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git.ipfire.org Git - thirdparty/glibc.git/blob - soft-fp/op-common.h
1 /* Software floating-point emulation. Common operations.
2 Copyright (C) 1997-2013 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 #define _FP_DECL(wc, X) \
33 _FP_I_TYPE X##_c __attribute__((unused)); \
34 _FP_I_TYPE X##_s __attribute__((unused)); \
38 /* Test whether the qNaN bit denotes a signaling NaN. */
39 #define _FP_FRAC_SNANP(fs, X) \
41 ? (_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs) \
42 : !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs))
43 #define _FP_FRAC_SNANP_SEMIRAW(fs, X) \
45 ? (_FP_FRAC_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs) \
46 : !(_FP_FRAC_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs))
49 * Finish truly unpacking a native fp value by classifying the kind
50 * of fp value and normalizing both the exponent and the fraction.
53 #define _FP_UNPACK_CANONICAL(fs, wc, X) \
58 _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \
59 _FP_FRAC_SLL_##wc(X, _FP_WORKBITS); \
60 X##_e -= _FP_EXPBIAS_##fs; \
61 X##_c = FP_CLS_NORMAL; \
65 if (_FP_FRAC_ZEROP_##wc(X)) \
66 X##_c = FP_CLS_ZERO; \
69 /* a denormalized number */ \
71 _FP_FRAC_CLZ_##wc(_shift, X); \
72 _shift -= _FP_FRACXBITS_##fs; \
73 _FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS)); \
74 X##_e -= _FP_EXPBIAS_##fs - 1 + _shift; \
75 X##_c = FP_CLS_NORMAL; \
76 FP_SET_EXCEPTION(FP_EX_DENORM); \
80 case _FP_EXPMAX_##fs: \
81 if (_FP_FRAC_ZEROP_##wc(X)) \
86 /* Check for signaling NaN */ \
87 if (_FP_FRAC_SNANP(fs, X)) \
88 FP_SET_EXCEPTION(FP_EX_INVALID); \
94 /* Finish unpacking an fp value in semi-raw mode: the mantissa is
95 shifted by _FP_WORKBITS but the implicit MSB is not inserted and
96 other classification is not done. */
97 #define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc(X, _FP_WORKBITS)
99 /* A semi-raw value has overflowed to infinity. Adjust the mantissa
100 and exponent appropriately. */
101 #define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \
103 if (FP_ROUNDMODE == FP_RND_NEAREST \
104 || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \
105 || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \
107 X##_e = _FP_EXPMAX_##fs; \
108 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
112 X##_e = _FP_EXPMAX_##fs - 1; \
113 _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
115 FP_SET_EXCEPTION(FP_EX_INEXACT); \
116 FP_SET_EXCEPTION(FP_EX_OVERFLOW); \
119 /* Check for a semi-raw value being a signaling NaN and raise the
120 invalid exception if so. */
121 #define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \
123 if (X##_e == _FP_EXPMAX_##fs \
124 && !_FP_FRAC_ZEROP_##wc(X) \
125 && _FP_FRAC_SNANP_SEMIRAW(fs, X)) \
126 FP_SET_EXCEPTION(FP_EX_INVALID); \
129 /* Choose a NaN result from an operation on two semi-raw NaN
131 #define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \
133 /* _FP_CHOOSENAN expects raw values, so shift as required. */ \
134 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
135 _FP_FRAC_SRL_##wc(Y, _FP_WORKBITS); \
136 _FP_CHOOSENAN(fs, wc, R, X, Y, OP); \
137 _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \
140 /* Make the fractional part a quiet NaN, preserving the payload
141 if possible, otherwise make it the canonical quiet NaN and set
142 the sign bit accordingly. */
143 #define _FP_SETQNAN(fs, wc, X) \
145 if (_FP_QNANNEGATEDP) \
147 _FP_FRAC_HIGH_RAW_##fs(X) &= _FP_QNANBIT_##fs - 1; \
148 if (_FP_FRAC_ZEROP_##wc(X)) \
150 X##_s = _FP_NANSIGN_##fs; \
151 _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
155 _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \
157 #define _FP_SETQNAN_SEMIRAW(fs, wc, X) \
159 if (_FP_QNANNEGATEDP) \
161 _FP_FRAC_HIGH_##fs(X) &= _FP_QNANBIT_SH_##fs - 1; \
162 if (_FP_FRAC_ZEROP_##wc(X)) \
164 X##_s = _FP_NANSIGN_##fs; \
165 _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
166 _FP_FRAC_SLL_##wc(X, _FP_WORKBITS); \
170 _FP_FRAC_HIGH_##fs(X) |= _FP_QNANBIT_SH_##fs; \
173 /* Test whether a biased exponent is normal (not zero or maximum). */
174 #define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1)
176 /* Prepare to pack an fp value in semi-raw mode: the mantissa is
177 rounded and shifted right, with the rounding possibly increasing
178 the exponent (including changing a finite value to infinity). */
179 #define _FP_PACK_SEMIRAW(fs, wc, X) \
182 if (X##_e == 0 && !_FP_FRAC_ZEROP_##wc(X)) \
184 if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
185 || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
186 FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
188 if (_FP_FRAC_HIGH_##fs(X) \
189 & (_FP_OVERFLOW_##fs >> 1)) \
191 _FP_FRAC_HIGH_##fs(X) &= ~(_FP_OVERFLOW_##fs >> 1); \
193 if (X##_e == _FP_EXPMAX_##fs) \
194 _FP_OVERFLOW_SEMIRAW(fs, wc, X); \
196 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
197 if (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
199 if (!_FP_KEEPNANFRACP) \
201 _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
202 X##_s = _FP_NANSIGN_##fs; \
205 _FP_SETQNAN(fs, wc, X); \
210 * Before packing the bits back into the native fp result, take care
211 * of such mundane things as rounding and overflow. Also, for some
212 * kinds of fp values, the original parts may not have been fully
213 * extracted -- but that is ok, we can regenerate them now.
