/*
* 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.
*/
#pragma weak fmal = __fmal
#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 },
{ 0x3ef00000u, 0 },
{ 0x3e700000u, 0 },
{ 0x41300000u, 0 },
{ 0x3e300000u, 0 },
{ 0x3b300000u, 0 },
{ 0x38300000u, 0 },
{ 0x42300000u, 0 },
{ 0x3df00000u, 0 },
{ 0x7fe00000u, 0 },
{ 0x00100000u, 0 },
{ 0x00100001u, 0 },
{ 0, 0 },
{ 0x7ff00000u, 0 },
{ 0x7ff00001u, 0 }
};
#define half C[0].d
#define two C[1].d
#define twom16 C[2].d
#define twom24 C[3].d
#define two20 C[4].d
#define twom28 C[5].d
#define twom76 C[6].d
#define twom124 C[7].d
#define two36 C[8].d
#define twom32 C[9].d
#define huge C[10].d
#define tiny C[11].d
#define tiny2 C[12].d
#define zero C[13].d
#define inf C[14].d
#define snan C[15].d
static const unsigned int fsr_rm = 0xc0000000u;
/*
* fmal for SPARC: 128-bit quad precision, big-endian
*/
long double
__fmal(long double x, long double y, long double z) {
union {
unsigned int i[4];
long double q;
} xx, yy, zz;
union {
unsigned int i[2];
double d;
} u;
double dx[5], dy[5], dxy[9], c, s;
unsigned int xy0, xy1, xy2, xy3, xy4, xy5, xy6, xy7;
unsigned int z0, z1, z2, z3, z4, z5, z6, z7;
unsigned int rm, sticky;
unsigned int fsr;
int hx, hy, hz, ex, ey, ez, exy, sxy, sz, e, ibit;
int cx, cy, cz;
volatile double dummy;
/* extract the high order words of the arguments */
xx.q = x;
yy.q = y;
zz.q = z;
hx = xx.i[0] & ~0x80000000;
hy = yy.i[0] & ~0x80000000;
hz = zz.i[0] & ~0x80000000;
/*
* distinguish zero, finite nonzero, infinite, and quiet nan
* arguments; raise invalid and return for signaling nans
*/
if (hx >= 0x7fff0000) {
if ((hx & 0xffff) | xx.i[1] | xx.i[2] | xx.i[3]) {
if (!(hx & 0x8000)) {
/* signaling nan, raise invalid */
dummy = snan;
dummy += snan;
xx.i[0] |= 0x8000;
return (xx.q);
}
cx = 3; /* quiet nan */
} else
cx = 2; /* inf */
} else if (hx == 0) {
cx = (xx.i[1] | xx.i[2] | xx.i[3]) ? 1 : 0;
/* subnormal or zero */
} else
cx = 1; /* finite nonzero */
if (hy >= 0x7fff0000) {
if ((hy & 0xffff) | yy.i[1] | yy.i[2] | yy.i[3]) {
if (!(hy & 0x8000)) {
dummy = snan;
dummy += snan;
yy.i[0] |= 0x8000;
return (yy.q);
}
cy = 3;
} else
cy = 2;
} else if (hy == 0) {
cy = (yy.i[1] | yy.i[2] | yy.i[3]) ? 1 : 0;
} else
cy = 1;
if (hz >= 0x7fff0000) {
if ((hz & 0xffff) | zz.i[1] | zz.i[2] | zz.i[3]) {
if (!(hz & 0x8000)) {
dummy = snan;
dummy += snan;
zz.i[0] |= 0x8000;
return (zz.q);
}
cz = 3;
} else
cz = 2;
} else if (hz == 0) {
cz = (zz.i[1] | zz.i[2] | zz.i[3]) ? 1 : 0;
} else
cz = 1;
/* get the fsr and clear current exceptions */
__fenv_getfsr32(&fsr);
fsr &= ~FSR_CEXC;
/* handle all other zero, inf, and nan cases */
if (cx != 1 || cy != 1 || cz != 1) {
/* if x or y is a quiet nan, return it */
if (cx == 3) {
__fenv_setfsr32(&fsr);
return (x);
}
if (cy == 3) {
__fenv_setfsr32(&fsr);
return (y);
}
