1 // SPDX-License-Identifier: GPL-2.0-or-later
2 /*
3
4 fp_arith.c: floating-point math routines for the Linux-m68k
5 floating point emulator.
6
7 Copyright (c) 1998-1999 David Huggins-Daines.
8
9 Somewhat based on the AlphaLinux floating point emulator, by David
10 Mosberger-Tang.
11
12 */
13
14 #include "fp_emu.h"
15 #include "multi_arith.h"
16 #include "fp_arith.h"
17
18 const struct fp_ext fp_QNaN =
19 {
20 .exp = 0x7fff,
21 .mant = { .m64 = ~0 }
22 };
23
24 const struct fp_ext fp_Inf =
25 {
26 .exp = 0x7fff,
27 };
28
29 /* let's start with the easy ones */
30
31 struct fp_ext *fp_fabs(struct fp_ext *dest, struct fp_ext *src)
32 {
33 dprint(PINSTR, "fabs\n");
34
35 fp_monadic_check(dest, src);
36
37 dest->sign = 0;
38
39 return dest;
40 }
41
42 struct fp_ext *fp_fneg(struct fp_ext *dest, struct fp_ext *src)
43 {
44 dprint(PINSTR, "fneg\n");
45
46 fp_monadic_check(dest, src);
47
48 dest->sign = !dest->sign;
49
50 return dest;
51 }
52
53 /* Now, the slightly harder ones */
54
55 /* fp_fadd: Implements the kernel of the FADD, FSADD, FDADD, FSUB,
56 FDSUB, and FCMP instructions. */
57
58 struct fp_ext *fp_fadd(struct fp_ext *dest, struct fp_ext *src)
59 {
60 int diff;
61
62 dprint(PINSTR, "fadd\n");
63
64 fp_dyadic_check(dest, src);
65
66 if (IS_INF(dest)) {
67 /* infinity - infinity == NaN */
68 if (IS_INF(src) && (src->sign != dest->sign))
69 fp_set_nan(dest);
70 return dest;
71 }
72 if (IS_INF(src)) {
73 fp_copy_ext(dest, src);
74 return dest;
75 }
76
77 if (IS_ZERO(dest)) {
78 if (IS_ZERO(src)) {
79 if (src->sign != dest->sign) {
80 if (FPDATA->rnd == FPCR_ROUND_RM)
81 dest->sign = 1;
82 else
83 dest->sign = 0;
84 }
85 } else
86 fp_copy_ext(dest, src);
87 return dest;
88 }
89
90 dest->lowmant = src->lowmant = 0;
91
92 if ((diff = dest->exp - src->exp) > 0)
93 fp_denormalize(src, diff);
94 else if ((diff = -diff) > 0)
95 fp_denormalize(dest, diff);
96
97 if (dest->sign == src->sign) {
98 if (fp_addmant(dest, src))
99 if (!fp_addcarry(dest))
100 return dest;
101 } else {
102 if (dest->mant.m64 < src->mant.m64) {
103 fp_submant(dest, src, dest);
104 dest->sign = !dest->sign;
105 } else
106 fp_submant(dest, dest, src);
107 }
108
109 return dest;
110 }
111
112 /* fp_fsub: Implements the kernel of the FSUB, FSSUB, and FDSUB
113 instructions.