216 #define _FP_PACK_CANONICAL(fs, wc, X) \
220 case FP_CLS_NORMAL: \
221 X##_e += _FP_EXPBIAS_##fs; \
225 if (_FP_FRAC_OVERP_##wc(fs, X)) \
227 _FP_FRAC_CLEAR_OVERP_##wc(fs, X); \
230 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
231 if (X##_e >= _FP_EXPMAX_##fs) \
234 switch (FP_ROUNDMODE) \
236 case FP_RND_NEAREST: \
237 X##_c = FP_CLS_INF; \
240 if (!X##_s) X##_c = FP_CLS_INF; \
243 if (X##_s) X##_c = FP_CLS_INF; \
246 if (X##_c == FP_CLS_INF) \
248 /* Overflow to infinity */ \
249 X##_e = _FP_EXPMAX_##fs; \
250 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
254 /* Overflow to maximum normal */ \
255 X##_e = _FP_EXPMAX_##fs - 1; \
256 _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
258 FP_SET_EXCEPTION(FP_EX_OVERFLOW); \
259 FP_SET_EXCEPTION(FP_EX_INEXACT); \
264 /* we've got a denormalized number */ \
265 X##_e = -X##_e + 1; \
266 if (X##_e <= _FP_WFRACBITS_##fs) \
268 _FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs); \
270 if (_FP_FRAC_HIGH_##fs(X) \
271 & (_FP_OVERFLOW_##fs >> 1)) \
274 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
275 FP_SET_EXCEPTION(FP_EX_INEXACT); \
280 _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
282 if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
283 || (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
284 FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
288 /* underflow to zero */ \
290 if (!_FP_FRAC_ZEROP_##wc(X)) \
292 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
294 _FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS); \
296 FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
303 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
307 X##_e = _FP_EXPMAX_##fs; \
308 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
312 X##_e = _FP_EXPMAX_##fs; \
313 if (!_FP_KEEPNANFRACP) \
315 _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
316 X##_s = _FP_NANSIGN_##fs; \
319 _FP_SETQNAN(fs, wc, X); \
324 /* This one accepts raw argument and not cooked, returns
325 * 1 if X is a signaling NaN.
