| blob | f52194ecd1c7909836b26ad7869057340ff9ca06 |
1 /* Software floating-point emulation. Common operations.
2 Copyright (C) 1997-2017 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; \
902 \
903 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
904 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
905 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
906 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
907 _FP_FRAC_COPY_##wc (R, X); \
908 R##_c = X##_c; \
909 break; \
910 \
911 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
912 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
913 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
914 R##_s = Y##_s; \
916 \
917 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
918 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
919 _FP_FRAC_COPY_##wc (R, Y); \
920 R##_c = Y##_c; \
921 break; \
922 \
923 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
924 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
925 R##_s = _FP_NANSIGN_##fs; \
926 R##_c = FP_CLS_NAN; \
927 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
928 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ); \
929 break; \
930 \
931 default: \
932 _FP_UNREACHABLE; \
933 } \
934 } \
935 while (0)
938 /* Fused multiply-add. The input values should be cooked. */
940 #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
941 do \
942 { \
943 __label__ done_fma; \
944 FP_DECL_##fs (_FP_FMA_T); \
945 _FP_FMA_T##_s = X##_s ^ Y##_s; \
946 _FP_FMA_T##_e = X##_e + Y##_e + 1; \
947 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
948 { \
949 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
950 switch (Z##_c) \
951 { \
952 case FP_CLS_INF: \
953 case FP_CLS_NAN: \
954 R##_s = Z##_s; \
955 _FP_FRAC_COPY_##wc (R, Z); \
956 R##_c = Z##_c; \
957 break; \
958 \
959 case FP_CLS_ZERO: \
960 R##_c = FP_CLS_NORMAL; \
961 R##_s = _FP_FMA_T##_s; \
962 R##_e = _FP_FMA_T##_e; \
963 \
964 _FP_MUL_MEAT_##fs (R, X, Y); \
965 \
966 if (_FP_FRAC_OVERP_##wc (fs, R)) \
967 _FP_FRAC_SRS_##wc (R, 1, _FP_WFRACBITS_##fs); \
968 else \
969 R##_e--; \
970 break; \
971 \
972 case FP_CLS_NORMAL:; \
973 _FP_FRAC_DECL_##dwc (_FP_FMA_TD); \
974 _FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \
975 _FP_FRAC_DECL_##dwc (_FP_FMA_RD); \
976 _FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \
977 R##_e = _FP_FMA_T##_e; \
978 int _FP_FMA_tsh \
979 = _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \
980 _FP_FMA_T##_e -= _FP_FMA_tsh; \
981 int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \
982 if (_FP_FMA_ediff >= 0) \
983 { \
984 int _FP_FMA_shift \
985 = _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \
986 if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \
987 _FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \
988 else \
989 { \
990 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
991 if (_FP_FMA_shift < 0) \
992 _FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \
993 _FP_WFRACBITS_DW_##fs); \
994 else if (_FP_FMA_shift > 0) \
995 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \
996 } \
997 R##_s = _FP_FMA_T##_s; \
998 if (_FP_FMA_T##_s == Z##_s) \
999 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
1000 _FP_FMA_ZD); \
1001 else \
1002 { \
1003 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
1004 _FP_FMA_ZD); \
1005 if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \
1006 { \
1007 R##_s = Z##_s; \
1008 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1009 _FP_FMA_TD); \
1010 } \
1011 } \
1012 } \
1013 else \
1014 { \
1015 R##_e = Z##_e; \
1016 R##_s = Z##_s; \
1017 _FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
1018 _FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \
1019 int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \
1020 if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \
1021 _FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \
1022 else if (_FP_FMA_shift > 0) \
1023 _FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \
1024 _FP_WFRACBITS_DW_##fs); \
1025 if (Z##_s == _FP_FMA_T##_s) \
1026 _FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1027 _FP_FMA_TD); \
1028 else \
1029 _FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
1030 _FP_FMA_TD); \
1031 } \
1032 if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \
1033 { \
1034 if (_FP_FMA_T##_s == Z##_s) \
1035 R##_s = Z##_s; \
1036 else \
1037 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1038 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1039 R##_c = FP_CLS_ZERO; \
1040 } \
1041 else \
1042 { \
1043 int _FP_FMA_rlz; \
1044 _FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \
1045 _FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \
1046 R##_e -= _FP_FMA_rlz; \
1047 int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \
1048 if (_FP_FMA_shift > 0) \
1049 _FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \
1050 _FP_WFRACBITS_DW_##fs); \
1051 else if (_FP_FMA_shift < 0) \
1052 _FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \
1053 _FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \
1054 R##_c = FP_CLS_NORMAL; \
1055 } \
1056 break; \
1057 } \
1058 goto done_fma; \
1059 \
1060 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1062 break; \
1063 \
1064 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1065 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1066 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1067 _FP_FMA_T##_s = X##_s; \
1069 \
