aboutsummaryrefslogblamecommitdiffstats
path: root/arch/m68k/math-emu/fp_arith.c
blob: 08f286db3c5af889f87e6a19c2aae24719f58c5c (plain) (tree)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701




























































































































































































































































































































































































































































































































































































































































































































                                                                                
/*

   fp_arith.c: floating-point math routines for the Linux-m68k
   floating point emulator.

   Copyright (c) 1998-1999 David Huggins-Daines.

   Somewhat based on the AlphaLinux floating point emulator, by David
   Mosberger-Tang.

   You may copy, modify, and redistribute this file under the terms of
   the GNU General Public License, version 2, or any later version, at
   your convenience.
 */

#include "fp_emu.h"
#include "multi_arith.h"
#include "fp_arith.h"

const struct fp_ext fp_QNaN =
{
	.exp = 0x7fff,
	.mant = { .m64 = ~0 }
};

const struct fp_ext fp_Inf =
{
	.exp = 0x7fff,
};

/* let's start with the easy ones */

struct fp_ext *
fp_fabs(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fabs\n");

	fp_monadic_check(dest, src);

	dest->sign = 0;

	return dest;
}

struct fp_ext *
fp_fneg(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fneg\n");

	fp_monadic_check(dest, src);

	dest->sign = !dest->sign;

	return dest;
}

/* Now, the slightly harder ones */

/* fp_fadd: Implements the kernel of the FADD, FSADD, FDADD, FSUB,
   FDSUB, and FCMP instructions. */

struct fp_ext *
fp_fadd(struct fp_ext *dest, struct fp_ext *src)
{
	int diff;

	dprint(PINSTR, "fadd\n");

	fp_dyadic_check(dest, src);

	if (IS_INF(dest)) {
		/* infinity - infinity == NaN */
		if (IS_INF(src) && (src->sign != dest->sign))
			fp_set_nan(dest);
		return dest;
	}
	if (IS_INF(src)) {
		fp_copy_ext(dest, src);
		return dest;
	}

	if (IS_ZERO(dest)) {
		if (IS_ZERO(src)) {
			if (src->sign != dest->sign) {
				if (FPDATA->rnd == FPCR_ROUND_RM)
					dest->sign = 1;
				else
					dest->sign = 0;
			}
		} else
			fp_copy_ext(dest, src);
		return dest;
	}

	dest->lowmant = src->lowmant = 0;

	if ((diff = dest->exp - src->exp) > 0)
		fp_denormalize(src, diff);
	else if ((diff = -diff) > 0)
		fp_denormalize(dest, diff);

	if (dest->sign == src->sign) {
		if (fp_addmant(dest, src))
			if (!fp_addcarry(dest))
				return dest;
	} else {
		if (dest->mant.m64 < src->mant.m64) {
			fp_submant(dest, src, dest);
			dest->sign = !dest->sign;
		} else
			fp_submant(dest, dest, src);
	}

	return dest;
}

/* fp_fsub: Implements the kernel of the FSUB, FSSUB, and FDSUB
   instructions.

   Remember that the arguments are in assembler-syntax order! */

struct fp_ext *
fp_fsub(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fsub ");

	src->sign = !src->sign;
	return fp_fadd(dest, src);
}


struct fp_ext *
fp_fcmp(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fcmp ");

	FPDATA->temp[1] = *dest;
	src->sign = !src->sign;
	return fp_fadd(&FPDATA->temp[1], src);
}

struct fp_ext *
fp_ftst(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "ftst\n");

	(void)dest;

	return src;
}

struct fp_ext *
fp_fmul(struct fp_ext *dest, struct fp_ext *src)
{
	union fp_mant128 temp;
	int exp;

	dprint(PINSTR, "fmul\n");

	fp_dyadic_check(dest, src);

	/* calculate the correct sign now, as it's necessary for infinities */
	dest->sign = src->sign ^ dest->sign;

