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d876f532 | 1 | /* Software floating-point emulation. Common operations. |
32c075e1 | 2 | Copyright (C) 1997,1998,1999,2006,2007 Free Software Foundation, Inc. |
d876f532 UD |
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). | |
8 | ||
9 | The GNU C Library is free software; you can redistribute it and/or | |
41bdb6e2 AJ |
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. | |
d876f532 | 13 | |
638a783c RM |
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.) | |
22 | ||
d876f532 UD |
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 | |
41bdb6e2 | 26 | Lesser General Public License for more details. |
d876f532 | 27 | |
41bdb6e2 AJ |
28 | You should have received a copy of the GNU Lesser General Public |
29 | License along with the GNU C Library; if not, write to the Free | |
638a783c RM |
30 | Software Foundation, 51 Franklin Street, Fifth Floor, Boston, |
31 | MA 02110-1301, USA. */ | |
d876f532 | 32 | |
fe0b1e85 RM |
33 | #define _FP_DECL(wc, X) \ |
34 | _FP_I_TYPE X##_c __attribute__((unused)), X##_s, X##_e; \ | |
d876f532 UD |
35 | _FP_FRAC_DECL_##wc(X) |
36 | ||
37 | /* | |
38 | * Finish truely unpacking a native fp value by classifying the kind | |
39 | * of fp value and normalizing both the exponent and the fraction. | |
40 | */ | |
41 | ||
42 | #define _FP_UNPACK_CANONICAL(fs, wc, X) \ | |
43 | do { \ | |
44 | switch (X##_e) \ | |
45 | { \ | |
46 | default: \ | |
47 | _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \ | |
48 | _FP_FRAC_SLL_##wc(X, _FP_WORKBITS); \ | |
49 | X##_e -= _FP_EXPBIAS_##fs; \ | |
50 | X##_c = FP_CLS_NORMAL; \ | |
51 | break; \ | |
52 | \ | |
53 | case 0: \ | |
54 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
55 | X##_c = FP_CLS_ZERO; \ | |
56 | else \ | |
57 | { \ | |
58 | /* a denormalized number */ \ | |
59 | _FP_I_TYPE _shift; \ | |
60 | _FP_FRAC_CLZ_##wc(_shift, X); \ | |
61 | _shift -= _FP_FRACXBITS_##fs; \ | |
62 | _FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS)); \ | |
63 | X##_e -= _FP_EXPBIAS_##fs - 1 + _shift; \ | |
64 | X##_c = FP_CLS_NORMAL; \ | |
65 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
66 | } \ | |
67 | break; \ | |
68 | \ | |
69 | case _FP_EXPMAX_##fs: \ | |
70 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
71 | X##_c = FP_CLS_INF; \ | |
72 | else \ | |
73 | { \ | |
74 | X##_c = FP_CLS_NAN; \ | |
75 | /* Check for signaling NaN */ \ | |
76 | if (!(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \ | |
77 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
78 | } \ | |
79 | break; \ | |
80 | } \ | |
81 | } while (0) | |
82 | ||
fe0b1e85 RM |
83 | /* Finish unpacking an fp value in semi-raw mode: the mantissa is |
84 | shifted by _FP_WORKBITS but the implicit MSB is not inserted and | |
85 | other classification is not done. */ | |
86 | #define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc(X, _FP_WORKBITS) | |
87 | ||
88 | /* A semi-raw value has overflowed to infinity. Adjust the mantissa | |
89 | and exponent appropriately. */ | |
90 | #define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \ | |
91 | do { \ | |
92 | if (FP_ROUNDMODE == FP_RND_NEAREST \ | |
93 | || (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \ | |
94 | || (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \ | |
95 | { \ | |
96 | X##_e = _FP_EXPMAX_##fs; \ | |
97 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
98 | } \ | |
99 | else \ | |
100 | { \ | |
101 | X##_e = _FP_EXPMAX_##fs - 1; \ | |
fe0b1e85 RM |
102 | _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \ |
103 | } \ | |
32c075e1 JJ |
104 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ |
105 | FP_SET_EXCEPTION(FP_EX_OVERFLOW); \ | |
fe0b1e85 RM |
106 | } while (0) |
107 | ||
108 | /* Check for a semi-raw value being a signaling NaN and raise the | |
109 | invalid exception if so. */ | |
110 | #define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \ | |
111 | do { \ | |
112 | if (X##_e == _FP_EXPMAX_##fs \ | |
113 | && !_FP_FRAC_ZEROP_##wc(X) \ | |
114 | && !(_FP_FRAC_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs)) \ | |
115 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
116 | } while (0) | |
117 | ||
118 | /* Choose a NaN result from an operation on two semi-raw NaN | |
119 | values. */ | |
120 | #define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \ | |
121 | do { \ | |
122 | /* _FP_CHOOSENAN expects raw values, so shift as required. */ \ | |
123 | _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ | |
124 | _FP_FRAC_SRL_##wc(Y, _FP_WORKBITS); \ | |
125 | _FP_CHOOSENAN(fs, wc, R, X, Y, OP); \ | |
126 | _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \ | |
127 | } while (0) | |
128 | ||
129 | /* Test whether a biased exponent is normal (not zero or maximum). */ | |
130 | #define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1) | |
131 | ||
132 | /* Prepare to pack an fp value in semi-raw mode: the mantissa is | |
133 | rounded and shifted right, with the rounding possibly increasing | |
134 | the exponent (including changing a finite value to infinity). */ | |
135 | #define _FP_PACK_SEMIRAW(fs, wc, X) \ | |
136 | do { \ | |
137 | _FP_ROUND(wc, X); \ | |
138 | if (_FP_FRAC_HIGH_##fs(X) \ | |
139 | & (_FP_OVERFLOW_##fs >> 1)) \ | |
140 | { \ | |
141 | _FP_FRAC_HIGH_##fs(X) &= ~(_FP_OVERFLOW_##fs >> 1); \ | |
142 | X##_e++; \ | |
143 | if (X##_e == _FP_EXPMAX_##fs) \ | |
144 | _FP_OVERFLOW_SEMIRAW(fs, wc, X); \ | |
145 | } \ | |
146 | _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ | |
147 | if (!_FP_EXP_NORMAL(fs, wc, X) && !_FP_FRAC_ZEROP_##wc(X)) \ | |
148 | { \ | |
149 | if (X##_e == 0) \ | |
150 | FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \ | |
151 | else \ | |
152 | { \ | |
153 | if (!_FP_KEEPNANFRACP) \ | |
