1 /*
2
3 fp_arith.c: floating-point math routines for the Linux-m68k
4 floating point emulator.
5
6 Copyright (c) 1998-1999 David Huggins-Daines.
7
8 Somewhat based on the AlphaLinux floating point emulator, by David
9 Mosberger-Tang.
10
11 You may copy, modify, and redistribute this file under the terms of
12 the GNU General Public License, version 2, or any later version, at
13 your convenience.
14 */
15
16 #include "fp_emu.h"
17 #include "multi_arith.h"
18 #include "fp_arith.h"
19
20 const struct fp_ext fp_QNaN =
21 {
22 .exp = 0x7fff,
23 .mant = { .m64 = ~0 }
24 };
25
26 const struct fp_ext fp_Inf =
27 {
28 .exp = 0x7fff,
29 };
30
31 /* let's start with the easy ones */
32
33 struct fp_ext *
fp_fabs(struct fp_ext * dest,struct fp_ext * src)34 fp_fabs(struct fp_ext *dest, struct fp_ext *src)
35 {
36 dprint(PINSTR, "fabs\n");
37
38 fp_monadic_check(dest, src);
39
40 dest->sign = 0;
41
42 return dest;
43 }
44
45 struct fp_ext *
fp_fneg(struct fp_ext * dest,struct fp_ext * src)46 fp_fneg(struct fp_ext *dest, struct fp_ext *src)
47 {
48 dprint(PINSTR, "fneg\n");
49
50 fp_monadic_check(dest, src);
51
52 dest->sign = !dest->sign;
53
54 return dest;
55 }
56
57 /* Now, the slightly harder ones */
58
59 /* fp_fadd: Implements the kernel of the FADD, FSADD, FDADD, FSUB,
60 FDSUB, and FCMP instructions. */
61
62 struct fp_ext *
fp_fadd(struct fp_ext * dest,struct fp_ext * src)63 fp_fadd(struct fp_ext *dest, struct fp_ext *src)
64 {
65 int diff;
66
67 dprint(PINSTR, "fadd\n");
68
69 fp_dyadic_check(dest, src);
70
71 if (IS_INF(dest)) {
72 /* infinity - infinity == NaN */
73 if (IS_INF(src) && (src->sign != dest->sign))
74 fp_set_nan(dest);
75 return dest;
76 }
77 if (IS_INF(src)) {
78 fp_copy_ext(dest, src);
79 return dest;
80 }
81
82 if (IS_ZERO(dest)) {
83 if (IS_ZERO(src)) {
84 if (src->sign != dest->sign) {
85 if (FPDATA->rnd == FPCR_ROUND_RM)
86 dest->sign = 1;
87 else
88 dest->sign = 0;
89 }
90 } else
91 fp_copy_ext(dest, src);
92 return dest;
93 }
94
95 dest->lowmant = src->lowmant = 0;
96
97 if ((diff = dest->exp - src->exp) > 0)
98 fp_denormalize(src, diff);
99 else if ((diff = -diff) > 0)
100 fp_denormalize(dest, diff);
101
102 if (dest->sign == src->sign) {
103 if (fp_addmant(dest, src))
104 if (!fp_addcarry(dest))
105 return dest;
106 } else {
107 if (dest->mant.m64 < src->mant.m64) {
108 fp_submant(dest, src, dest);
109 dest->sign = !dest->sign;
110 } else
111 fp_submant(dest, dest, src);
112 }
113
114 return dest;
115 }
116
117 /* fp_fsub: Implements the kernel of the FSUB, FSSUB, and FDSUB
118 instructions.