1070 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1071 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1072 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1073 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1074 _FP_FRAC_COPY_##wc (_FP_FMA_T, X); \
1075 _FP_FMA_T##_c = X##_c; \
1076 break; \
1077 \
1078 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
1079 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1080 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1081 _FP_FMA_T##_s = Y##_s; \
1083 \
1084 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
1085 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
1086 _FP_FRAC_COPY_##wc (_FP_FMA_T, Y); \
1087 _FP_FMA_T##_c = Y##_c; \
1088 break; \
1089 \
1090 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1091 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1092 _FP_FMA_T##_s = _FP_NANSIGN_##fs; \
1093 _FP_FMA_T##_c = FP_CLS_NAN; \
1094 _FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \
1095 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \
1096 break; \
1097 \
1098 default: \
1099 _FP_UNREACHABLE; \
1100 } \
1101 \
1103 switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \
1104 { \
1105 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1107 break; \
1108 \
1109 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1110 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1111 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1112 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1113 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1114 R##_s = _FP_FMA_T##_s; \
1115 _FP_FRAC_COPY_##wc (R, _FP_FMA_T); \
1116 R##_c = _FP_FMA_T##_c; \
1117 break; \
1118 \
1119 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1120 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1121 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1122 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1123 R##_s = Z##_s; \
1124 _FP_FRAC_COPY_##wc (R, Z); \
1125 R##_c = Z##_c; \
1126 R##_e = Z##_e; \
1127 break; \
1128 \
1129 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1130 if (_FP_FMA_T##_s == Z##_s) \
1131 { \
1132 R##_s = Z##_s; \
1133 _FP_FRAC_COPY_##wc (R, Z); \
1134 R##_c = Z##_c; \
1135 } \
1136 else \
1137 { \
1138 R##_s = _FP_NANSIGN_##fs; \
1139 R##_c = FP_CLS_NAN; \
1140 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1141 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_ISI); \
1142 } \
1143 break; \
1144 \
1145 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1146 if (_FP_FMA_T##_s == Z##_s) \
1147 R##_s = Z##_s; \
1148 else \
1149 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1150 _FP_FRAC_COPY_##wc (R, Z); \
1151 R##_c = Z##_c; \
1152 break; \
1153 \
1154 default: \
1155 _FP_UNREACHABLE; \
1156 } \
1157 done_fma: ; \
1158 } \
1159 while (0)
1162 /* Main division routine. The input values should be cooked. */
1164 #define _FP_DIV(fs, wc, R, X, Y) \
1165 do \
1166 { \
1167 R##_s = X##_s ^ Y##_s; \
1168 R##_e = X##_e - Y##_e; \
1169 switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
1170 { \
1171 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
1172 R##_c = FP_CLS_NORMAL; \
1173 \
1174 _FP_DIV_MEAT_##fs (R, X, Y); \
1175 break; \
1176 \
1177 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
1179 break; \
1180 \
1181 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NORMAL): \
1182 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_INF): \
1183 case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_ZERO): \
1184 R##_s = X##_s; \
1185 _FP_FRAC_COPY_##wc (R, X); \
1186 R##_c = X##_c; \
1187 break; \
1188 \
1189 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NAN): \
1190 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
1191 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
1192 R##_s = Y##_s; \
1193 _FP_FRAC_COPY_##wc (R, Y); \
1194 R##_c = Y##_c; \
1195 break; \
1196 \
1197 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_INF): \
1198 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
1199 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
1200 R##_c = FP_CLS_ZERO; \
1201 break; \
1202 \
1203 case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_ZERO): \
1204 FP_SET_EXCEPTION (FP_EX_DIVZERO); \
1206 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
1207 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
1208 R##_c = FP_CLS_INF; \
1209 break; \
1210 \
1211 case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
1212 case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
1213 R##_s = _FP_NANSIGN_##fs; \
1214 R##_c = FP_CLS_NAN; \
1215 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1216 FP_SET_EXCEPTION (FP_EX_INVALID \
1217 | (X##_c == FP_CLS_INF \
1218 ? FP_EX_INVALID_IDI \
1219 : FP_EX_INVALID_ZDZ)); \
1220 break; \
1221 \
1222 default: \
1223 _FP_UNREACHABLE; \
1224 } \
1225 } \
1226 while (0)
1229 /* Helper for comparisons. EX is 0 not to raise exceptions, 1 to
1230 raise exceptions for signaling NaN operands, 2 to raise exceptions
1231 for all NaN operands. Conditionals are organized to allow the
1232 compiler to optimize away code based on the value of EX. */
1234 #define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \
1235 do \
1236 { \
1237 /* The arguments are unordered, which may or may not result in \
1239 if (ex) \
1240 { \
1241 /* At least some cases of unordered arguments result in \
1243 if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \
1244 { \
1245 /* Check separately for each case of "invalid" \
1247 if ((ex) == 2) \
1248 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \
1249 if (_FP_ISSIGNAN (fs, wc, X) \
1250 || _FP_ISSIGNAN (fs, wc, Y)) \
1251 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