327 #define _FP_ISSIGNAN(fs, wc, X) \
330 if (X##_e == _FP_EXPMAX_##fs) \
332 if (!_FP_FRAC_ZEROP_##wc(X) \
333 && _FP_FRAC_SNANP(fs, X)) \
343 /* Addition on semi-raw values. */
344 #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
346 if (X##_s == Y##_s) \
350 int ediff = X##_e - Y##_e; \
356 /* Y is zero or denormalized. */ \
357 if (_FP_FRAC_ZEROP_##wc(Y)) \
359 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
360 _FP_FRAC_COPY_##wc(R, X); \
365 FP_SET_EXCEPTION(FP_EX_DENORM); \
369 _FP_FRAC_ADD_##wc(R, X, Y); \
372 if (X##_e == _FP_EXPMAX_##fs) \
374 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
375 _FP_FRAC_COPY_##wc(R, X); \
381 else if (X##_e == _FP_EXPMAX_##fs) \
383 /* X is NaN or Inf, Y is normal. */ \
384 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
385 _FP_FRAC_COPY_##wc(R, X); \
389 /* Insert implicit MSB of Y. */ \
390 _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
393 /* Shift the mantissa of Y to the right EDIFF steps; \
394 remember to account later for the implicit MSB of X. */ \
395 if (ediff <= _FP_WFRACBITS_##fs) \
396 _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
397 else if (!_FP_FRAC_ZEROP_##wc(Y)) \
398 _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
399 _FP_FRAC_ADD_##wc(R, X, Y); \
401 else if (ediff < 0) \
407 /* X is zero or denormalized. */ \
408 if (_FP_FRAC_ZEROP_##wc(X)) \
410 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
411 _FP_FRAC_COPY_##wc(R, Y); \
416 FP_SET_EXCEPTION(FP_EX_DENORM); \
420 _FP_FRAC_ADD_##wc(R, Y, X); \
423 if (Y##_e == _FP_EXPMAX_##fs) \
425 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
426 _FP_FRAC_COPY_##wc(R, Y); \
432 else if (Y##_e == _FP_EXPMAX_##fs) \
434 /* Y is NaN or Inf, X is normal. */ \
435 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
436 _FP_FRAC_COPY_##wc(R, Y); \
440 /* Insert implicit MSB of X. */ \
441 _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
444 /* Shift the mantissa of X to the right EDIFF steps; \
445 remember to account later for the implicit MSB of Y. */ \
446 if (ediff <= _FP_WFRACBITS_##fs) \
447 _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
448 else if (!_FP_FRAC_ZEROP_##wc(X)) \
449 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
450 _FP_FRAC_ADD_##wc(R, Y, X); \
455 if (!_FP_EXP_NORMAL(fs, wc, X)) \
459 /* X and Y are zero or denormalized. */ \
461 if (_FP_FRAC_ZEROP_##wc(X)) \
463 if (!_FP_FRAC_ZEROP_##wc(Y)) \
464 FP_SET_EXCEPTION(FP_EX_DENORM); \
465 _FP_FRAC_COPY_##wc(R, Y); \
468 else if (_FP_FRAC_ZEROP_##wc(Y)) \
470 FP_SET_EXCEPTION(FP_EX_DENORM); \
471 _FP_FRAC_COPY_##wc(R, X); \
476 FP_SET_EXCEPTION(FP_EX_DENORM); \
477 _FP_FRAC_ADD_##wc(R, X, Y); \
478 if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
480 /* Normalized result. */ \
481 _FP_FRAC_HIGH_##fs(R) \
482 &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
490 /* X and Y are NaN or Inf. */ \
491 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
492 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
493 R##_e = _FP_EXPMAX_##fs; \
494 if (_FP_FRAC_ZEROP_##wc(X)) \
495 _FP_FRAC_COPY_##wc(R, Y); \
496 else if (_FP_FRAC_ZEROP_##wc(Y)) \
497 _FP_FRAC_COPY_##wc(R, X); \
499 _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
503 /* The exponents of X and Y, both normal, are equal. The \
504 implicit MSBs will always add to increase the \
506 _FP_FRAC_ADD_##wc(R, X, Y); \
508 _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
509 if (R##_e == _FP_EXPMAX_##fs) \
510 /* Overflow to infinity (depending on rounding mode). */ \
511 _FP_OVERFLOW_SEMIRAW(fs, wc, R); \
515 if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
518 _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
520 _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
521 if (R##_e == _FP_EXPMAX_##fs) \
522 /* Overflow to infinity (depending on rounding mode). */ \
523 _FP_OVERFLOW_SEMIRAW(fs, wc, R); \
530 int ediff = X##_e - Y##_e; \
537 /* Y is zero or denormalized. */ \
538 if (_FP_FRAC_ZEROP_##wc(Y)) \
540 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
541 _FP_FRAC_COPY_##wc(R, X); \
546 FP_SET_EXCEPTION(FP_EX_DENORM); \
550 _FP_FRAC_SUB_##wc(R, X, Y); \
553 if (X##_e == _FP_EXPMAX_##fs) \
555 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