/* if x*y is 0*inf, raise invalid and return the default nan */
if ((cx == 0 && cy == 2) || (cx == 2 && cy == 0)) {
dummy = zero;
dummy *= inf;
zz.i[0] = 0x7fffffff;
zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
return (zz.q);
}
/* if z is a quiet nan, return it */
if (cz == 3) {
__fenv_setfsr32(&fsr);
return (z);
}
/*
* now none of x, y, or z is nan; handle cases where x or y
* is inf
*/
if (cx == 2 || cy == 2) {
/*
* if z is also inf, either we have inf-inf or
* the result is the same as z depending on signs
*/
if (cz == 2) {
if ((int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) < 0) {
dummy = inf;
dummy -= inf;
zz.i[0] = 0x7fffffff;
zz.i[1] = zz.i[2] = zz.i[3] =
0xffffffff;
return (zz.q);
}
__fenv_setfsr32(&fsr);
return (z);
}
/* otherwise the result is inf with appropriate sign */
zz.i[0] = ((xx.i[0] ^ yy.i[0]) & 0x80000000) |
0x7fff0000;
zz.i[1] = zz.i[2] = zz.i[3] = 0;
__fenv_setfsr32(&fsr);
return (zz.q);
}
/* if z is inf, return it */
if (cz == 2) {
__fenv_setfsr32(&fsr);
return (z);
}
/*
* now x, y, and z are all finite; handle cases where x or y
* is zero
*/
if (cx == 0 || cy == 0) {
/* either we have 0-0 or the result is the same as z */
if (cz == 0 && (int) ((xx.i[0] ^ yy.i[0]) ^ zz.i[0]) <
0) {
zz.i[0] = (fsr >> 30) == FSR_RM ? 0x80000000 :
0;
__fenv_setfsr32(&fsr);
return (zz.q);
}
__fenv_setfsr32(&fsr);
return (z);
}
/* if we get here, x and y are nonzero finite, z must be zero */
return (x * y);
}
/*
* now x, y, and z are all finite and nonzero; set round-to-
* negative-infinity mode
*/
__fenv_setfsr32(&fsr_rm);
/*
* get the signs and exponents and normalize the significands
* of x and y
*/
sxy = (xx.i[0] ^ yy.i[0]) & 0x80000000;
ex = hx >> 16;
hx &= 0xffff;
if (!ex) {
if (hx | (xx.i[1] & 0xfffe0000)) {
ex = 1;
} else if (xx.i[1] | (xx.i[2] & 0xfffe0000)) {
hx = xx.i[1];
xx.i[1] = xx.i[2];
xx.i[2] = xx.i[3];
xx.i[3] = 0;
ex = -31;
} else if (xx.i[2] | (xx.i[3] & 0xfffe0000)) {
hx = xx.i[2];
xx.i[1] = xx.i[3];
xx.i[2] = xx.i[3] = 0;
ex = -63;
} else {
hx = xx.i[3];
xx.i[1] = xx.i[2] = xx.i[3] = 0;
ex = -95;
}
while ((hx & 0x10000) == 0) {
hx = (hx << 1) | (xx.i[1] >> 31);
xx.i[1] = (xx.i[1] << 1) | (xx.i[2] >> 31);
xx.i[2] = (xx.i[2] << 1) | (xx.i[3] >> 31);
xx.i[3] <<= 1;
ex--;
}
} else
hx |= 0x10000;
ey = hy >> 16;
hy &= 0xffff;
if (!ey) {
if (hy | (yy.i[1] & 0xfffe0000)) {
ey = 1;
} else if (yy.i[1] | (yy.i[2] & 0xfffe0000)) {
hy = yy.i[1];
yy.i[1] = yy.i[2];
yy.i[2] = yy.i[3];
yy.i[3] = 0;
ey = -31;
} else if (yy.i[2] | (yy.i[3] & 0xfffe0000)) {
hy = yy.i[2];
yy.i[1] = yy.i[3];
yy.i[2] = yy.i[3] = 0;
ey = -63;
} else {
hy = yy.i[3];
yy.i[1] = yy.i[2] = yy.i[3] = 0;
ey = -95;
}
while ((hy & 0x10000) == 0) {
hy = (hy << 1) | (yy.i[1] >> 31);
yy.i[1] = (yy.i[1] << 1) | (yy.i[2] >> 31);
yy.i[2] = (yy.i[2] << 1) | (yy.i[3] >> 31);
yy.i[3] <<= 1;
ey--;
}
} else
hy |= 0x10000;
