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c906108c SS |
1 | /* This is a software floating point library which can be used instead of |
2 | the floating point routines in libgcc1.c for targets without hardware | |
3 | floating point. */ | |
4 | ||
6aba47ca | 5 | /* Copyright (C) 1994, 2007 Free Software Foundation, Inc. |
c906108c | 6 | |
4744ac1b JB |
7 | This program is free software; you can redistribute it and/or modify |
8 | it under the terms of the GNU General Public License as published by | |
9 | the Free Software Foundation; either version 3 of the License, or | |
10 | (at your option) any later version. | |
c906108c | 11 | |
4744ac1b JB |
12 | This program is distributed in the hope that it will be useful, |
13 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | GNU General Public License for more details. | |
c906108c SS |
16 | |
17 | You should have received a copy of the GNU General Public License | |
4744ac1b | 18 | along with this program. If not, see <http://www.gnu.org/licenses/>. */ |
c906108c SS |
19 | |
20 | /* As a special exception, if you link this library with other files, | |
21 | some of which are compiled with GCC, to produce an executable, | |
22 | this library does not by itself cause the resulting executable | |
23 | to be covered by the GNU General Public License. | |
24 | This exception does not however invalidate any other reasons why | |
25 | the executable file might be covered by the GNU General Public License. */ | |
26 | ||
27 | /* This implements IEEE 754 format arithmetic, but does not provide a | |
28 | mechanism for setting the rounding mode, or for generating or handling | |
29 | exceptions. | |
30 | ||
31 | The original code by Steve Chamberlain, hacked by Mark Eichin and Jim | |
32 | Wilson, all of Cygnus Support. */ | |
33 | ||
34 | /* The intended way to use this file is to make two copies, add `#define FLOAT' | |
35 | to one copy, then compile both copies and add them to libgcc.a. */ | |
36 | ||
37 | /* The following macros can be defined to change the behaviour of this file: | |
38 | FLOAT: Implement a `float', aka SFmode, fp library. If this is not | |
39 | defined, then this file implements a `double', aka DFmode, fp library. | |
40 | FLOAT_ONLY: Used with FLOAT, to implement a `float' only library, i.e. | |
41 | don't include float->double conversion which requires the double library. | |
42 | This is useful only for machines which can't support doubles, e.g. some | |
43 | 8-bit processors. | |
44 | CMPtype: Specify the type that floating point compares should return. | |
45 | This defaults to SItype, aka int. | |
46 | US_SOFTWARE_GOFAST: This makes all entry points use the same names as the | |
47 | US Software goFast library. If this is not defined, the entry points use | |
48 | the same names as libgcc1.c. | |
49 | _DEBUG_BITFLOAT: This makes debugging the code a little easier, by adding | |
50 | two integers to the FLO_union_type. | |
51 | NO_NANS: Disable nan and infinity handling | |
52 | SMALL_MACHINE: Useful when operations on QIs and HIs are faster | |
53 | than on an SI */ | |
54 | ||
55 | #ifndef SFtype | |
56 | typedef SFtype __attribute__ ((mode (SF))); | |
57 | #endif | |
58 | #ifndef DFtype | |
59 | typedef DFtype __attribute__ ((mode (DF))); | |
60 | #endif | |
61 | ||
62 | #ifndef HItype | |
63 | typedef int HItype __attribute__ ((mode (HI))); | |
64 | #endif | |
65 | #ifndef SItype | |
66 | typedef int SItype __attribute__ ((mode (SI))); | |
67 | #endif | |
68 | #ifndef DItype | |
69 | typedef int DItype __attribute__ ((mode (DI))); | |
70 | #endif | |
71 | ||
72 | /* The type of the result of a fp compare */ | |
73 | #ifndef CMPtype | |
74 | #define CMPtype SItype | |
75 | #endif | |
76 | ||
77 | #ifndef UHItype | |
78 | typedef unsigned int UHItype __attribute__ ((mode (HI))); | |
79 | #endif | |
80 | #ifndef USItype | |
81 | typedef unsigned int USItype __attribute__ ((mode (SI))); | |
82 | #endif | |
83 | #ifndef UDItype | |
84 | typedef unsigned int UDItype __attribute__ ((mode (DI))); | |
85 | #endif | |
86 | ||
87 | #define MAX_SI_INT ((SItype) ((unsigned) (~0)>>1)) | |
88 | #define MAX_USI_INT ((USItype) ~0) | |
89 | ||
90 | ||
91 | #ifdef FLOAT_ONLY | |
92 | #define NO_DI_MODE | |
93 | #endif | |
94 | ||
95 | #ifdef FLOAT | |
96 | # define NGARDS 7L | |
97 | # define GARDROUND 0x3f | |
98 | # define GARDMASK 0x7f | |
99 | # define GARDMSB 0x40 | |
100 | # define EXPBITS 8 | |
101 | # define EXPBIAS 127 | |
102 | # define FRACBITS 23 | |
103 | # define EXPMAX (0xff) | |
104 | # define QUIET_NAN 0x100000L | |
105 | # define FRAC_NBITS 32 | |
106 | # define FRACHIGH 0x80000000L | |
107 | # define FRACHIGH2 0xc0000000L | |
