1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #if defined(ELFOBJ)
31 #pragma weak fma = __fma
32 #endif
33
34 #include "libm.h"
35 #include "fma.h"
36 #include "fenv_inlines.h"
37
38 #if defined(__sparc)
39
40 static const union {
41 unsigned i[2];
42 double d;
43 } C[] = {
44 { 0x3fe00000u, 0 },
45 { 0x40000000u, 0 },
46 { 0x43300000u, 0 },
47 { 0x41a00000u, 0 },
48 { 0x3e500000u, 0 },
49 { 0x3df00000u, 0 },
50 { 0x3bf00000u, 0 },
51 { 0x7fe00000u, 0 },
52 { 0x00100000u, 0 },
53 { 0x00100001u, 0 }
54 };
55
56 #define half C[0].d
57 #define two C[1].d
58 #define two52 C[2].d
59 #define two27 C[3].d
60 #define twom26 C[4].d
61 #define twom32 C[5].d
62 #define twom64 C[6].d
63 #define huge C[7].d
64 #define tiny C[8].d
65 #define tiny2 C[9].d
66
67 static const unsigned int fsr_rm = 0xc0000000u;
68
69 /*
70 * fma for SPARC: 64-bit double precision, big-endian
71 */
72 double
73 __fma(double x, double y, double z) {
74 union {
75 unsigned i[2];
76 double d;
77 } xx, yy, zz;
78 double xhi, yhi, xlo, ylo, t;
79 unsigned int xy0, xy1, xy2, xy3, z0, z1, z2, z3, fsr, rm, sticky;
80 int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
81 volatile double dummy;
82
83 /* extract the high order words of the arguments */
84 xx.d = x;
85 yy.d = y;
86 zz.d = z;
87 hx = xx.i[0] & ~0x80000000;
88 hy = yy.i[0] & ~0x80000000;
89 hz = zz.i[0] & ~0x80000000;
90
91 /* dispense with inf, nan, and zero cases */
92 if (hx >= 0x7ff00000 || hy >= 0x7ff00000 || (hx | xx.i[1]) == 0 ||
93 (hy | yy.i[1]) == 0) /* x or y is inf, nan, or zero */
94 return (x * y + z);
95
96 if (hz >= 0x7ff00000) /* z is inf or nan */
97 return (x + z); /* avoid spurious under/overflow in x * y */
98
99 if ((hz | zz.i[1]) == 0) /* z is zero */
100 /*
101 * x * y isn't zero but could underflow to zero,
102 * so don't add z, lest we perturb the sign
103 */
104 return (x * y);
105
106 /*
107 * now x, y, and z are all finite and nonzero; save the fsr and
108 * set round-to-negative-infinity mode (and clear nonstandard
109 * mode before we try to scale subnormal operands)
110 */
111 __fenv_getfsr32(&fsr);
112 __fenv_setfsr32(&fsr_rm);
113
114 /* extract signs and exponents, and normalize subnormals */
115 sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
116 sz = zz.i[0] & 0x80000000;
117 ex = hx >> 20;
118 if (!ex) {
119 xx.d = x * two52;
120 ex = ((xx.i[0] & ~0x80000000) >> 20) - 52;
121 }
122 ey = hy >> 20;
123 if (!ey) {
124 yy.d = y * two52;
125 ey = ((yy.i[0] & ~0x80000000) >> 20) - 52;
126 }
127 ez = hz >> 20;
128 if (!ez) {
129 zz.d = z * two52;
130 ez = ((zz.i[0] & ~0x80000000) >> 20) - 52;
131 }
132
133 /* multiply x*y to 106 bits */
134 exy = ex + ey - 0x3ff;
135 xx.i[0] = (xx.i[0] & 0xfffff) | 0x3ff00000;
136 yy.i[0] = (yy.i[0] & 0xfffff) | 0x3ff00000;
137 x = xx.d;
138 y = yy.d;
139 xhi = ((x + twom26) + two27) - two27;
140 yhi = ((y + twom26) + two27) - two27;