exy = ex + ey - 0x3fff;
/* convert the significands of x and y to doubles */
c = twom16;
dx[0] = (double) ((int) hx) * c;
dy[0] = (double) ((int) hy) * c;
c *= twom24;
dx[1] = (double) ((int) (xx.i[1] >> 8)) * c;
dy[1] = (double) ((int) (yy.i[1] >> 8)) * c;
c *= twom24;
dx[2] = (double) ((int) (((xx.i[1] << 16) | (xx.i[2] >> 16)) &
0xffffff)) * c;
dy[2] = (double) ((int) (((yy.i[1] << 16) | (yy.i[2] >> 16)) &
0xffffff)) * c;
c *= twom24;
dx[3] = (double) ((int) (((xx.i[2] << 8) | (xx.i[3] >> 24)) &
0xffffff)) * c;
dy[3] = (double) ((int) (((yy.i[2] << 8) | (yy.i[3] >> 24)) &
0xffffff)) * c;
c *= twom24;
dx[4] = (double) ((int) (xx.i[3] & 0xffffff)) * c;
dy[4] = (double) ((int) (yy.i[3] & 0xffffff)) * c;
/* form the "digits" of the product */
dxy[0] = dx[0] * dy[0];
dxy[1] = dx[0] * dy[1] + dx[1] * dy[0];
dxy[2] = dx[0] * dy[2] + dx[1] * dy[1] + dx[2] * dy[0];
dxy[3] = dx[0] * dy[3] + dx[1] * dy[2] + dx[2] * dy[1] +
dx[3] * dy[0];
dxy[4] = dx[0] * dy[4] + dx[1] * dy[3] + dx[2] * dy[2] +
dx[3] * dy[1] + dx[4] * dy[0];
dxy[5] = dx[1] * dy[4] + dx[2] * dy[3] + dx[3] * dy[2] +
dx[4] * dy[1];
dxy[6] = dx[2] * dy[4] + dx[3] * dy[3] + dx[4] * dy[2];
dxy[7] = dx[3] * dy[4] + dx[4] * dy[3];
dxy[8] = dx[4] * dy[4];
/* split odd-numbered terms and combine into even-numbered terms */
c = (dxy[1] + two20) - two20;
dxy[0] += c;
dxy[1] -= c;
c = (dxy[3] + twom28) - twom28;
dxy[2] += c + dxy[1];
dxy[3] -= c;
c = (dxy[5] + twom76) - twom76;
dxy[4] += c + dxy[3];
dxy[5] -= c;
c = (dxy[7] + twom124) - twom124;
dxy[6] += c + dxy[5];
dxy[8] += (dxy[7] - c);
/* propagate carries, adjusting the exponent if need be */
dxy[7] = dxy[6] + dxy[8];
dxy[5] = dxy[4] + dxy[7];
dxy[3] = dxy[2] + dxy[5];
dxy[1] = dxy[0] + dxy[3];
if (dxy[1] >= two) {
dxy[0] *= half;
dxy[1] *= half;
dxy[2] *= half;
dxy[3] *= half;
dxy[4] *= half;
dxy[5] *= half;
dxy[6] *= half;
dxy[7] *= half;
dxy[8] *= half;
exy++;
}
/* extract the significand of x*y */
s = two36;
u.d = c = dxy[1] + s;
xy0 = u.i[1];
c -= s;
dxy[1] -= c;
dxy[0] -= c;
s *= twom32;
u.d = c = dxy[1] + s;
xy1 = u.i[1];
c -= s;
dxy[2] += (dxy[0] - c);
dxy[3] = dxy[2] + dxy[5];
s *= twom32;
u.d = c = dxy[3] + s;
xy2 = u.i[1];
c -= s;
dxy[4] += (dxy[2] - c);
dxy[5] = dxy[4] + dxy[7];
s *= twom32;
u.d = c = dxy[5] + s;
xy3 = u.i[1];
c -= s;
dxy[4] -= c;
dxy[5] = dxy[4] + dxy[7];
s *= twom32;
u.d = c = dxy[5] + s;
xy4 = u.i[1];
c -= s;
dxy[6] += (dxy[4] - c);
dxy[7] = dxy[6] + dxy[8];
s *= twom32;
u.d = c = dxy[7] + s;
xy5 = u.i[1];
c -= s;
dxy[8] += (dxy[6] - c);
s *= twom32;
u.d = c = dxy[8] + s;
xy6 = u.i[1];
c -= s;
dxy[8] -= c;
s *= twom32;
u.d = c = dxy[8] + s;
xy7 = u.i[1];
/* extract the sign, exponent, and significand of z */
sz = zz.i[0] & 0x80000000;
ez = hz >> 16;
z0 = hz & 0xffff;
if (!ez) {
if (z0 | (zz.i[1] & 0xfffe0000)) {
z1 = zz.i[1];
z2 = zz.i[2];
