1 /*
2 * Copyright (c) 1992, 1993
3 * The Regents of the University of California. All rights reserved.
4 *
5 * This software was developed by the Computer Systems Engineering group
6 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
7 * contributed to Berkeley.
8 *
9 * All advertising materials mentioning features or use of this software
10 * must display the following acknowledgement:
11 * This product includes software developed by the University of
12 * California, Lawrence Berkeley Laboratory.
13 *
14 * Redistribution and use in source and binary forms, with or without
15 * modification, are permitted provided that the following conditions
16 * are met:
17 * 1. Redistributions of source code must retain the above copyright
18 * notice, this list of conditions and the following disclaimer.
19 * 2. Redistributions in binary form must reproduce the above copyright
20 * notice, this list of conditions and the following disclaimer in the
21 * documentation and/or other materials provided with the distribution.
22 * 3. Neither the name of the University nor the names of its contributors
23 * may be used to endorse or promote products derived from this software
24 * without specific prior written permission.
25 *
26 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
27 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
28 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
29 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
30 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
31 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
32 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
33 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
34 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
35 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
36 * SUCH DAMAGE.
37 *
38 * @(#)fpu_implode.c 8.1 (Berkeley) 6/11/93
39 * $NetBSD: fpu_implode.c,v 1.8 2001/08/26 05:44:46 eeh Exp $
40 */
41
42 #include <sys/cdefs.h>
43 __FBSDID("$FreeBSD$");
44
45 /*
46 * FPU subroutines: `implode' internal format numbers into the machine's
47 * `packed binary' format.
48 */
49
50 #include <sys/param.h>
51
52 #ifdef FPU_DEBUG
53 #include <stdio.h>
54 #endif
55
56 #include <machine/frame.h>
57 #include <machine/fp.h>
58 #include <machine/fsr.h>
59 #include <machine/ieee.h>
60 #include <machine/instr.h>
61
62 #include "fpu_arith.h"
63 #include "fpu_emu.h"
64 #include "fpu_extern.h"
65 #include "__sparc_utrap_private.h"
66
67 static int fpround(struct fpemu *, struct fpn *);
68 static int toinf(struct fpemu *, int);
69
70 /*
71 * Round a number (algorithm from Motorola MC68882 manual, modified for
72 * our internal format). Set inexact exception if rounding is required.
73 * Return true iff we rounded up.
74 *
75 * After rounding, we discard the guard and round bits by shifting right
76 * 2 bits (a la fpu_shr(), but we do not bother with fp->fp_sticky).
77 * This saves effort later.
78 *
79 * Note that we may leave the value 2.0 in fp->fp_mant; it is the caller's
80 * responsibility to fix this if necessary.
81 */
82 static int
fpround(struct fpemu * fe,struct fpn * fp)83 fpround(struct fpemu *fe, struct fpn *fp)
84 {
85 u_int m0, m1, m2, m3;
86 int gr, s;
87
88 m0 = fp->fp_mant[0];
89 m1 = fp->fp_mant[1];
90 m2 = fp->fp_mant[2];
91 m3 = fp->fp_mant[3];
92 gr = m3 & 3;
93 s = fp->fp_sticky;
94
95 /* mant >>= FP_NG */
96 m3 = (m3 >> FP_NG) | (m2 << (32 - FP_NG));
97 m2 = (m2 >> FP_NG) | (m1 << (32 - FP_NG));
98 m1 = (m1 >> FP_NG) | (m0 << (32 - FP_NG));
99 m0 >>= FP_NG;
100
101 if ((gr | s) == 0) /* result is exact: no rounding needed */
102 goto rounddown;
103
104 fe->fe_cx |= FSR_NX; /* inexact */
105
106 /* Go to rounddown to round down; break to round up. */
107 switch (FSR_GET_RD(fe->fe_fsr)) {
108 case FSR_RD_N:
109 default:
110 /*
111 * Round only if guard is set (gr & 2). If guard is set,
112 * but round & sticky both clear, then we want to round
113 * but have a tie, so round to even, i.e., add 1 iff odd.