108 | typedef USItype fractype; | |
109 | typedef UHItype halffractype; | |
110 | typedef SFtype FLO_type; | |
111 | typedef SItype intfrac; | |
112 | ||
113 | #else | |
114 | # define PREFIXFPDP dp | |
115 | # define PREFIXSFDF df | |
116 | # define NGARDS 8L | |
117 | # define GARDROUND 0x7f | |
118 | # define GARDMASK 0xff | |
119 | # define GARDMSB 0x80 | |
120 | # define EXPBITS 11 | |
121 | # define EXPBIAS 1023 | |
122 | # define FRACBITS 52 | |
123 | # define EXPMAX (0x7ff) | |
124 | # define QUIET_NAN 0x8000000000000LL | |
125 | # define FRAC_NBITS 64 | |
126 | # define FRACHIGH 0x8000000000000000LL | |
127 | # define FRACHIGH2 0xc000000000000000LL | |
128 | typedef UDItype fractype; | |
129 | typedef USItype halffractype; | |
130 | typedef DFtype FLO_type; | |
131 | typedef DItype intfrac; | |
132 | #endif | |
133 | ||
134 | #ifdef US_SOFTWARE_GOFAST | |
135 | # ifdef FLOAT | |
136 | # define add fpadd | |
137 | # define sub fpsub | |
138 | # define multiply fpmul | |
139 | # define divide fpdiv | |
140 | # define compare fpcmp | |
141 | # define si_to_float sitofp | |
142 | # define float_to_si fptosi | |
143 | # define float_to_usi fptoui | |
144 | # define negate __negsf2 | |
145 | # define sf_to_df fptodp | |
146 | # define dptofp dptofp | |
147 | #else | |
148 | # define add dpadd | |
149 | # define sub dpsub | |
150 | # define multiply dpmul | |
151 | # define divide dpdiv | |
152 | # define compare dpcmp | |
153 | # define si_to_float litodp | |
154 | # define float_to_si dptoli | |
155 | # define float_to_usi dptoul | |
156 | # define negate __negdf2 | |
157 | # define df_to_sf dptofp | |
158 | #endif | |
159 | #else | |
160 | # ifdef FLOAT | |
161 | # define add __addsf3 | |
162 | # define sub __subsf3 | |
163 | # define multiply __mulsf3 | |
164 | # define divide __divsf3 | |
165 | # define compare __cmpsf2 | |
166 | # define _eq_f2 __eqsf2 | |
167 | # define _ne_f2 __nesf2 | |
168 | # define _gt_f2 __gtsf2 | |
169 | # define _ge_f2 __gesf2 | |
170 | # define _lt_f2 __ltsf2 | |
171 | # define _le_f2 __lesf2 | |
172 | # define si_to_float __floatsisf | |
173 | # define float_to_si __fixsfsi | |
174 | # define float_to_usi __fixunssfsi | |
175 | # define negate __negsf2 | |
176 | # define sf_to_df __extendsfdf2 | |
177 | #else | |
178 | # define add __adddf3 | |
179 | # define sub __subdf3 | |
180 | # define multiply __muldf3 | |
181 | # define divide __divdf3 | |
182 | # define compare __cmpdf2 | |
183 | # define _eq_f2 __eqdf2 | |
184 | # define _ne_f2 __nedf2 | |
185 | # define _gt_f2 __gtdf2 | |
186 | # define _ge_f2 __gedf2 | |
187 | # define _lt_f2 __ltdf2 | |
188 | # define _le_f2 __ledf2 | |
189 | # define si_to_float __floatsidf | |
190 | # define float_to_si __fixdfsi | |
191 | # define float_to_usi __fixunsdfsi | |
192 | # define negate __negdf2 | |
193 | # define df_to_sf __truncdfsf2 | |
194 | # endif | |
195 | #endif | |
196 | ||
197 | ||
198 | #ifndef INLINE | |
199 | #define INLINE __inline__ | |
200 | #endif | |
201 | ||
202 | /* Preserve the sticky-bit when shifting fractions to the right. */ | |
203 | #define LSHIFT(a) { a = (a & 1) | (a >> 1); } | |
204 | ||
205 | /* numeric parameters */ | |
206 | /* F_D_BITOFF is the number of bits offset between the MSB of the mantissa | |
207 | of a float and of a double. Assumes there are only two float types. | |
208 | (double::FRAC_BITS+double::NGARGS-(float::FRAC_BITS-float::NGARDS)) | |
209 | */ | |
210 | #define F_D_BITOFF (52+8-(23+7)) | |
211 | ||
212 | ||
213 | #define NORMAL_EXPMIN (-(EXPBIAS)+1) | |
214 | #define IMPLICIT_1 (1LL<<(FRACBITS+NGARDS)) | |
215 | #define IMPLICIT_2 (1LL<<(FRACBITS+1+NGARDS)) | |
216 | ||
217 | /* common types */ | |
218 | ||
219 | typedef enum | |
220 | { | |
221 | CLASS_SNAN, | |
222 | CLASS_QNAN, | |
223 | CLASS_ZERO, | |
224 | CLASS_NUMBER, | |
225 | CLASS_INFINITY | |
226 | } fp_class_type; | |
227 | ||
228 | typedef struct | |
229 | { | |
230 | #ifdef SMALL_MACHINE | |
231 | char class; | |
232 | unsigned char sign; | |
233 | short normal_exp; | |
234 | #else | |
235 | fp_class_type class; | |
236 | unsigned int sign; | |
237 | int normal_exp; | |
238 | #endif | |
239 | ||
240 | union | |
241 | { | |
242 | fractype ll; | |
243 | halffractype l[2]; | |
244 | } fraction; | |
245 | } fp_number_type; | |
246 | ||
247 | typedef union | |
248 | { | |
249 | FLO_type value; | |
250 | #ifdef _DEBUG_BITFLOAT | |
251 | int l[2]; | |
252 | #endif | |
253 | struct | |
254 | { | |
255 | #ifndef FLOAT_BIT_ORDER_MISMATCH | |
256 | unsigned int sign:1 __attribute__ ((packed)); | |
257 | unsigned int exp:EXPBITS __attribute__ ((packed)); | |
258 | fractype fraction:FRACBITS __attribute__ ((packed)); | |
259 | #else | |