556 _FP_FRAC_COPY_##wc(R, X); \
562 else if (X##_e == _FP_EXPMAX_##fs) \
564 /* X is NaN or Inf, Y is normal. */ \
565 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
566 _FP_FRAC_COPY_##wc(R, X); \
570 /* Insert implicit MSB of Y. */ \
571 _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
574 /* Shift the mantissa of Y to the right EDIFF steps; \
575 remember to account later for the implicit MSB of X. */ \
576 if (ediff <= _FP_WFRACBITS_##fs) \
577 _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
578 else if (!_FP_FRAC_ZEROP_##wc(Y)) \
579 _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
580 _FP_FRAC_SUB_##wc(R, X, Y); \
582 else if (ediff < 0) \
589 /* X is zero or denormalized. */ \
590 if (_FP_FRAC_ZEROP_##wc(X)) \
592 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
593 _FP_FRAC_COPY_##wc(R, Y); \
598 FP_SET_EXCEPTION(FP_EX_DENORM); \
602 _FP_FRAC_SUB_##wc(R, Y, X); \
605 if (Y##_e == _FP_EXPMAX_##fs) \
607 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
608 _FP_FRAC_COPY_##wc(R, Y); \
614 else if (Y##_e == _FP_EXPMAX_##fs) \
616 /* Y is NaN or Inf, X is normal. */ \
617 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
618 _FP_FRAC_COPY_##wc(R, Y); \
622 /* Insert implicit MSB of X. */ \
623 _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
626 /* Shift the mantissa of X to the right EDIFF steps; \
627 remember to account later for the implicit MSB of Y. */ \
628 if (ediff <= _FP_WFRACBITS_##fs) \
629 _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
630 else if (!_FP_FRAC_ZEROP_##wc(X)) \
631 _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
632 _FP_FRAC_SUB_##wc(R, Y, X); \
637 if (!_FP_EXP_NORMAL(fs, wc, X)) \
641 /* X and Y are zero or denormalized. */ \
643 if (_FP_FRAC_ZEROP_##wc(X)) \
645 _FP_FRAC_COPY_##wc(R, Y); \
646 if (_FP_FRAC_ZEROP_##wc(Y)) \
647 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
650 FP_SET_EXCEPTION(FP_EX_DENORM); \
655 else if (_FP_FRAC_ZEROP_##wc(Y)) \
657 FP_SET_EXCEPTION(FP_EX_DENORM); \
658 _FP_FRAC_COPY_##wc(R, X); \
664 FP_SET_EXCEPTION(FP_EX_DENORM); \
665 _FP_FRAC_SUB_##wc(R, X, Y); \
667 if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
669 /* |X| < |Y|, negate result. */ \
670 _FP_FRAC_SUB_##wc(R, Y, X); \
673 else if (_FP_FRAC_ZEROP_##wc(R)) \
674 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
680 /* X and Y are NaN or Inf, of opposite signs. */ \
681 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
682 _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
683 R##_e = _FP_EXPMAX_##fs; \
684 if (_FP_FRAC_ZEROP_##wc(X)) \
686 if (_FP_FRAC_ZEROP_##wc(Y)) \
689 R##_s = _FP_NANSIGN_##fs; \
690 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
691 _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \
692 FP_SET_EXCEPTION(FP_EX_INVALID); \
698 _FP_FRAC_COPY_##wc(R, Y); \
703 if (_FP_FRAC_ZEROP_##wc(Y)) \
707 _FP_FRAC_COPY_##wc(R, X); \
712 _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
718 /* The exponents of X and Y, both normal, are equal. The \
719 implicit MSBs cancel. */ \
721 _FP_FRAC_SUB_##wc(R, X, Y); \
723 if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
725 /* |X| < |Y|, negate result. */ \
726 _FP_FRAC_SUB_##wc(R, Y, X); \
729 else if (_FP_FRAC_ZEROP_##wc(R)) \
732 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
738 if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
741 /* Carry into most significant bit of larger one of X and Y, \
742 canceling it; renormalize. */ \
743 _FP_FRAC_HIGH_##fs(R) &= _FP_IMPLBIT_SH_##fs - 1; \
745 _FP_FRAC_CLZ_##wc(diff, R); \
746 diff -= _FP_WFRACXBITS_##fs; \
747 _FP_FRAC_SLL_##wc(R, diff); \
750 /* R is denormalized. */ \
751 diff = diff - R##_e + 1; \
752 _FP_FRAC_SRS_##wc(R, diff, _FP_WFRACBITS_##fs); \
758 _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
765 #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
766 #define _FP_SUB(fs, wc, R, X, Y) \
768 if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) Y##_s ^= 1; \
769 _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \
774 * Main negation routine. The input value is raw.
777 #define _FP_NEG(fs, wc, R, X) \
779 _FP_FRAC_COPY_##wc(R, X); \
786 * Main multiplication routine. The input values should be cooked.