141 xlo = x - xhi;
142 ylo = y - yhi;
143 x *= y;
144 y = ((xhi * yhi - x) + xhi * ylo + xlo * yhi) + xlo * ylo;
145 if (x >= two) {
146 x *= half;
147 y *= half;
148 exy++;
149 }
150
151 /* extract the significands */
152 xx.d = x;
153 xy0 = (xx.i[0] & 0xfffff) | 0x100000;
154 xy1 = xx.i[1];
155 yy.d = t = y + twom32;
156 xy2 = yy.i[1];
157 yy.d = (y - (t - twom32)) + twom64;
158 xy3 = yy.i[1];
159 z0 = (zz.i[0] & 0xfffff) | 0x100000;
160 z1 = zz.i[1];
161 z2 = z3 = 0;
162
163 /*
164 * now x*y is represented by sxy, exy, and xy[0-3], and z is
165 * represented likewise; swap if need be so |xy| <= |z|
166 */
167 if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 &&
168 (xy1 > z1 || (xy1 == z1 && (xy2 | xy3) != 0)))))) {
169 e = sxy; sxy = sz; sz = e;
170 e = exy; exy = ez; ez = e;
171 e = xy0; xy0 = z0; z0 = e;
172 e = xy1; xy1 = z1; z1 = e;
173 z2 = xy2; xy2 = 0;
174 z3 = xy3; xy3 = 0;
175 }
176
177 /* shift the significand of xy keeping a sticky bit */
178 e = ez - exy;
179 if (e > 116) {
180 xy0 = xy1 = xy2 = 0;
181 xy3 = 1;
182 } else if (e >= 96) {
183 sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (127 - e));
184 xy3 = xy0 >> (e - 96);
185 if (sticky)
186 xy3 |= 1;
187 xy0 = xy1 = xy2 = 0;
188 } else if (e >= 64) {
189 sticky = xy3 | xy2 | ((xy1 << 1) << (95 - e));
190 xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
191 if (sticky)
192 xy3 |= 1;
193 xy2 = xy0 >> (e - 64);
194 xy0 = xy1 = 0;
195 } else if (e >= 32) {
196 sticky = xy3 | ((xy2 << 1) << (63 - e));
197 xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
198 if (sticky)
199 xy3 |= 1;
200 xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
201 xy1 = xy0 >> (e - 32);
202 xy0 = 0;
203 } else if (e) {
204 sticky = (xy3 << 1) << (31 - e);
205 xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
206 if (sticky)
207 xy3 |= 1;
208 xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
209 xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
210 xy0 >>= e;
211 }
212
213 /* if this is a magnitude subtract, negate the significand of xy */
214 if (sxy ^ sz) {
215 xy0 = ~xy0;
216 xy1 = ~xy1;
217 xy2 = ~xy2;
218 xy3 = -xy3;
219 if (xy3 == 0)
220 if (++xy2 == 0)
221 if (++xy1 == 0)
222 xy0++;
223 }
224
225 /* add, propagating carries */
226 z3 += xy3;
227 e = (z3 < xy3);
228 z2 += xy2;
229 if (e) {
230 z2++;
231 e = (z2 <= xy2);
232 } else
233 e = (z2 < xy2);
234 z1 += xy1;
235 if (e) {
236 z1++;
237 e = (z1 <= xy1);
238 } else
239 e = (z1 < xy1);
240 z0 += xy0;
241 if (e)
242 z0++;
243
244 /* postnormalize and collect rounding information into z2 */
245 if (ez < 1) {
246 /* result is tiny; shift right until exponent is within range */
247 e = 1 - ez;
248 if (e > 56) {
249 z2 = 1; /* result can't be exactly zero */
250 z0 = z1 = 0;
251 } else if (e >= 32) {
252 sticky = z3 | z2 | ((z1 << 1) << (63 - e));
253 z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