260 | fractype fraction:FRACBITS __attribute__ ((packed)); | |
261 | unsigned int exp:EXPBITS __attribute__ ((packed)); | |
262 | unsigned int sign:1 __attribute__ ((packed)); | |
263 | #endif | |
264 | } | |
265 | bits; | |
266 | } | |
267 | FLO_union_type; | |
268 | ||
269 | ||
270 | /* end of header */ | |
271 | ||
272 | /* IEEE "special" number predicates */ | |
273 | ||
274 | #ifdef NO_NANS | |
275 | ||
276 | #define nan() 0 | |
277 | #define isnan(x) 0 | |
278 | #define isinf(x) 0 | |
279 | #else | |
280 | ||
281 | INLINE | |
282 | static fp_number_type * | |
283 | nan () | |
284 | { | |
285 | static fp_number_type thenan; | |
286 | ||
287 | return &thenan; | |
288 | } | |
289 | ||
290 | INLINE | |
291 | static int | |
292 | isnan ( fp_number_type * x) | |
293 | { | |
294 | return x->class == CLASS_SNAN || x->class == CLASS_QNAN; | |
295 | } | |
296 | ||
297 | INLINE | |
298 | static int | |
299 | isinf ( fp_number_type * x) | |
300 | { | |
301 | return x->class == CLASS_INFINITY; | |
302 | } | |
303 | ||
304 | #endif | |
305 | ||
306 | INLINE | |
307 | static int | |
308 | iszero ( fp_number_type * x) | |
309 | { | |
310 | return x->class == CLASS_ZERO; | |
311 | } | |
312 | ||
313 | INLINE | |
314 | static void | |
315 | flip_sign ( fp_number_type * x) | |
316 | { | |
317 | x->sign = !x->sign; | |
318 | } | |
319 | ||
320 | static FLO_type | |
321 | pack_d ( fp_number_type * src) | |
322 | { | |
323 | FLO_union_type dst; | |
324 | fractype fraction = src->fraction.ll; /* wasn't unsigned before? */ | |
325 | ||
326 | dst.bits.sign = src->sign; | |
327 | ||
328 | if (isnan (src)) | |
329 | { | |
330 | dst.bits.exp = EXPMAX; | |
331 | dst.bits.fraction = src->fraction.ll; | |
332 | if (src->class == CLASS_QNAN || 1) | |
333 | { | |
334 | dst.bits.fraction |= QUIET_NAN; | |
335 | } | |
336 | } | |
337 | else if (isinf (src)) | |
338 | { | |
339 | dst.bits.exp = EXPMAX; | |
340 | dst.bits.fraction = 0; | |
341 | } | |
342 | else if (iszero (src)) | |
343 | { | |
344 | dst.bits.exp = 0; | |
345 | dst.bits.fraction = 0; | |
346 | } | |
347 | else if (fraction == 0) | |
348 | { | |
349 | dst.value = 0; | |
350 | } | |
351 | else | |
352 | { | |
353 | if (src->normal_exp < NORMAL_EXPMIN) | |
354 | { | |
355 | /* This number's exponent is too low to fit into the bits | |
356 | available in the number, so we'll store 0 in the exponent and | |
357 | shift the fraction to the right to make up for it. */ | |
358 | ||
359 | int shift = NORMAL_EXPMIN - src->normal_exp; | |
360 | ||
361 | dst.bits.exp = 0; | |
362 | ||
363 | if (shift > FRAC_NBITS - NGARDS) | |
364 | { | |
365 | /* No point shifting, since it's more that 64 out. */ | |
366 | fraction = 0; | |
367 | } | |
368 | else | |
369 | { | |
370 | /* Shift by the value */ | |
371 | fraction >>= shift; | |
372 | } | |
373 | fraction >>= NGARDS; | |
374 | dst.bits.fraction = fraction; | |
375 | } | |
376 | else if (src->normal_exp > EXPBIAS) | |
377 | { | |
378 | dst.bits.exp = EXPMAX; | |
379 | dst.bits.fraction = 0; | |
380 | } | |
381 | else | |
382 | { | |
383 | dst.bits.exp = src->normal_exp + EXPBIAS; | |
384 | /* IF the gard bits are the all zero, but the first, then we're | |
385 | half way between two numbers, choose the one which makes the | |
386 | lsb of the answer 0. */ | |
387 | if ((fraction & GARDMASK) == GARDMSB) | |
388 | { | |
389 | if (fraction & (1 << NGARDS)) | |
390 | fraction += GARDROUND + 1; | |
391 | } | |
392 | else | |
393 | { | |
394 | /* Add a one to the guards to round up */ | |
395 | fraction += GARDROUND; | |
396 | } | |
397 | if (fraction >= IMPLICIT_2) | |
398 | { | |
399 | fraction >>= 1; | |
400 | dst.bits.exp += 1; | |
401 | } | |
402 | fraction >>= NGARDS; | |
403 | dst.bits.fraction = fraction; | |
404 | } | |
405 | } | |
406 | return dst.value; | |
407 | } | |
408 | ||
409 | static void | |
410 | unpack_d (FLO_union_type * src, fp_number_type * dst) | |
411 | { | |
412 | fractype fraction = src->bits.fraction; | |
413 | ||
414 | dst->sign = src->bits.sign; | |
415 | if (src->bits.exp == 0) | |
416 | { | |
417 | /* Hmm. Looks like 0 */ | |
418 | if (fraction == 0) | |
419 | { | |
420 | /* tastes like zero */ | |
421 | dst->class = CLASS_ZERO; | |
422 | } | |
423 | else | |
424 | { | |
425 | /* Zero exponent with non zero fraction - it's denormalized, | |
426 | so there isn't a leading implicit one - we'll shift it so | |
427 | it gets one. */ | |
428 | dst->normal_exp = src->bits.exp - EXPBIAS + 1; | |
429 | fraction <<= NGARDS; | |
430 | ||
431 | dst->class = CLASS_NUMBER; | |
432 | #if 1 | |
433 | while (fraction < IMPLICIT_1) | |
434 | { | |
435 | fraction <<= 1; | |
436 | dst->normal_exp--; | |
437 | } | |
438 | #endif | |