1252 } \
1253 /* Otherwise, we only need to check whether to raise an \
1255 else if ((ex) == 2 \
1256 || _FP_ISSIGNAN (fs, wc, X) \
1257 || _FP_ISSIGNAN (fs, wc, Y)) \
1258 FP_SET_EXCEPTION (FP_EX_INVALID); \
1259 } \
1260 } \
1261 while (0)
1263 /* Helper for comparisons. If denormal operands would raise an
1264 exception, check for them, and flush to zero as appropriate
1265 (otherwise, we need only check and flush to zero if it might affect
1266 the result, which is done later with _FP_CMP_CHECK_FLUSH_ZERO). */
1267 #define _FP_CMP_CHECK_DENORM(fs, wc, X, Y) \
1268 do \
1269 { \
1270 if (FP_EX_DENORM != 0) \
1271 { \
1272 /* We must ensure the correct exceptions are raised for \
1273 denormal operands, even though this may not affect the \
1275 if (FP_DENORM_ZERO) \
1276 { \
1277 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1278 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1279 } \
1280 else \
1281 { \
1282 if ((X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X)) \
1283 || (Y##_e == 0 && !_FP_FRAC_ZEROP_##wc (Y))) \
1284 FP_SET_EXCEPTION (FP_EX_DENORM); \
1285 } \
1286 } \
1287 } \
1288 while (0)
1290 /* Helper for comparisons. Check for flushing denormals for zero if
1291 we didn't need to check earlier for any denormal operands. */
1292 #define _FP_CMP_CHECK_FLUSH_ZERO(fs, wc, X, Y) \
1293 do \
1294 { \
1295 if (FP_EX_DENORM == 0) \
1296 { \
1297 _FP_CHECK_FLUSH_ZERO (fs, wc, X); \
1298 _FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
1299 } \
1300 } \
1301 while (0)
1303 /* Main differential comparison routine. The inputs should be raw not
1304 cooked. The return is -1, 0, 1 for normal values, UN
1305 otherwise. */
1307 #define _FP_CMP(fs, wc, ret, X, Y, un, ex) \
1308 do \
1309 { \
1310 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1312 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1313 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1314 { \
1315 (ret) = (un); \
1316 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1317 } \
1318 else \
1319 { \
1320 int _FP_CMP_is_zero_x; \
1321 int _FP_CMP_is_zero_y; \
1322 \
1323 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1324 \
1325 _FP_CMP_is_zero_x \
1326 = (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
1327 _FP_CMP_is_zero_y \
1328 = (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
1329 \
1330 if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \
1331 (ret) = 0; \
1332 else if (_FP_CMP_is_zero_x) \
1333 (ret) = Y##_s ? 1 : -1; \
1334 else if (_FP_CMP_is_zero_y) \
1335 (ret) = X##_s ? -1 : 1; \
1336 else if (X##_s != Y##_s) \
1337 (ret) = X##_s ? -1 : 1; \
1338 else if (X##_e > Y##_e) \
1339 (ret) = X##_s ? -1 : 1; \
1340 else if (X##_e < Y##_e) \
1341 (ret) = X##_s ? 1 : -1; \
1342 else if (_FP_FRAC_GT_##wc (X, Y)) \
1343 (ret) = X##_s ? -1 : 1; \
1344 else if (_FP_FRAC_GT_##wc (Y, X)) \
1345 (ret) = X##_s ? 1 : -1; \
1346 else \
1347 (ret) = 0; \
1348 } \
1349 } \
1350 while (0)
1353 /* Simplification for strict equality. */
1355 #define _FP_CMP_EQ(fs, wc, ret, X, Y, ex) \
1356 do \
1357 { \
1358 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1360 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1361 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))) \
1362 { \
1363 (ret) = 1; \
1364 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1365 } \
1366 else \
1367 { \
1368 _FP_CMP_CHECK_FLUSH_ZERO (fs, wc, X, Y); \
1369 \
1370 (ret) = !(X##_e == Y##_e \
1371 && _FP_FRAC_EQ_##wc (X, Y) \
1372 && (X##_s == Y##_s \
1373 || (!X##_e && _FP_FRAC_ZEROP_##wc (X)))); \
1374 } \
1375 } \
1376 while (0)
1378 /* Version to test unordered. */
1380 #define _FP_CMP_UNORD(fs, wc, ret, X, Y, ex) \
1381 do \
1382 { \
1383 _FP_CMP_CHECK_DENORM (fs, wc, X, Y); \
1384 (ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
1385 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
1386 if (ret) \
1387 _FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
1388 } \
1389 while (0)
1391 /* Main square root routine. The input value should be cooked. */
1393 #define _FP_SQRT(fs, wc, R, X) \
1394 do \
1395 { \
1396 _FP_FRAC_DECL_##wc (_FP_SQRT_T); \
1397 _FP_FRAC_DECL_##wc (_FP_SQRT_S); \
1398 _FP_W_TYPE _FP_SQRT_q; \
1399 switch (X##_c) \
1400 { \
1401 case FP_CLS_NAN: \
1402 _FP_FRAC_COPY_##wc (R, X); \
1403 R##_s = X##_s; \
1404 R##_c = FP_CLS_NAN; \
1405 break; \
1406 case FP_CLS_INF: \
1407 if (X##_s) \
1408 { \
1409 R##_s = _FP_NANSIGN_##fs; \
1411 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1412 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1413 } \
1414 else \
1415 { \
1416 R##_s = 0; \
1418 } \
1419 break; \
1420 case FP_CLS_ZERO: \
1421 R##_s = X##_s; \
1423 break; \
1424 case FP_CLS_NORMAL: \
1425 R##_s = 0; \
1426 if (X##_s) \
1427 { \
1429 R##_s = _FP_NANSIGN_##fs; \
1430 _FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
1431 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
1432 break; \
1433 } \
1434 R##_c = FP_CLS_NORMAL; \
1435 if (X##_e & 1) \
1436 _FP_FRAC_SLL_##wc (X, 1); \
1437 R##_e = X##_e >> 1; \
1438 _FP_FRAC_SET_##wc (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \
1439 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1440 _FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \
1441 _FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \
1442 _FP_SQRT_q); \
1443 } \
1444 } \
1445 while (0)
1447 /* Convert from FP to integer. Input is raw. */
1449 /* RSIGNED can have following values:
1450 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
1451 the result is either 0 or (2^rsize)-1 depending on the sign in such
1452 case.