114 */
115 if ((gr & 2) == 0)
116 goto rounddown;
117 if ((gr & 1) || fp->fp_sticky || (m3 & 1))
118 break;
119 goto rounddown;
120
121 case FSR_RD_Z:
122 /* Round towards zero, i.e., down. */
123 goto rounddown;
124
125 case FSR_RD_NINF:
126 /* Round towards -Inf: up if negative, down if positive. */
127 if (fp->fp_sign)
128 break;
129 goto rounddown;
130
131 case FSR_RD_PINF:
132 /* Round towards +Inf: up if positive, down otherwise. */
133 if (!fp->fp_sign)
134 break;
135 goto rounddown;
136 }
137
138 /* Bump low bit of mantissa, with carry. */
139 FPU_ADDS(m3, m3, 1);
140 FPU_ADDCS(m2, m2, 0);
141 FPU_ADDCS(m1, m1, 0);
142 FPU_ADDC(m0, m0, 0);
143 fp->fp_mant[0] = m0;
144 fp->fp_mant[1] = m1;
145 fp->fp_mant[2] = m2;
146 fp->fp_mant[3] = m3;
147 return (1);
148
149 rounddown:
150 fp->fp_mant[0] = m0;
151 fp->fp_mant[1] = m1;
152 fp->fp_mant[2] = m2;
153 fp->fp_mant[3] = m3;
154 return (0);
155 }
156
157 /*
158 * For overflow: return true if overflow is to go to +/-Inf, according
159 * to the sign of the overflowing result. If false, overflow is to go
160 * to the largest magnitude value instead.
161 */
162 static int
toinf(struct fpemu * fe,int sign)163 toinf(struct fpemu *fe, int sign)
164 {
165 int inf;
166
167 /* look at rounding direction */
168 switch (FSR_GET_RD(fe->fe_fsr)) {
169 default:
170 case FSR_RD_N: /* the nearest value is always Inf */
171 inf = 1;
172 break;
173
174 case FSR_RD_Z: /* toward 0 => never towards Inf */
175 inf = 0;
176 break;
177
178 case FSR_RD_PINF: /* toward +Inf iff positive */
179 inf = sign == 0;
180 break;
181
182 case FSR_RD_NINF: /* toward -Inf iff negative */
183 inf = sign;
184 break;
185 }
186 return (inf);
187 }
188
189 /*
190 * fpn -> int (int value returned as return value).
191 *
192 * N.B.: this conversion always rounds towards zero (this is a peculiarity
193 * of the SPARC instruction set).
194 */
195 u_int
__fpu_ftoi(fe,fp)196 __fpu_ftoi(fe, fp)
197 struct fpemu *fe;
198 struct fpn *fp;
199 {
200 u_int i;
201 int sign, exp;
202
203 sign = fp->fp_sign;
204 switch (fp->fp_class) {
205 case FPC_ZERO:
206 return (0);
207
208 case FPC_NUM:
209 /*
210 * If exp >= 2^32, overflow. Otherwise shift value right
211 * into last mantissa word (this will not exceed 0xffffffff),
212 * shifting any guard and round bits out into the sticky
213 * bit. Then ``round'' towards zero, i.e., just set an
214 * inexact exception if sticky is set (see round()).
215 * If the result is > 0x80000000, or is positive and equals
216 * 0x80000000, overflow; otherwise the last fraction word
217 * is the result.
218 */
219 if ((exp = fp->fp_exp) >= 32)
220 break;
221 /* NB: the following includes exp < 0 cases */
222 if (__fpu_shr(fp, FP_NMANT - 1 - exp) != 0)
223 fe->fe_cx |= FSR_NX;
224 i = fp->fp_mant[3];
225 if (i >= ((u_int)0x80000000 + sign))
226 break;
227 return (sign ? -i : i);
228
229 default: /* Inf, qNaN, sNaN */
230 break;
231 }
232 /* overflow: replace any inexact exception with invalid */
233 fe->fe_cx = (fe->fe_cx & ~FSR_NX) | FSR_NV;
234 return (0x7fffffff + sign);
235 }
236
237 /*
238 * fpn -> extended int (high bits of int value returned as return value).
239 *
240 * N.B.: this conversion always rounds towards zero (this is a peculiarity
241 * of the SPARC instruction set).