154 | { \ | |
155 | _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \ | |
156 | X##_s = _FP_NANSIGN_##fs; \ | |
157 | } \ | |
158 | else \ | |
159 | _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \ | |
160 | } \ | |
161 | } \ | |
162 | } while (0) | |
163 | ||
d876f532 UD |
164 | /* |
165 | * Before packing the bits back into the native fp result, take care | |
166 | * of such mundane things as rounding and overflow. Also, for some | |
167 | * kinds of fp values, the original parts may not have been fully | |
168 | * extracted -- but that is ok, we can regenerate them now. | |
169 | */ | |
170 | ||
171 | #define _FP_PACK_CANONICAL(fs, wc, X) \ | |
172 | do { \ | |
173 | switch (X##_c) \ | |
174 | { \ | |
175 | case FP_CLS_NORMAL: \ | |
176 | X##_e += _FP_EXPBIAS_##fs; \ | |
177 | if (X##_e > 0) \ | |
178 | { \ | |
179 | _FP_ROUND(wc, X); \ | |
180 | if (_FP_FRAC_OVERP_##wc(fs, X)) \ | |
181 | { \ | |
cf299341 | 182 | _FP_FRAC_CLEAR_OVERP_##wc(fs, X); \ |
d876f532 UD |
183 | X##_e++; \ |
184 | } \ | |
cf299341 | 185 | _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ |
d876f532 UD |
186 | if (X##_e >= _FP_EXPMAX_##fs) \ |
187 | { \ | |
188 | /* overflow */ \ | |
189 | switch (FP_ROUNDMODE) \ | |
190 | { \ | |
191 | case FP_RND_NEAREST: \ | |
192 | X##_c = FP_CLS_INF; \ | |
193 | break; \ | |
194 | case FP_RND_PINF: \ | |
195 | if (!X##_s) X##_c = FP_CLS_INF; \ | |
196 | break; \ | |
197 | case FP_RND_MINF: \ | |
198 | if (X##_s) X##_c = FP_CLS_INF; \ | |
199 | break; \ | |
200 | } \ | |
201 | if (X##_c == FP_CLS_INF) \ | |
202 | { \ | |
203 | /* Overflow to infinity */ \ | |
204 | X##_e = _FP_EXPMAX_##fs; \ | |
205 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
206 | } \ | |
207 | else \ | |
208 | { \ | |
209 | /* Overflow to maximum normal */ \ | |
210 | X##_e = _FP_EXPMAX_##fs - 1; \ | |
211 | _FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \ | |
212 | } \ | |
213 | FP_SET_EXCEPTION(FP_EX_OVERFLOW); \ | |
214 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
215 | } \ | |
216 | } \ | |
217 | else \ | |
218 | { \ | |
219 | /* we've got a denormalized number */ \ | |
220 | X##_e = -X##_e + 1; \ | |
221 | if (X##_e <= _FP_WFRACBITS_##fs) \ | |
222 | { \ | |
223 | _FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs); \ | |
224 | _FP_ROUND(wc, X); \ | |
225 | if (_FP_FRAC_HIGH_##fs(X) \ | |
226 | & (_FP_OVERFLOW_##fs >> 1)) \ | |
227 | { \ | |
228 | X##_e = 1; \ | |
229 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
230 | } \ | |
231 | else \ | |
232 | { \ | |
233 | X##_e = 0; \ | |
234 | _FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \ | |
235 | FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \ | |
236 | } \ | |
237 | } \ | |
238 | else \ | |
239 | { \ | |
240 | /* underflow to zero */ \ | |
241 | X##_e = 0; \ | |
242 | if (!_FP_FRAC_ZEROP_##wc(X)) \ | |
243 | { \ | |
244 | _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ | |
245 | _FP_ROUND(wc, X); \ | |
246 | _FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS); \ | |
247 | } \ | |
248 | FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \ | |
249 | } \ | |
250 | } \ | |
251 | break; \ | |
252 | \ | |
253 | case FP_CLS_ZERO: \ | |
254 | X##_e = 0; \ | |
255 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
256 | break; \ | |
257 | \ | |
258 | case FP_CLS_INF: \ | |
259 | X##_e = _FP_EXPMAX_##fs; \ | |
260 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
261 | break; \ | |
262 | \ | |
263 | case FP_CLS_NAN: \ | |
264 | X##_e = _FP_EXPMAX_##fs; \ | |
265 | if (!_FP_KEEPNANFRACP) \ | |
266 | { \ | |
267 | _FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \ | |
268 | X##_s = _FP_NANSIGN_##fs; \ | |
269 | } \ | |
270 | else \ | |
271 | _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \ | |
272 | break; \ | |
273 | } \ | |
274 | } while (0) | |
275 | ||
276 | /* This one accepts raw argument and not cooked, returns | |
277 | * 1 if X is a signaling NaN. | |
278 | */ | |
279 | #define _FP_ISSIGNAN(fs, wc, X) \ | |
280 | ({ \ | |
281 | int __ret = 0; \ | |
282 | if (X##_e == _FP_EXPMAX_##fs) \ | |
283 | { \ | |
284 | if (!_FP_FRAC_ZEROP_##wc(X) \ | |
285 | && !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \ | |
286 | __ret = 1; \ | |
287 | } \ | |
288 | __ret; \ | |
289 | }) | |
290 | ||
291 | ||
292 | ||
293 | ||
294 | ||
fe0b1e85 RM |
295 | /* Addition on semi-raw values. */ |
296 | #define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \ | |
297 | do { \ | |
298 | if (X##_s == Y##_s) \ | |
299 | { \ | |
300 | /* Addition. */ \ | |
301 | R##_s = X##_s; \ | |
302 | int ediff = X##_e - Y##_e; \ | |
303 | if (ediff > 0) \ | |
304 | { \ | |
305 | R##_e = X##_e; \ | |
306 | if (Y##_e == 0) \ | |
307 | { \ | |
308 | /* Y is zero or denormalized. */ \ | |
309 | if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
310 | { \ | |
311 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
312 | _FP_FRAC_COPY_##wc(R, X); \ | |
313 | goto add_done; \ | |
314 | } \ | |
315 | else \ | |
316 | { \ | |
317 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
318 | ediff--; \ | |
319 | if (ediff == 0) \ | |
320 | { \ | |
321 | _FP_FRAC_ADD_##wc(R, X, Y); \ | |
322 | goto add3; \ | |
323 | } \ | |
324 | if (X##_e == _FP_EXPMAX_##fs) \ | |
325 | { \ | |
326 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
327 | _FP_FRAC_COPY_##wc(R, X); \ | |
328 | goto add_done; \ | |
329 | } \ | |
330 | goto add1; \ | |
331 | } \ | |
332 | } \ | |
333 | else if (X##_e == _FP_EXPMAX_##fs) \ | |
334 | { \ | |
335 | /* X is NaN or Inf, Y is normal. */ \ | |
336 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
337 | _FP_FRAC_COPY_##wc(R, X); \ | |
338 | goto add_done; \ | |
339 | } \ | |
340 | \ | |
341 | /* Insert implicit MSB of Y. */ \ | |