z3 = zz.i[3];
ez = 1;
} else if (zz.i[1] | (zz.i[2] & 0xfffe0000)) {
z0 = zz.i[1];
z1 = zz.i[2];
z2 = zz.i[3];
z3 = 0;
ez = -31;
} else if (zz.i[2] | (zz.i[3] & 0xfffe0000)) {
z0 = zz.i[2];
z1 = zz.i[3];
z2 = z3 = 0;
ez = -63;
} else {
z0 = zz.i[3];
z1 = z2 = z3 = 0;
ez = -95;
}
while ((z0 & 0x10000) == 0) {
z0 = (z0 << 1) | (z1 >> 31);
z1 = (z1 << 1) | (z2 >> 31);
z2 = (z2 << 1) | (z3 >> 31);
z3 <<= 1;
ez--;
}
} else {
z0 |= 0x10000;
z1 = zz.i[1];
z2 = zz.i[2];
z3 = zz.i[3];
}
z4 = z5 = z6 = z7 = 0;
/*
* now x*y is represented by sxy, exy, and xy[0-7], 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 > z2 || (xy2 == z2 && (xy3 > z3 ||
(xy3 == z3 && (xy4 | xy5 | xy6 | xy7) != 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;
e = xy2; xy2 = z2; z2 = e;
e = xy3; xy3 = z3; z3 = e;
z4 = xy4; xy4 = 0;
z5 = xy5; xy5 = 0;
z6 = xy6; xy6 = 0;
z7 = xy7; xy7 = 0;
}
/* shift the significand of xy keeping a sticky bit */
e = ez - exy;
if (e > 236) {
xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
xy7 = 1;
} else if (e >= 224) {
sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 | xy1 |
((xy0 << 1) << (255 - e));
xy7 = xy0 >> (e - 224);
if (sticky)
xy7 |= 1;
xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = xy6 = 0;
} else if (e >= 192) {
sticky = xy7 | xy6 | xy5 | xy4 | xy3 | xy2 |
((xy1 << 1) << (223 - e));
xy7 = (xy1 >> (e - 192)) | ((xy0 << 1) << (223 - e));
if (sticky)
xy7 |= 1;
xy6 = xy0 >> (e - 192);
xy0 = xy1 = xy2 = xy3 = xy4 = xy5 = 0;
} else if (e >= 160) {
sticky = xy7 | xy6 | xy5 | xy4 | xy3 |
((xy2 << 1) << (191 - e));
xy7 = (xy2 >> (e - 160)) | ((xy1 << 1) << (191 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy1 >> (e - 160)) | ((xy0 << 1) << (191 - e));
xy5 = xy0 >> (e - 160);
xy0 = xy1 = xy2 = xy3 = xy4 = 0;
} else if (e >= 128) {
sticky = xy7 | xy6 | xy5 | xy4 | ((xy3 << 1) << (159 - e));
xy7 = (xy3 >> (e - 128)) | ((xy2 << 1) << (159 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy2 >> (e - 128)) | ((xy1 << 1) << (159 - e));
xy5 = (xy1 >> (e - 128)) | ((xy0 << 1) << (159 - e));
xy4 = xy0 >> (e - 128);
xy0 = xy1 = xy2 = xy3 = 0;
} else if (e >= 96) {
sticky = xy7 | xy6 | xy5 | ((xy4 << 1) << (127 - e));
xy7 = (xy4 >> (e - 96)) | ((xy3 << 1) << (127 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy3 >> (e - 96)) | ((xy2 << 1) << (127 - e));
xy5 = (xy2 >> (e - 96)) | ((xy1 << 1) << (127 - e));
xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
xy3 = xy0 >> (e - 96);
xy0 = xy1 = xy2 = 0;
} else if (e >= 64) {
sticky = xy7 | xy6 | ((xy5 << 1) << (95 - e));
xy7 = (xy5 >> (e - 64)) | ((xy4 << 1) << (95 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy4 >> (e - 64)) | ((xy3 << 1) << (95 - e));
xy5 = (xy3 >> (e - 64)) | ((xy2 << 1) << (95 - e));
xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
xy2 = xy0 >> (e - 64);
xy0 = xy1 = 0;
