fma.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#if defined(ELFOBJ)
#pragma weak fma = __fma
#endif
#include "libm.h"
#include "fma.h"
#include "fenv_inlines.h"
#if defined(__sparc)
static const union {
unsigned i[2];
double d;
} C[] = {
{ 0x3fe00000u, 0 },
{ 0x40000000u, 0 },
{ 0x43300000u, 0 },
{ 0x41a00000u, 0 },
{ 0x3e500000u, 0 },
{ 0x3df00000u, 0 },
{ 0x3bf00000u, 0 },
{ 0x7fe00000u, 0 },
{ 0x00100000u, 0 },
{ 0x00100001u, 0 }
};
#define half C[0].d
#define two C[1].d
#define two52 C[2].d
#define two27 C[3].d
#define twom26 C[4].d
#define twom32 C[5].d
#define twom64 C[6].d
#define huge C[7].d
#define tiny C[8].d
#define tiny2 C[9].d
static const unsigned int fsr_rm = 0xc0000000u;
/*
* fma for SPARC: 64-bit double precision, big-endian
*/
double
__fma(double x, double y, double z) {
union {
unsigned i[2];
double d;
} xx, yy, zz;
double xhi, yhi, xlo, ylo, t;
unsigned int xy0, xy1, xy2, xy3, z0, z1, z2, z3, fsr, rm, sticky;
int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
volatile double dummy;
/* extract the high order words of the arguments */
xx.d = x;
yy.d = y;
zz.d = z;
hx = xx.i[0] & ~0x80000000;
hy = yy.i[0] & ~0x80000000;
hz = zz.i[0] & ~0x80000000;
/* dispense with inf, nan, and zero cases */
if (hx >= 0x7ff00000 || hy >= 0x7ff00000 || (hx | xx.i[1]) == 0 ||
(hy | yy.i[1]) == 0) /* x or y is inf, nan, or zero */
return (x * y + z);
if (hz >= 0x7ff00000) /* z is inf or nan */
return (x + z); /* avoid spurious under/overflow in x * y */
if ((hz | zz.i[1]) == 0) /* z is zero */
/*
* x * y isn't zero but could underflow to zero,
* so don't add z, lest we perturb the sign
*/
return (x * y);
/*
* now x, y, and z are all finite and nonzero; save the fsr and
* set round-to-negative-infinity mode (and clear nonstandard
* mode before we try to scale subnormal operands)
*/
__fenv_getfsr32(&fsr);
__fenv_setfsr32(&fsr_rm);
/* extract signs and exponents, and normalize subnormals */
sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
sz = zz.i[0] & 0x80000000;
ex = hx >> 20;
if (!ex) {
xx.d = x * two52;
ex = ((xx.i[0] & ~0x80000000) >> 20) - 52;
}
ey = hy >> 20;
if (!ey) {
yy.d = y * two52;
ey = ((yy.i[0] & ~0x80000000) >> 20) - 52;
}
ez = hz >> 20;
if (!ez) {
zz.d = z * two52;
ez = ((zz.i[0] & ~0x80000000) >> 20) - 52;
}
/* multiply x*y to 106 bits */
exy = ex + ey - 0x3ff;
xx.i[0] = (xx.i[0] & 0xfffff) | 0x3ff00000;
yy.i[0] = (yy.i[0] & 0xfffff) | 0x3ff00000;
x = xx.d;
y = yy.d;
xhi = ((x + twom26) + two27) - two27;
yhi = ((y + twom26) + two27) - two27;
xlo = x - xhi;
ylo = y - yhi;
x *= y;
y = ((xhi * yhi - x) + xhi * ylo + xlo * yhi) + xlo * ylo;
if (x >= two) {
x *= half;
y *= half;
exy++;
}
/* extract the significands */
xx.d = x;
xy0 = (xx.i[0] & 0xfffff) | 0x100000;
xy1 = xx.i[1];
yy.d = t = y + twom32;
xy2 = yy.i[1];
yy.d = (y - (t - twom32)) + twom64;
xy3 = yy.i[1];
z0 = (zz.i[0] & 0xfffff) | 0x100000;
z1 = zz.i[1];
z2 = z3 = 0;
/*
* now x*y is represented by sxy, exy, and xy[0-3], and z is
* represented likewise; swap if need be so |xy| <= |z|
*/
if (exy > ez || (exy == ez && (xy0 > z0 || (xy0 == z0 &&
(xy1 > z1 || (xy1 == z1 && (xy2 | xy3) != 0)))))) {
e = sxy; sxy = sz; sz = e;
e = exy; exy = ez; ez = e;
e = xy0; xy0 = z0; z0 = e;