	/* Handle infinities */
	if (IS_INF(dest)) {
		if (IS_ZERO(src))
			fp_set_nan(dest);
		return dest;
	}
	if (IS_INF(src)) {
		if (IS_ZERO(dest))
			fp_set_nan(dest);
		else
			fp_copy_ext(dest, src);
		return dest;
	}

	/* Of course, as we all know, zero * anything = zero.  You may
	   not have known that it might be a positive or negative
	   zero... */
	if (IS_ZERO(dest) || IS_ZERO(src)) {
		dest->exp = 0;
		dest->mant.m64 = 0;
		dest->lowmant = 0;

		return dest;
	}

	exp = dest->exp + src->exp - 0x3ffe;

	/* shift up the mantissa for denormalized numbers,
	   so that the highest bit is set, this makes the
	   shift of the result below easier */
	if ((long)dest->mant.m32[0] >= 0)
		exp -= fp_overnormalize(dest);
	if ((long)src->mant.m32[0] >= 0)
		exp -= fp_overnormalize(src);

	/* now, do a 64-bit multiply with expansion */
	fp_multiplymant(&temp, dest, src);

	/* normalize it back to 64 bits and stuff it back into the
	   destination struct */
	if ((long)temp.m32[0] > 0) {
		exp--;
		fp_putmant128(dest, &temp, 1);
	} else
		fp_putmant128(dest, &temp, 0);

	if (exp >= 0x7fff) {
		fp_set_ovrflw(dest);
		return dest;
	}
	dest->exp = exp;
	if (exp < 0) {
		fp_set_sr(FPSR_EXC_UNFL);
		fp_denormalize(dest, -exp);
	}

	return dest;
}

/* fp_fdiv: Implements the "kernel" of the FDIV, FSDIV, FDDIV and
   FSGLDIV instructions.

   Note that the order of the operands is counter-intuitive: instead
   of src / dest, the result is actually dest / src. */

struct fp_ext *
fp_fdiv(struct fp_ext *dest, struct fp_ext *src)
{
	union fp_mant128 temp;
	int exp;

	dprint(PINSTR, "fdiv\n");

	fp_dyadic_check(dest, src);

	/* calculate the correct sign now, as it's necessary for infinities */
	dest->sign = src->sign ^ dest->sign;

	/* Handle infinities */
	if (IS_INF(dest)) {
		/* infinity / infinity = NaN (quiet, as always) */
		if (IS_INF(src))
			fp_set_nan(dest);
		/* infinity / anything else = infinity (with approprate sign) */
		return dest;
	}
	if (IS_INF(src)) {
		/* anything / infinity = zero (with appropriate sign) */
		dest->exp = 0;
		dest->mant.m64 = 0;
		dest->lowmant = 0;

		return dest;
	}

	/* zeroes */
	if (IS_ZERO(dest)) {
		/* zero / zero = NaN */
		if (IS_ZERO(src))
			fp_set_nan(dest);
		/* zero / anything else = zero */
		return dest;
	}
	if (IS_ZERO(src)) {
		/* anything / zero = infinity (with appropriate sign) */
		fp_set_sr(FPSR_EXC_DZ);
		dest->exp = 0x7fff;
		dest->mant.m64 = 0;

		return dest;
	}

	exp = dest->exp - src->exp + 0x3fff;

	/* shift up the mantissa for denormalized numbers,
	   so that the highest bit is set, this makes lots
	   of things below easier */
	if ((long)dest->mant.m32[0] >= 0)
		exp -= fp_overnormalize(dest);
	if ((long)src->mant.m32[0] >= 0)
		exp -= fp_overnormalize(src);

	/* now, do the 64-bit divide */
	fp_dividemant(&temp, dest, src);