242 */
243 u_int
__fpu_ftox(fe,fp,res)244 __fpu_ftox(fe, fp, res)
245 struct fpemu *fe;
246 struct fpn *fp;
247 u_int *res;
248 {
249 u_int64_t i;
250 int sign, exp;
251
252 sign = fp->fp_sign;
253 switch (fp->fp_class) {
254 case FPC_ZERO:
255 i = 0;
256 goto done;
257
258 case FPC_NUM:
259 /*
260 * If exp >= 2^64, overflow. Otherwise shift value
261 * right into last mantissa word (this will not exceed
262 * 0xffffffffffffffff), shifting any guard and round
263 * bits out into the sticky bit. Then ``round'' towards
264 * zero, i.e., just set an inexact exception if sticky
265 * is set (see round()).
266 * If the result is > 0x8000000000000000, or is positive
267 * and equals 0x8000000000000000, overflow; otherwise
268 * the last fraction word is the result.
269 */
270 if ((exp = fp->fp_exp) >= 64)
271 break;
272 /* NB: the following includes exp < 0 cases */
273 if (__fpu_shr(fp, FP_NMANT - 1 - exp) != 0)
274 fe->fe_cx |= FSR_NX;
275 i = ((u_int64_t)fp->fp_mant[2]<<32)|fp->fp_mant[3];
276 if (i >= ((u_int64_t)0x8000000000000000LL + sign))
277 break;
278 if (sign)
279 i = -i;
280 goto done;
281
282 default: /* Inf, qNaN, sNaN */
283 break;
284 }
285 /* overflow: replace any inexact exception with invalid */
286 fe->fe_cx = (fe->fe_cx & ~FSR_NX) | FSR_NV;
287 i = 0x7fffffffffffffffLL + sign;
288 done:
289 res[1] = i & 0xffffffff;
290 return (i >> 32);
291 }
292
293 /*
294 * fpn -> single (32 bit single returned as return value).
295 * We assume <= 29 bits in a single-precision fraction (1.f part).
296 */
297 u_int
__fpu_ftos(fe,fp)298 __fpu_ftos(fe, fp)
299 struct fpemu *fe;
300 struct fpn *fp;
301 {
302 u_int sign = fp->fp_sign << 31;
303 int exp;
304
305 #define SNG_EXP(e) ((e) << SNG_FRACBITS) /* makes e an exponent */
306 #define SNG_MASK (SNG_EXP(1) - 1) /* mask for fraction */
307
308 /* Take care of non-numbers first. */
309 if (ISNAN(fp)) {
310 /*
311 * Preserve upper bits of NaN, per SPARC V8 appendix N.
312 * Note that fp->fp_mant[0] has the quiet bit set,
313 * even if it is classified as a signalling NaN.
314 */
315 (void) __fpu_shr(fp, FP_NMANT - 1 - SNG_FRACBITS);
316 exp = SNG_EXP_INFNAN;
317 goto done;
318 }
319 if (ISINF(fp))
320 return (sign | SNG_EXP(SNG_EXP_INFNAN));
321 if (ISZERO(fp))
322 return (sign);
323
324 /*
325 * Normals (including subnormals). Drop all the fraction bits
326 * (including the explicit ``implied'' 1 bit) down into the
327 * single-precision range. If the number is subnormal, move
328 * the ``implied'' 1 into the explicit range as well, and shift
329 * right to introduce leading zeroes. Rounding then acts
330 * differently for normals and subnormals: the largest subnormal
331 * may round to the smallest normal (1.0 x 2^minexp), or may
332 * remain subnormal. A number that is subnormal before rounding
333 * will signal an underflow if the result is inexact or if underflow
334 * traps are enabled.
335 *
336 * Rounding a normal, on the other hand, always produces another
337 * normal (although either way the result might be too big for
338 * single precision, and cause an overflow). If rounding a
339 * normal produces 2.0 in the fraction, we need not adjust that
340 * fraction at all, since both 1.0 and 2.0 are zero under the
341 * fraction mask.
342 *
343 * Note that the guard and round bits vanish from the number after
344 * rounding.