e = xy1; xy1 = z1; z1 = e;
z2 = xy2; xy2 = 0;
z3 = xy3; xy3 = 0;
}
/* shift the significand of xy keeping a sticky bit */
e = ez - exy;
if (e > 116) {
xy0 = xy1 = xy2 = 0;
xy3 = 1;
} else if (e >= 96) {
sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (127 - e));
xy3 = xy0 >> (e - 96);
if (sticky)
xy3 |= 1;
xy0 = xy1 = xy2 = 0;
} else if (e >= 64) {
sticky = xy3 | xy2 | ((xy1 << 1) << (95 - e));
xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
if (sticky)
xy3 |= 1;
xy2 = xy0 >> (e - 64);
xy0 = xy1 = 0;
} else if (e >= 32) {
sticky = xy3 | ((xy2 << 1) << (63 - e));
xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
if (sticky)
xy3 |= 1;
xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
xy1 = xy0 >> (e - 32);
xy0 = 0;
} else if (e) {
sticky = (xy3 << 1) << (31 - e);
xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
if (sticky)
xy3 |= 1;
xy2 = (xy2 >> e) | ((xy1 << 1) << (31 - e));
xy1 = (xy1 >> e) | ((xy0 << 1) << (31 - e));
xy0 >>= e;
}
/* if this is a magnitude subtract, negate the significand of xy */
if (sxy ^ sz) {
xy0 = ~xy0;
xy1 = ~xy1;
xy2 = ~xy2;
xy3 = -xy3;
if (xy3 == 0)
if (++xy2 == 0)
if (++xy1 == 0)
xy0++;
}
/* add, propagating carries */
z3 += xy3;
e = (z3 < xy3);
z2 += xy2;
if (e) {
z2++;
e = (z2 <= xy2);
} else
e = (z2 < xy2);
z1 += xy1;
if (e) {
z1++;
e = (z1 <= xy1);
} else
e = (z1 < xy1);
z0 += xy0;
if (e)
z0++;
/* postnormalize and collect rounding information into z2 */
if (ez < 1) {
/* result is tiny; shift right until exponent is within range */
e = 1 - ez;
if (e > 56) {
z2 = 1; /* result can't be exactly zero */
z0 = z1 = 0;
} else if (e >= 32) {
sticky = z3 | z2 | ((z1 << 1) << (63 - e));
z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
if (sticky)
z2 |= 1;
z1 = z0 >> (e - 32);
z0 = 0;
} else {
sticky = z3 | (z2 << 1) << (31 - e);
z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
if (sticky)
z2 |= 1;
z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
z0 >>= e;
}
ez = 1;
} else if (z0 >= 0x200000) {
/* carry out; shift right by one */
sticky = (z2 & 1) | z3;
z2 = (z2 >> 1) | (z1 << 31);
if (sticky)
z2 |= 1;
z1 = (z1 >> 1) | (z0 << 31);
z0 >>= 1;
ez++;
} else {
if (z0 < 0x100000 && (z0 | z1 | z2 | z3) != 0) {
/*
* borrow/cancellation; shift left as much as
* exponent allows
*/
while (!(z0 | (z1 & 0xffe00000)) && ez >= 33) {
z0 = z1;
z1 = z2;
z2 = z3;
z3 = 0;
ez -= 32;
}
while (z0 < 0x100000 && ez > 1) {
z0 = (z0 << 1) | (z1 >> 31);
z1 = (z1 << 1) | (z2 >> 31);
z2 = (z2 << 1) | (z3 >> 31);
z3 <<= 1;
ez--;
}
}
if (z3)
z2 |= 1;
}
/* get the rounding mode and clear current exceptions */
rm = fsr >> 30;
fsr &= ~FSR_CEXC;
/* strip off the integer bit, if there is one */
ibit = z0 & 0x100000;
if (ibit)
z0 -= 0x100000;
else {
ez = 0;
if (!(z0 | z1 | z2)) { /* exact zero */
zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
zz.i[1] = 0;
__fenv_setfsr32(&fsr);
return (zz.d);
}
}
/*
* flip the sense of directed roundings if the result is negative;
* the logic below applies to a positive result
*/
if (sz)
rm ^= rm >> 1;
/* round and raise exceptions */
if (z2) {
fsr |= FSR_NXC;
/* decide whether to round the fraction up */
if (rm == FSR_RP || (rm == FSR_RN && (z2 > 0x80000000u ||
(z2 == 0x80000000u && (z1 & 1))))) {