342 | _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \ | |
343 | \ | |
344 | add1: \ | |
345 | /* Shift the mantissa of Y to the right EDIFF steps; \ | |
346 | remember to account later for the implicit MSB of X. */ \ | |
347 | if (ediff <= _FP_WFRACBITS_##fs) \ | |
348 | _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \ | |
349 | else if (!_FP_FRAC_ZEROP_##wc(Y)) \ | |
350 | _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \ | |
351 | _FP_FRAC_ADD_##wc(R, X, Y); \ | |
352 | } \ | |
353 | else if (ediff < 0) \ | |
354 | { \ | |
355 | ediff = -ediff; \ | |
356 | R##_e = Y##_e; \ | |
357 | if (X##_e == 0) \ | |
358 | { \ | |
359 | /* X is zero or denormalized. */ \ | |
360 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
361 | { \ | |
362 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
363 | _FP_FRAC_COPY_##wc(R, Y); \ | |
364 | goto add_done; \ | |
365 | } \ | |
366 | else \ | |
367 | { \ | |
368 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
369 | ediff--; \ | |
370 | if (ediff == 0) \ | |
371 | { \ | |
372 | _FP_FRAC_ADD_##wc(R, Y, X); \ | |
373 | goto add3; \ | |
374 | } \ | |
375 | if (Y##_e == _FP_EXPMAX_##fs) \ | |
376 | { \ | |
377 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
378 | _FP_FRAC_COPY_##wc(R, Y); \ | |
379 | goto add_done; \ | |
380 | } \ | |
381 | goto add2; \ | |
382 | } \ | |
383 | } \ | |
384 | else if (Y##_e == _FP_EXPMAX_##fs) \ | |
385 | { \ | |
386 | /* Y is NaN or Inf, X is normal. */ \ | |
387 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
388 | _FP_FRAC_COPY_##wc(R, Y); \ | |
389 | goto add_done; \ | |
390 | } \ | |
391 | \ | |
392 | /* Insert implicit MSB of X. */ \ | |
393 | _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \ | |
394 | \ | |
395 | add2: \ | |
396 | /* Shift the mantissa of X to the right EDIFF steps; \ | |
397 | remember to account later for the implicit MSB of Y. */ \ | |
398 | if (ediff <= _FP_WFRACBITS_##fs) \ | |
399 | _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \ | |
400 | else if (!_FP_FRAC_ZEROP_##wc(X)) \ | |
401 | _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ | |
402 | _FP_FRAC_ADD_##wc(R, Y, X); \ | |
403 | } \ | |
404 | else \ | |
405 | { \ | |
406 | /* ediff == 0. */ \ | |
407 | if (!_FP_EXP_NORMAL(fs, wc, X)) \ | |
408 | { \ | |
409 | if (X##_e == 0) \ | |
410 | { \ | |
411 | /* X and Y are zero or denormalized. */ \ | |
412 | R##_e = 0; \ | |
413 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
414 | { \ | |
415 | if (!_FP_FRAC_ZEROP_##wc(Y)) \ | |
416 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
417 | _FP_FRAC_COPY_##wc(R, Y); \ | |
418 | goto add_done; \ | |
419 | } \ | |
420 | else if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
421 | { \ | |
422 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
423 | _FP_FRAC_COPY_##wc(R, X); \ | |
424 | goto add_done; \ | |
425 | } \ | |
426 | else \ | |
427 | { \ | |
428 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
429 | _FP_FRAC_ADD_##wc(R, X, Y); \ | |
430 | if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ | |
431 | { \ | |
432 | /* Normalized result. */ \ | |
433 | _FP_FRAC_HIGH_##fs(R) \ | |
434 | &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ | |
435 | R##_e = 1; \ | |
436 | } \ | |
437 | goto add_done; \ | |
438 | } \ | |
439 | } \ | |
440 | else \ | |
441 | { \ | |
442 | /* X and Y are NaN or Inf. */ \ | |
443 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
444 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
445 | R##_e = _FP_EXPMAX_##fs; \ | |
446 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
447 | _FP_FRAC_COPY_##wc(R, Y); \ | |
448 | else if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
449 | _FP_FRAC_COPY_##wc(R, X); \ | |
450 | else \ | |
451 | _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \ | |
452 | goto add_done; \ | |
453 | } \ | |
454 | } \ | |
455 | /* The exponents of X and Y, both normal, are equal. The \ | |
456 | implicit MSBs will always add to increase the \ | |
457 | exponent. */ \ | |
458 | _FP_FRAC_ADD_##wc(R, X, Y); \ | |
459 | R##_e = X##_e + 1; \ | |
460 | _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ | |
461 | if (R##_e == _FP_EXPMAX_##fs) \ | |
462 | /* Overflow to infinity (depending on rounding mode). */ \ | |
463 | _FP_OVERFLOW_SEMIRAW(fs, wc, R); \ | |
464 | goto add_done; \ | |
465 | } \ | |
466 | add3: \ | |
467 | if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ | |
468 | { \ | |
469 | /* Overflow. */ \ | |
470 | _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ | |
471 | R##_e++; \ | |
472 | _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ | |
473 | if (R##_e == _FP_EXPMAX_##fs) \ | |
474 | /* Overflow to infinity (depending on rounding mode). */ \ | |
475 | _FP_OVERFLOW_SEMIRAW(fs, wc, R); \ | |
476 | } \ | |
477 | add_done: ; \ | |
478 | } \ | |
479 | else \ | |
480 | { \ | |
481 | /* Subtraction. */ \ | |
482 | int ediff = X##_e - Y##_e; \ | |
483 | if (ediff > 0) \ | |
484 | { \ | |
485 | R##_e = X##_e; \ | |
486 | R##_s = X##_s; \ | |
487 | if (Y##_e == 0) \ | |
488 | { \ | |
489 | /* Y is zero or denormalized. */ \ | |
490 | if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
491 | { \ | |
492 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
493 | _FP_FRAC_COPY_##wc(R, X); \ | |
494 | goto sub_done; \ | |
495 | } \ | |
496 | else \ | |
497 | { \ | |
498 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
499 | ediff--; \ | |
500 | if (ediff == 0) \ | |
501 | { \ | |
502 | _FP_FRAC_SUB_##wc(R, X, Y); \ | |
503 | goto sub3; \ | |
504 | } \ | |
505 | if (X##_e == _FP_EXPMAX_##fs) \ | |
506 | { \ | |
507 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
508 | _FP_FRAC_COPY_##wc(R, X); \ | |
509 | goto sub_done; \ | |
510 | } \ | |
511 | goto sub1; \ | |
512 | } \ | |
513 | } \ | |