1453 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1454 NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1455 depending on the sign in such case.
1456 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1457 NV is set plus the result is reduced modulo 2^rsize.
1458 -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
1459 set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1460 depending on the sign in such case. */
1461 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
1462 do \
1463 { \
1464 if (X##_e < _FP_EXPBIAS_##fs) \
1465 { \
1466 (r) = 0; \
1467 if (X##_e == 0) \
1468 { \
1469 if (!_FP_FRAC_ZEROP_##wc (X)) \
1470 { \
1471 if (!FP_DENORM_ZERO) \
1472 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1473 FP_SET_EXCEPTION (FP_EX_DENORM); \
1474 } \
1475 } \
1476 else \
1477 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1478 } \
1479 else if ((rsigned) == 2 \
1480 && (X##_e \
1481 >= ((_FP_EXPMAX_##fs \
1482 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1483 ? _FP_EXPMAX_##fs \
1484 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1485 { \
1487 (r) = 0; \
1488 FP_SET_EXCEPTION (FP_EX_INVALID \
1489 | FP_EX_INVALID_CVI \
1490 | ((FP_EX_INVALID_SNAN \
1491 && _FP_ISSIGNAN (fs, wc, X)) \
1492 ? FP_EX_INVALID_SNAN \
1493 : 0)); \
1494 } \
1495 else if ((rsigned) != 2 \
1496 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1497 ? _FP_EXPMAX_##fs \
1498 : (_FP_EXPBIAS_##fs + (rsize) \
1499 - ((rsigned) > 0 || X##_s))) \
1500 || (!(rsigned) && X##_s))) \
1501 { \
1503 if (rsigned) \
1504 { \
1505 (r) = 1; \
1506 (r) <<= (rsize) - 1; \
1507 (r) -= 1 - X##_s; \
1508 } \
1509 else \
1510 { \
1511 (r) = 0; \
1512 if (!X##_s) \
1513 (r) = ~(r); \
1514 } \
1515 \
1516 if (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \
1517 && (rsigned) \
1518 && X##_s \
1519 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \
1520 { \
1521 /* Possibly converting to most negative integer; check the \
1523 int _FP_TO_INT_inexact = 0; \
1524 (void) ((_FP_FRACBITS_##fs > (rsize)) \
1525 ? ({ \
1526 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1527 _FP_FRACBITS_##fs - (rsize), \
1528 _FP_FRACBITS_##fs); \
1529 0; \
1530 }) \
1531 : 0); \
1532 if (!_FP_FRAC_ZEROP_##wc (X)) \
1533 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1534 else if (_FP_TO_INT_inexact) \
1535 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1536 } \
1537 else \
1538 FP_SET_EXCEPTION (FP_EX_INVALID \
1539 | FP_EX_INVALID_CVI \
1540 | ((FP_EX_INVALID_SNAN \
1541 && _FP_ISSIGNAN (fs, wc, X)) \
1542 ? FP_EX_INVALID_SNAN \
1543 : 0)); \
1544 } \
1545 else \
1546 { \
1547 int _FP_TO_INT_inexact = 0; \
1548 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1549 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1550 { \
1551 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1552 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1553 } \
1554 else \
1555 { \
1556 _FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
1557 (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
1558 - X##_e), \
1559 _FP_FRACBITS_##fs); \
1560 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1561 } \
1562 if ((rsigned) && X##_s) \
1563 (r) = -(r); \
1564 if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \
1565 { \
1567 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1568 || !X##_s \
1569 || (r) != (((typeof (r)) 1) << ((rsize) - 1))) \
1570 { \
1571 _FP_TO_INT_inexact = 0; \
1572 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1573 } \
1574 } \
1575 if (_FP_TO_INT_inexact) \
1576 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1577 } \
1578 } \
1579 while (0)