119
120 Remember that the arguments are in assembler-syntax order! */
121
122 struct fp_ext *
fp_fsub(struct fp_ext * dest,struct fp_ext * src)123 fp_fsub(struct fp_ext *dest, struct fp_ext *src)
124 {
125 dprint(PINSTR, "fsub ");
126
127 src->sign = !src->sign;
128 return fp_fadd(dest, src);
129 }
130
131
132 struct fp_ext *
fp_fcmp(struct fp_ext * dest,struct fp_ext * src)133 fp_fcmp(struct fp_ext *dest, struct fp_ext *src)
134 {
135 dprint(PINSTR, "fcmp ");
136
137 FPDATA->temp[1] = *dest;
138 src->sign = !src->sign;
139 return fp_fadd(&FPDATA->temp[1], src);
140 }
141
142 struct fp_ext *
fp_ftst(struct fp_ext * dest,struct fp_ext * src)143 fp_ftst(struct fp_ext *dest, struct fp_ext *src)
144 {
145 dprint(PINSTR, "ftst\n");
146
147 (void)dest;
148
149 return src;
150 }
151
152 struct fp_ext *
fp_fmul(struct fp_ext * dest,struct fp_ext * src)153 fp_fmul(struct fp_ext *dest, struct fp_ext *src)
154 {
155 union fp_mant128 temp;
156 int exp;
157
158 dprint(PINSTR, "fmul\n");
159
160 fp_dyadic_check(dest, src);
161
162 /* calculate the correct sign now, as it's necessary for infinities */
163 dest->sign = src->sign ^ dest->sign;
164
165 /* Handle infinities */
166 if (IS_INF(dest)) {
167 if (IS_ZERO(src))
168 fp_set_nan(dest);
169 return dest;
170 }
171 if (IS_INF(src)) {
172 if (IS_ZERO(dest))
173 fp_set_nan(dest);
174 else
175 fp_copy_ext(dest, src);
176 return dest;
177 }
178
179 /* Of course, as we all know, zero * anything = zero. You may
180 not have known that it might be a positive or negative
181 zero... */
182 if (IS_ZERO(dest) || IS_ZERO(src)) {
183 dest->exp = 0;
184 dest->mant.m64 = 0;
185 dest->lowmant = 0;
186
187 return dest;
188 }
189
190 exp = dest->exp + src->exp - 0x3ffe;
191
192 /* shift up the mantissa for denormalized numbers,
193 so that the highest bit is set, this makes the
194 shift of the result below easier */
195 if ((long)dest->mant.m32[0] >= 0)
196 exp -= fp_overnormalize(dest);
197 if ((long)src->mant.m32[0] >= 0)
198 exp -= fp_overnormalize(src);
199
200 /* now, do a 64-bit multiply with expansion */
201 fp_multiplymant(&temp, dest, src);
202
203 /* normalize it back to 64 bits and stuff it back into the
204 destination struct */
205 if ((long)temp.m32[0] > 0) {
206 exp--;
207 fp_putmant128(dest, &temp, 1);
208 } else
209 fp_putmant128(dest, &temp, 0);
210
211 if (exp >= 0x7fff) {
212 fp_set_ovrflw(dest);
213 return dest;
214 }
215 dest->exp = exp;
216 if (exp < 0) {
217 fp_set_sr(FPSR_EXC_UNFL);
218 fp_denormalize(dest, -exp);
219 }
220
221 return dest;
222 }
223
224 /* fp_fdiv: Implements the "kernel" of the FDIV, FSDIV, FDDIV and
225 FSGLDIV instructions.
226
227 Note that the order of the operands is counter-intuitive: instead
228 of src / dest, the result is actually dest / src. */
229
230 struct fp_ext *
fp_fdiv(struct fp_ext * dest,struct fp_ext * src)231 fp_fdiv(struct fp_ext *dest, struct fp_ext *src)
232 {
233 union fp_mant128 temp;
234 int exp;
235
236 dprint(PINSTR, "fdiv\n");
237
238 fp_dyadic_check(dest, src);
239
240 /* calculate the correct sign now, as it's necessary for infinities */
241 dest->sign = src->sign ^ dest->sign;
242
243 /* Handle infinities */
244 if (IS_INF(dest)) {
245 /* infinity / infinity = NaN (quiet, as always) */
246 if (IS_INF(src))
247 fp_set_nan(dest);
248 /* infinity / anything else = infinity (with approprate sign) */
249 return dest;
250 }
251 if (IS_INF(src)) {
252 /* anything / infinity = zero (with appropriate sign) */
253 dest->exp = 0;
254 dest->mant.m64 = 0;
255 dest->lowmant = 0;
256
257 return dest;
258 }
259
260 /* zeroes */
261 if (IS_ZERO(dest)) {
262 /* zero / zero = NaN */
263 if (IS_ZERO(src))
264 fp_set_nan(dest);
265 /* zero / anything else = zero */
266 return dest;
267 }
268 if (IS_ZERO(src)) {
269 /* anything / zero = infinity (with appropriate sign) */
270 fp_set_sr(FPSR_EXC_DZ);
271 dest->exp = 0x7fff;
272 dest->mant.m64 = 0;
273
274 return dest;
275 }
276
277 exp = dest->exp - src->exp + 0x3fff;
278
279 /* shift up the mantissa for denormalized numbers,
280 so that the highest bit is set, this makes lots