439 | dst->fraction.ll = fraction; | |
440 | } | |
441 | } | |
442 | else if (src->bits.exp == EXPMAX) | |
443 | { | |
444 | /* Huge exponent*/ | |
445 | if (fraction == 0) | |
446 | { | |
447 | /* Attached to a zero fraction - means infinity */ | |
448 | dst->class = CLASS_INFINITY; | |
449 | } | |
450 | else | |
451 | { | |
452 | /* Non zero fraction, means nan */ | |
453 | if (dst->sign) | |
454 | { | |
455 | dst->class = CLASS_SNAN; | |
456 | } | |
457 | else | |
458 | { | |
459 | dst->class = CLASS_QNAN; | |
460 | } | |
461 | /* Keep the fraction part as the nan number */ | |
462 | dst->fraction.ll = fraction; | |
463 | } | |
464 | } | |
465 | else | |
466 | { | |
467 | /* Nothing strange about this number */ | |
468 | dst->normal_exp = src->bits.exp - EXPBIAS; | |
469 | dst->class = CLASS_NUMBER; | |
470 | dst->fraction.ll = (fraction << NGARDS) | IMPLICIT_1; | |
471 | } | |
472 | } | |
473 | ||
474 | static fp_number_type * | |
475 | _fpadd_parts (fp_number_type * a, | |
476 | fp_number_type * b, | |
477 | fp_number_type * tmp) | |
478 | { | |
479 | intfrac tfraction; | |
480 | ||
481 | /* Put commonly used fields in local variables. */ | |
482 | int a_normal_exp; | |
483 | int b_normal_exp; | |
484 | fractype a_fraction; | |
485 | fractype b_fraction; | |
486 | ||
487 | if (isnan (a)) | |
488 | { | |
489 | return a; | |
490 | } | |
491 | if (isnan (b)) | |
492 | { | |
493 | return b; | |
494 | } | |
495 | if (isinf (a)) | |
496 | { | |
497 | /* Adding infinities with opposite signs yields a NaN. */ | |
498 | if (isinf (b) && a->sign != b->sign) | |
499 | return nan (); | |
500 | return a; | |
501 | } | |
502 | if (isinf (b)) | |
503 | { | |
504 | return b; | |
505 | } | |
506 | if (iszero (b)) | |
507 | { | |
508 | return a; | |
509 | } | |
510 | if (iszero (a)) | |
511 | { | |
512 | return b; | |
513 | } | |
514 | ||
515 | /* Got two numbers. shift the smaller and increment the exponent till | |
516 | they're the same */ | |
517 | { | |
518 | int diff; | |
519 | ||
520 | a_normal_exp = a->normal_exp; | |
521 | b_normal_exp = b->normal_exp; | |
522 | a_fraction = a->fraction.ll; | |
523 | b_fraction = b->fraction.ll; | |
524 | ||
525 | diff = a_normal_exp - b_normal_exp; | |
526 | ||
527 | if (diff < 0) | |
528 | diff = -diff; | |
529 | if (diff < FRAC_NBITS) | |
530 | { | |
531 | /* ??? This does shifts one bit at a time. Optimize. */ | |
532 | while (a_normal_exp > b_normal_exp) | |
533 | { | |
534 | b_normal_exp++; | |
535 | LSHIFT (b_fraction); | |
536 | } | |
537 | while (b_normal_exp > a_normal_exp) | |
538 | { | |
539 | a_normal_exp++; | |
540 | LSHIFT (a_fraction); | |
541 | } | |
542 | } | |
543 | else | |
544 | { | |
545 | /* Somethings's up.. choose the biggest */ | |
546 | if (a_normal_exp > b_normal_exp) | |
547 | { | |
548 | b_normal_exp = a_normal_exp; | |
549 | b_fraction = 0; | |
550 | } | |
551 | else | |
552 | { | |
553 | a_normal_exp = b_normal_exp; | |
554 | a_fraction = 0; | |
555 | } | |
556 | } | |
557 | } | |
558 | ||
559 | if (a->sign != b->sign) | |
560 | { | |
561 | if (a->sign) | |
562 | { | |
563 | tfraction = -a_fraction + b_fraction; | |
564 | } | |
565 | else | |
566 | { | |
567 | tfraction = a_fraction - b_fraction; | |
568 | } | |
569 | if (tfraction > 0) | |
570 | { | |
571 | tmp->sign = 0; | |
572 | tmp->normal_exp = a_normal_exp; | |
573 | tmp->fraction.ll = tfraction; | |
574 | } | |
575 | else | |
576 | { | |
577 | tmp->sign = 1; | |
578 | tmp->normal_exp = a_normal_exp; | |
579 | tmp->fraction.ll = -tfraction; | |
580 | } | |
581 | /* and renormalize it */ | |
582 | ||
583 | while (tmp->fraction.ll < IMPLICIT_1 && tmp->fraction.ll) | |
584 | { | |
585 | tmp->fraction.ll <<= 1; | |
586 | tmp->normal_exp--; | |
587 | } | |
588 | } | |
589 | else | |
590 | { | |
591 | tmp->sign = a->sign; | |
592 | tmp->normal_exp = a_normal_exp; | |
593 | tmp->fraction.ll = a_fraction + b_fraction; | |
594 | } | |
595 | tmp->class = CLASS_NUMBER; | |
596 | /* Now the fraction is added, we have to shift down to renormalize the | |
597 | number */ | |
598 | ||
599 | if (tmp->fraction.ll >= IMPLICIT_2) | |
600 | { | |
601 | LSHIFT (tmp->fraction.ll); | |
602 | tmp->normal_exp++; | |
603 | } | |
604 | return tmp; | |
605 | ||
606 | } | |
607 | ||
608 | FLO_type | |
609 | add (FLO_type arg_a, FLO_type arg_b) | |
610 | { | |
611 | fp_number_type a; | |
612 | fp_number_type b; | |
613 | fp_number_type tmp; | |
614 | fp_number_type *res; | |
615 | ||
616 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
617 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
618 | ||
619 | res = _fpadd_parts (&a, &b, &tmp); | |
620 | ||
621 | return pack_d (res); | |
622 | } | |
623 | ||
624 | FLO_type | |