114
115 Remember that the arguments are in assembler-syntax order! */
116
117 struct fp_ext *fp_fsub(struct fp_ext *dest, struct fp_ext *src)
118 {
119 dprint(PINSTR, "fsub ");
120
121 src->sign = !src->sign;
122 return fp_fadd(dest, src);
123 }
124
125
126 struct fp_ext *fp_fcmp(struct fp_ext *dest, struct fp_ext *src)
127 {
128 dprint(PINSTR, "fcmp ");
129
130 FPDATA->temp[1] = *dest;
131 src->sign = !src->sign;
132 return fp_fadd(&FPDATA->temp[1], src);
133 }
134
135 struct fp_ext *fp_ftst(struct fp_ext *dest, struct fp_ext *src)
136 {
137 dprint(PINSTR, "ftst\n");
138
139 (void)dest;
140
141 return src;
142 }
143
144 struct fp_ext *fp_fmul(struct fp_ext *dest, struct fp_ext *src)
145 {
146 union fp_mant128 temp;
147 int exp;
148
149 dprint(PINSTR, "fmul\n");
150
151 fp_dyadic_check(dest, src);
152
153 /* calculate the correct sign now, as it's necessary for infinities */
154 dest->sign = src->sign ^ dest->sign;
155
156 /* Handle infinities */
157 if (IS_INF(dest)) {
158 if (IS_ZERO(src))
159 fp_set_nan(dest);
160 return dest;
161 }
162 if (IS_INF(src)) {
163 if (IS_ZERO(dest))
164 fp_set_nan(dest);
165 else
166 fp_copy_ext(dest, src);
167 return dest;
168 }
169
170 /* Of course, as we all know, zero * anything = zero. You may
171 not have known that it might be a positive or negative
172 zero... */
173 if (IS_ZERO(dest) || IS_ZERO(src)) {
174 dest->exp = 0;
175 dest->mant.m64 = 0;
176 dest->lowmant = 0;
177
178 return dest;
179 }
180
181 exp = dest->exp + src->exp - 0x3ffe;
182
183 /* shift up the mantissa for denormalized numbers,
184 so that the highest bit is set, this makes the
185 shift of the result below easier */
186 if ((long)dest->mant.m32[0] >= 0)
187 exp -= fp_overnormalize(dest);
188 if ((long)src->mant.m32[0] >= 0)
189 exp -= fp_overnormalize(src);
190
191 /* now, do a 64-bit multiply with expansion */
192 fp_multiplymant(&temp, dest, src);
193
194 /* normalize it back to 64 bits and stuff it back into the
195 destination struct */
196 if ((long)temp.m32[0] > 0) {
197 exp--;
198 fp_putmant128(dest, &temp, 1);
199 } else
200 fp_putmant128(dest, &temp, 0);
201
202 if (exp >= 0x7fff) {
203 fp_set_ovrflw(dest);
204 return dest;
205 }
206 dest->exp = exp;
207 if (exp < 0) {
208 fp_set_sr(FPSR_EXC_UNFL);
209 fp_denormalize(dest, -exp);
210 }
211
212 return dest;
213 }
214
215 /* fp_fdiv: Implements the "kernel" of the FDIV, FSDIV, FDDIV and
216 FSGLDIV instructions.
217
218 Note that the order of the operands is counter-intuitive: instead
219 of src / dest, the result is actually dest / src. */
220
221 struct fp_ext *fp_fdiv(struct fp_ext *dest, struct fp_ext *src)
222 {
223 union fp_mant128 temp;
224 int exp;
225
226 dprint(PINSTR, "fdiv\n");
227
228 fp_dyadic_check(dest, src);
229
230 /* calculate the correct sign now, as it's necessary for infinities */
231 dest->sign = src->sign ^ dest->sign;
232
233 /* Handle infinities */
234 if (IS_INF(dest)) {
235 /* infinity / infinity = NaN (quiet, as always) */
236 if (IS_INF(src))
237 fp_set_nan(dest);
238 /* infinity / anything else = infinity (with appropriate sign) */
239 return dest;
240 }
241 if (IS_INF(src)) {
242 /* anything / infinity = zero (with appropriate sign) */
243 dest->exp = 0;
244 dest->mant.m64 = 0;
245 dest->lowmant = 0;
246
247 return dest;
248 }
249
250 /* zeroes */
251 if (IS_ZERO(dest)) {
252 /* zero / zero = NaN */
253 if (IS_ZERO(src))
254 fp_set_nan(dest);
255 /* zero / anything else = zero */
256 return dest;
257 }
258 if (IS_ZERO(src)) {
259 /* anything / zero = infinity (with appropriate sign) */
260 fp_set_sr(FPSR_EXC_DZ);
261 dest->exp = 0x7fff;
262 dest->mant.m64 = 0;
263
264 return dest;
265 }
266
267 exp = dest->exp - src->exp + 0x3fff;
268
269 /* shift up the mantissa for denormalized numbers,
270 so that the highest bit is set, this makes lots
271 of things below easier */
272 if ((long)dest->mant.m32[0] >= 0)