789 #define _FP_MUL(fs, wc, R, X, Y) \
791 R##_s = X##_s ^ Y##_s; \
792 R##_e = X##_e + Y##_e + 1; \
793 switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
795 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
796 R##_c = FP_CLS_NORMAL; \
798 _FP_MUL_MEAT_##fs(R,X,Y); \
800 if (_FP_FRAC_OVERP_##wc(fs, R)) \
801 _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
806 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
807 _FP_CHOOSENAN(fs, wc, R, X, Y, '*'); \
810 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
811 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
812 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
815 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
816 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
817 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
818 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
819 _FP_FRAC_COPY_##wc(R, X); \
823 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
824 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
825 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
828 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
829 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
830 _FP_FRAC_COPY_##wc(R, Y); \
834 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
835 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
836 R##_s = _FP_NANSIGN_##fs; \
837 R##_c = FP_CLS_NAN; \
838 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
839 FP_SET_EXCEPTION(FP_EX_INVALID); \
848 /* Fused multiply-add. The input values should be cooked. */
850 #define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
853 T##_s = X##_s ^ Y##_s; \
854 T##_e = X##_e + Y##_e + 1; \
855 switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
857 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
863 _FP_FRAC_COPY_##wc(R, Z); \
868 R##_c = FP_CLS_NORMAL; \
872 _FP_MUL_MEAT_##fs(R, X, Y); \
874 if (_FP_FRAC_OVERP_##wc(fs, R)) \
875 _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
880 case FP_CLS_NORMAL:; \
881 _FP_FRAC_DECL_##dwc(TD); \
882 _FP_FRAC_DECL_##dwc(ZD); \
883 _FP_FRAC_DECL_##dwc(RD); \
884 _FP_MUL_MEAT_DW_##fs(TD, X, Y); \
886 int tsh = _FP_FRAC_HIGHBIT_DW_##dwc(fs, TD) == 0; \
888 int ediff = T##_e - Z##_e; \
891 int shift = _FP_WFRACBITS_##fs - tsh - ediff; \
892 if (shift <= -_FP_WFRACBITS_##fs) \
893 _FP_FRAC_SET_##dwc(ZD, _FP_MINFRAC_##dwc); \
896 _FP_FRAC_COPY_##dwc##_##wc(ZD, Z); \
898 _FP_FRAC_SRS_##dwc(ZD, -shift, \
899 _FP_WFRACBITS_DW_##fs); \
900 else if (shift > 0) \
901 _FP_FRAC_SLL_##dwc(ZD, shift); \
904 if (T##_s == Z##_s) \
905 _FP_FRAC_ADD_##dwc(RD, TD, ZD); \
908 _FP_FRAC_SUB_##dwc(RD, TD, ZD); \
909 if (_FP_FRAC_NEGP_##dwc(RD)) \
912 _FP_FRAC_SUB_##dwc(RD, ZD, TD); \
920 _FP_FRAC_COPY_##dwc##_##wc(ZD, Z); \
921 _FP_FRAC_SLL_##dwc(ZD, _FP_WFRACBITS_##fs); \
922 int shift = -ediff - tsh; \
923 if (shift >= _FP_WFRACBITS_DW_##fs) \
924 _FP_FRAC_SET_##dwc(TD, _FP_MINFRAC_##dwc); \
925 else if (shift > 0) \
926 _FP_FRAC_SRS_##dwc(TD, shift, \
927 _FP_WFRACBITS_DW_##fs); \
928 if (Z##_s == T##_s) \
929 _FP_FRAC_ADD_##dwc(RD, ZD, TD); \
931 _FP_FRAC_SUB_##dwc(RD, ZD, TD); \
933 if (_FP_FRAC_ZEROP_##dwc(RD)) \
935 if (T##_s == Z##_s) \
938 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
939 _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc); \
940 R##_c = FP_CLS_ZERO; \
945 _FP_FRAC_CLZ_##dwc(rlz, RD); \
946 rlz -= _FP_WFRACXBITS_DW_##fs; \
948 int shift = _FP_WFRACBITS_##fs - rlz; \
950 _FP_FRAC_SRS_##dwc(RD, shift, \
951 _FP_WFRACBITS_DW_##fs); \
952 else if (shift < 0) \
953 _FP_FRAC_SLL_##dwc(RD, -shift); \
954 _FP_FRAC_COPY_##wc##_##dwc(R, RD); \
955 R##_c = FP_CLS_NORMAL; \
961 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
962 _FP_CHOOSENAN(fs, wc, T, X, Y, '*'); \
965 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
966 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
967 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
970 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
971 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
972 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
973 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
974 _FP_FRAC_COPY_##wc(T, X); \
978 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
979 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
980 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
983 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
984 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
985 _FP_FRAC_COPY_##wc(T, Y); \
989 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
990 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
991 T##_s = _FP_NANSIGN_##fs; \
992 T##_c = FP_CLS_NAN; \
993 _FP_FRAC_SET_##wc(T, _FP_NANFRAC_##fs); \
994 FP_SET_EXCEPTION(FP_EX_INVALID); \
1001 /* T = X * Y is zero, infinity or NaN. */ \
1002 switch (_FP_CLS_COMBINE(T##_c, Z##_c)) \
1004 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
1005 _FP_CHOOSENAN(fs, wc, R, T, Z, '+'); \
1008 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
1009 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
1010 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
1011 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
1012 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
1014 _FP_FRAC_COPY_##wc(R, T); \
1018 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
1019 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
1020 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
1021 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
1023 _FP_FRAC_COPY_##wc(R, Z); \
1027 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
1028 if (T##_s == Z##_s) \
1031 _FP_FRAC_COPY_##wc(R, Z); \
1036 R##_s = _FP_NANSIGN_##fs; \
1037 R##_c = FP_CLS_NAN; \
1038 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
1039 FP_SET_EXCEPTION(FP_EX_INVALID); \
1043 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
1044 if (T##_s == Z##_s) \
1047 R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
1048 _FP_FRAC_COPY_##wc(R, Z); \
1060 * Main division routine. The input values should be cooked.