/* round up and renormalize if necessary */
if (++z1 == 0) {
if (++z0 == 0x100000) {
z0 = 0;
ez++;
}
}
}
}
/* check for under/overflow */
if (ez >= 0x7ff) {
if (rm == FSR_RN || rm == FSR_RP) {
zz.i[0] = sz | 0x7ff00000;
zz.i[1] = 0;
} else {
zz.i[0] = sz | 0x7fefffff;
zz.i[1] = 0xffffffff;
}
fsr |= FSR_OFC | FSR_NXC;
} else {
zz.i[0] = sz | (ez << 20) | z0;
zz.i[1] = z1;
/*
* !ibit => exact result was tiny before rounding,
* z2 nonzero => result delivered is inexact
*/
if (!ibit) {
if (z2)
fsr |= FSR_UFC | FSR_NXC;
else if (fsr & FSR_UFM)
fsr |= FSR_UFC;
}
}
/* restore the fsr and emulate exceptions as needed */
if ((fsr & FSR_CEXC) & (fsr >> 23)) {
__fenv_setfsr32(&fsr);
if (fsr & FSR_OFC) {
dummy = huge;
dummy *= huge;
} else if (fsr & FSR_UFC) {
dummy = tiny;
if (fsr & FSR_NXC)
dummy *= tiny;
else
dummy -= tiny2;
} else {
dummy = huge;
dummy += tiny;
}
} else {
fsr |= (fsr & 0x1f) << 5;
__fenv_setfsr32(&fsr);
}
return (zz.d);
}
#elif defined(__x86)
#if defined(__amd64)
#define NI 4
#else
#define NI 3
#endif
/*
* fma for x86: 64-bit double precision, little-endian
*/
double
__fma(double x, double y, double z) {
union {
unsigned i[NI];
long double e;
} xx, yy, zz;
long double xe, ye, xhi, xlo, yhi, ylo;
int ex, ey, ez;
unsigned cwsw, oldcwsw, rm;
/* convert the operands to double extended */
xx.e = (long double) x;
yy.e = (long double) y;
zz.e = (long double) z;
/* extract the exponents of the arguments */
ex = xx.i[2] & 0x7fff;
ey = yy.i[2] & 0x7fff;
ez = zz.i[2] & 0x7fff;
/* dispense with inf, nan, and zero cases */
if (ex == 0x7fff || ey == 0x7fff || ex == 0 || ey == 0)
/* x or y is inf, nan, or zero */
return ((double) (xx.e * yy.e + zz.e));
if (ez >= 0x7fff) /* z is inf or nan */
return ((double) (xx.e + zz.e));
/* avoid spurious inexact in x * y */
/*
* save the control and status words, mask all exceptions, and
* set rounding to 64-bit precision and to-nearest
*/
__fenv_getcwsw(&oldcwsw);
cwsw = (oldcwsw & 0xf0c0ffff) | 0x033f0000;
__fenv_setcwsw(&cwsw);
/* multiply x*y to 106 bits */
xe = xx.e;
xx.i[0] = 0;
xhi = xx.e; /* hi 32 bits */
xlo = xe - xhi; /* lo 21 bits */
ye = yy.e;
yy.i[0] = 0;
yhi = yy.e;
ylo = ye - yhi;
xe = xe * ye;
ye = ((xhi * yhi - xe) + xhi * ylo + xlo * yhi) + xlo * ylo;
/* distill the sum of xe, ye, and z */
xhi = ye + zz.e;
yhi = xhi - ye;
xlo = (zz.e - yhi) + (ye - (xhi - yhi));
/* now (xhi,xlo) = ye + z */
yhi = xe + xhi;
ye = yhi - xe;
ylo = (xhi - ye) + (xe - (yhi - ye)); /* now (yhi,ylo) = xe + xhi */
xhi = xlo + ylo;
xe = xhi - xlo;
xlo = (ylo - xe) + (xlo - (xhi - xe)); /* now (xhi,xlo) = xlo + ylo */
yy.e = yhi + xhi;
ylo = (yhi - yy.e) + xhi; /* now (yy.e,ylo) = xhi + yhi */
if (yy.i[1] != 0) { /* yy.e is nonzero */
/* perturb yy.e if its least significant 10 bits are zero */
if (!(yy.i[0] & 0x3ff)) {
xx.e = ylo + xlo;
if (xx.i[1] != 0) {
xx.i[2] = (xx.i[2] & 0x8000) |
((yy.i[2] & 0x7fff) - 63);
xx.i[1] = 0x80000000;
xx.i[0] = 0;
yy.e += xx.e;
}
}
} else {
/* set sign of zero result according to rounding direction */
rm = oldcwsw & 0x0c000000;
yy.i[2] = ((rm == FCW_RM)? 0x8000 : 0);
}
/*
* restore the control and status words and convert the result
* to double
*/
__fenv_setcwsw(&oldcwsw);
return ((double) yy.e);
}
#else
#error Unknown architecture
#endif