625 | sub (FLO_type arg_a, FLO_type arg_b) | |
626 | { | |
627 | fp_number_type a; | |
628 | fp_number_type b; | |
629 | fp_number_type tmp; | |
630 | fp_number_type *res; | |
631 | ||
632 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
633 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
634 | ||
635 | b.sign ^= 1; | |
636 | ||
637 | res = _fpadd_parts (&a, &b, &tmp); | |
638 | ||
639 | return pack_d (res); | |
640 | } | |
641 | ||
642 | static fp_number_type * | |
643 | _fpmul_parts ( fp_number_type * a, | |
644 | fp_number_type * b, | |
645 | fp_number_type * tmp) | |
646 | { | |
647 | fractype low = 0; | |
648 | fractype high = 0; | |
649 | ||
650 | if (isnan (a)) | |
651 | { | |
652 | a->sign = a->sign != b->sign; | |
653 | return a; | |
654 | } | |
655 | if (isnan (b)) | |
656 | { | |
657 | b->sign = a->sign != b->sign; | |
658 | return b; | |
659 | } | |
660 | if (isinf (a)) | |
661 | { | |
662 | if (iszero (b)) | |
663 | return nan (); | |
664 | a->sign = a->sign != b->sign; | |
665 | return a; | |
666 | } | |
667 | if (isinf (b)) | |
668 | { | |
669 | if (iszero (a)) | |
670 | { | |
671 | return nan (); | |
672 | } | |
673 | b->sign = a->sign != b->sign; | |
674 | return b; | |
675 | } | |
676 | if (iszero (a)) | |
677 | { | |
678 | a->sign = a->sign != b->sign; | |
679 | return a; | |
680 | } | |
681 | if (iszero (b)) | |
682 | { | |
683 | b->sign = a->sign != b->sign; | |
684 | return b; | |
685 | } | |
686 | ||
687 | /* Calculate the mantissa by multiplying both 64bit numbers to get a | |
688 | 128 bit number */ | |
689 | { | |
690 | fractype x = a->fraction.ll; | |
691 | fractype ylow = b->fraction.ll; | |
692 | fractype yhigh = 0; | |
693 | int bit; | |
694 | ||
695 | #if defined(NO_DI_MODE) | |
696 | { | |
697 | /* ??? This does multiplies one bit at a time. Optimize. */ | |
698 | for (bit = 0; bit < FRAC_NBITS; bit++) | |
699 | { | |
700 | int carry; | |
701 | ||
702 | if (x & 1) | |
703 | { | |
704 | carry = (low += ylow) < ylow; | |
705 | high += yhigh + carry; | |
706 | } | |
707 | yhigh <<= 1; | |
708 | if (ylow & FRACHIGH) | |
709 | { | |
710 | yhigh |= 1; | |
711 | } | |
712 | ylow <<= 1; | |
713 | x >>= 1; | |
714 | } | |
715 | } | |
716 | #elif defined(FLOAT) | |
717 | { | |
718 | /* Multiplying two 32 bit numbers to get a 64 bit number on | |
719 | a machine with DI, so we're safe */ | |
720 | ||
721 | DItype answer = (DItype)(a->fraction.ll) * (DItype)(b->fraction.ll); | |
722 | ||
723 | high = answer >> 32; | |
724 | low = answer; | |
725 | } | |
726 | #else | |
727 | /* Doing a 64*64 to 128 */ | |
728 | { | |
729 | UDItype nl = a->fraction.ll & 0xffffffff; | |
730 | UDItype nh = a->fraction.ll >> 32; | |
731 | UDItype ml = b->fraction.ll & 0xffffffff; | |
732 | UDItype mh = b->fraction.ll >>32; | |
733 | UDItype pp_ll = ml * nl; | |
734 | UDItype pp_hl = mh * nl; | |
735 | UDItype pp_lh = ml * nh; | |
736 | UDItype pp_hh = mh * nh; | |
737 | UDItype res2 = 0; | |
738 | UDItype res0 = 0; | |
739 | UDItype ps_hh__ = pp_hl + pp_lh; | |
740 | if (ps_hh__ < pp_hl) | |
741 | res2 += 0x100000000LL; | |
742 | pp_hl = (ps_hh__ << 32) & 0xffffffff00000000LL; | |
743 | res0 = pp_ll + pp_hl; | |
744 | if (res0 < pp_ll) | |
745 | res2++; | |
746 | res2 += ((ps_hh__ >> 32) & 0xffffffffL) + pp_hh; | |
747 | high = res2; | |
748 | low = res0; | |
749 | } | |
750 | #endif | |
751 | } | |
752 | ||
753 | tmp->normal_exp = a->normal_exp + b->normal_exp; | |
754 | tmp->sign = a->sign != b->sign; | |
755 | #ifdef FLOAT | |
756 | tmp->normal_exp += 2; /* ??????????????? */ | |
757 | #else | |
758 | tmp->normal_exp += 4; /* ??????????????? */ | |
759 | #endif | |
760 | while (high >= IMPLICIT_2) | |
761 | { | |
762 | tmp->normal_exp++; | |
763 | if (high & 1) | |
764 | { | |
765 | low >>= 1; | |
766 | low |= FRACHIGH; | |
767 | } | |
768 | high >>= 1; | |
769 | } | |
770 | while (high < IMPLICIT_1) | |
771 | { | |
772 | tmp->normal_exp--; | |
773 | ||
774 | high <<= 1; | |
775 | if (low & FRACHIGH) | |
776 | high |= 1; | |
777 | low <<= 1; | |
778 | } | |
779 | /* rounding is tricky. if we only round if it won't make us round later. */ | |
780 | #if 0 | |
781 | if (low & FRACHIGH2) | |
782 | { | |
783 | if (((high & GARDMASK) != GARDMSB) | |
784 | && (((high + 1) & GARDMASK) == GARDMSB)) | |
785 | { | |
786 | /* don't round, it gets done again later. */ | |
787 | } | |
788 | else | |
789 | { | |
790 | high++; | |
791 | } | |
792 | } | |
793 | #endif | |
794 | if ((high & GARDMASK) == GARDMSB) | |
795 | { | |
796 | if (high & (1 << NGARDS)) | |
797 | { | |
798 | /* half way, so round to even */ | |
799 | high += GARDROUND + 1; | |
800 | } | |
801 | else if (low) | |
802 | { | |
803 | /* but we really weren't half way */ | |