} else if (e >= 32) {
sticky = xy7 | ((xy6 << 1) << (63 - e));
xy7 = (xy6 >> (e - 32)) | ((xy5 << 1) << (63 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy5 >> (e - 32)) | ((xy4 << 1) << (63 - e));
xy5 = (xy4 >> (e - 32)) | ((xy3 << 1) << (63 - e));
xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
xy1 = xy0 >> (e - 32);
xy0 = 0;
} else if (e) {
sticky = (xy7 << 1) << (31 - e);
xy7 = (xy7 >> e) | ((xy6 << 1) << (31 - e));
if (sticky)
xy7 |= 1;
xy6 = (xy6 >> e) | ((xy5 << 1) << (31 - e));
xy5 = (xy5 >> e) | ((xy4 << 1) << (31 - e));
xy4 = (xy4 >> e) | ((xy3 << 1) << (31 - e));
xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
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;
xy4 = ~xy4;
xy5 = ~xy5;
xy6 = ~xy6;
xy7 = -xy7;
if (xy7 == 0)
if (++xy6 == 0)
if (++xy5 == 0)
if (++xy4 == 0)
if (++xy3 == 0)
if (++xy2 == 0)
if (++xy1 == 0)
xy0++;
}
/* add, propagating carries */
z7 += xy7;
e = (z7 < xy7);
z6 += xy6;
if (e) {
z6++;
e = (z6 <= xy6);
} else
e = (z6 < xy6);
z5 += xy5;
if (e) {
z5++;
e = (z5 <= xy5);
} else
e = (z5 < xy5);
z4 += xy4;
if (e) {
z4++;
e = (z4 <= xy4);
} else
e = (z4 < xy4);
z3 += xy3;
if (e) {
z3++;
e = (z3 <= xy3);
} else
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 z4 */
if (ez < 1) {
/* result is tiny; shift right until exponent is within range */
e = 1 - ez;
if (e > 116) {
z4 = 1; /* result can't be exactly zero */
z0 = z1 = z2 = z3 = 0;
} else if (e >= 96) {
sticky = z7 | z6 | z5 | z4 | z3 | z2 |
((z1 << 1) << (127 - e));
z4 = (z1 >> (e - 96)) | ((z0 << 1) << (127 - e));
if (sticky)
z4 |= 1;
z3 = z0 >> (e - 96);
z0 = z1 = z2 = 0;
} else if (e >= 64) {
sticky = z7 | z6 | z5 | z4 | z3 |
((z2 << 1) << (95 - e));
z4 = (z2 >> (e - 64)) | ((z1 << 1) << (95 - e));
if (sticky)
z4 |= 1;
z3 = (z1 >> (e - 64)) | ((z0 << 1) << (95 - e));
z2 = z0 >> (e - 64);
z0 = z1 = 0;
} else if (e >= 32) {
sticky = z7 | z6 | z5 | z4 | ((z3 << 1) << (63 - e));
z4 = (z3 >> (e - 32)) | ((z2 << 1) << (63 - e));
if (sticky)
z4 |= 1;
z3 = (z2 >> (e - 32)) | ((z1 << 1) << (63 - e));
z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
z1 = z0 >> (e - 32);
z0 = 0;
} else {
sticky = z7 | z6 | z5 | (z4 << 1) << (31 - e);
z4 = (z4 >> e) | ((z3 << 1) << (31 - e));
if (sticky)
z4 |= 1;
z3 = (z3 >> e) | ((z2 << 1) << (31 - e));
z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
z0 >>= e;
}
ez = 1;
} else if (z0 >= 0x20000) {
/* carry out; shift right by one */
sticky = (z4 & 1) | z5 | z6 | z7;
z4 = (z4 >> 1) | (z3 << 31);
if (sticky)
z4 |= 1;
z3 = (z3 >> 1) | (z2 << 31);
z2 = (z2 >> 1) | (z1 << 31);
z1 = (z1 >> 1) | (z0 << 31);
z0 >>= 1;
ez++;
} else {
if (z0 < 0x10000 && (z0 | z1 | z2 | z3 | z4 | z5 | z6 | z7)
!= 0) {
/*
* borrow/cancellation; shift left as much as
* exponent allows
*/
while (!(z0 | (z1 & 0xfffe0000)) && ez >= 33) {
z0 = z1;
z1 = z2;
z2 = z3;