254 if (sticky)
255 z2 |= 1;
256 z1 = z0 >> (e - 32);
257 z0 = 0;
258 } else {
259 sticky = z3 | (z2 << 1) << (31 - e);
260 z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
261 if (sticky)
262 z2 |= 1;
263 z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
264 z0 >>= e;
265 }
266 ez = 1;
267 } else if (z0 >= 0x200000) {
268 /* carry out; shift right by one */
269 sticky = (z2 & 1) | z3;
270 z2 = (z2 >> 1) | (z1 << 31);
271 if (sticky)
272 z2 |= 1;
273 z1 = (z1 >> 1) | (z0 << 31);
274 z0 >>= 1;
275 ez++;
276 } else {
277 if (z0 < 0x100000 && (z0 | z1 | z2 | z3) != 0) {
278 /*
279 * borrow/cancellation; shift left as much as
280 * exponent allows
281 */
282 while (!(z0 | (z1 & 0xffe00000)) && ez >= 33) {
283 z0 = z1;
284 z1 = z2;
285 z2 = z3;
286 z3 = 0;
287 ez -= 32;
288 }
289 while (z0 < 0x100000 && ez > 1) {
290 z0 = (z0 << 1) | (z1 >> 31);
291 z1 = (z1 << 1) | (z2 >> 31);
292 z2 = (z2 << 1) | (z3 >> 31);
293 z3 <<= 1;
294 ez--;
295 }
296 }
297 if (z3)
298 z2 |= 1;
299 }
300
301 /* get the rounding mode and clear current exceptions */
302 rm = fsr >> 30;
303 fsr &= ~FSR_CEXC;
304
305 /* strip off the integer bit, if there is one */
306 ibit = z0 & 0x100000;
307 if (ibit)
308 z0 -= 0x100000;
309 else {
310 ez = 0;
311 if (!(z0 | z1 | z2)) { /* exact zero */
312 zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
313 zz.i[1] = 0;
314 __fenv_setfsr32(&fsr);
315 return (zz.d);
316 }
317 }
318
319 /*
320 * flip the sense of directed roundings if the result is negative;
321 * the logic below applies to a positive result
322 */
323 if (sz)
324 rm ^= rm >> 1;
325
326 /* round and raise exceptions */
327 if (z2) {
328 fsr |= FSR_NXC;
329
330 /* decide whether to round the fraction up */
331 if (rm == FSR_RP || (rm == FSR_RN && (z2 > 0x80000000u ||
332 (z2 == 0x80000000u && (z1 & 1))))) {
333 /* round up and renormalize if necessary */
334 if (++z1 == 0) {
335 if (++z0 == 0x100000) {
336 z0 = 0;
337 ez++;
338 }
339 }
340 }
341 }
342
343 /* check for under/overflow */
344 if (ez >= 0x7ff) {
345 if (rm == FSR_RN || rm == FSR_RP) {
346 zz.i[0] = sz | 0x7ff00000;
347 zz.i[1] = 0;
348 } else {
349 zz.i[0] = sz | 0x7fefffff;
350 zz.i[1] = 0xffffffff;
351 }
352 fsr |= FSR_OFC | FSR_NXC;
353 } else {
354 zz.i[0] = sz | (ez << 20) | z0;
355 zz.i[1] = z1;
356
357 /*
358 * !ibit => exact result was tiny before rounding,
359 * z2 nonzero => result delivered is inexact
360 */
361 if (!ibit) {
362 if (z2)
363 fsr |= FSR_UFC | FSR_NXC;
364 else if (fsr & FSR_UFM)
365 fsr |= FSR_UFC;
366 }
367 }
368
369 /* restore the fsr and emulate exceptions as needed */
370 if ((fsr & FSR_CEXC) & (fsr >> 23)) {
371 __fenv_setfsr32(&fsr);
372 if (fsr & FSR_OFC) {
373 dummy = huge;
374 dummy *= huge;
375 } else if (fsr & FSR_UFC) {
376 dummy = tiny;
377 if (fsr & FSR_NXC)
378 dummy *= tiny;
379 else
380 dummy -= tiny2;
381 } else {