804 | high += GARDROUND + 1; | |
805 | } | |
806 | } | |
807 | tmp->fraction.ll = high; | |
808 | tmp->class = CLASS_NUMBER; | |
809 | return tmp; | |
810 | } | |
811 | ||
812 | FLO_type | |
813 | multiply (FLO_type arg_a, FLO_type arg_b) | |
814 | { | |
815 | fp_number_type a; | |
816 | fp_number_type b; | |
817 | fp_number_type tmp; | |
818 | fp_number_type *res; | |
819 | ||
820 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
821 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
822 | ||
823 | res = _fpmul_parts (&a, &b, &tmp); | |
824 | ||
825 | return pack_d (res); | |
826 | } | |
827 | ||
828 | static fp_number_type * | |
829 | _fpdiv_parts (fp_number_type * a, | |
830 | fp_number_type * b, | |
831 | fp_number_type * tmp) | |
832 | { | |
833 | fractype low = 0; | |
834 | fractype high = 0; | |
835 | fractype r0, r1, y0, y1, bit; | |
836 | fractype q; | |
837 | fractype numerator; | |
838 | fractype denominator; | |
839 | fractype quotient; | |
840 | fractype remainder; | |
841 | ||
842 | if (isnan (a)) | |
843 | { | |
844 | return a; | |
845 | } | |
846 | if (isnan (b)) | |
847 | { | |
848 | return b; | |
849 | } | |
850 | if (isinf (a) || iszero (a)) | |
851 | { | |
852 | if (a->class == b->class) | |
853 | return nan (); | |
854 | return a; | |
855 | } | |
856 | a->sign = a->sign ^ b->sign; | |
857 | ||
858 | if (isinf (b)) | |
859 | { | |
860 | a->fraction.ll = 0; | |
861 | a->normal_exp = 0; | |
862 | return a; | |
863 | } | |
864 | if (iszero (b)) | |
865 | { | |
866 | a->class = CLASS_INFINITY; | |
867 | return b; | |
868 | } | |
869 | ||
870 | /* Calculate the mantissa by multiplying both 64bit numbers to get a | |
871 | 128 bit number */ | |
872 | { | |
873 | int carry; | |
874 | intfrac d0, d1; /* weren't unsigned before ??? */ | |
875 | ||
876 | /* quotient = | |
877 | ( numerator / denominator) * 2^(numerator exponent - denominator exponent) | |
878 | */ | |
879 | ||
880 | a->normal_exp = a->normal_exp - b->normal_exp; | |
881 | numerator = a->fraction.ll; | |
882 | denominator = b->fraction.ll; | |
883 | ||
884 | if (numerator < denominator) | |
885 | { | |
886 | /* Fraction will be less than 1.0 */ | |
887 | numerator *= 2; | |
888 | a->normal_exp--; | |
889 | } | |
890 | bit = IMPLICIT_1; | |
891 | quotient = 0; | |
892 | /* ??? Does divide one bit at a time. Optimize. */ | |
893 | while (bit) | |
894 | { | |
895 | if (numerator >= denominator) | |
896 | { | |
897 | quotient |= bit; | |
898 | numerator -= denominator; | |
899 | } | |
900 | bit >>= 1; | |
901 | numerator *= 2; | |
902 | } | |
903 | ||
904 | if ((quotient & GARDMASK) == GARDMSB) | |
905 | { | |
906 | if (quotient & (1 << NGARDS)) | |
907 | { | |
908 | /* half way, so round to even */ | |
909 | quotient += GARDROUND + 1; | |
910 | } | |
911 | else if (numerator) | |
912 | { | |
913 | /* but we really weren't half way, more bits exist */ | |
914 | quotient += GARDROUND + 1; | |
915 | } | |
916 | } | |
917 | ||
918 | a->fraction.ll = quotient; | |
919 | return (a); | |
920 | } | |
921 | } | |
922 | ||
923 | FLO_type | |
924 | divide (FLO_type arg_a, FLO_type arg_b) | |
925 | { | |
926 | fp_number_type a; | |
927 | fp_number_type b; | |
928 | fp_number_type tmp; | |
929 | fp_number_type *res; | |
930 | ||
931 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
932 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
933 | ||
934 | res = _fpdiv_parts (&a, &b, &tmp); | |
935 | ||
936 | return pack_d (res); | |
937 | } | |
938 | ||
939 | /* according to the demo, fpcmp returns a comparison with 0... thus | |
940 | a<b -> -1 | |
941 | a==b -> 0 | |
942 | a>b -> +1 | |
943 | */ | |
944 | ||
945 | static int | |
946 | _fpcmp_parts (fp_number_type * a, fp_number_type * b) | |
947 | { | |
948 | #if 0 | |
949 | /* either nan -> unordered. Must be checked outside of this routine. */ | |
950 | if (isnan (a) && isnan (b)) | |
951 | { | |
952 | return 1; /* still unordered! */ | |
953 | } | |
954 | #endif | |
955 | ||
956 | if (isnan (a) || isnan (b)) | |
957 | { | |
958 | return 1; /* how to indicate unordered compare? */ | |
959 | } | |
960 | if (isinf (a) && isinf (b)) | |
961 | { | |
962 | /* +inf > -inf, but +inf != +inf */ | |
963 | /* b \a| +inf(0)| -inf(1) | |
964 | ______\+--------+-------- | |
965 | +inf(0)| a==b(0)| a<b(-1) | |
966 | -------+--------+-------- | |
967 | -inf(1)| a>b(1) | a==b(0) | |
968 | -------+--------+-------- | |
969 | So since unordered must be non zero, just line up the columns... | |
970 | */ | |
971 | return b->sign - a->sign; | |
972 | } | |
973 | /* but not both... */ | |
974 | if (isinf (a)) | |
975 | { | |
976 | return a->sign ? -1 : 1; | |
977 | } | |
978 | if (isinf (b)) | |
979 | { | |