514 | else if (X##_e == _FP_EXPMAX_##fs) \ | |
515 | { \ | |
516 | /* X is NaN or Inf, Y is normal. */ \ | |
517 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
518 | _FP_FRAC_COPY_##wc(R, X); \ | |
519 | goto sub_done; \ | |
520 | } \ | |
521 | \ | |
522 | /* Insert implicit MSB of Y. */ \ | |
523 | _FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \ | |
524 | \ | |
525 | sub1: \ | |
526 | /* Shift the mantissa of Y to the right EDIFF steps; \ | |
527 | remember to account later for the implicit MSB of X. */ \ | |
528 | if (ediff <= _FP_WFRACBITS_##fs) \ | |
529 | _FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \ | |
530 | else if (!_FP_FRAC_ZEROP_##wc(Y)) \ | |
531 | _FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \ | |
532 | _FP_FRAC_SUB_##wc(R, X, Y); \ | |
533 | } \ | |
534 | else if (ediff < 0) \ | |
535 | { \ | |
536 | ediff = -ediff; \ | |
537 | R##_e = Y##_e; \ | |
538 | R##_s = Y##_s; \ | |
539 | if (X##_e == 0) \ | |
540 | { \ | |
541 | /* X is zero or denormalized. */ \ | |
542 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
543 | { \ | |
544 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
545 | _FP_FRAC_COPY_##wc(R, Y); \ | |
546 | goto sub_done; \ | |
547 | } \ | |
548 | else \ | |
549 | { \ | |
550 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
551 | ediff--; \ | |
552 | if (ediff == 0) \ | |
553 | { \ | |
554 | _FP_FRAC_SUB_##wc(R, Y, X); \ | |
555 | goto sub3; \ | |
556 | } \ | |
557 | if (Y##_e == _FP_EXPMAX_##fs) \ | |
558 | { \ | |
559 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
560 | _FP_FRAC_COPY_##wc(R, Y); \ | |
561 | goto sub_done; \ | |
562 | } \ | |
563 | goto sub2; \ | |
564 | } \ | |
565 | } \ | |
566 | else if (Y##_e == _FP_EXPMAX_##fs) \ | |
567 | { \ | |
568 | /* Y is NaN or Inf, X is normal. */ \ | |
569 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
570 | _FP_FRAC_COPY_##wc(R, Y); \ | |
571 | goto sub_done; \ | |
572 | } \ | |
573 | \ | |
574 | /* Insert implicit MSB of X. */ \ | |
575 | _FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \ | |
576 | \ | |
577 | sub2: \ | |
578 | /* Shift the mantissa of X to the right EDIFF steps; \ | |
579 | remember to account later for the implicit MSB of Y. */ \ | |
580 | if (ediff <= _FP_WFRACBITS_##fs) \ | |
581 | _FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \ | |
582 | else if (!_FP_FRAC_ZEROP_##wc(X)) \ | |
583 | _FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \ | |
584 | _FP_FRAC_SUB_##wc(R, Y, X); \ | |
585 | } \ | |
586 | else \ | |
587 | { \ | |
588 | /* ediff == 0. */ \ | |
589 | if (!_FP_EXP_NORMAL(fs, wc, X)) \ | |
590 | { \ | |
591 | if (X##_e == 0) \ | |
592 | { \ | |
593 | /* X and Y are zero or denormalized. */ \ | |
594 | R##_e = 0; \ | |
595 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
596 | { \ | |
597 | _FP_FRAC_COPY_##wc(R, Y); \ | |
598 | if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
599 | R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ | |
600 | else \ | |
601 | { \ | |
602 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
603 | R##_s = Y##_s; \ | |
604 | } \ | |
605 | goto sub_done; \ | |
606 | } \ | |
607 | else if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
608 | { \ | |
609 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
610 | _FP_FRAC_COPY_##wc(R, X); \ | |
611 | R##_s = X##_s; \ | |
612 | goto sub_done; \ | |
613 | } \ | |
614 | else \ | |
615 | { \ | |
616 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
617 | _FP_FRAC_SUB_##wc(R, X, Y); \ | |
618 | R##_s = X##_s; \ | |
619 | if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ | |
620 | { \ | |
621 | /* |X| < |Y|, negate result. */ \ | |
622 | _FP_FRAC_SUB_##wc(R, Y, X); \ | |
623 | R##_s = Y##_s; \ | |
624 | } \ | |
625 | else if (_FP_FRAC_ZEROP_##wc(R)) \ | |
626 | R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ | |
627 | goto sub_done; \ | |
628 | } \ | |
629 | } \ | |
630 | else \ | |
631 | { \ | |
632 | /* X and Y are NaN or Inf, of opposite signs. */ \ | |
633 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \ | |
634 | _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \ | |
635 | R##_e = _FP_EXPMAX_##fs; \ | |
636 | if (_FP_FRAC_ZEROP_##wc(X)) \ | |
637 | { \ | |
638 | if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
639 | { \ | |
640 | /* Inf - Inf. */ \ | |
641 | R##_s = _FP_NANSIGN_##fs; \ | |
642 | _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ | |
643 | _FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \ | |
644 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
645 | } \ | |
646 | else \ | |
647 | { \ | |
648 | /* Inf - NaN. */ \ | |
649 | R##_s = Y##_s; \ | |
650 | _FP_FRAC_COPY_##wc(R, Y); \ | |
651 | } \ | |
652 | } \ | |
653 | else \ | |
654 | { \ | |
655 | if (_FP_FRAC_ZEROP_##wc(Y)) \ | |
656 | { \ | |
657 | /* NaN - Inf. */ \ | |
658 | R##_s = X##_s; \ | |
659 | _FP_FRAC_COPY_##wc(R, X); \ | |
660 | } \ | |
661 | else \ | |
662 | { \ | |
663 | /* NaN - NaN. */ \ | |
664 | _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \ | |
665 | } \ | |
666 | } \ | |
667 | goto sub_done; \ | |
668 | } \ | |
669 | } \ | |
670 | /* The exponents of X and Y, both normal, are equal. The \ | |
671 | implicit MSBs cancel. */ \ | |
672 | R##_e = X##_e; \ | |
673 | _FP_FRAC_SUB_##wc(R, X, Y); \ | |
674 | R##_s = X##_s; \ | |
675 | if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ | |
676 | { \ | |
677 | /* |X| < |Y|, negate result. */ \ | |
678 | _FP_FRAC_SUB_##wc(R, Y, X); \ | |
679 | R##_s = Y##_s; \ | |
680 | } \ | |
681 | else if (_FP_FRAC_ZEROP_##wc(R)) \ | |
682 | { \ | |
683 | R##_e = 0; \ | |
684 | R##_s = (FP_ROUNDMODE == FP_RND_MINF); \ | |
685 | goto sub_done; \ | |
686 | } \ | |
687 | goto norm; \ | |
688 | } \ | |
689 | sub3: \ | |