	/* normalize it back to 64 bits and stuff it back into the
	   destination struct */
	if (!temp.m32[0]) {
		exp--;
		fp_putmant128(dest, &temp, 32);
	} else
		fp_putmant128(dest, &temp, 31);

	if (exp >= 0x7fff) {
		fp_set_ovrflw(dest);
		return dest;
	}
	dest->exp = exp;
	if (exp < 0) {
		fp_set_sr(FPSR_EXC_UNFL);
		fp_denormalize(dest, -exp);
	}

	return dest;
}

struct fp_ext *
fp_fsglmul(struct fp_ext *dest, struct fp_ext *src)
{
	int exp;

	dprint(PINSTR, "fsglmul\n");

	fp_dyadic_check(dest, src);

	/* calculate the correct sign now, as it's necessary for infinities */
	dest->sign = src->sign ^ dest->sign;

	/* Handle infinities */
	if (IS_INF(dest)) {
		if (IS_ZERO(src))
			fp_set_nan(dest);
		return dest;
	}
	if (IS_INF(src)) {
		if (IS_ZERO(dest))
			fp_set_nan(dest);
		else
			fp_copy_ext(dest, src);
		return dest;
	}

	/* Of course, as we all know, zero * anything = zero.  You may
	   not have known that it might be a positive or negative
	   zero... */
	if (IS_ZERO(dest) || IS_ZERO(src)) {
		dest->exp = 0;
		dest->mant.m64 = 0;
		dest->lowmant = 0;

		return dest;
	}

	exp = dest->exp + src->exp - 0x3ffe;

	/* do a 32-bit multiply */
	fp_mul64(dest->mant.m32[0], dest->mant.m32[1],
		 dest->mant.m32[0] & 0xffffff00,
		 src->mant.m32[0] & 0xffffff00);

	if (exp >= 0x7fff) {
		fp_set_ovrflw(dest);
		return dest;
	}
	dest->exp = exp;
	if (exp < 0) {
		fp_set_sr(FPSR_EXC_UNFL);
		fp_denormalize(dest, -exp);
	}

	return dest;
}

struct fp_ext *
fp_fsgldiv(struct fp_ext *dest, struct fp_ext *src)
{
	int exp;
	unsigned long quot, rem;

	dprint(PINSTR, "fsgldiv\n");

	fp_dyadic_check(dest, src);

	/* calculate the correct sign now, as it's necessary for infinities */
	dest->sign = src->sign ^ dest->sign;

	/* Handle infinities */
	if (IS_INF(dest)) {
		/* infinity / infinity = NaN (quiet, as always) */
		if (IS_INF(src))
			fp_set_nan(dest);
		/* infinity / anything else = infinity (with approprate sign) */
		return dest;
	}
	if (IS_INF(src)) {
		/* anything / infinity = zero (with appropriate sign) */
		dest->exp = 0;
		dest->mant.m64 = 0;
		dest->lowmant = 0;

		return dest;
	}

	/* zeroes */
	if (IS_ZERO(dest)) {
		/* zero / zero = NaN */
		if (IS_ZERO(src))
			fp_set_nan(dest);
		/* zero / anything else = zero */
		return dest;
	}
	if (IS_ZERO(src)) {
		/* anything / zero = infinity (with appropriate sign) */
		fp_set_sr(FPSR_EXC_DZ);
		dest->exp = 0x7fff;
		dest->mant.m64 = 0;

		return dest;
	}

	exp = dest->exp - src->exp + 0x3fff;

	dest->mant.m32[0] &= 0xffffff00;
	src->mant.m32[0] &= 0xffffff00;

	/* do the 32-bit divide */
	if (dest->mant.m32[0] >= src->mant.m32[0]) {
		fp_sub64(dest->mant, src->mant);
		fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
		dest->mant.m32[0] = 0x80000000 | (quot >> 1);
		dest->mant.m32[1] = (quot & 1) | rem;	/* only for rounding */
	} else {
		fp_div64(quot, rem, dest->mant.m32[0], 0, src->mant.m32[0]);
		dest->mant.m32[0] = quot;
		dest->mant.m32[1] = rem;		/* only for rounding */
		exp--;
	}

	if (exp >= 0x7fff) {
		fp_set_ovrflw(dest);
		return dest;
	}
	dest->exp = exp;
	if (exp < 0) {
		fp_set_sr(FPSR_EXC_UNFL);
		fp_denormalize(dest, -exp);
	}

	return dest;
}

/* fp_roundint: Internal rounding function for use by several of these
   emulated instructions.