345 */
346 if ((exp = fp->fp_exp + SNG_EXP_BIAS) <= 0) { /* subnormal */
347 /* -NG for g,r; -SNG_FRACBITS-exp for fraction */
348 (void) __fpu_shr(fp, FP_NMANT - FP_NG - SNG_FRACBITS - exp);
349 if (fpround(fe, fp) && fp->fp_mant[3] == SNG_EXP(1)) {
350 fe->fe_cx |= FSR_UF;
351 return (sign | SNG_EXP(1) | 0);
352 }
353 if ((fe->fe_cx & FSR_NX) ||
354 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT)))
355 fe->fe_cx |= FSR_UF;
356 return (sign | SNG_EXP(0) | fp->fp_mant[3]);
357 }
358 /* -FP_NG for g,r; -1 for implied 1; -SNG_FRACBITS for fraction */
359 (void) __fpu_shr(fp, FP_NMANT - FP_NG - 1 - SNG_FRACBITS);
360 #ifdef DIAGNOSTIC
361 if ((fp->fp_mant[3] & SNG_EXP(1 << FP_NG)) == 0)
362 __utrap_panic("fpu_ftos");
363 #endif
364 if (fpround(fe, fp) && fp->fp_mant[3] == SNG_EXP(2))
365 exp++;
366 if (exp >= SNG_EXP_INFNAN) {
367 /* overflow to inf or to max single */
368 fe->fe_cx |= FSR_OF | FSR_NX;
369 if (toinf(fe, sign))
370 return (sign | SNG_EXP(SNG_EXP_INFNAN));
371 return (sign | SNG_EXP(SNG_EXP_INFNAN - 1) | SNG_MASK);
372 }
373 done:
374 /* phew, made it */
375 return (sign | SNG_EXP(exp) | (fp->fp_mant[3] & SNG_MASK));
376 }
377
378 /*
379 * fpn -> double (32 bit high-order result returned; 32-bit low order result
380 * left in res[1]). Assumes <= 61 bits in double precision fraction.
381 *
382 * This code mimics fpu_ftos; see it for comments.
383 */
384 u_int
__fpu_ftod(fe,fp,res)385 __fpu_ftod(fe, fp, res)
386 struct fpemu *fe;
387 struct fpn *fp;
388 u_int *res;
389 {
390 u_int sign = fp->fp_sign << 31;
391 int exp;
392
393 #define DBL_EXP(e) ((e) << (DBL_FRACBITS & 31))
394 #define DBL_MASK (DBL_EXP(1) - 1)
395
396 if (ISNAN(fp)) {
397 (void) __fpu_shr(fp, FP_NMANT - 1 - DBL_FRACBITS);
398 exp = DBL_EXP_INFNAN;
399 goto done;
400 }
401 if (ISINF(fp)) {
402 sign |= DBL_EXP(DBL_EXP_INFNAN);
403 goto zero;
404 }
405 if (ISZERO(fp)) {
406 zero: res[1] = 0;
407 return (sign);
408 }
409
410 if ((exp = fp->fp_exp + DBL_EXP_BIAS) <= 0) {
411 (void) __fpu_shr(fp, FP_NMANT - FP_NG - DBL_FRACBITS - exp);
412 if (fpround(fe, fp) && fp->fp_mant[2] == DBL_EXP(1)) {
413 fe->fe_cx |= FSR_UF;
414 res[1] = 0;
415 return (sign | DBL_EXP(1) | 0);
416 }
417 if ((fe->fe_cx & FSR_NX) ||
418 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT)))
419 fe->fe_cx |= FSR_UF;
420 exp = 0;
421 goto done;
422 }
423 (void) __fpu_shr(fp, FP_NMANT - FP_NG - 1 - DBL_FRACBITS);
424 if (fpround(fe, fp) && fp->fp_mant[2] == DBL_EXP(2))
425 exp++;
426 if (exp >= DBL_EXP_INFNAN) {
427 fe->fe_cx |= FSR_OF | FSR_NX;
428 if (toinf(fe, sign)) {
429 res[1] = 0;
430 return (sign | DBL_EXP(DBL_EXP_INFNAN) | 0);
431 }
432 res[1] = ~0;
433 return (sign | DBL_EXP(DBL_EXP_INFNAN - 1) | DBL_MASK);
434 }
435 done:
436 res[1] = fp->fp_mant[3];
437 return (sign | DBL_EXP(exp) | (fp->fp_mant[2] & DBL_MASK));
438 }
439
440 /*
441 * fpn -> extended (32 bit high-order result returned; low-order fraction
442 * words left in res[1]..res[3]). Like ftod, which is like ftos ... but
443 * our internal format *is* extended precision, plus 2 bits for guard/round,
444 * so we can avoid a small bit of work.