281 of things below easier */
282 if ((long)dest->mant.m32[0] >= 0)
283 exp -= fp_overnormalize(dest);
284 if ((long)src->mant.m32[0] >= 0)
285 exp -= fp_overnormalize(src);
286
287 /* now, do the 64-bit divide */
288 fp_dividemant(&temp, dest, src);
289
290 /* normalize it back to 64 bits and stuff it back into the
291 destination struct */
292 if (!temp.m32[0]) {
293 exp--;
294 fp_putmant128(dest, &temp, 32);
295 } else
296 fp_putmant128(dest, &temp, 31);
297
298 if (exp >= 0x7fff) {
299 fp_set_ovrflw(dest);
300 return dest;
301 }
302 dest->exp = exp;
303 if (exp < 0) {
304 fp_set_sr(FPSR_EXC_UNFL);
305 fp_denormalize(dest, -exp);
306 }
307
308 return dest;
309 }
310
311 struct fp_ext *
fp_fsglmul(struct fp_ext * dest,struct fp_ext * src)312 fp_fsglmul(struct fp_ext *dest, struct fp_ext *src)
313 {
314 int exp;
315
316 dprint(PINSTR, "fsglmul\n");
317
318 fp_dyadic_check(dest, src);
319
320 /* calculate the correct sign now, as it's necessary for infinities */
321 dest->sign = src->sign ^ dest->sign;
322
323 /* Handle infinities */
324 if (IS_INF(dest)) {
325 if (IS_ZERO(src))
326 fp_set_nan(dest);
327 return dest;
328 }
329 if (IS_INF(src)) {
330 if (IS_ZERO(dest))
331 fp_set_nan(dest);
332 else
333 fp_copy_ext(dest, src);
334 return dest;
335 }
336
337 /* Of course, as we all know, zero * anything = zero. You may
338 not have known that it might be a positive or negative
339 zero... */
340 if (IS_ZERO(dest) || IS_ZERO(src)) {
341 dest->exp = 0;
342 dest->mant.m64 = 0;
343 dest->lowmant = 0;
344
345 return dest;
346 }
347
348 exp = dest->exp + src->exp - 0x3ffe;
349
350 /* do a 32-bit multiply */
351 fp_mul64(dest->mant.m32[0], dest->mant.m32[1],
352 dest->mant.m32[0] & 0xffffff00,
353 src->mant.m32[0] & 0xffffff00);
354
355 if (exp >= 0x7fff) {
356 fp_set_ovrflw(dest);
357 return dest;
358 }
359 dest->exp = exp;
360 if (exp < 0) {
361 fp_set_sr(FPSR_EXC_UNFL);
362 fp_denormalize(dest, -exp);
363 }
364
365 return dest;
366 }
367
368 struct fp_ext *
fp_fsgldiv(struct fp_ext * dest,struct fp_ext * src)369 fp_fsgldiv(struct fp_ext *dest, struct fp_ext *src)
370 {
371 int exp;
372 unsigned long quot, rem;
373
374 dprint(PINSTR, "fsgldiv\n");
375
376 fp_dyadic_check(dest, src);
377
378 /* calculate the correct sign now, as it's necessary for infinities */
379 dest->sign = src->sign ^ dest->sign;
380
381 /* Handle infinities */
382 if (IS_INF(dest)) {
383 /* infinity / infinity = NaN (quiet, as always) */
384 if (IS_INF(src))
385 fp_set_nan(dest);
386 /* infinity / anything else = infinity (with approprate sign) */
387 return dest;
388 }
389 if (IS_INF(src)) {
390 /* anything / infinity = zero (with appropriate sign) */
391 dest->exp = 0;
392 dest->mant.m64 = 0;
393 dest->lowmant = 0;
394
395 return dest;
396 }
397
398 /* zeroes */
399 if (IS_ZERO(dest)) {
400 /* zero / zero = NaN */
401 if (IS_ZERO(src))
402 fp_set_nan(dest);
403 /* zero / anything else = zero */
404 return dest;
405 }
406 if (IS_ZERO(src)) {
407 /* anything / zero = infinity (with appropriate sign) */
408 fp_set_sr(FPSR_EXC_DZ);
409 dest->exp = 0x7fff;
410 dest->mant.m64 = 0;
411
412 return dest;
413 }
414
415 exp = dest->exp - src->exp + 0x3fff;
416
417 dest->mant.m32[0] &= 0xffffff00;
418 src->mant.m32[0] &= 0xffffff00;
419
420 /* do the 32-bit divide */
421 if (dest->mant.m32[0] >= src->mant.m32[0]) {
422 fp_sub64(dest->mant, src->mant);
423 fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
424 dest->mant.m32[0] = 0x80000000 | (quot >> 1);
425 dest->mant.m32[1] = (quot & 1) | rem; /* only for rounding */
426 } else {
427 fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
428 dest->mant.m32[0] = quot;
429 dest->mant.m32[1] = rem; /* only for rounding */
430 exp--;
431 }
432
433 if (exp >= 0x7fff) {
434 fp_set_ovrflw(dest);
435 return dest;
436 }
437 dest->exp = exp;
438 if (exp < 0) {
439 fp_set_sr(FPSR_EXC_UNFL);
440 fp_denormalize(dest, -exp);
441 }
442
443 return dest;
444 }
445
446 /* fp_roundint: Internal rounding function for use by several of these
447 emulated instructions.