   This one rounds off the fractional part using the rounding mode
   specified. */

static void fp_roundint(struct fp_ext *dest, int mode)
{
	union fp_mant64 oldmant;
	unsigned long mask;

	if (!fp_normalize_ext(dest))
		return;

	/* infinities and zeroes */
	if (IS_INF(dest) || IS_ZERO(dest))
		return;

	/* first truncate the lower bits */
	oldmant = dest->mant;
	switch (dest->exp) {
	case 0 ... 0x3ffe:
		dest->mant.m64 = 0;
		break;
	case 0x3fff ... 0x401e:
		dest->mant.m32[0] &= 0xffffffffU << (0x401e - dest->exp);
		dest->mant.m32[1] = 0;
		if (oldmant.m64 == dest->mant.m64)
			return;
		break;
	case 0x401f ... 0x403e:
		dest->mant.m32[1] &= 0xffffffffU << (0x403e - dest->exp);
		if (oldmant.m32[1] == dest->mant.m32[1])
			return;
		break;
	default:
		return;
	}
	fp_set_sr(FPSR_EXC_INEX2);

	/* We might want to normalize upwards here... however, since
	   we know that this is only called on the output of fp_fdiv,
	   or with the input to fp_fint or fp_fintrz, and the inputs
	   to all these functions are either normal or denormalized
	   (no subnormals allowed!), there's really no need.

	   In the case of fp_fdiv, observe that 0x80000000 / 0xffff =
	   0xffff8000, and the same holds for 128-bit / 64-bit. (i.e. the
	   smallest possible normal dividend and the largest possible normal
	   divisor will still produce a normal quotient, therefore, (normal
	   << 64) / normal is normal in all cases) */

	switch (mode) {
	case FPCR_ROUND_RN:
		switch (dest->exp) {
		case 0 ... 0x3ffd:
			return;
		case 0x3ffe:
			/* As noted above, the input is always normal, so the
			   guard bit (bit 63) is always set.  therefore, the
			   only case in which we will NOT round to 1.0 is when
			   the input is exactly 0.5. */
			if (oldmant.m64 == (1ULL << 63))
				return;
			break;
		case 0x3fff ... 0x401d:
			mask = 1 << (0x401d - dest->exp);
			if (!(oldmant.m32[0] & mask))
				return;
			if (oldmant.m32[0] & (mask << 1))
				break;
			if (!(oldmant.m32[0] << (dest->exp - 0x3ffd)) &&
					!oldmant.m32[1])
				return;
			break;
		case 0x401e:
			if (!(oldmant.m32[1] >= 0))
				return;
			if (oldmant.m32[0] & 1)
				break;
			if (!(oldmant.m32[1] << 1))
				return;
			break;
		case 0x401f ... 0x403d:
			mask = 1 << (0x403d - dest->exp);
			if (!(oldmant.m32[1] & mask))
				return;
			if (oldmant.m32[1] & (mask << 1))
				break;
			if (!(oldmant.m32[1] << (dest->exp - 0x401d)))
				return;
			break;
		default:
			return;
		}
		break;
	case FPCR_ROUND_RZ:
		return;
	default:
		if (dest->sign ^ (mode - FPCR_ROUND_RM))
			break;
		return;
	}

	switch (dest->exp) {
	case 0 ... 0x3ffe:
		dest->exp = 0x3fff;
		dest->mant.m64 = 1ULL << 63;
		break;
	case 0x3fff ... 0x401e:
		mask = 1 << (0x401e - dest->exp);
		if (dest->mant.m32[0] += mask)
			break;
		dest->mant.m32[0] = 0x80000000;
		dest->exp++;
		break;
	case 0x401f ... 0x403e:
		mask = 1 << (0x403e - dest->exp);
		if (dest->mant.m32[1] += mask)
			break;
		if (dest->mant.m32[0] += 1)
                        break;
		dest->mant.m32[0] = 0x80000000;
                dest->exp++;
		break;
	}
}