273 exp -= fp_overnormalize(dest);
274 if ((long)src->mant.m32[0] >= 0)
275 exp -= fp_overnormalize(src);
276
277 /* now, do the 64-bit divide */
278 fp_dividemant(&temp, dest, src);
279
280 /* normalize it back to 64 bits and stuff it back into the
281 destination struct */
282 if (!temp.m32[0]) {
283 exp--;
284 fp_putmant128(dest, &temp, 32);
285 } else
286 fp_putmant128(dest, &temp, 31);
287
288 if (exp >= 0x7fff) {
289 fp_set_ovrflw(dest);
290 return dest;
291 }
292 dest->exp = exp;
293 if (exp < 0) {
294 fp_set_sr(FPSR_EXC_UNFL);
295 fp_denormalize(dest, -exp);
296 }
297
298 return dest;
299 }
300
301 struct fp_ext *fp_fsglmul(struct fp_ext *dest, struct fp_ext *src)
302 {
303 int exp;
304
305 dprint(PINSTR, "fsglmul\n");
306
307 fp_dyadic_check(dest, src);
308
309 /* calculate the correct sign now, as it's necessary for infinities */
310 dest->sign = src->sign ^ dest->sign;
311
312 /* Handle infinities */
313 if (IS_INF(dest)) {
314 if (IS_ZERO(src))
315 fp_set_nan(dest);
316 return dest;
317 }
318 if (IS_INF(src)) {
319 if (IS_ZERO(dest))
320 fp_set_nan(dest);
321 else
322 fp_copy_ext(dest, src);
323 return dest;
324 }
325
326 /* Of course, as we all know, zero * anything = zero. You may
327 not have known that it might be a positive or negative
328 zero... */
329 if (IS_ZERO(dest) || IS_ZERO(src)) {
330 dest->exp = 0;
331 dest->mant.m64 = 0;
332 dest->lowmant = 0;
333
334 return dest;
335 }
336
337 exp = dest->exp + src->exp - 0x3ffe;
338
339 /* do a 32-bit multiply */
340 fp_mul64(dest->mant.m32[0], dest->mant.m32[1],
341 dest->mant.m32[0] & 0xffffff00,
342 src->mant.m32[0] & 0xffffff00);
343
344 if (exp >= 0x7fff) {
345 fp_set_ovrflw(dest);
346 return dest;
347 }
348 dest->exp = exp;
349 if (exp < 0) {
350 fp_set_sr(FPSR_EXC_UNFL);
351 fp_denormalize(dest, -exp);
352 }
353
354 return dest;
355 }
356
357 struct fp_ext *fp_fsgldiv(struct fp_ext *dest, struct fp_ext *src)
358 {
359 int exp;
360 unsigned long quot, rem;
361
362 dprint(PINSTR, "fsgldiv\n");
363
364 fp_dyadic_check(dest, src);
365
366 /* calculate the correct sign now, as it's necessary for infinities */
367 dest->sign = src->sign ^ dest->sign;
368
369 /* Handle infinities */
370 if (IS_INF(dest)) {
371 /* infinity / infinity = NaN (quiet, as always) */
372 if (IS_INF(src))
373 fp_set_nan(dest);
374 /* infinity / anything else = infinity (with approprate sign) */
375 return dest;
376 }
377 if (IS_INF(src)) {
378 /* anything / infinity = zero (with appropriate sign) */
379 dest->exp = 0;
380 dest->mant.m64 = 0;
381 dest->lowmant = 0;
382
383 return dest;
384 }
385
386 /* zeroes */
387 if (IS_ZERO(dest)) {
388 /* zero / zero = NaN */
389 if (IS_ZERO(src))
390 fp_set_nan(dest);
391 /* zero / anything else = zero */
392 return dest;
393 }
394 if (IS_ZERO(src)) {
395 /* anything / zero = infinity (with appropriate sign) */
396 fp_set_sr(FPSR_EXC_DZ);
397 dest->exp = 0x7fff;
398 dest->mant.m64 = 0;
399
400 return dest;
401 }
402
403 exp = dest->exp - src->exp + 0x3fff;
404
405 dest->mant.m32[0] &= 0xffffff00;
406 src->mant.m32[0] &= 0xffffff00;
407
408 /* do the 32-bit divide */
409 if (dest->mant.m32[0] >= src->mant.m32[0]) {
410 fp_sub64(dest->mant, src->mant);
411 fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
412 dest->mant.m32[0] = 0x80000000 | (quot >> 1);
413 dest->mant.m32[1] = (quot & 1) | rem; /* only for rounding */
414 } else {
415 fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
416 dest->mant.m32[0] = quot;
417 dest->mant.m32[1] = rem; /* only for rounding */
418 exp--;
419 }
420
421 if (exp >= 0x7fff) {
422 fp_set_ovrflw(dest);
423 return dest;
424 }
425 dest->exp = exp;
426 if (exp < 0) {
427 fp_set_sr(FPSR_EXC_UNFL);
428 fp_denormalize(dest, -exp);
429 }
430
431 return dest;
432 }
433
434 /* fp_roundint: Internal rounding function for use by several of these
435 emulated instructions.