448
449 This one rounds off the fractional part using the rounding mode
450 specified. */
451
fp_roundint(struct fp_ext * dest,int mode)452 static void fp_roundint(struct fp_ext *dest, int mode)
453 {
454 union fp_mant64 oldmant;
455 unsigned long mask;
456
457 if (!fp_normalize_ext(dest))
458 return;
459
460 /* infinities and zeroes */
461 if (IS_INF(dest) || IS_ZERO(dest))
462 return;
463
464 /* first truncate the lower bits */
465 oldmant = dest->mant;
466 switch (dest->exp) {
467 case 0 ... 0x3ffe:
468 dest->mant.m64 = 0;
469 break;
470 case 0x3fff ... 0x401e:
471 dest->mant.m32[0] &= 0xffffffffU << (0x401e - dest->exp);
472 dest->mant.m32[1] = 0;
473 if (oldmant.m64 == dest->mant.m64)
474 return;
475 break;
476 case 0x401f ... 0x403e:
477 dest->mant.m32[1] &= 0xffffffffU << (0x403e - dest->exp);
478 if (oldmant.m32[1] == dest->mant.m32[1])
479 return;
480 break;
481 default:
482 return;
483 }
484 fp_set_sr(FPSR_EXC_INEX2);
485
486 /* We might want to normalize upwards here... however, since
487 we know that this is only called on the output of fp_fdiv,
488 or with the input to fp_fint or fp_fintrz, and the inputs
489 to all these functions are either normal or denormalized
490 (no subnormals allowed!), there's really no need.
491
492 In the case of fp_fdiv, observe that 0x80000000 / 0xffff =
493 0xffff8000, and the same holds for 128-bit / 64-bit. (i.e. the
494 smallest possible normal dividend and the largest possible normal
495 divisor will still produce a normal quotient, therefore, (normal
496 << 64) / normal is normal in all cases) */
497
498 switch (mode) {
499 case FPCR_ROUND_RN:
500 switch (dest->exp) {
501 case 0 ... 0x3ffd:
502 return;
503 case 0x3ffe:
504 /* As noted above, the input is always normal, so the
505 guard bit (bit 63) is always set. therefore, the
506 only case in which we will NOT round to 1.0 is when
507 the input is exactly 0.5. */
508 if (oldmant.m64 == (1ULL << 63))
509 return;
510 break;
511 case 0x3fff ... 0x401d:
512 mask = 1 << (0x401d - dest->exp);
513 if (!(oldmant.m32[0] & mask))
514 return;
515 if (oldmant.m32[0] & (mask << 1))
516 break;
517 if (!(oldmant.m32[0] << (dest->exp - 0x3ffd)) &&
518 !oldmant.m32[1])
519 return;
520 break;
521 case 0x401e:
522 if (!(oldmant.m32[1] >= 0))
523 return;
524 if (oldmant.m32[0] & 1)
525 break;
526 if (!(oldmant.m32[1] << 1))
527 return;
528 break;
529 case 0x401f ... 0x403d:
530 mask = 1 << (0x403d - dest->exp);
531 if (!(oldmant.m32[1] & mask))
532 return;
533 if (oldmant.m32[1] & (mask << 1))
534 break;
535 if (!(oldmant.m32[1] << (dest->exp - 0x401d)))
536 return;
537 break;
538 default:
539 return;
540 }
541 break;
542 case FPCR_ROUND_RZ:
543 return;
544 default:
545 if (dest->sign ^ (mode - FPCR_ROUND_RM))
546 break;
547 return;
548 }
549
550 switch (dest->exp) {
551 case 0 ... 0x3ffe:
552 dest->exp = 0x3fff;
553 dest->mant.m64 = 1ULL << 63;
554 break;
555 case 0x3fff ... 0x401e:
556 mask = 1 << (0x401e - dest->exp);
557 if (dest->mant.m32[0] += mask)
558 break;
559 dest->mant.m32[0] = 0x80000000;
560 dest->exp++;
561 break;
562 case 0x401f ... 0x403e:
563 mask = 1 << (0x403e - dest->exp);
564 if (dest->mant.m32[1] += mask)
565 break;
566 if (dest->mant.m32[0] += 1)
567 break;
568 dest->mant.m32[0] = 0x80000000;
569 dest->exp++;
570 break;
571 }