z3 = z4;
z4 = z5;
z5 = z6;
z6 = z7;
z7 = 0;
ez -= 32;
}
while (z0 < 0x10000 && ez > 1) {
z0 = (z0 << 1) | (z1 >> 31);
z1 = (z1 << 1) | (z2 >> 31);
z2 = (z2 << 1) | (z3 >> 31);
z3 = (z3 << 1) | (z4 >> 31);
z4 = (z4 << 1) | (z5 >> 31);
z5 = (z5 << 1) | (z6 >> 31);
z6 = (z6 << 1) | (z7 >> 31);
z7 <<= 1;
ez--;
}
}
if (z5 | z6 | z7)
z4 |= 1;
}
/* get the rounding mode */
rm = fsr >> 30;
/* strip off the integer bit, if there is one */
ibit = z0 & 0x10000;
if (ibit)
z0 -= 0x10000;
else {
ez = 0;
if (!(z0 | z1 | z2 | z3 | z4)) { /* exact zero */
zz.i[0] = rm == FSR_RM ? 0x80000000 : 0;
zz.i[1] = zz.i[2] = zz.i[3] = 0;
__fenv_setfsr32(&fsr);
return (zz.q);
}
}
/*
* 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 (z4) {
fsr |= FSR_NXC;
/* decide whether to round the fraction up */
if (rm == FSR_RP || (rm == FSR_RN && (z4 > 0x80000000u ||
(z4 == 0x80000000u && (z3 & 1))))) {
/* round up and renormalize if necessary */
if (++z3 == 0)
if (++z2 == 0)
if (++z1 == 0)
if (++z0 == 0x10000) {
z0 = 0;
ez++;
}
}
}
/* check for under/overflow */
if (ez >= 0x7fff) {
if (rm == FSR_RN || rm == FSR_RP) {
zz.i[0] = sz | 0x7fff0000;
zz.i[1] = zz.i[2] = zz.i[3] = 0;
} else {
zz.i[0] = sz | 0x7ffeffff;
zz.i[1] = zz.i[2] = zz.i[3] = 0xffffffff;
}
fsr |= FSR_OFC | FSR_NXC;
} else {
zz.i[0] = sz | (ez << 16) | z0;
zz.i[1] = z1;
zz.i[2] = z2;
zz.i[3] = z3;
/*
* !ibit => exact result was tiny before rounding,
* z4 nonzero => result delivered is inexact
*/
if (!ibit) {
if (z4)
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.q);
}
#elif defined(__x86)
static const union {
unsigned i[2];
double d;
} C[] = {
{ 0, 0x3fe00000u },
{ 0, 0x40000000u },
{ 0, 0x3df00000u },
{ 0, 0x3bf00000u },
{ 0, 0x41f00000u },
{ 0, 0x43e00000u },
{ 0, 0x7fe00000u },
{ 0, 0x00100000u },
{ 0, 0x00100001u }
};
#define half C[0].d
#define two C[1].d
#define twom32 C[2].d
#define twom64 C[3].d
#define two32 C[4].d
#define two63 C[5].d
#define huge C[6].d
#define tiny C[7].d
#define tiny2 C[8].d
#if defined(__amd64)
#define NI 4
#else
#define NI 3
#endif
/*
* fmal for x86: 80-bit extended double precision, little-endian
*/
long double
__fmal(long double x, long double y, long double z) {
union {
unsigned i[NI];
long double e;
} xx, yy, zz;
long double xhi, yhi, xlo, ylo, t;
unsigned xy0, xy1, xy2, xy3, xy4, z0, z1, z2, z3, z4;
unsigned oldcwsw, cwsw, rm, sticky, carry;
int ex, ey, ez, exy, sxy, sz, e, tinyafter;
volatile double dummy;
/* extract the exponents of the arguments */
xx.e = x;
yy.e = y;
zz.e = z;
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 | xx.i[1] | xx.i[0]) == 0 ||
(ey | yy.i[1] | yy.i[0]) == 0) /* x or y is inf, nan, or 0 */
return (x * y + z);
if (ez == 0x7fff) /* z is inf or nan */
return (x + z); /* avoid spurious under/overflow in x * y */
if ((ez | zz.i[1] | zz.i[0]) == 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; extract signs and