1581 /* Convert from floating point to integer, rounding according to the
1582 current rounding direction. Input is raw. RSIGNED is as for
1583 _FP_TO_INT. */
1584 #define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \
1585 do \
1586 { \
1587 __label__ _FP_TO_INT_ROUND_done; \
1588 if (X##_e < _FP_EXPBIAS_##fs) \
1589 { \
1590 int _FP_TO_INT_ROUND_rounds_away = 0; \
1591 if (X##_e == 0) \
1592 { \
1593 if (_FP_FRAC_ZEROP_##wc (X)) \
1594 { \
1595 (r) = 0; \
1596 goto _FP_TO_INT_ROUND_done; \
1597 } \
1598 else \
1599 { \
1600 FP_SET_EXCEPTION (FP_EX_DENORM); \
1601 if (FP_DENORM_ZERO) \
1602 { \
1603 (r) = 0; \
1604 goto _FP_TO_INT_ROUND_done; \
1605 } \
1606 } \
1607 } \
1608 /* The result is 0, 1 or -1 depending on the rounding mode; \
1610 switch (FP_ROUNDMODE) \
1611 { \
1612 case FP_RND_NEAREST: \
1613 _FP_TO_INT_ROUND_rounds_away \
1614 = (X##_e == _FP_EXPBIAS_##fs - 1 \
1615 && !_FP_FRAC_ZEROP_##wc (X)); \
1616 break; \
1617 case FP_RND_ZERO: \
1619 break; \
1620 case FP_RND_PINF: \
1621 _FP_TO_INT_ROUND_rounds_away = !X##_s; \
1622 break; \
1623 case FP_RND_MINF: \
1624 _FP_TO_INT_ROUND_rounds_away = X##_s; \
1625 break; \
1626 } \
1627 if ((rsigned) == 0 && _FP_TO_INT_ROUND_rounds_away && X##_s) \
1628 { \
1630 (r) = 0; \
1631 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1632 } \
1633 else if ((rsize) == 1 && (rsigned) > 0 \
1634 && _FP_TO_INT_ROUND_rounds_away && !X##_s) \
1635 { \
1636 /* Converting to a 1-bit signed bit-field, which cannot \
1638 (r) = ((rsigned) == 2 ? -1 : 0); \
1639 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1640 } \
1641 else \
1642 { \
1643 (r) = (_FP_TO_INT_ROUND_rounds_away \
1644 ? (X##_s ? -1 : 1) \
1645 : 0); \
1646 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1647 } \
1648 } \
1649 else if ((rsigned) == 2 \
1650 && (X##_e \
1651 >= ((_FP_EXPMAX_##fs \
1652 < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
1653 ? _FP_EXPMAX_##fs \
1654 : _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
1655 { \
1657 (r) = 0; \
1658 FP_SET_EXCEPTION (FP_EX_INVALID \
1659 | FP_EX_INVALID_CVI \
1660 | ((FP_EX_INVALID_SNAN \
1661 && _FP_ISSIGNAN (fs, wc, X)) \
1662 ? FP_EX_INVALID_SNAN \
1663 : 0)); \
1664 } \
1665 else if ((rsigned) != 2 \
1666 && (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
1667 ? _FP_EXPMAX_##fs \
1668 : (_FP_EXPBIAS_##fs + (rsize) \
1669 - ((rsigned) > 0 && !X##_s))) \
1670 || ((rsigned) == 0 && X##_s))) \
1671 { \
1673 if ((rsigned) != 0) \
1674 { \
1675 (r) = 1; \
1676 (r) <<= (rsize) - 1; \
1677 (r) -= 1 - X##_s; \
1678 } \
1679 else \
1680 { \
1681 (r) = 0; \
1682 if (!X##_s) \
1683 (r) = ~(r); \
1684 } \
1685 \
1686 FP_SET_EXCEPTION (FP_EX_INVALID \
1687 | FP_EX_INVALID_CVI \
1688 | ((FP_EX_INVALID_SNAN \
1689 && _FP_ISSIGNAN (fs, wc, X)) \
1690 ? FP_EX_INVALID_SNAN \
1691 : 0)); \
1692 } \
1693 else \
1694 { \
1695 /* The value is finite, with magnitude at least 1. If \
1696 the conversion is unsigned, the value is positive. \
1697 If RSIGNED is not 2, the value does not definitely \
1698 overflow by virtue of its exponent, but may still turn \
1699 out to overflow after rounding; if RSIGNED is 2, the \
1700 exponent may be such that the value definitely overflows, \
1702 int _FP_TO_INT_ROUND_inexact = 0; \
1703 _FP_FRAC_HIGH_RAW_##fs (X) |= _FP_IMPLBIT_##fs; \
1704 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1705 { \
1707 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1708 (r) <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1709 } \
1710 else \
1711 { \
1712 /* May need to shift in order to round (unless there \
1714 int _FP_TO_INT_ROUND_rshift \
