OpenSolaris_b135/lib/libc/sparc/fp/_Q_div.c
/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License, Version 1.0 only
* (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 2003 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma ident "%Z%%M% %I% %E% SMI"
#include "quad.h"
static const double C[] = {
0.0,
1.0,
68719476736.0,
402653184.0,
24.0,
16.0,
3.66210937500000000000e-04,
1.52587890625000000000e-05,
1.43051147460937500000e-06,
5.96046447753906250000e-08,
3.72529029846191406250e-09,
2.18278728425502777100e-11,
8.52651282912120223045e-14,
3.55271367880050092936e-15,
1.30104260698260532081e-18,
8.67361737988403547206e-19,
2.16840434497100886801e-19,
3.17637355220362627151e-22,
7.75481824268463445192e-26,
4.62223186652936604733e-33,
9.62964972193617926528e-35,
4.70197740328915003187e-38,
2.75506488473973634680e-40,
};
#define zero C[0]
#define one C[1]
#define two36 C[2]
#define three2p27 C[3]
#define three2p3 C[4]
#define two4 C[5]
#define three2m13 C[6]
#define twom16 C[7]
#define three2m21 C[8]
#define twom24 C[9]
#define twom28 C[10]
#define three2m37 C[11]
#define three2m45 C[12]
#define twom48 C[13]
#define three2m61 C[14]
#define twom60 C[15]
#define twom62 C[16]
#define three2m73 C[17]
#define three2m85 C[18]
#define three2m109 C[19]
#define twom113 C[20]
#define twom124 C[21]
#define three2m133 C[22]
static const unsigned int
fsr_re = 0x00000000u,
fsr_rn = 0xc0000000u;
#ifdef __sparcv9
/*
* _Qp_div(pz, x, y) sets *pz = *x / *y.
*/
void
_Qp_div(union longdouble *pz, const union longdouble *x,
const union longdouble *y)
#else
/*
* _Q_div(x, y) returns *x / *y.
*/
union longdouble
_Q_div(const union longdouble *x, const union longdouble *y)
#endif /* __sparcv9 */
{
union longdouble z;
union xdouble u;
double c, d, ry, xx[4], yy[5], zz[5];
unsigned int xm, ym, fsr, lx, ly, wx[3], wy[3];
unsigned int msw, frac2, frac3, frac4, rm;
int ibit, ex, ey, ez, sign;
xm = x->l.msw & 0x7fffffff;
ym = y->l.msw & 0x7fffffff;
sign = (x->l.msw ^ y->l.msw) & ~0x7fffffff;
__quad_getfsrp(&fsr);
/* handle nan and inf cases */
if (xm >= 0x7fff0000 || ym >= 0x7fff0000) {
/* handle nan cases according to V9 app. B */
if (QUAD_ISNAN(*y)) {
if (!(y->l.msw & 0x8000)) {
/* snan, signal invalid */
if (fsr & FSR_NVM) {
__quad_fdivq(x, y, &Z);
} else {
Z = *y;
Z.l.msw |= 0x8000;
fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
FSR_NVC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
} else if (QUAD_ISNAN(*x) && !(x->l.msw & 0x8000)) {
/* snan, signal invalid */
if (fsr & FSR_NVM) {
__quad_fdivq(x, y, &Z);
} else {
Z = *x;
Z.l.msw |= 0x8000;
fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
FSR_NVC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}
Z = *y;
QUAD_RETURN(Z);
}
if (QUAD_ISNAN(*x)) {
if (!(x->l.msw & 0x8000)) {
/* snan, signal invalid */
if (fsr & FSR_NVM) {
__quad_fdivq(x, y, &Z);
} else {
Z = *x;
Z.l.msw |= 0x8000;
fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
FSR_NVC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}
Z = *x;
QUAD_RETURN(Z);
}
if (xm == 0x7fff0000) {
/* x is inf */
if (ym == 0x7fff0000) {
/* inf / inf, signal invalid */
if (fsr & FSR_NVM) {
__quad_fdivq(x, y, &Z);
} else {
Z.l.msw = 0x7fffffff;
Z.l.frac2 = Z.l.frac3 =
Z.l.frac4 = 0xffffffff;
fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
FSR_NVC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}
/* inf / finite, return inf */
Z.l.msw = sign | 0x7fff0000;
Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0;