* normalize the significands (this will raise the denormal operand
* exception if need be)
*/
sxy = (xx.i[2] ^ yy.i[2]) & 0x8000;
sz = zz.i[2] & 0x8000;
if (!ex) {
xx.e = x * two63;
ex = (xx.i[2] & 0x7fff) - 63;
}
if (!ey) {
yy.e = y * two63;
ey = (yy.i[2] & 0x7fff) - 63;
}
if (!ez) {
zz.e = z * two63;
ez = (zz.i[2] & 0x7fff) - 63;
}
/*
* save the control and status words, mask all exceptions, and
* set rounding to 64-bit precision and toward-zero
*/
__fenv_getcwsw(&oldcwsw);
cwsw = (oldcwsw & 0xf0c0ffff) | 0x0f3f0000;
__fenv_setcwsw(&cwsw);
/* multiply x*y to 128 bits */
exy = ex + ey - 0x3fff;
xx.i[2] = 0x3fff;
yy.i[2] = 0x3fff;
x = xx.e;
y = yy.e;
xhi = ((x + twom32) + two32) - two32;
yhi = ((y + twom32) + two32) - two32;
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.e = x;
xy0 = xx.i[1];
xy1 = xx.i[0];
yy.e = t = y + twom32;
xy2 = yy.i[0];
yy.e = (y - (t - twom32)) + twom64;
xy3 = yy.i[0];
xy4 = 0;
z0 = zz.i[1];
z1 = zz.i[0];
z2 = z3 = z4 = 0;
/*
* now x*y is represented by sxy, exy, and xy[0-4], 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 > 130) {
xy0 = xy1 = xy2 = xy3 = 0;
xy4 = 1;
} else if (e >= 128) {
sticky = xy3 | xy2 | xy1 | ((xy0 << 1) << (159 - e));
xy4 = xy0 >> (e - 128);
if (sticky)
xy4 |= 1;
xy0 = xy1 = xy2 = xy3 = 0;
} else if (e >= 96) {
sticky = xy3 | xy2 | ((xy1 << 1) << (127 - e));
xy4 = (xy1 >> (e - 96)) | ((xy0 << 1) << (127 - e));
if (sticky)
xy4 |= 1;
xy3 = xy0 >> (e - 96);
xy0 = xy1 = xy2 = 0;
} else if (e >= 64) {
sticky = xy3 | ((xy2 << 1) << (95 - e));
xy4 = (xy2 >> (e - 64)) | ((xy1 << 1) << (95 - e));
if (sticky)
xy4 |= 1;
xy3 = (xy1 >> (e - 64)) | ((xy0 << 1) << (95 - e));
xy2 = xy0 >> (e - 64);
xy0 = xy1 = 0;
} else if (e >= 32) {
sticky = (xy3 << 1) << (63 - e);
xy4 = (xy3 >> (e - 32)) | ((xy2 << 1) << (63 - e));
if (sticky)
xy4 |= 1;
xy3 = (xy2 >> (e - 32)) | ((xy1 << 1) << (63 - e));
xy2 = (xy1 >> (e - 32)) | ((xy0 << 1) << (63 - e));
xy1 = xy0 >> (e - 32);
xy0 = 0;
} else if (e) {
xy4 = (xy3 << 1) << (31 - e);
xy3 = (xy3 >> e) | ((xy2 << 1) << (31 - e));
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;
xy4 = -xy4;
if (xy4 == 0)
if (++xy3 == 0)
if (++xy2 == 0)
if (++xy1 == 0)
xy0++;
}
/* add, propagating carries */
z4 += xy4;
carry = (z4 < xy4);
z3 += xy3;
if (carry) {
z3++;
carry = (z3 <= xy3);
} else
carry = (z3 < xy3);
z2 += xy2;
if (carry) {
z2++;
carry = (z2 <= xy2);
} else
carry = (z2 < xy2);
z1 += xy1;
if (carry) {
z1++;
carry = (z1 <= xy1);
} else
carry = (z1 < xy1);
z0 += xy0;
if (carry) {
z0++;
carry = (z0 <= xy0);
} else
carry = (z0 < xy0);
/* for a magnitude subtract, ignore the last carry out */
if (sxy ^ sz)
carry = 0;
/* 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 > 67) {
z2 = 1; /* result can't be exactly zero */
z0 = z1 = 0;
} else if (e >= 64) {