1715 = (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs \
1716 - 1 - _FP_WORKBITS - X##_e); \
1717 if (_FP_TO_INT_ROUND_rshift > 0) \
1718 _FP_FRAC_SRS_##wc (X, _FP_TO_INT_ROUND_rshift, \
1719 _FP_WFRACBITS_##fs); \
1720 else if (_FP_TO_INT_ROUND_rshift < 0) \
1721 _FP_FRAC_SLL_##wc (X, -_FP_TO_INT_ROUND_rshift); \
1722 /* Round like _FP_ROUND, but setting \
1723 _FP_TO_INT_ROUND_inexact instead of directly setting \
1724 the "inexact" exception, since it may turn out we \
1726 if (_FP_FRAC_LOW_##wc (X) & 7) \
1727 { \
1728 _FP_TO_INT_ROUND_inexact = 1; \
1729 switch (FP_ROUNDMODE) \
1730 { \
1731 case FP_RND_NEAREST: \
1732 _FP_ROUND_NEAREST (wc, X); \
1733 break; \
1734 case FP_RND_ZERO: \
1735 _FP_ROUND_ZERO (wc, X); \
1736 break; \
1737 case FP_RND_PINF: \
1738 _FP_ROUND_PINF (wc, X); \
1739 break; \
1740 case FP_RND_MINF: \
1741 _FP_ROUND_MINF (wc, X); \
1742 break; \
1743 } \
1744 } \
1745 _FP_FRAC_SRL_##wc (X, _FP_WORKBITS); \
1746 _FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
1747 } \
1748 if ((rsigned) != 0 && X##_s) \
1749 (r) = -(r); \
1750 /* An exponent of RSIZE - 1 always needs testing for \
1751 overflow (either directly overflowing, or overflowing \
1752 when rounding up results in 2^RSIZE). An exponent of \
1753 RSIZE - 2 can overflow for positive values when rounding \
1754 up to 2^(RSIZE-1), but cannot overflow for negative \
1756 if (X##_e >= (_FP_EXPBIAS_##fs + (rsize) - 1 \
1757 - ((rsigned) > 0 && !X##_s))) \
1758 { \
1759 if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
1760 || (X##_e == _FP_EXPBIAS_##fs + (rsize) - 1 \
1761 && (X##_s \
1762 ? (r) != (((typeof (r)) 1) << ((rsize) - 1)) \
1763 : ((rsigned) > 0 || (r) == 0))) \
1764 || ((rsigned) > 0 \
1765 && !X##_s \
1766 && X##_e == _FP_EXPBIAS_##fs + (rsize) - 2 \
1767 && (r) == (((typeof (r)) 1) << ((rsize) - 1)))) \
1768 { \
1769 if ((rsigned) != 2) \
1770 { \
1771 if ((rsigned) != 0) \
1772 { \
1773 (r) = 1; \
1774 (r) <<= (rsize) - 1; \
1775 (r) -= 1 - X##_s; \
1776 } \
1777 else \
1778 { \
1779 (r) = 0; \
1780 (r) = ~(r); \
1781 } \
1782 } \
1783 _FP_TO_INT_ROUND_inexact = 0; \
1784 FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
1785 } \
1786 } \
1787 if (_FP_TO_INT_ROUND_inexact) \
1788 FP_SET_EXCEPTION (FP_EX_INEXACT); \
1789 } \
1790 _FP_TO_INT_ROUND_done: ; \
1791 } \
1792 while (0)
1794 /* Convert integer to fp. Output is raw. RTYPE is unsigned even if
1795 input is signed. */
1796 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
1797 do \
1798 { \
1799 __label__ pack_semiraw; \
1800 if (r) \
1801 { \
1802 rtype _FP_FROM_INT_ur = (r); \
1803 \
1804 if ((X##_s = ((r) < 0))) \
1805 _FP_FROM_INT_ur = -_FP_FROM_INT_ur; \
1806 \
1807 _FP_STATIC_ASSERT ((rsize) <= 2 * _FP_W_TYPE_SIZE, \
1809 (void) (((rsize) <= _FP_W_TYPE_SIZE) \
1810 ? ({ \
1811 int _FP_FROM_INT_lz; \
1812 __FP_CLZ (_FP_FROM_INT_lz, \
1813 (_FP_W_TYPE) _FP_FROM_INT_ur); \
1814 X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \
1815 - _FP_FROM_INT_lz); \
1816 }) \
1817 : ({ \
1818 int _FP_FROM_INT_lz; \
1819 __FP_CLZ_2 (_FP_FROM_INT_lz, \
1820 (_FP_W_TYPE) (_FP_FROM_INT_ur \
1821 >> _FP_W_TYPE_SIZE), \
1822 (_FP_W_TYPE) _FP_FROM_INT_ur); \
1823 X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
1824 - _FP_FROM_INT_lz); \
1825 })); \
1826 \
1827 if ((rsize) - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
1828 && X##_e >= _FP_EXPMAX_##fs) \
1829 { \
1830 /* Exponent too big; overflow to infinity. (May also \
1832 _FP_OVERFLOW_SEMIRAW (fs, wc, X); \
1833 goto pack_semiraw; \
1834 } \
1835 \
1836 if ((rsize) <= _FP_FRACBITS_##fs \
1837 || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
1838 { \