436
437 This one rounds off the fractional part using the rounding mode
438 specified. */
439
440 static void fp_roundint(struct fp_ext *dest, int mode)
441 {
442 union fp_mant64 oldmant;
443 unsigned long mask;
444
445 if (!fp_normalize_ext(dest))
446 return;
447
448 /* infinities and zeroes */
449 if (IS_INF(dest) || IS_ZERO(dest))
450 return;
451
452 /* first truncate the lower bits */
453 oldmant = dest->mant;
454 switch (dest->exp) {
455 case 0 ... 0x3ffe:
456 dest->mant.m64 = 0;
457 break;
458 case 0x3fff ... 0x401e:
459 dest->mant.m32[0] &= 0xffffffffU << (0x401e - dest->exp);
460 dest->mant.m32[1] = 0;
461 if (oldmant.m64 == dest->mant.m64)
462 return;
463 break;
464 case 0x401f ... 0x403e:
465 dest->mant.m32[1] &= 0xffffffffU << (0x403e - dest->exp);
466 if (oldmant.m32[1] == dest->mant.m32[1])
467 return;
468 break;
469 default:
470 return;
471 }
472 fp_set_sr(FPSR_EXC_INEX2);
473
474 /* We might want to normalize upwards here... however, since
475 we know that this is only called on the output of fp_fdiv,
476 or with the input to fp_fint or fp_fintrz, and the inputs
477 to all these functions are either normal or denormalized
478 (no subnormals allowed!), there's really no need.
479
480 In the case of fp_fdiv, observe that 0x80000000 / 0xffff =
481 0xffff8000, and the same holds for 128-bit / 64-bit. (i.e. the
482 smallest possible normal dividend and the largest possible normal
483 divisor will still produce a normal quotient, therefore, (normal
484 << 64) / normal is normal in all cases) */
485
486 switch (mode) {
487 case FPCR_ROUND_RN:
488 switch (dest->exp) {
489 case 0 ... 0x3ffd:
490 return;
491 case 0x3ffe:
492 /* As noted above, the input is always normal, so the
493 guard bit (bit 63) is always set. therefore, the
494 only case in which we will NOT round to 1.0 is when
495 the input is exactly 0.5. */
496 if (oldmant.m64 == (1ULL << 63))
497 return;
498 break;
499 case 0x3fff ... 0x401d:
500 mask = 1 << (0x401d - dest->exp);
501 if (!(oldmant.m32[0] & mask))
502 return;
503 if (oldmant.m32[0] & (mask << 1))
504 break;
505 if (!(oldmant.m32[0] << (dest->exp - 0x3ffd)) &&
506 !oldmant.m32[1])
507 return;
508 break;
509 case 0x401e:
510 if (oldmant.m32[1] & 0x80000000)
511 return;
512 if (oldmant.m32[0] & 1)
513 break;
514 if (!(oldmant.m32[1] << 1))
515 return;
516 break;
517 case 0x401f ... 0x403d:
518 mask = 1 << (0x403d - dest->exp);
519 if (!(oldmant.m32[1] & mask))
520 return;
521 if (oldmant.m32[1] & (mask << 1))
522 break;
523 if (!(oldmant.m32[1] << (dest->exp - 0x401d)))
524 return;
525 break;
526 default:
527 return;
528 }
529 break;
530 case FPCR_ROUND_RZ:
531 return;
532 default:
533 if (dest->sign ^ (mode - FPCR_ROUND_RM))
534 break;
535 return;
536 }
537
538 switch (dest->exp) {
539 case 0 ... 0x3ffe:
540 dest->exp = 0x3fff;
541 dest->mant.m64 = 1ULL << 63;
542 break;
543 case 0x3fff ... 0x401e:
544 mask = 1 << (0x401e - dest->exp);
545 if (dest->mant.m32[0] += mask)
546 break;
547 dest->mant.m32[0] = 0x80000000;
548 dest->exp++;
549 break;
550 case 0x401f ... 0x403e:
551 mask = 1 << (0x403e - dest->exp);
552 if (dest->mant.m32[1] += mask)