sticky = z4 | z3 | z2 | z1 | ((z0 << 1) << (95 - e));
z2 = (z0 >> (e - 64)) | ((carry << 1) << (95 - e));
if (sticky)
z2 |= 1;
z1 = carry >> (e - 64);
z0 = 0;
} else if (e >= 32) {
sticky = z4 | z3 | z2 | ((z1 << 1) << (63 - e));
z2 = (z1 >> (e - 32)) | ((z0 << 1) << (63 - e));
if (sticky)
z2 |= 1;
z1 = (z0 >> (e - 32)) | ((carry << 1) << (63 - e));
z0 = carry >> (e - 32);
} else {
sticky = z4 | z3 | (z2 << 1) << (31 - e);
z2 = (z2 >> e) | ((z1 << 1) << (31 - e));
if (sticky)
z2 |= 1;
z1 = (z1 >> e) | ((z0 << 1) << (31 - e));
z0 = (z0 >> e) | ((carry << 1) << (31 - e));
}
ez = 1;
} else if (carry) {
/* carry out; shift right by one */
sticky = (z2 & 1) | z3 | z4;
z2 = (z2 >> 1) | (z1 << 31);
if (sticky)
z2 |= 1;
z1 = (z1 >> 1) | (z0 << 31);
z0 = (z0 >> 1) | 0x80000000;
ez++;
} else {
if (z0 < 0x80000000u && (z0 | z1 | z2 | z3 | z4) != 0) {
/*
* borrow/cancellation; shift left as much as
* exponent allows
*/
while (!z0 && ez >= 33) {
z0 = z1;
z1 = z2;
z2 = z3;
z3 = z4;
z4 = 0;
ez -= 32;
}
while (z0 < 0x80000000u && ez > 1) {
z0 = (z0 << 1) | (z1 >> 31);
z1 = (z1 << 1) | (z2 >> 31);
z2 = (z2 << 1) | (z3 >> 31);
z3 = (z3 << 1) | (z4 >> 31);
z4 <<= 1;
ez--;
}
}
if (z3 | z4)
z2 |= 1;
}
/* get the rounding mode */
rm = oldcwsw & 0x0c000000;
/* adjust exponent if result is subnormal */
tinyafter = 0;
if (!(z0 & 0x80000000)) {
ez = 0;
tinyafter = 1;
if (!(z0 | z1 | z2)) { /* exact zero */
zz.i[2] = rm == FCW_RM ? 0x8000 : 0;
zz.i[1] = zz.i[0] = 0;
__fenv_setcwsw(&oldcwsw);
return (zz.e);
}
}
/*
* flip the sense of directed roundings if the result is negative;
* the logic below applies to a positive result
*/
if (sz && (rm == FCW_RM || rm == FCW_RP))
rm = (FCW_RM + FCW_RP) - rm;
/* round */
if (z2) {
if (rm == FCW_RP || (rm == FCW_RN && (z2 > 0x80000000u ||
(z2 == 0x80000000u && (z1 & 1))))) {
/* round up and renormalize if necessary */
if (++z1 == 0) {
if (++z0 == 0) {
z0 = 0x80000000;
ez++;
} else if (z0 == 0x80000000) {
/* rounded up to smallest normal */
ez = 1;
if ((rm == FCW_RP && z2 >
0x80000000u) || (rm == FCW_RN &&
z2 >= 0xc0000000u))
/*
* would have rounded up to
* smallest normal even with
* unbounded range
*/
tinyafter = 0;
}
}
}
}
/* restore the control and status words, check for over/underflow */
__fenv_setcwsw(&oldcwsw);
if (ez >= 0x7fff) {
if (rm == FCW_RN || rm == FCW_RP) {
zz.i[2] = sz | 0x7fff;
zz.i[1] = 0x80000000;
zz.i[0] = 0;
} else {
zz.i[2] = sz | 0x7ffe;
zz.i[1] = 0xffffffff;
zz.i[0] = 0xffffffff;
}
dummy = huge;
dummy *= huge;
} else {
zz.i[2] = sz | ez;
zz.i[1] = z0;
zz.i[0] = z1;
/*
* tinyafter => result rounded w/ unbounded range would be tiny,
* z2 nonzero => result delivered is inexact
*/
if (tinyafter) {
dummy = tiny;
if (z2)
dummy *= tiny;
else
dummy -= tiny2;
} else if (z2) {
dummy = huge;
dummy += tiny;
}
}
return (zz.e);
}
#else
#error Unknown architecture
#endif