1840 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \
1841 if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \
1842 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
1843 + _FP_FRACBITS_##fs - 1 - X##_e)); \
1844 } \
1845 else \
1846 { \
1847 /* More bits in integer than in floating type; need to \
1849 if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
1850 _FP_FROM_INT_ur \
1851 = ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \
1852 - _FP_WFRACBITS_##fs + 1)) \
1853 | ((_FP_FROM_INT_ur \
1854 << ((rsize) - (X##_e - _FP_EXPBIAS_##fs \
1855 - _FP_WFRACBITS_##fs + 1))) \
1856 != 0)); \
1857 _FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_ur, (rsize)); \
1858 if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
1859 _FP_FRAC_SLL_##wc (X, (_FP_EXPBIAS_##fs \
1860 + _FP_WFRACBITS_##fs - 1 - X##_e)); \
1861 _FP_FRAC_HIGH_##fs (X) &= ~(_FP_W_TYPE) _FP_IMPLBIT_SH_##fs; \
1862 pack_semiraw: \
1863 _FP_PACK_SEMIRAW (fs, wc, X); \
1864 } \
1865 } \
1866 else \
1867 { \
1868 X##_s = 0; \
1869 X##_e = 0; \
1870 _FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
1871 } \
1872 } \
1873 while (0)
1876 /* Extend from a narrower floating-point format to a wider one. Input
1877 and output are raw. If CHECK_NAN, then signaling NaNs are
1878 converted to quiet with the "invalid" exception raised; otherwise
1879 signaling NaNs remain signaling with no exception. */
1880 #define _FP_EXTEND_CNAN(dfs, sfs, dwc, swc, D, S, check_nan) \
1881 do \
1882 { \
1883 _FP_STATIC_ASSERT (_FP_FRACBITS_##dfs >= _FP_FRACBITS_##sfs, \
1885 _FP_STATIC_ASSERT ((_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
1886 >= _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs), \
1889 _FP_STATIC_ASSERT (((_FP_EXPBIAS_##dfs \
1890 >= (_FP_EXPBIAS_##sfs \
1891 + _FP_FRACBITS_##sfs - 1)) \
1892 || (_FP_EXPBIAS_##dfs == _FP_EXPBIAS_##sfs)), \
1895 D##_s = S##_s; \
1896 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
1897 if (_FP_EXP_NORMAL (sfs, swc, S)) \
1898 { \
1899 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1900 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
1901 } \
1902 else \
1903 { \
1904 if (S##_e == 0) \
1905 { \
1906 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
1907 if (_FP_FRAC_ZEROP_##swc (S)) \
1908 D##_e = 0; \
1909 else if (_FP_EXPBIAS_##dfs \
1910 < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
1911 { \
1912 FP_SET_EXCEPTION (FP_EX_DENORM); \
1913 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
1914 - _FP_FRACBITS_##sfs)); \
1915 D##_e = 0; \
1916 if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \
1917 FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
1918 } \
1919 else \
1920 { \
1921 int FP_EXTEND_lz; \
1922 FP_SET_EXCEPTION (FP_EX_DENORM); \
1923 _FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \
1924 _FP_FRAC_SLL_##dwc (D, \
1925 FP_EXTEND_lz + _FP_FRACBITS_##dfs \
1926 - _FP_FRACTBITS_##sfs); \
1927 D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
1928 + _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \
1929 } \
1930 } \
1931 else \
1932 { \
1933 D##_e = _FP_EXPMAX_##dfs; \
1934 if (!_FP_FRAC_ZEROP_##swc (S)) \
1935 { \
1936 if (check_nan && _FP_FRAC_SNANP (sfs, S)) \
1937 FP_SET_EXCEPTION (FP_EX_INVALID \
1938 | FP_EX_INVALID_SNAN); \
1939 _FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
1940 - _FP_FRACBITS_##sfs)); \
1941 if (check_nan) \
1942 _FP_SETQNAN (dfs, dwc, D); \
1943 } \
1944 } \
1945 } \
1946 } \
1947 while (0)
1949 #define FP_EXTEND(dfs, sfs, dwc, swc, D, S) \
1950 _FP_EXTEND_CNAN (dfs, sfs, dwc, swc, D, S, 1)
1952 /* Truncate from a wider floating-point format to a narrower one.