1063 #define _FP_DIV(fs, wc, R, X, Y) \
1065 R##_s = X##_s ^ Y##_s; \
1066 R##_e = X##_e - Y##_e; \
1067 switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
1069 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
1070 R##_c = FP_CLS_NORMAL; \
1072 _FP_DIV_MEAT_##fs(R,X,Y); \
1075 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
1076 _FP_CHOOSENAN(fs, wc, R, X, Y, '/'); \
1079 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
1080 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
1081 case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
1083 _FP_FRAC_COPY_##wc(R, X); \
1087 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
1088 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
1089 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
1091 _FP_FRAC_COPY_##wc(R, Y); \
1095 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
1096 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
1097 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
1098 R##_c = FP_CLS_ZERO; \
1101 case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
1102 FP_SET_EXCEPTION(FP_EX_DIVZERO); \
1103 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
1104 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
1105 R##_c = FP_CLS_INF; \
1108 case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
1109 case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
1110 R##_s = _FP_NANSIGN_##fs; \
1111 R##_c = FP_CLS_NAN; \
1112 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
1113 FP_SET_EXCEPTION(FP_EX_INVALID); \
1123 * Main differential comparison routine. The inputs should be raw not
1124 * cooked. The return is -1,0,1 for normal values, 2 otherwise.
1127 #define _FP_CMP(fs, wc, ret, X, Y, un) \
1129 /* NANs are unordered */ \
1130 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
1131 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
1140 __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0; \
1141 __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0; \
1143 if (__is_zero_x && __is_zero_y) \
1145 else if (__is_zero_x) \
1146 ret = Y##_s ? 1 : -1; \
1147 else if (__is_zero_y) \
1148 ret = X##_s ? -1 : 1; \
1149 else if (X##_s != Y##_s) \
1150 ret = X##_s ? -1 : 1; \
1151 else if (X##_e > Y##_e) \
1152 ret = X##_s ? -1 : 1; \
1153 else if (X##_e < Y##_e) \
1154 ret = X##_s ? 1 : -1; \
1155 else if (_FP_FRAC_GT_##wc(X, Y)) \
1156 ret = X##_s ? -1 : 1; \
1157 else if (_FP_FRAC_GT_##wc(Y, X)) \
1158 ret = X##_s ? 1 : -1; \
1165 /* Simplification for strict equality. */
1167 #define _FP_CMP_EQ(fs, wc, ret, X, Y) \
1169 /* NANs are unordered */ \
1170 if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
1171 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
1177 ret = !(X##_e == Y##_e \
1178 && _FP_FRAC_EQ_##wc(X, Y) \
1179 && (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc(X)))); \
1183 /* Version to test unordered. */
1185 #define _FP_CMP_UNORD(fs, wc, ret, X, Y) \
1187 ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
1188 || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))); \
1192 * Main square root routine. The input value should be cooked.
1195 #define _FP_SQRT(fs, wc, R, X) \
1197 _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S); \
1202 _FP_FRAC_COPY_##wc(R, X); \
1204 R##_c = FP_CLS_NAN; \
1209 R##_s = _FP_NANSIGN_##fs; \
1210 R##_c = FP_CLS_NAN; /* NAN */ \
1211 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
1212 FP_SET_EXCEPTION(FP_EX_INVALID); \
1217 R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \
1222 R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \
1224 case FP_CLS_NORMAL: \
1228 R##_c = FP_CLS_NAN; /* NAN */ \
1229 R##_s = _FP_NANSIGN_##fs; \
1230 _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
1231 FP_SET_EXCEPTION(FP_EX_INVALID); \
1234 R##_c = FP_CLS_NORMAL; \
1236 _FP_FRAC_SLL_##wc(X, 1); \
1237 R##_e = X##_e >> 1; \
1238 _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc); \
1239 _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc); \
1240 q = _FP_OVERFLOW_##fs >> 1; \
1241 _FP_SQRT_MEAT_##wc(R, S, T, X, q); \
1246 * Convert from FP to integer. Input is raw.