690 | if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \ | |
691 | { \ | |
692 | int diff; \ | |
693 | /* Carry into most significant bit of larger one of X and Y, \ | |
694 | canceling it; renormalize. */ \ | |
695 | _FP_FRAC_HIGH_##fs(R) &= _FP_IMPLBIT_SH_##fs - 1; \ | |
696 | norm: \ | |
697 | _FP_FRAC_CLZ_##wc(diff, R); \ | |
698 | diff -= _FP_WFRACXBITS_##fs; \ | |
699 | _FP_FRAC_SLL_##wc(R, diff); \ | |
700 | if (R##_e <= diff) \ | |
701 | { \ | |
702 | /* R is denormalized. */ \ | |
703 | diff = diff - R##_e + 1; \ | |
704 | _FP_FRAC_SRS_##wc(R, diff, _FP_WFRACBITS_##fs); \ | |
705 | R##_e = 0; \ | |
706 | } \ | |
707 | else \ | |
708 | { \ | |
709 | R##_e -= diff; \ | |
710 | _FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ | |
711 | } \ | |
712 | } \ | |
713 | sub_done: ; \ | |
714 | } \ | |
d876f532 UD |
715 | } while (0) |
716 | ||
717 | #define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+') | |
fe0b1e85 RM |
718 | #define _FP_SUB(fs, wc, R, X, Y) \ |
719 | do { \ | |
720 | if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) Y##_s ^= 1; \ | |
721 | _FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \ | |
d876f532 UD |
722 | } while (0) |
723 | ||
724 | ||
725 | /* | |
726 | * Main negation routine. FIXME -- when we care about setting exception | |
727 | * bits reliably, this will not do. We should examine all of the fp classes. | |
728 | */ | |
729 | ||
730 | #define _FP_NEG(fs, wc, R, X) \ | |
731 | do { \ | |
732 | _FP_FRAC_COPY_##wc(R, X); \ | |
733 | R##_c = X##_c; \ | |
734 | R##_e = X##_e; \ | |
735 | R##_s = 1 ^ X##_s; \ | |
736 | } while (0) | |
737 | ||
738 | ||
739 | /* | |
740 | * Main multiplication routine. The input values should be cooked. | |
741 | */ | |
742 | ||
743 | #define _FP_MUL(fs, wc, R, X, Y) \ | |
744 | do { \ | |
745 | R##_s = X##_s ^ Y##_s; \ | |
746 | switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \ | |
747 | { \ | |
748 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \ | |
749 | R##_c = FP_CLS_NORMAL; \ | |
750 | R##_e = X##_e + Y##_e + 1; \ | |
751 | \ | |
752 | _FP_MUL_MEAT_##fs(R,X,Y); \ | |
753 | \ | |
754 | if (_FP_FRAC_OVERP_##wc(fs, R)) \ | |
755 | _FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \ | |
756 | else \ | |
757 | R##_e--; \ | |
758 | break; \ | |
759 | \ | |
760 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \ | |
761 | _FP_CHOOSENAN(fs, wc, R, X, Y, '*'); \ | |
762 | break; \ | |
763 | \ | |
764 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \ | |
765 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \ | |
766 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \ | |
767 | R##_s = X##_s; \ | |
768 | \ | |
769 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \ | |
770 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \ | |
771 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \ | |
772 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \ | |
773 | _FP_FRAC_COPY_##wc(R, X); \ | |
774 | R##_c = X##_c; \ | |
775 | break; \ | |
776 | \ | |
777 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \ | |
778 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \ | |
779 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \ | |
780 | R##_s = Y##_s; \ | |
781 | \ | |
782 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \ | |
783 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \ | |
784 | _FP_FRAC_COPY_##wc(R, Y); \ | |
785 | R##_c = Y##_c; \ | |
786 | break; \ | |
787 | \ | |
788 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \ | |
789 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \ | |
790 | R##_s = _FP_NANSIGN_##fs; \ | |
791 | R##_c = FP_CLS_NAN; \ | |
792 | _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ | |
793 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
794 | break; \ | |
795 | \ | |
796 | default: \ | |
797 | abort(); \ | |
798 | } \ | |
799 | } while (0) | |
800 | ||
801 | ||
802 | /* | |
803 | * Main division routine. The input values should be cooked. | |
804 | */ | |
805 | ||
806 | #define _FP_DIV(fs, wc, R, X, Y) \ | |
807 | do { \ | |
808 | R##_s = X##_s ^ Y##_s; \ | |
809 | switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \ | |
810 | { \ | |
811 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \ | |
812 | R##_c = FP_CLS_NORMAL; \ | |
813 | R##_e = X##_e - Y##_e; \ | |
814 | \ | |
815 | _FP_DIV_MEAT_##fs(R,X,Y); \ | |
816 | break; \ | |
817 | \ | |
818 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \ | |
819 | _FP_CHOOSENAN(fs, wc, R, X, Y, '/'); \ | |
820 | break; \ | |
821 | \ | |
822 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \ | |
823 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \ | |
824 | case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \ | |
825 | R##_s = X##_s; \ | |
826 | _FP_FRAC_COPY_##wc(R, X); \ | |
827 | R##_c = X##_c; \ | |
828 | break; \ | |
829 | \ | |
830 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \ | |
831 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \ | |
832 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \ | |
833 | R##_s = Y##_s; \ | |
834 | _FP_FRAC_COPY_##wc(R, Y); \ | |
835 | R##_c = Y##_c; \ | |
836 | break; \ | |
837 | \ | |
838 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \ | |
839 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \ | |
840 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \ | |
841 | R##_c = FP_CLS_ZERO; \ | |
842 | break; \ | |
843 | \ | |
844 | case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \ | |
845 | FP_SET_EXCEPTION(FP_EX_DIVZERO); \ | |
846 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \ | |
847 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \ | |
848 | R##_c = FP_CLS_INF; \ | |
849 | break; \ | |
850 | \ | |
851 | case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \ | |
852 | case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \ | |
853 | R##_s = _FP_NANSIGN_##fs; \ | |
854 | R##_c = FP_CLS_NAN; \ | |
855 | _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ | |
856 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
857 | break; \ | |
858 | \ | |
859 | default: \ | |
860 | abort(); \ | |
861 | } \ | |
862 | } while (0) | |
863 | ||
864 | ||
865 | /* | |
866 | * Main differential comparison routine. The inputs should be raw not | |
867 | * cooked. The return is -1,0,1 for normal values, 2 otherwise. | |
868 | */ | |
869 | ||
870 | #define _FP_CMP(fs, wc, ret, X, Y, un) \ | |
871 | do { \ | |
872 | /* NANs are unordered */ \ | |
873 | if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \ | |
874 | || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \ | |
875 | { \ | |
876 | ret = un; \ | |
877 | } \ | |
878 | else \ | |
879 | { \ | |
880 | int __is_zero_x; \ | |
881 | int __is_zero_y; \ | |
882 | \ | |
883 | __is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0; \ | |
884 | __is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0; \ | |
885 | \ | |
886 | if (__is_zero_x && __is_zero_y) \ | |
887 | ret = 0; \ | |
888 | else if (__is_zero_x) \ | |
889 | ret = Y##_s ? 1 : -1; \ | |
890 | else if (__is_zero_y) \ | |
891 | ret = X##_s ? -1 : 1; \ | |
892 | else if (X##_s != Y##_s) \ | |
893 | ret = X##_s ? -1 : 1; \ | |
894 | else if (X##_e > Y##_e) \ | |
895 | ret = X##_s ? -1 : 1; \ | |
896 | else if (X##_e < Y##_e) \ | |
897 | ret = X##_s ? 1 : -1; \ | |
898 | else if (_FP_FRAC_GT_##wc(X, Y)) \ | |
899 | ret = X##_s ? -1 : 1; \ | |
900 | else if (_FP_FRAC_GT_##wc(Y, X)) \ | |
901 | ret = X##_s ? 1 : -1; \ | |
902 | else \ | |
903 | ret = 0; \ | |
904 | } \ | |
905 | } while (0) | |
906 | ||
907 | ||
908 | /* Simplification for strict equality. */ | |
909 | ||
fe0b1e85 RM |
910 | #define _FP_CMP_EQ(fs, wc, ret, X, Y) \ |
911 | do { \ | |
912 | /* NANs are unordered */ \ | |
913 | if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \ | |
914 | || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \ | |
915 | { \ | |
916 | ret = 1; \ | |
917 | } \ | |
918 | else \ | |
919 | { \ | |
920 | ret = !(X##_e == Y##_e \ | |
921 | && _FP_FRAC_EQ_##wc(X, Y) \ | |
922 | && (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc(X)))); \ | |
923 | } \ | |
d876f532 UD |
924 | } while (0) |
925 | ||
e7b8c7bc RM |
926 | /* Version to test unordered. */ |
927 | ||
928 | #define _FP_CMP_UNORD(fs, wc, ret, X, Y) \ | |
929 | do { \ | |
930 | ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \ | |
931 | || (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))); \ | |
932 | } while (0) | |
933 | ||
d876f532 UD |
934 | /* |
935 | * Main square root routine. The input value should be cooked. | |
936 | */ | |
937 | ||
938 | #define _FP_SQRT(fs, wc, R, X) \ | |
939 | do { \ | |
940 | _FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S); \ | |
941 | _FP_W_TYPE q; \ | |
942 | switch (X##_c) \ | |
943 | { \ | |
944 | case FP_CLS_NAN: \ | |
945 | _FP_FRAC_COPY_##wc(R, X); \ | |
946 | R##_s = X##_s; \ | |
947 | R##_c = FP_CLS_NAN; \ | |
948 | break; \ | |
949 | case FP_CLS_INF: \ | |
950 | if (X##_s) \ | |
951 | { \ | |
952 | R##_s = _FP_NANSIGN_##fs; \ | |
953 | R##_c = FP_CLS_NAN; /* NAN */ \ | |
954 | _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ | |
955 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
956 | } \ | |
957 | else \ | |
958 | { \ | |
959 | R##_s = 0; \ | |
960 | R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \ | |
961 | } \ | |
962 | break; \ | |
963 | case FP_CLS_ZERO: \ | |
964 | R##_s = X##_s; \ | |
965 | R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \ | |
966 | break; \ | |
967 | case FP_CLS_NORMAL: \ | |
968 | R##_s = 0; \ | |
969 | if (X##_s) \ | |
970 | { \ | |
971 | R##_c = FP_CLS_NAN; /* sNAN */ \ | |
972 | R##_s = _FP_NANSIGN_##fs; \ | |
973 | _FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \ | |
974 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
975 | break; \ | |
976 | } \ | |
977 | R##_c = FP_CLS_NORMAL; \ | |
978 | if (X##_e & 1) \ | |
979 | _FP_FRAC_SLL_##wc(X, 1); \ | |
980 | R##_e = X##_e >> 1; \ | |
981 | _FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc); \ | |
982 | _FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc); \ | |
983 | q = _FP_OVERFLOW_##fs >> 1; \ | |
984 | _FP_SQRT_MEAT_##wc(R, S, T, X, q); \ | |
985 | } \ | |
986 | } while (0) | |
987 | ||
988 | /* | |
fe0b1e85 | 989 | * Convert from FP to integer. Input is raw. |
d876f532 UD |
990 | */ |
991 | ||
992 | /* RSIGNED can have following values: | |
993 | * 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus | |
fe0b1e85 RM |
994 | * the result is either 0 or (2^rsize)-1 depending on the sign in such |
995 | * case. | |
996 | * 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, | |
997 | * NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 | |
998 | * depending on the sign in such case. | |
d876f532 | 999 | * -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is |
fe0b1e85 RM |
1000 | * set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 |
1001 | * depending on the sign in such case. | |
d876f532 | 1002 | */ |
fe0b1e85 RM |
1003 | #define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \ |
1004 | do { \ | |
1005 | if (X##_e < _FP_EXPBIAS_##fs) \ | |
1006 | { \ | |
1007 | r = 0; \ | |
1008 | if (X##_e == 0) \ | |
1009 | { \ | |
1010 | if (!_FP_FRAC_ZEROP_##wc(X)) \ | |
1011 | { \ | |
1012 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
1013 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
1014 | } \ | |
1015 | } \ | |
1016 | else \ | |
1017 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
1018 | } \ | |
1019 | else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \ | |
1020 | || (!rsigned && X##_s)) \ | |
1021 | { \ | |
1022 | /* Overflow or converting to the most negative integer. */ \ | |
1023 | if (rsigned) \ | |
1024 | { \ | |
1025 | r = 1; \ | |
1026 | r <<= rsize - 1; \ | |
1027 | r -= 1 - X##_s; \ | |
1028 | } else { \ | |
1029 | r = 0; \ | |
1030 | if (X##_s) \ | |
1031 | r = ~r; \ | |
1032 | } \ | |
a334319f | 1033 | \ |
fe0b1e85 RM |
1034 | if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \ |
1035 | { \ | |
1036 | /* Possibly converting to most negative integer; check the \ | |
1037 | mantissa. */ \ | |
1038 | int inexact = 0; \ | |
1039 | (void)((_FP_FRACBITS_##fs > rsize) \ | |
1040 | ? ({ _FP_FRAC_SRST_##wc(X, inexact, \ | |
1041 | _FP_FRACBITS_##fs - rsize, \ | |
1042 | _FP_FRACBITS_##fs); 0; }) \ | |
1043 | : 0); \ | |
1044 | if (!_FP_FRAC_ZEROP_##wc(X)) \ | |
1045 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
1046 | else if (inexact) \ | |
1047 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
1048 | } \ | |
1049 | else \ | |
1050 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
1051 | } \ | |
1052 | else \ | |
1053 | { \ | |
1054 | _FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \ | |
1055 | if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \ | |
1056 | { \ | |
1057 | _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ | |
1058 | r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \ | |
1059 | } \ | |
1060 | else \ | |
1061 | { \ | |
1062 | int inexact; \ | |
1063 | _FP_FRAC_SRST_##wc(X, inexact, \ | |
1064 | (_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \ | |
1065 | - X##_e), \ | |
1066 | _FP_FRACBITS_##fs); \ | |
1067 | if (inexact) \ | |
1068 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
1069 | _FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \ | |
1070 | } \ | |
1071 | if (rsigned && X##_s) \ | |
1072 | r = -r; \ | |
1073 | } \ | |
1074 | } while (0) | |
1075 | ||
1076 | /* Convert integer to fp. Output is raw. RTYPE is unsigned even if | |
1077 | input is signed. */ | |
1078 | #define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \ | |
1079 | do { \ | |
1080 | if (r) \ | |
1081 | { \ | |
1082 | rtype ur_; \ | |
1083 | \ | |
1084 | if ((X##_s = (r < 0))) \ | |
1085 | r = -(rtype)r; \ | |
1086 | \ | |
1087 | ur_ = (rtype) r; \ | |
1088 | (void)((rsize <= _FP_W_TYPE_SIZE) \ | |
1089 | ? ({ \ | |
1090 | int lz_; \ | |
1091 | __FP_CLZ(lz_, (_FP_W_TYPE)ur_); \ | |
1092 | X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \ | |
1093 | }) \ | |
1094 | : ((rsize <= 2 * _FP_W_TYPE_SIZE) \ | |
1095 | ? ({ \ | |
1096 | int lz_; \ | |
1097 | __FP_CLZ_2(lz_, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \ | |
1098 | (_FP_W_TYPE)ur_); \ | |
1099 | X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \ | |
1100 | - lz_); \ | |
1101 | }) \ | |
1102 | : (abort(), 0))); \ | |
1103 | \ | |
1104 | if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \ | |
1105 | && X##_e >= _FP_EXPMAX_##fs) \ | |
1106 | { \ | |
1107 | /* Exponent too big; overflow to infinity. (May also \ | |
1108 | happen after rounding below.) */ \ | |
1109 | _FP_OVERFLOW_SEMIRAW(fs, wc, X); \ | |
1110 | goto pack_semiraw; \ | |
1111 | } \ | |
1112 | \ | |
1113 | if (rsize <= _FP_FRACBITS_##fs \ | |
1114 | || X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \ | |
1115 | { \ | |
1116 | /* Exactly representable; shift left. */ \ | |
1117 | _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \ | |
1118 | _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \ | |
1119 | + _FP_FRACBITS_##fs - 1 - X##_e)); \ | |
1120 | } \ | |
1121 | else \ | |
1122 | { \ | |
1123 | /* More bits in integer than in floating type; need to \ | |
1124 | round. */ \ | |
1125 | if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \ | |
1126 | ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \ | |
1127 | - _FP_WFRACBITS_##fs + 1)) \ | |
1128 | | ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \ | |
1129 | - _FP_WFRACBITS_##fs + 1))) \ | |
1130 | != 0)); \ | |
1131 | _FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \ | |
1132 | if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \ | |
1133 | _FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \ | |
1134 | + _FP_WFRACBITS_##fs - 1 - X##_e)); \ | |
1135 | _FP_FRAC_HIGH_##fs(X) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \ | |
1136 | pack_semiraw: \ | |
1137 | _FP_PACK_SEMIRAW(fs, wc, X); \ | |
1138 | } \ | |
1139 | } \ | |
1140 | else \ | |
1141 | { \ | |
1142 | X##_s = 0; \ | |
1143 | X##_e = 0; \ | |
1144 | _FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \ | |
1145 | } \ | |
a334319f | 1146 | } while (0) |
d876f532 | 1147 | |
0ecb606c | 1148 | |
fe0b1e85 RM |
1149 | /* Extend from a narrower floating-point format to a wider one. Input |
1150 | and output are raw. */ | |
1151 | #define FP_EXTEND(dfs,sfs,dwc,swc,D,S) \ | |
1152 | do { \ | |
1153 | if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \ | |
1154 | || (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \ | |
1155 | < _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \ | |
1156 | || _FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \ | |
1157 | abort(); \ | |
1158 | D##_s = S##_s; \ | |
1159 | _FP_FRAC_COPY_##dwc##_##swc(D, S); \ | |
1160 | if (_FP_EXP_NORMAL(sfs, swc, S)) \ | |
1161 | { \ | |
1162 | D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ | |
1163 | _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \ | |
1164 | } \ | |
1165 | else \ | |
1166 | { \ | |
1167 | if (S##_e == 0) \ | |
1168 | { \ | |
1169 | if (_FP_FRAC_ZEROP_##swc(S)) \ | |
1170 | D##_e = 0; \ | |
1171 | else \ | |
1172 | { \ | |
1173 | int _lz; \ | |
1174 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
1175 | _FP_FRAC_CLZ_##swc(_lz, S); \ | |
1176 | _FP_FRAC_SLL_##dwc(D, \ | |
1177 | _lz + _FP_FRACBITS_##dfs \ | |