1953 Input and output are semi-raw. */
1954 #define FP_TRUNC(dfs, sfs, dwc, swc, D, S) \
1955 do \
1956 { \
1957 _FP_STATIC_ASSERT (_FP_FRACBITS_##sfs >= _FP_FRACBITS_##dfs, \
1959 _FP_STATIC_ASSERT (((_FP_EXPBIAS_##sfs \
1960 >= (_FP_EXPBIAS_##dfs \
1961 + _FP_FRACBITS_##dfs - 1)) \
1962 || _FP_EXPBIAS_##sfs == _FP_EXPBIAS_##dfs), \
1965 D##_s = S##_s; \
1966 if (_FP_EXP_NORMAL (sfs, swc, S)) \
1967 { \
1968 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1969 if (D##_e >= _FP_EXPMAX_##dfs) \
1970 _FP_OVERFLOW_SEMIRAW (dfs, dwc, D); \
1971 else \
1972 { \
1973 if (D##_e <= 0) \
1974 { \
1975 if (D##_e < 1 - _FP_FRACBITS_##dfs) \
1976 { \
1977 _FP_FRAC_SET_##swc (S, _FP_ZEROFRAC_##swc); \
1978 _FP_FRAC_LOW_##swc (S) |= 1; \
1979 } \
1980 else \
1981 { \
1982 _FP_FRAC_HIGH_##sfs (S) |= _FP_IMPLBIT_SH_##sfs; \
1983 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
1984 - _FP_WFRACBITS_##dfs \
1985 + 1 - D##_e), \
1986 _FP_WFRACBITS_##sfs); \
1987 } \
1988 D##_e = 0; \
1989 } \
1990 else \
1991 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
1992 - _FP_WFRACBITS_##dfs), \
1993 _FP_WFRACBITS_##sfs); \
1994 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
1995 } \
1996 } \
1997 else \
1998 { \
1999 if (S##_e == 0) \
2000 { \
2001 _FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
2002 D##_e = 0; \
2003 if (_FP_FRAC_ZEROP_##swc (S)) \
2004 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2005 else \
2006 { \
2007 FP_SET_EXCEPTION (FP_EX_DENORM); \
2008 if (_FP_EXPBIAS_##sfs \
2009 < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
2010 { \
2011 _FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
2012 - _FP_WFRACBITS_##dfs), \
2013 _FP_WFRACBITS_##sfs); \
2014 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
2015 } \
2016 else \
2017 { \
2018 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2019 _FP_FRAC_LOW_##dwc (D) |= 1; \
2020 } \
2021 } \
2022 } \
2023 else \
2024 { \
2025 D##_e = _FP_EXPMAX_##dfs; \
2026 if (_FP_FRAC_ZEROP_##swc (S)) \
2027 _FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
2028 else \
2029 { \
2030 _FP_CHECK_SIGNAN_SEMIRAW (sfs, swc, S); \
2031 _FP_FRAC_SRL_##swc (S, (_FP_WFRACBITS_##sfs \
2032 - _FP_WFRACBITS_##dfs)); \
2033 _FP_FRAC_COPY_##dwc##_##swc (D, S); \
2035 _FP_FRAC_LOW_##dwc (D) \
2036 &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
2037 _FP_SETQNAN_SEMIRAW (dfs, dwc, D); \
2038 } \
2039 } \
2040 } \
2041 } \
2042 while (0)
2044 /* Helper primitives. */
2046 /* Count leading zeros in a word. */
2048 #ifndef __FP_CLZ
2049 /* GCC 3.4 and later provide the builtins for us. */
2050 # define __FP_CLZ(r, x) \
2051 do \
2052 { \
2053 _FP_STATIC_ASSERT ((sizeof (_FP_W_TYPE) == sizeof (unsigned int) \
2054 || (sizeof (_FP_W_TYPE) \
2055 == sizeof (unsigned long)) \
2056 || (sizeof (_FP_W_TYPE) \
2057 == sizeof (unsigned long long))), \
2059 if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
2060 (r) = __builtin_clz (x); \
2061 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
2062 (r) = __builtin_clzl (x); \
2064 (r) = __builtin_clzll (x); \
2065 } \
2066 while (0)
2069 #define _FP_DIV_HELP_imm(q, r, n, d) \
2070 do \
2071 { \
2072 (q) = (n) / (d), (r) = (n) % (d); \
2073 } \
2074 while (0)
2077 /* A restoring bit-by-bit division primitive. */
2079 #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
2080 do \
2081 { \
2082 int _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \
2083 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \
2084 _FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \
2085 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \
2086 _FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \
2087 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
2089 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \
2090 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_v, _FP_WFRACXBITS_##fs); \
2091 /* First round. Since the operands are normalized, either the \
2092 first or second bit will be set in the fraction. Produce a \
2093 normalized result by checking which and adjusting the loop \
2095 if (_FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \
2096 { \
2097 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2098 _FP_DIV_MEAT_N_loop_u, \
2099 _FP_DIV_MEAT_N_loop_v); \
2100 _FP_FRAC_LOW_##wc (R) |= 1; \
2101 _FP_DIV_MEAT_N_loop_count--; \
2102 } \
2103 else \
2104 R##_e--; \
2106 do \
2107 { \
2108 int _FP_DIV_MEAT_N_loop_msb \
2109 = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \
2110 _FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \
2111 _FP_FRAC_SLL_##wc (R, 1); \
2112 if (_FP_DIV_MEAT_N_loop_msb \
2113 || _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \
2114 _FP_DIV_MEAT_N_loop_v)) \
2115 { \
2116 _FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
2117 _FP_DIV_MEAT_N_loop_u, \
2118 _FP_DIV_MEAT_N_loop_v); \
2119 _FP_FRAC_LOW_##wc (R) |= 1; \
2120 } \
2121 } \
2122 while (--_FP_DIV_MEAT_N_loop_count > 0); \
2123 /* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \
2125 _FP_FRAC_LOW_##wc (R) \
2126 |= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \
2127 } \
2128 while (0)
2130 #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
2131 #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
2132 #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)