1249 /* RSIGNED can have following values:
1250 * 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
1251 * the result is either 0 or (2^rsize)-1 depending on the sign in such
1253 * 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
1254 * NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1255 * depending on the sign in such case.
1256 * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
1257 * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
1258 * depending on the sign in such case.
1260 #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
1262 if (X##_e < _FP_EXPBIAS_##fs) \
1267 if (!_FP_FRAC_ZEROP_##wc(X)) \
1269 FP_SET_EXCEPTION(FP_EX_INEXACT); \
1270 FP_SET_EXCEPTION(FP_EX_DENORM); \
1274 FP_SET_EXCEPTION(FP_EX_INEXACT); \
1276 else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \
1277 || (!rsigned && X##_s)) \
1279 /* Overflow or converting to the most negative integer. */ \
1291 if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \
1293 /* Possibly converting to most negative integer; check the \
1296 (void)((_FP_FRACBITS_##fs > rsize) \
1297 ? ({ _FP_FRAC_SRST_##wc(X, inexact, \
1298 _FP_FRACBITS_##fs - rsize, \
1299 _FP_FRACBITS_##fs); 0; }) \
1301 if (!_FP_FRAC_ZEROP_##wc(X)) \
1302 FP_SET_EXCEPTION(FP_EX_INVALID); \
1304 FP_SET_EXCEPTION(FP_EX_INEXACT); \
1307 FP_SET_EXCEPTION(FP_EX_INVALID); \
1311 _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \
1312 if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
1314 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
1315 r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
1320 _FP_FRAC_SRST_##wc(X, inexact, \
1321 (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
1323 _FP_FRACBITS_##fs); \
1325 FP_SET_EXCEPTION(FP_EX_INEXACT); \
1326 _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
1328 if (rsigned && X##_s) \
1333 /* Convert integer to fp. Output is raw. RTYPE is unsigned even if
1335 #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
1341 if ((X##_s = (r < 0))) \
1345 (void)((rsize <= _FP_W_TYPE_SIZE) \
1348 __FP_CLZ(lz_, (_FP_W_TYPE)ur_); \
1349 X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \
1351 : ((rsize <= 2 * _FP_W_TYPE_SIZE) \
1354 __FP_CLZ_2(lz_, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \
1356 X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
1361 if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
1362 && X##_e >= _FP_EXPMAX_##fs) \
1364 /* Exponent too big; overflow to infinity. (May also \
1365 happen after rounding below.) */ \
1366 _FP_OVERFLOW_SEMIRAW(fs, wc, X); \
1367 goto pack_semiraw; \
1370 if (rsize <= _FP_FRACBITS_##fs \
1371 || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
1373 /* Exactly representable; shift left. */ \
1374 _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
1375 if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \
1376 _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
1377 + _FP_FRACBITS_##fs - 1 - X##_e)); \
1381 /* More bits in integer than in floating type; need to \
1383 if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
1384 ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \
1385 - _FP_WFRACBITS_##fs + 1)) \
1386 | ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \
1387 - _FP_WFRACBITS_##fs + 1))) \
1389 _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
1390 if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
1391 _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
1392 + _FP_WFRACBITS_##fs - 1 - X##_e)); \
1393 _FP_FRAC_HIGH_##fs(X) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
1395 _FP_PACK_SEMIRAW(fs, wc, X); \
1402 _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
1407 /* Extend from a narrower floating-point format to a wider one. Input
1408 and output are raw. */
1409 #define FP_EXTEND(dfs,sfs,dwc,swc,D,S) \
1411 if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \
1412 || (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
1413 < _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \
1414 || (_FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1 \
1415 && _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \
1418 _FP_FRAC_COPY_##dwc##_##swc(D, S); \
1419 if (_FP_EXP_NORMAL(sfs, swc, S)) \
1421 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1422 _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
1428 if (_FP_FRAC_ZEROP_##swc(S)) \
1430 else if (_FP_EXPBIAS_##dfs \
1431 < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
1433 FP_SET_EXCEPTION(FP_EX_DENORM); \
1434 _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \
1435 - _FP_FRACBITS_##sfs)); \
1441 FP_SET_EXCEPTION(FP_EX_DENORM); \
1442 _FP_FRAC_CLZ_##swc(_lz, S); \
1443 _FP_FRAC_SLL_##dwc(D, \
1444 _lz + _FP_FRACBITS_##dfs \
1445 - _FP_FRACTBITS_##sfs); \
1446 D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
1447 + _FP_FRACXBITS_##sfs - _lz); \
1452 D##_e = _FP_EXPMAX_##dfs; \
1453 if (!_FP_FRAC_ZEROP_##swc(S)) \
1455 if (_FP_FRAC_SNANP(sfs, S)) \
1456 FP_SET_EXCEPTION(FP_EX_INVALID); \
1457 _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \
1458 - _FP_FRACBITS_##sfs)); \
1464 /* Truncate from a wider floating-point format to a narrower one.