980 | return b->sign ? 1 : -1; | |
981 | } | |
982 | if (iszero (a) && iszero (b)) | |
983 | { | |
984 | return 0; | |
985 | } | |
986 | if (iszero (a)) | |
987 | { | |
988 | return b->sign ? 1 : -1; | |
989 | } | |
990 | if (iszero (b)) | |
991 | { | |
992 | return a->sign ? -1 : 1; | |
993 | } | |
994 | /* now both are "normal". */ | |
995 | if (a->sign != b->sign) | |
996 | { | |
997 | /* opposite signs */ | |
998 | return a->sign ? -1 : 1; | |
999 | } | |
1000 | /* same sign; exponents? */ | |
1001 | if (a->normal_exp > b->normal_exp) | |
1002 | { | |
1003 | return a->sign ? -1 : 1; | |
1004 | } | |
1005 | if (a->normal_exp < b->normal_exp) | |
1006 | { | |
1007 | return a->sign ? 1 : -1; | |
1008 | } | |
1009 | /* same exponents; check size. */ | |
1010 | if (a->fraction.ll > b->fraction.ll) | |
1011 | { | |
1012 | return a->sign ? -1 : 1; | |
1013 | } | |
1014 | if (a->fraction.ll < b->fraction.ll) | |
1015 | { | |
1016 | return a->sign ? 1 : -1; | |
1017 | } | |
1018 | /* after all that, they're equal. */ | |
1019 | return 0; | |
1020 | } | |
1021 | ||
1022 | CMPtype | |
1023 | compare (FLO_type arg_a, FLO_type arg_b) | |
1024 | { | |
1025 | fp_number_type a; | |
1026 | fp_number_type b; | |
1027 | ||
1028 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1029 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1030 | ||
1031 | return _fpcmp_parts (&a, &b); | |
1032 | } | |
1033 | ||
1034 | #ifndef US_SOFTWARE_GOFAST | |
1035 | ||
1036 | /* These should be optimized for their specific tasks someday. */ | |
1037 | ||
1038 | CMPtype | |
1039 | _eq_f2 (FLO_type arg_a, FLO_type arg_b) | |
1040 | { | |
1041 | fp_number_type a; | |
1042 | fp_number_type b; | |
1043 | ||
1044 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1045 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1046 | ||
1047 | if (isnan (&a) || isnan (&b)) | |
1048 | return 1; /* false, truth == 0 */ | |
1049 | ||
1050 | return _fpcmp_parts (&a, &b) ; | |
1051 | } | |
1052 | ||
1053 | CMPtype | |
1054 | _ne_f2 (FLO_type arg_a, FLO_type arg_b) | |
1055 | { | |
1056 | fp_number_type a; | |
1057 | fp_number_type b; | |
1058 | ||
1059 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1060 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1061 | ||
1062 | if (isnan (&a) || isnan (&b)) | |
1063 | return 1; /* true, truth != 0 */ | |
1064 | ||
1065 | return _fpcmp_parts (&a, &b) ; | |
1066 | } | |
1067 | ||
1068 | CMPtype | |
1069 | _gt_f2 (FLO_type arg_a, FLO_type arg_b) | |
1070 | { | |
1071 | fp_number_type a; | |
1072 | fp_number_type b; | |
1073 | ||
1074 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1075 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1076 | ||
1077 | if (isnan (&a) || isnan (&b)) | |
1078 | return -1; /* false, truth > 0 */ | |
1079 | ||
1080 | return _fpcmp_parts (&a, &b); | |
1081 | } | |
1082 | ||
1083 | CMPtype | |
1084 | _ge_f2 (FLO_type arg_a, FLO_type arg_b) | |
1085 | { | |
1086 | fp_number_type a; | |
1087 | fp_number_type b; | |
1088 | ||
1089 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1090 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1091 | ||
1092 | if (isnan (&a) || isnan (&b)) | |
1093 | return -1; /* false, truth >= 0 */ | |
1094 | return _fpcmp_parts (&a, &b) ; | |
1095 | } | |
1096 | ||
1097 | CMPtype | |
1098 | _lt_f2 (FLO_type arg_a, FLO_type arg_b) | |
1099 | { | |
1100 | fp_number_type a; | |
1101 | fp_number_type b; | |
1102 | ||
1103 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1104 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1105 | ||
1106 | if (isnan (&a) || isnan (&b)) | |
1107 | return 1; /* false, truth < 0 */ | |
1108 | ||
1109 | return _fpcmp_parts (&a, &b); | |
1110 | } | |
1111 | ||
1112 | CMPtype | |
1113 | _le_f2 (FLO_type arg_a, FLO_type arg_b) | |
1114 | { | |
1115 | fp_number_type a; | |
1116 | fp_number_type b; | |
1117 | ||
1118 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1119 | unpack_d ((FLO_union_type *) & arg_b, &b); | |
1120 | ||
1121 | if (isnan (&a) || isnan (&b)) | |
1122 | return 1; /* false, truth <= 0 */ | |
1123 | ||
1124 | return _fpcmp_parts (&a, &b) ; | |
1125 | } | |
1126 | ||
1127 | #endif /* ! US_SOFTWARE_GOFAST */ | |
1128 | ||
1129 | FLO_type | |
1130 | si_to_float (SItype arg_a) | |
1131 | { | |
1132 | fp_number_type in; | |
1133 | ||
1134 | in.class = CLASS_NUMBER; | |
1135 | in.sign = arg_a < 0; | |
1136 | if (!arg_a) | |
1137 | { | |
1138 | in.class = CLASS_ZERO; | |
1139 | } | |
1140 | else | |
1141 | { | |
1142 | in.normal_exp = FRACBITS + NGARDS; | |
1143 | if (in.sign) | |
1144 | { | |
1145 | /* Special case for minint, since there is no +ve integer | |
1146 | representation for it */ | |