1178 | - _FP_FRACTBITS_##sfs); \ | |
1179 | D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \ | |
1180 | + _FP_FRACXBITS_##sfs - _lz); \ | |
1181 | } \ | |
1182 | } \ | |
1183 | else \ | |
1184 | { \ | |
1185 | D##_e = _FP_EXPMAX_##dfs; \ | |
1186 | if (!_FP_FRAC_ZEROP_##swc(S)) \ | |
1187 | { \ | |
1188 | if (!(_FP_FRAC_HIGH_RAW_##sfs(S) & _FP_QNANBIT_##sfs)) \ | |
1189 | FP_SET_EXCEPTION(FP_EX_INVALID); \ | |
1190 | _FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \ | |
1191 | - _FP_FRACBITS_##sfs)); \ | |
1192 | } \ | |
1193 | } \ | |
1194 | } \ | |
1195 | } while (0) | |
1196 | ||
1197 | /* Truncate from a wider floating-point format to a narrower one. | |
1198 | Input and output are semi-raw. */ | |
1199 | #define FP_TRUNC(dfs,sfs,dwc,swc,D,S) \ | |
1200 | do { \ | |
1201 | if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \ | |
1202 | || _FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \ | |
1203 | abort(); \ | |
1204 | D##_s = S##_s; \ | |
1205 | if (_FP_EXP_NORMAL(sfs, swc, S)) \ | |
1206 | { \ | |
1207 | D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \ | |
1208 | if (D##_e >= _FP_EXPMAX_##dfs) \ | |
1209 | _FP_OVERFLOW_SEMIRAW(dfs, dwc, D); \ | |
1210 | else \ | |
1211 | { \ | |
1212 | if (D##_e <= 0) \ | |
1213 | { \ | |
1214 | if (D##_e <= 1 - _FP_FRACBITS_##dfs) \ | |
1215 | _FP_FRAC_SET_##swc(S, _FP_ZEROFRAC_##swc); \ | |
1216 | else \ | |
1217 | { \ | |
1218 | _FP_FRAC_HIGH_##sfs(S) |= _FP_IMPLBIT_SH_##sfs; \ | |
1219 | _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \ | |
1220 | - _FP_WFRACBITS_##dfs + 1 - D##_e), \ | |
1221 | _FP_WFRACBITS_##sfs); \ | |
1222 | } \ | |
1223 | D##_e = 0; \ | |
1224 | } \ | |
1225 | else \ | |
1226 | _FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \ | |
1227 | - _FP_WFRACBITS_##dfs), \ | |
1228 | _FP_WFRACBITS_##sfs); \ | |
1229 | _FP_FRAC_COPY_##dwc##_##swc(D, S); \ | |
1230 | } \ | |
1231 | } \ | |
1232 | else \ | |
1233 | { \ | |
1234 | if (S##_e == 0) \ | |
1235 | { \ | |
1236 | D##_e = 0; \ | |
1237 | _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \ | |
1238 | if (!_FP_FRAC_ZEROP_##swc(S)) \ | |
1239 | { \ | |
1240 | FP_SET_EXCEPTION(FP_EX_DENORM); \ | |
1241 | FP_SET_EXCEPTION(FP_EX_INEXACT); \ | |
1242 | } \ | |
1243 | } \ | |
1244 | else \ | |
1245 | { \ | |
1246 | D##_e = _FP_EXPMAX_##dfs; \ | |
1247 | if (_FP_FRAC_ZEROP_##swc(S)) \ | |
1248 | _FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \ | |
1249 | else \ | |
1250 | { \ | |
1251 | _FP_CHECK_SIGNAN_SEMIRAW(sfs, swc, S); \ | |
1252 | _FP_FRAC_SRL_##swc(S, (_FP_WFRACBITS_##sfs \ | |
1253 | - _FP_WFRACBITS_##dfs)); \ | |
1254 | _FP_FRAC_COPY_##dwc##_##swc(D, S); \ | |
32c075e1 JJ |
1255 | /* Semi-raw NaN must have all workbits cleared. */ \ |
1256 | _FP_FRAC_LOW_##dwc(D) \ | |
1257 | &= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \ | |
fe0b1e85 RM |
1258 | _FP_FRAC_HIGH_##dfs(D) |= _FP_QNANBIT_SH_##dfs; \ |
1259 | } \ | |
1260 | } \ | |
1261 | } \ | |
1262 | } while (0) | |
d876f532 UD |
1263 | |
1264 | /* | |
1265 | * Helper primitives. | |
1266 | */ | |
1267 | ||
1268 | /* Count leading zeros in a word. */ | |
1269 | ||
1270 | #ifndef __FP_CLZ | |
0d86378f RM |
1271 | /* GCC 3.4 and later provide the builtins for us. */ |
1272 | #define __FP_CLZ(r, x) \ | |
1273 | do { \ | |
1274 | if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \ | |
1275 | r = __builtin_clz (x); \ | |
1276 | else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \ | |
1277 | r = __builtin_clzl (x); \ | |
1278 | else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \ | |
1279 | r = __builtin_clzll (x); \ | |
1280 | else \ | |
1281 | abort (); \ | |
d876f532 | 1282 | } while (0) |
d876f532 UD |
1283 | #endif /* ndef __FP_CLZ */ |
1284 | ||
1285 | #define _FP_DIV_HELP_imm(q, r, n, d) \ | |
1286 | do { \ | |
1287 | q = n / d, r = n % d; \ | |
1288 | } while (0) | |
1289 | ||
1a8aaf91 UD |
1290 | |
1291 | /* A restoring bit-by-bit division primitive. */ | |
1292 | ||
1293 | #define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \ | |
1294 | do { \ | |
1295 | int count = _FP_WFRACBITS_##fs; \ | |
1296 | _FP_FRAC_DECL_##wc (u); \ | |
1297 | _FP_FRAC_DECL_##wc (v); \ | |
1298 | _FP_FRAC_COPY_##wc (u, X); \ | |
1299 | _FP_FRAC_COPY_##wc (v, Y); \ | |
1300 | _FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \ | |
1301 | /* Normalize U and V. */ \ | |
1302 | _FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \ | |
1303 | _FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \ | |
1304 | /* First round. Since the operands are normalized, either the \ | |
1305 | first or second bit will be set in the fraction. Produce a \ | |
1306 | normalized result by checking which and adjusting the loop \ | |
1307 | count and exponent accordingly. */ \ | |
1308 | if (_FP_FRAC_GE_1 (u, v)) \ | |
1309 | { \ | |
1310 | _FP_FRAC_SUB_##wc (u, u, v); \ | |
1311 | _FP_FRAC_LOW_##wc (R) |= 1; \ | |
1312 | count--; \ | |
1313 | } \ | |
1314 | else \ | |
1315 | R##_e--; \ | |
1316 | /* Subsequent rounds. */ \ | |
1317 | do { \ | |
1318 | int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \ | |
1319 | _FP_FRAC_SLL_##wc (u, 1); \ | |
1320 | _FP_FRAC_SLL_##wc (R, 1); \ | |
1321 | if (msb || _FP_FRAC_GE_1 (u, v)) \ | |
1322 | { \ | |
1323 | _FP_FRAC_SUB_##wc (u, u, v); \ | |
1324 | _FP_FRAC_LOW_##wc (R) |= 1; \ | |
1325 | } \ | |
1326 | } while (--count > 0); \ | |
1327 | /* If there's anything left in U, the result is inexact. */ \ | |
1328 | _FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \ | |
1329 | } while (0) | |
1330 | ||
1331 | #define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y) | |
1332 | #define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y) | |
1333 | #define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y) |