382 dummy = huge;
383 dummy += tiny;
384 }
385 } else {
386 fsr |= (fsr & 0x1f) << 5;
387 __fenv_setfsr32(&fsr);
388 }
389 return (zz.d);
390 }
391
392 #elif defined(__x86)
393
394 #if defined(__amd64)
395 #define NI 4
396 #else
397 #define NI 3
398 #endif
399
400 /*
401 * fma for x86: 64-bit double precision, little-endian
402 */
403 double
404 __fma(double x, double y, double z) {
405 union {
406 unsigned i[NI];
407 long double e;
408 } xx, yy, zz;
409 long double xe, ye, xhi, xlo, yhi, ylo;
410 int ex, ey, ez;
411 unsigned cwsw, oldcwsw, rm;
412
413 /* convert the operands to double extended */
414 xx.e = (long double) x;
415 yy.e = (long double) y;
416 zz.e = (long double) z;
417
418 /* extract the exponents of the arguments */
419 ex = xx.i[2] & 0x7fff;
420 ey = yy.i[2] & 0x7fff;
421 ez = zz.i[2] & 0x7fff;
422
423 /* dispense with inf, nan, and zero cases */
424 if (ex == 0x7fff || ey == 0x7fff || ex == 0 || ey == 0)
425 /* x or y is inf, nan, or zero */
426 return ((double) (xx.e * yy.e + zz.e));
427
428 if (ez >= 0x7fff) /* z is inf or nan */
429 return ((double) (xx.e + zz.e));
430 /* avoid spurious inexact in x * y */
431
432 /*
433 * save the control and status words, mask all exceptions, and
434 * set rounding to 64-bit precision and to-nearest
435 */
436 __fenv_getcwsw(&oldcwsw);
437 cwsw = (oldcwsw & 0xf0c0ffff) | 0x033f0000;
438 __fenv_setcwsw(&cwsw);
439
440 /* multiply x*y to 106 bits */
441 xe = xx.e;
442 xx.i[0] = 0;
443 xhi = xx.e; /* hi 32 bits */
444 xlo = xe - xhi; /* lo 21 bits */
445 ye = yy.e;
446 yy.i[0] = 0;
447 yhi = yy.e;
448 ylo = ye - yhi;
449 xe = xe * ye;
450 ye = ((xhi * yhi - xe) + xhi * ylo + xlo * yhi) + xlo * ylo;
451
452 /* distill the sum of xe, ye, and z */
453 xhi = ye + zz.e;
454 yhi = xhi - ye;
455 xlo = (zz.e - yhi) + (ye - (xhi - yhi));
456 /* now (xhi,xlo) = ye + z */
457
458 yhi = xe + xhi;
459 ye = yhi - xe;
460 ylo = (xhi - ye) + (xe - (yhi - ye)); /* now (yhi,ylo) = xe + xhi */
461
462 xhi = xlo + ylo;
463 xe = xhi - xlo;
464 xlo = (ylo - xe) + (xlo - (xhi - xe)); /* now (xhi,xlo) = xlo + ylo */
465
466 yy.e = yhi + xhi;
467 ylo = (yhi - yy.e) + xhi; /* now (yy.e,ylo) = xhi + yhi */
468
469 if (yy.i[1] != 0) { /* yy.e is nonzero */
470 /* perturb yy.e if its least significant 10 bits are zero */
471 if (!(yy.i[0] & 0x3ff)) {
472 xx.e = ylo + xlo;
473 if (xx.i[1] != 0) {
474 xx.i[2] = (xx.i[2] & 0x8000) |
475 ((yy.i[2] & 0x7fff) - 63);
476 xx.i[1] = 0x80000000;
477 xx.i[0] = 0;
478 yy.e += xx.e;
479 }
480 }
481 } else {
482 /* set sign of zero result according to rounding direction */
483 rm = oldcwsw & 0x0c000000;
484 yy.i[2] = ((rm == FCW_RM)? 0x8000 : 0);
485 }
486
487 /*
488 * restore the control and status words and convert the result
489 * to double
490 */
491 __fenv_setcwsw(&oldcwsw);
492 return ((double) yy.e);
493 }
494
495 #else
496 #error Unknown architecture
497 #endif