572 }
573
574 /* modrem_kernel: Implementation of the FREM and FMOD instructions
575 (which are exactly the same, except for the rounding used on the
576 intermediate value) */
577
578 static struct fp_ext *
modrem_kernel(struct fp_ext * dest,struct fp_ext * src,int mode)579 modrem_kernel(struct fp_ext *dest, struct fp_ext *src, int mode)
580 {
581 struct fp_ext tmp;
582
583 fp_dyadic_check(dest, src);
584
585 /* Infinities and zeros */
586 if (IS_INF(dest) || IS_ZERO(src)) {
587 fp_set_nan(dest);
588 return dest;
589 }
590 if (IS_ZERO(dest) || IS_INF(src))
591 return dest;
592
593 /* FIXME: there is almost certainly a smarter way to do this */
594 fp_copy_ext(&tmp, dest);
595 fp_fdiv(&tmp, src); /* NOTE: src might be modified */
596 fp_roundint(&tmp, mode);
597 fp_fmul(&tmp, src);
598 fp_fsub(dest, &tmp);
599
600 /* set the quotient byte */
601 fp_set_quotient((dest->mant.m64 & 0x7f) | (dest->sign << 7));
602 return dest;
603 }
604
605 /* fp_fmod: Implements the kernel of the FMOD instruction.
606
607 Again, the argument order is backwards. The result, as defined in
608 the Motorola manuals, is:
609
610 fmod(src,dest) = (dest - (src * floor(dest / src))) */
611
612 struct fp_ext *
fp_fmod(struct fp_ext * dest,struct fp_ext * src)613 fp_fmod(struct fp_ext *dest, struct fp_ext *src)
614 {
615 dprint(PINSTR, "fmod\n");
616 return modrem_kernel(dest, src, FPCR_ROUND_RZ);
617 }
618
619 /* fp_frem: Implements the kernel of the FREM instruction.
620
621 frem(src,dest) = (dest - (src * round(dest / src)))
622 */
623
624 struct fp_ext *
fp_frem(struct fp_ext * dest,struct fp_ext * src)625 fp_frem(struct fp_ext *dest, struct fp_ext *src)
626 {
627 dprint(PINSTR, "frem\n");
628 return modrem_kernel(dest, src, FPCR_ROUND_RN);
629 }
630
631 struct fp_ext *
fp_fint(struct fp_ext * dest,struct fp_ext * src)632 fp_fint(struct fp_ext *dest, struct fp_ext *src)
633 {
634 dprint(PINSTR, "fint\n");
635
636 fp_copy_ext(dest, src);
637
638 fp_roundint(dest, FPDATA->rnd);
639
640 return dest;
641 }
642
643 struct fp_ext *
fp_fintrz(struct fp_ext * dest,struct fp_ext * src)644 fp_fintrz(struct fp_ext *dest, struct fp_ext *src)
645 {
646 dprint(PINSTR, "fintrz\n");
647
648 fp_copy_ext(dest, src);
649
650 fp_roundint(dest, FPCR_ROUND_RZ);
651
652 return dest;
653 }
654
655 struct fp_ext *
fp_fscale(struct fp_ext * dest,struct fp_ext * src)656 fp_fscale(struct fp_ext *dest, struct fp_ext *src)
657 {
658 int scale, oldround;
659
660 dprint(PINSTR, "fscale\n");
661
662 fp_dyadic_check(dest, src);
663
664 /* Infinities */
665 if (IS_INF(src)) {
666 fp_set_nan(dest);
667 return dest;
668 }
669 if (IS_INF(dest))
670 return dest;
671
672 /* zeroes */
673 if (IS_ZERO(src) || IS_ZERO(dest))
674 return dest;
675
676 /* Source exponent out of range */
677 if (src->exp >= 0x400c) {
678 fp_set_ovrflw(dest);
679 return dest;
680 }
681
682 /* src must be rounded with round to zero. */
683 oldround = FPDATA->rnd;
684 FPDATA->rnd = FPCR_ROUND_RZ;
685 scale = fp_conv_ext2long(src);
686 FPDATA->rnd = oldround;
687
688 /* new exponent */
689 scale += dest->exp;
690
691 if (scale >= 0x7fff) {
692 fp_set_ovrflw(dest);
693 } else if (scale <= 0) {
694 fp_set_sr(FPSR_EXC_UNFL);
695 fp_denormalize(dest, -scale);
696 } else
697 dest->exp = scale;
698
699 return dest;
700 }
701
702