445 */
446 u_int
__fpu_ftoq(fe,fp,res)447 __fpu_ftoq(fe, fp, res)
448 struct fpemu *fe;
449 struct fpn *fp;
450 u_int *res;
451 {
452 u_int sign = fp->fp_sign << 31;
453 int exp;
454
455 #define EXT_EXP(e) ((e) << (EXT_FRACBITS & 31))
456 #define EXT_MASK (EXT_EXP(1) - 1)
457
458 if (ISNAN(fp)) {
459 (void) __fpu_shr(fp, 2); /* since we are not rounding */
460 exp = EXT_EXP_INFNAN;
461 goto done;
462 }
463 if (ISINF(fp)) {
464 sign |= EXT_EXP(EXT_EXP_INFNAN);
465 goto zero;
466 }
467 if (ISZERO(fp)) {
468 zero: res[1] = res[2] = res[3] = 0;
469 return (sign);
470 }
471
472 if ((exp = fp->fp_exp + EXT_EXP_BIAS) <= 0) {
473 (void) __fpu_shr(fp, FP_NMANT - FP_NG - EXT_FRACBITS - exp);
474 if (fpround(fe, fp) && fp->fp_mant[0] == EXT_EXP(1)) {
475 fe->fe_cx |= FSR_UF;
476 res[1] = res[2] = res[3] = 0;
477 return (sign | EXT_EXP(1) | 0);
478 }
479 if ((fe->fe_cx & FSR_NX) ||
480 (fe->fe_fsr & (FSR_UF << FSR_TEM_SHIFT)))
481 fe->fe_cx |= FSR_UF;
482 exp = 0;
483 goto done;
484 }
485 /* Since internal == extended, no need to shift here. */
486 if (fpround(fe, fp) && fp->fp_mant[0] == EXT_EXP(2))
487 exp++;
488 if (exp >= EXT_EXP_INFNAN) {
489 fe->fe_cx |= FSR_OF | FSR_NX;
490 if (toinf(fe, sign)) {
491 res[1] = res[2] = res[3] = 0;
492 return (sign | EXT_EXP(EXT_EXP_INFNAN) | 0);
493 }
494 res[1] = res[2] = res[3] = ~0;
495 return (sign | EXT_EXP(EXT_EXP_INFNAN - 1) | EXT_MASK);
496 }
497 done:
498 res[1] = fp->fp_mant[1];
499 res[2] = fp->fp_mant[2];
500 res[3] = fp->fp_mant[3];
501 return (sign | EXT_EXP(exp) | (fp->fp_mant[0] & EXT_MASK));
502 }
503
504 /*
505 * Implode an fpn, writing the result into the given space.
506 */
507 void
__fpu_implode(fe,fp,type,space)508 __fpu_implode(fe, fp, type, space)
509 struct fpemu *fe;
510 struct fpn *fp;
511 int type;
512 u_int *space;
513 {
514
515 switch (type) {
516 case FTYPE_LNG:
517 space[0] = __fpu_ftox(fe, fp, space);
518 break;
519
520 case FTYPE_INT:
521 space[0] = __fpu_ftoi(fe, fp);
522 break;
523
524 case FTYPE_SNG:
525 space[0] = __fpu_ftos(fe, fp);
526 break;
527
528 case FTYPE_DBL:
529 space[0] = __fpu_ftod(fe, fp, space);
530 break;
531
532 case FTYPE_EXT:
533 /* funky rounding precision options ?? */
534 space[0] = __fpu_ftoq(fe, fp, space);
535 break;
536
537 default:
538 __utrap_panic("fpu_implode");
539 }
540 DPRINTF(FPE_REG, ("fpu_implode: %x %x %x %x\n",
541 space[0], space[1], space[2], space[3]));
542 }
543