \
1736 _FP_ROUND_MINF (wc, X); \
1737 break; \
1738 } \
1739 } \
1740 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
1741 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1742 } \
1743 if ((rsigned) != 0 && X##_s) \
1744 (r) = -(r); \
1745 /* An exponent of RSIZE - 1 always needs testing for \
1746 overflow (either directly overflowing, or overflowing \
1747 when rounding up results in 2^RSIZE). An exponent of \
1748 RSIZE - 2 can overflow for positive values when rounding \
1749 up to 2^(RSIZE-1), but cannot overflow for negative \
1751 if (X##_e >= (_FP_EXPBIAS_##fs + (rsize) - 1 \
1752 - ((rsigned) > 0 && !X##_s))) \
1753 { \
1754 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1755 || (X##_e == _FP_EXPBIAS_##fs + (rsize) - 1 \
1756 && (X##_s \
1757 ? (r) != (((typeof (r)) 1) << ((rsize) - 1)) \
1758 : ((rsigned) > 0 || (r) == 0))) \
1759 || ((rsigned) > 0 \
1760 && !X##_s \
1761 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 2 \
1762 && (r) == (((typeof (r)) 1) << ((rsize) - 1)))) \
1763 { \
1764 if ((rsigned) != 2) \
1765 { \
1766 if ((rsigned) != 0) \
1767 { \
1768 (r) = 1; \
1769 (r) <<= (rsize) - 1; \
1770 (r) -= 1 - X##_s; \
1771 } \
1772 else \
1773 { \
1774 (r) = 0; \
1775 (r) = ~(r); \
1776 } \
1777 } \
1778 _FP_TO_INT_ROUND_inexact = 0; \
1779 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1780 } \
1781 } \
1782 if (_FP_TO_INT_ROUND_inexact) \
1783 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1784 } \
1785 _FP_TO_INT_ROUND_done: ; \
1786 } \
1787 while (0)
1789 /* Convert integer to fp. Output is raw. RTYPE is unsigned even if
1790 input is signed. */
1791 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
1792 do \
1793 { \
1794 __label__ pack_semiraw; \
1795 if (r) \
1796 { \
1797 rtype _FP_FROM_INT_ur; \
1798 \
1799 if ((X##_s = ((r) < 0))) \
1800 (r) = -(rtype) (r); \
1801 \
1802 _FP_FROM_INT_ur = (rtype) (r); \
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 /* Helper primitives. */
2042 /* Count leading zeros in a word. */
2044 #ifndef __FP_CLZ
2045 /* GCC 3.4 and later provide the builtins for us. */
2046 # define __FP_CLZ(r, x) \
2047 do \
2048 { \
2049 _FP_STATIC_ASSERT ((sizeof (_FP_W_TYPE) == sizeof (unsigned int) \
2050 || (sizeof (_FP_W_TYPE) \
2051 == sizeof (unsigned long)) \
2052 || (sizeof (_FP_W_TYPE) \
2053 == sizeof (unsigned long long))), \
2055 if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
2056 (r) = __builtin_clz (x); \
2057 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
2058 (r) = __builtin_clzl (x); \
2060 (r) = __builtin_clzll (x); \
2061 } \
2062 while (0)
2065 #define _FP_DIV_HELP_imm(q, r, n, d) \
2066 do \
2067 { \
2068 (q) = (n) / (d), (r) = (n) % (d); \
2069 } \
2070 while (0)
2073 /* A restoring bit-by-bit division primitive. */
2075 #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
2076 do \
2077 { \
2078 int _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \
2079 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \
2080 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \
2081 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \
2082 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \
2083 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
2085 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \
2086 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_v, _FP_WFRACXBITS_##fs); \
2087 /* First round. Since the operands are normalized, either the \
2088 first or second bit will be set in the fraction. Produce a \
2089 normalized result by checking which and adjusting the loop \
2091 if (_FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \
2092 { \
2093 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2094 _FP_DIV_MEAT_N_loop_u, \
2095 _FP_DIV_MEAT_N_loop_v); \
2096 _FP_FRAC_LOW_##wc (R) |= 1; \
2097 _FP_DIV_MEAT_N_loop_count--; \
2098 } \
2099 else \
2100 R##_e--; \
2102 do \
2103 { \
2104 int _FP_DIV_MEAT_N_loop_msb \
2105 = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \
2106 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \
2107 _FP_FRAC_SLL_##wc (R, 1); \
2108 if (_FP_DIV_MEAT_N_loop_msb \
2109 || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \
2110 _FP_DIV_MEAT_N_loop_v)) \
2111 { \
2112 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2113 _FP_DIV_MEAT_N_loop_u, \
2114 _FP_DIV_MEAT_N_loop_v); \
2115 _FP_FRAC_LOW_##wc (R) |= 1; \
2116 } \
2117 } \
2118 while (--_FP_DIV_MEAT_N_loop_count > 0); \
2119 /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \
2121 _FP_FRAC_LOW_##wc (R) \
2122 |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \
2123 } \
2124 while (0)
2126 #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
2127 #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
2128 #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)