1147 | if (arg_a == 0x80000000) | |
1148 | { | |
1149 | return -2147483648.0; | |
1150 | } | |
1151 | in.fraction.ll = (-arg_a); | |
1152 | } | |
1153 | else | |
1154 | in.fraction.ll = arg_a; | |
1155 | ||
1156 | while (in.fraction.ll < (1LL << (FRACBITS + NGARDS))) | |
1157 | { | |
1158 | in.fraction.ll <<= 1; | |
1159 | in.normal_exp -= 1; | |
1160 | } | |
1161 | } | |
1162 | return pack_d (&in); | |
1163 | } | |
1164 | ||
1165 | SItype | |
1166 | float_to_si (FLO_type arg_a) | |
1167 | { | |
1168 | fp_number_type a; | |
1169 | SItype tmp; | |
1170 | ||
1171 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1172 | if (iszero (&a)) | |
1173 | return 0; | |
1174 | if (isnan (&a)) | |
1175 | return 0; | |
1176 | /* get reasonable MAX_SI_INT... */ | |
1177 | if (isinf (&a)) | |
1178 | return a.sign ? MAX_SI_INT : (-MAX_SI_INT)-1; | |
1179 | /* it is a number, but a small one */ | |
1180 | if (a.normal_exp < 0) | |
1181 | return 0; | |
1182 | if (a.normal_exp > 30) | |
1183 | return a.sign ? (-MAX_SI_INT)-1 : MAX_SI_INT; | |
1184 | tmp = a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp); | |
1185 | return a.sign ? (-tmp) : (tmp); | |
1186 | } | |
1187 | ||
1188 | #ifdef US_SOFTWARE_GOFAST | |
1189 | /* While libgcc2.c defines its own __fixunssfsi and __fixunsdfsi routines, | |
1190 | we also define them for GOFAST because the ones in libgcc2.c have the | |
1191 | wrong names and I'd rather define these here and keep GOFAST CYG-LOC's | |
1192 | out of libgcc2.c. We can't define these here if not GOFAST because then | |
1193 | there'd be duplicate copies. */ | |
1194 | ||
1195 | USItype | |
1196 | float_to_usi (FLO_type arg_a) | |
1197 | { | |
1198 | fp_number_type a; | |
1199 | ||
1200 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1201 | if (iszero (&a)) | |
1202 | return 0; | |
1203 | if (isnan (&a)) | |
1204 | return 0; | |
1205 | /* get reasonable MAX_USI_INT... */ | |
1206 | if (isinf (&a)) | |
1207 | return a.sign ? MAX_USI_INT : 0; | |
1208 | /* it is a negative number */ | |
1209 | if (a.sign) | |
1210 | return 0; | |
1211 | /* it is a number, but a small one */ | |
1212 | if (a.normal_exp < 0) | |
1213 | return 0; | |
1214 | if (a.normal_exp > 31) | |
1215 | return MAX_USI_INT; | |
1216 | else if (a.normal_exp > (FRACBITS + NGARDS)) | |
1217 | return a.fraction.ll << ((FRACBITS + NGARDS) - a.normal_exp); | |
1218 | else | |
1219 | return a.fraction.ll >> ((FRACBITS + NGARDS) - a.normal_exp); | |
1220 | } | |
1221 | #endif | |
1222 | ||
1223 | FLO_type | |
1224 | negate (FLO_type arg_a) | |
1225 | { | |
1226 | fp_number_type a; | |
1227 | ||
1228 | unpack_d ((FLO_union_type *) & arg_a, &a); | |
1229 | flip_sign (&a); | |
1230 | return pack_d (&a); | |
1231 | } | |
1232 | ||
1233 | #ifdef FLOAT | |
1234 | ||
1235 | SFtype | |
1236 | __make_fp(fp_class_type class, | |
1237 | unsigned int sign, | |
1238 | int exp, | |
1239 | USItype frac) | |
1240 | { | |
1241 | fp_number_type in; | |
1242 | ||
1243 | in.class = class; | |
1244 | in.sign = sign; | |
1245 | in.normal_exp = exp; | |
1246 | in.fraction.ll = frac; | |
1247 | return pack_d (&in); | |
1248 | } | |
1249 | ||
1250 | #ifndef FLOAT_ONLY | |
1251 | ||
1252 | /* This enables one to build an fp library that supports float but not double. | |
1253 | Otherwise, we would get an undefined reference to __make_dp. | |
1254 | This is needed for some 8-bit ports that can't handle well values that | |
1255 | are 8-bytes in size, so we just don't support double for them at all. */ | |
1256 | ||
1257 | extern DFtype __make_dp (fp_class_type, unsigned int, int, UDItype frac); | |
1258 | ||
1259 | DFtype | |
1260 | sf_to_df (SFtype arg_a) | |
1261 | { | |
1262 | fp_number_type in; | |
1263 | ||
1264 | unpack_d ((FLO_union_type *) & arg_a, &in); | |
1265 | return __make_dp (in.class, in.sign, in.normal_exp, | |
1266 | ((UDItype) in.fraction.ll) << F_D_BITOFF); | |
1267 | } | |
1268 | ||
1269 | #endif | |
1270 | #endif | |
1271 | ||
1272 | #ifndef FLOAT | |
1273 | ||
1274 | extern SFtype __make_fp (fp_class_type, unsigned int, int, USItype); | |
1275 | ||
1276 | DFtype | |
1277 | __make_dp (fp_class_type class, unsigned int sign, int exp, UDItype frac) | |
1278 | { | |
1279 | fp_number_type in; | |
1280 | ||
1281 | in.class = class; | |
1282 | in.sign = sign; | |
1283 | in.normal_exp = exp; | |
1284 | in.fraction.ll = frac; | |
1285 | return pack_d (&in); | |
1286 | } | |
1287 | ||
1288 | SFtype | |
1289 | df_to_sf (DFtype arg_a) | |
1290 | { | |
1291 | fp_number_type in; | |
1292 | ||
1293 | unpack_d ((FLO_union_type *) & arg_a, &in); | |
1294 | return __make_fp (in.class, in.sign, in.normal_exp, | |
1295 | in.fraction.ll >> F_D_BITOFF); | |
1296 | } | |
1297 | ||
1298 | #endif |