553 break;
554 if (dest->mant.m32[0] += 1)
555 break;
556 dest->mant.m32[0] = 0x80000000;
557 dest->exp++;
558 break;
559 }
560 }
561
562 /* modrem_kernel: Implementation of the FREM and FMOD instructions
563 (which are exactly the same, except for the rounding used on the
564 intermediate value) */
565
566 static struct fp_ext *modrem_kernel(struct fp_ext *dest, struct fp_ext *src,
567 int mode)
568 {
569 struct fp_ext tmp;
570
571 fp_dyadic_check(dest, src);
572
573 /* Infinities and zeros */
574 if (IS_INF(dest) || IS_ZERO(src)) {
575 fp_set_nan(dest);
576 return dest;
577 }
578 if (IS_ZERO(dest) || IS_INF(src))
579 return dest;
580
581 /* FIXME: there is almost certainly a smarter way to do this */
582 fp_copy_ext(&tmp, dest);
583 fp_fdiv(&tmp, src); /* NOTE: src might be modified */
584 fp_roundint(&tmp, mode);
585 fp_fmul(&tmp, src);
586 fp_fsub(dest, &tmp);
587
588 /* set the quotient byte */
589 fp_set_quotient((dest->mant.m64 & 0x7f) | (dest->sign << 7));
590 return dest;
591 }
592
593 /* fp_fmod: Implements the kernel of the FMOD instruction.
594
595 Again, the argument order is backwards. The result, as defined in
596 the Motorola manuals, is:
597
598 fmod(src,dest) = (dest - (src * floor(dest / src))) */
599
600 struct fp_ext *fp_fmod(struct fp_ext *dest, struct fp_ext *src)
601 {
602 dprint(PINSTR, "fmod\n");
603 return modrem_kernel(dest, src, FPCR_ROUND_RZ);
604 }
605
606 /* fp_frem: Implements the kernel of the FREM instruction.
607
608 frem(src,dest) = (dest - (src * round(dest / src)))
609 */
610
611 struct fp_ext *fp_frem(struct fp_ext *dest, struct fp_ext *src)
612 {
613 dprint(PINSTR, "frem\n");
614 return modrem_kernel(dest, src, FPCR_ROUND_RN);
615 }
616
617 struct fp_ext *fp_fint(struct fp_ext *dest, struct fp_ext *src)
618 {
619 dprint(PINSTR, "fint\n");
620
621 fp_copy_ext(dest, src);
622
623 fp_roundint(dest, FPDATA->rnd);
624
625 return dest;
626 }
627
628 struct fp_ext *fp_fintrz(struct fp_ext *dest, struct fp_ext *src)
629 {
630 dprint(PINSTR, "fintrz\n");
631
632 fp_copy_ext(dest, src);
633
634 fp_roundint(dest, FPCR_ROUND_RZ);
635
636 return dest;
637 }
638
639 struct fp_ext *fp_fscale(struct fp_ext *dest, struct fp_ext *src)
640 {
641 int scale, oldround;
642
643 dprint(PINSTR, "fscale\n");
644
645 fp_dyadic_check(dest, src);
646
647 /* Infinities */
648 if (IS_INF(src)) {
649 fp_set_nan(dest);
650 return dest;
651 }
652 if (IS_INF(dest))
653 return dest;
654
655 /* zeroes */
656 if (IS_ZERO(src) || IS_ZERO(dest))
657 return dest;
658
659 /* Source exponent out of range */
660 if (src->exp >= 0x400c) {
661 fp_set_ovrflw(dest);
662 return dest;
663 }
664
665 /* src must be rounded with round to zero. */
666 oldround = FPDATA->rnd;
667 FPDATA->rnd = FPCR_ROUND_RZ;
668 scale = fp_conv_ext2long(src);
669 FPDATA->rnd = oldround;
670
671 /* new exponent */
672 scale += dest->exp;
673
674 if (scale >= 0x7fff) {
675 fp_set_ovrflw(dest);
676 } else if (scale <= 0) {
677 fp_set_sr(FPSR_EXC_UNFL);
678 fp_denormalize(dest, -scale);
679 } else
680 dest->exp = scale;
681
682 return dest;
683 }
684
685
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