1465 Input and output are semi-raw. */
1466 #define FP_TRUNC(dfs,sfs,dwc,swc,D,S) \
1468 if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \
1469 || (_FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1 \
1470 && _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \
1473 if (_FP_EXP_NORMAL(sfs, swc, S)) \
1475 D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
1476 if (D##_e >= _FP_EXPMAX_##dfs) \
1477 _FP_OVERFLOW_SEMIRAW(dfs, dwc, D); \
1482 if (D##_e < 1 - _FP_FRACBITS_##dfs) \
1484 _FP_FRAC_SET_##swc(S, _FP_ZEROFRAC_##swc); \
1485 _FP_FRAC_LOW_##swc(S) |= 1; \
1489 _FP_FRAC_HIGH_##sfs(S) |= _FP_IMPLBIT_SH_##sfs; \
1490 _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
1491 - _FP_WFRACBITS_##dfs + 1 - D##_e), \
1492 _FP_WFRACBITS_##sfs); \
1497 _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
1498 - _FP_WFRACBITS_##dfs), \
1499 _FP_WFRACBITS_##sfs); \
1500 _FP_FRAC_COPY_##dwc##_##swc(D, S); \
1508 if (_FP_FRAC_ZEROP_##swc(S)) \
1509 _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
1512 FP_SET_EXCEPTION(FP_EX_DENORM); \
1513 if (_FP_EXPBIAS_##sfs \
1514 < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
1516 _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
1517 - _FP_WFRACBITS_##dfs), \
1518 _FP_WFRACBITS_##sfs); \
1519 _FP_FRAC_COPY_##dwc##_##swc(D, S); \
1523 _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
1524 _FP_FRAC_LOW_##dwc(D) |= 1; \
1530 D##_e = _FP_EXPMAX_##dfs; \
1531 if (_FP_FRAC_ZEROP_##swc(S)) \
1532 _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
1535 _FP_CHECK_SIGNAN_SEMIRAW(sfs, swc, S); \
1536 _FP_FRAC_SRL_##swc(S, (_FP_WFRACBITS_##sfs \
1537 - _FP_WFRACBITS_##dfs)); \
1538 _FP_FRAC_COPY_##dwc##_##swc(D, S); \
1539 /* Semi-raw NaN must have all workbits cleared. */ \
1540 _FP_FRAC_LOW_##dwc(D) \
1541 &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
1542 _FP_SETQNAN_SEMIRAW(dfs, dwc, D); \
1549 * Helper primitives.
1552 /* Count leading zeros in a word. */
1555 /* GCC 3.4 and later provide the builtins for us. */
1556 #define __FP_CLZ(r, x) \
1558 if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
1559 r = __builtin_clz (x); \
1560 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
1561 r = __builtin_clzl (x); \
1562 else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \
1563 r = __builtin_clzll (x); \
1567 #endif /* ndef __FP_CLZ */
1569 #define _FP_DIV_HELP_imm(q, r, n, d) \
1571 q = n / d, r = n % d; \
1575 /* A restoring bit-by-bit division primitive. */
1577 #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
1579 int count = _FP_WFRACBITS_##fs; \
1580 _FP_FRAC_DECL_##wc (u); \
1581 _FP_FRAC_DECL_##wc (v); \
1582 _FP_FRAC_COPY_##wc (u, X); \
1583 _FP_FRAC_COPY_##wc (v, Y); \
1584 _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
1585 /* Normalize U and V. */ \
1586 _FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \
1587 _FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \
1588 /* First round. Since the operands are normalized, either the \
1589 first or second bit will be set in the fraction. Produce a \
1590 normalized result by checking which and adjusting the loop \
1591 count and exponent accordingly. */ \
1592 if (_FP_FRAC_GE_1 (u, v)) \
1594 _FP_FRAC_SUB_##wc (u, u, v); \
1595 _FP_FRAC_LOW_##wc (R) |= 1; \
1600 /* Subsequent rounds. */ \
1602 int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \
1603 _FP_FRAC_SLL_##wc (u, 1); \
1604 _FP_FRAC_SLL_##wc (R, 1); \
1605 if (msb || _FP_FRAC_GE_1 (u, v)) \
1607 _FP_FRAC_SUB_##wc (u, u, v); \
1608 _FP_FRAC_LOW_##wc (R) |= 1; \
1610 } while (--count > 0); \
1611 /* If there's anything left in U, the result is inexact. */ \
1612 _FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \
1615 #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
1616 #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
1617 #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)