/* modrem_kernel: Implementation of the FREM and FMOD instructions
   (which are exactly the same, except for the rounding used on the
   intermediate value) */

static struct fp_ext *
modrem_kernel(struct fp_ext *dest, struct fp_ext *src, int mode)
{
	struct fp_ext tmp;

	fp_dyadic_check(dest, src);

	/* Infinities and zeros */
	if (IS_INF(dest) || IS_ZERO(src)) {
		fp_set_nan(dest);
		return dest;
	}
	if (IS_ZERO(dest) || IS_INF(src))
		return dest;

	/* FIXME: there is almost certainly a smarter way to do this */
	fp_copy_ext(&tmp, dest);
	fp_fdiv(&tmp, src);		/* NOTE: src might be modified */
	fp_roundint(&tmp, mode);
	fp_fmul(&tmp, src);
	fp_fsub(dest, &tmp);

	/* set the quotient byte */
	fp_set_quotient((dest->mant.m64 & 0x7f) | (dest->sign << 7));
	return dest;
}

/* fp_fmod: Implements the kernel of the FMOD instruction.

   Again, the argument order is backwards.  The result, as defined in
   the Motorola manuals, is:

   fmod(src,dest) = (dest - (src * floor(dest / src))) */

struct fp_ext *
fp_fmod(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fmod\n");
	return modrem_kernel(dest, src, FPCR_ROUND_RZ);
}

/* fp_frem: Implements the kernel of the FREM instruction.

   frem(src,dest) = (dest - (src * round(dest / src)))
 */

struct fp_ext *
fp_frem(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "frem\n");
	return modrem_kernel(dest, src, FPCR_ROUND_RN);
}

struct fp_ext *
fp_fint(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fint\n");

	fp_copy_ext(dest, src);

	fp_roundint(dest, FPDATA->rnd);

	return dest;
}

struct fp_ext *
fp_fintrz(struct fp_ext *dest, struct fp_ext *src)
{
	dprint(PINSTR, "fintrz\n");

	fp_copy_ext(dest, src);

	fp_roundint(dest, FPCR_ROUND_RZ);

	return dest;
}

struct fp_ext *
fp_fscale(struct fp_ext *dest, struct fp_ext *src)
{
	int scale, oldround;

	dprint(PINSTR, "fscale\n");

	fp_dyadic_check(dest, src);

	/* Infinities */
	if (IS_INF(src)) {
		fp_set_nan(dest);
		return dest;
	}
	if (IS_INF(dest))
		return dest;

	/* zeroes */
	if (IS_ZERO(src) || IS_ZERO(dest))
		return dest;

	/* Source exponent out of range */
	if (src->exp >= 0x400c) {
		fp_set_ovrflw(dest);
		return dest;
	}

	/* src must be rounded with round to zero. */
	oldround = FPDATA->rnd;
	FPDATA->rnd = FPCR_ROUND_RZ;
	scale = fp_conv_ext2long(src);
	FPDATA->rnd = oldround;

	/* new exponent */
	scale += dest->exp;

	if (scale >= 0x7fff) {
		fp_set_ovrflw(dest);
	} else if (scale <= 0) {
		fp_set_sr(FPSR_EXC_UNFL);
		fp_denormalize(dest, -scale);
	} else
		dest->exp = scale;

	return dest;
}