QUAD_RETURN(Z);
}
/* y is inf */
Z.l.msw = sign;
Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0;
QUAD_RETURN(Z);
}
/* handle zero cases */
if (xm == 0 || ym == 0) {
if (QUAD_ISZERO(*x)) {
if (QUAD_ISZERO(*y)) {
/* zero / zero, signal invalid */
if (fsr & FSR_NVM) {
__quad_fdivq(x, y, &Z);
} else {
Z.l.msw = 0x7fffffff;
Z.l.frac2 = Z.l.frac3 =
Z.l.frac4 = 0xffffffff;
fsr = (fsr & ~FSR_CEXC) | FSR_NVA |
FSR_NVC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}
/* zero / nonzero, return zero */
Z.l.msw = sign;
Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0;
QUAD_RETURN(Z);
}
if (QUAD_ISZERO(*y)) {
/* nonzero / zero, signal zero divide */
if (fsr & FSR_DZM) {
__quad_fdivq(x, y, &Z);
} else {
Z.l.msw = sign | 0x7fff0000;
Z.l.frac2 = Z.l.frac3 = Z.l.frac4 = 0;
fsr = (fsr & ~FSR_CEXC) | FSR_DZA | FSR_DZC;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}
}
/* now x and y are finite, nonzero */
__quad_setfsrp(&fsr_re);
/* get their normalized significands and exponents */
ex = (int)(xm >> 16);
lx = xm & 0xffff;
if (ex) {
lx |= 0x10000;
wx[0] = x->l.frac2;
wx[1] = x->l.frac3;
wx[2] = x->l.frac4;
} else {
if (lx | (x->l.frac2 & 0xfffe0000)) {
wx[0] = x->l.frac2;
wx[1] = x->l.frac3;
wx[2] = x->l.frac4;
ex = 1;
} else if (x->l.frac2 | (x->l.frac3 & 0xfffe0000)) {
lx = x->l.frac2;
wx[0] = x->l.frac3;
wx[1] = x->l.frac4;
wx[2] = 0;
ex = -31;
} else if (x->l.frac3 | (x->l.frac4 & 0xfffe0000)) {
lx = x->l.frac3;
wx[0] = x->l.frac4;
wx[1] = wx[2] = 0;
ex = -63;
} else {
lx = x->l.frac4;
wx[0] = wx[1] = wx[2] = 0;
ex = -95;
}
while ((lx & 0x10000) == 0) {
lx = (lx << 1) | (wx[0] >> 31);
wx[0] = (wx[0] << 1) | (wx[1] >> 31);
wx[1] = (wx[1] << 1) | (wx[2] >> 31);
wx[2] <<= 1;
ex--;
}
}
ez = ex;
ey = (int)(ym >> 16);
ly = ym & 0xffff;
if (ey) {
ly |= 0x10000;
wy[0] = y->l.frac2;
wy[1] = y->l.frac3;
wy[2] = y->l.frac4;
} else {
if (ly | (y->l.frac2 & 0xfffe0000)) {
wy[0] = y->l.frac2;
wy[1] = y->l.frac3;
wy[2] = y->l.frac4;
ey = 1;
} else if (y->l.frac2 | (y->l.frac3 & 0xfffe0000)) {
ly = y->l.frac2;
wy[0] = y->l.frac3;
wy[1] = y->l.frac4;
wy[2] = 0;
ey = -31;
} else if (y->l.frac3 | (y->l.frac4 & 0xfffe0000)) {
ly = y->l.frac3;
wy[0] = y->l.frac4;
wy[1] = wy[2] = 0;
ey = -63;
} else {
ly = y->l.frac4;
wy[0] = wy[1] = wy[2] = 0;
ey = -95;
}
while ((ly & 0x10000) == 0) {
ly = (ly << 1) | (wy[0] >> 31);
wy[0] = (wy[0] << 1) | (wy[1] >> 31);
wy[1] = (wy[1] << 1) | (wy[2] >> 31);
wy[2] <<= 1;
ey--;
}
}
ez -= ey - 0x3fff;
/* extract the significands into doubles */
c = twom16;
xx[0] = (double)((int)lx) * c;
yy[0] = (double)((int)ly) * c;
c *= twom24;
xx[0] += (double)((int)(wx[0] >> 8)) * c;
yy[1] = (double)((int)(wy[0] >> 8)) * c;
c *= twom24;
xx[1] = (double)((int)(((wx[0] << 16) |
(wx[1] >> 16)) & 0xffffff)) * c;
yy[2] = (double)((int)(((wy[0] << 16) |
(wy[1] >> 16)) & 0xffffff)) * c;
c *= twom24;
xx[2] = (double)((int)(((wx[1] << 8) |
(wx[2] >> 24)) & 0xffffff)) * c;
yy[3] = (double)((int)(((wy[1] << 8) |
(wy[2] >> 24)) & 0xffffff)) * c;
c *= twom24;
xx[3] = (double)((int)(wx[2] & 0xffffff)) * c;
yy[4] = (double)((int)(wy[2] & 0xffffff)) * c;
/* approximate the reciprocal of y */
ry = one / ((yy[0] + yy[1]) + yy[2]);
/* compute the first five "digits" of the quotient */
zz[0] = (ry * (xx[0] + xx[1]) + three2p27) - three2p27;
xx[0] = ((xx[0] - zz[0] * yy[0]) - zz[0] * yy[1]) + xx[1];
d = zz[0] * yy[2];
c = (d + three2m13) - three2m13;
xx[0] -= c;
xx[1] = xx[2] - (d - c);
d = zz[0] * yy[3];
c = (d + three2m37) - three2m37;
xx[1] -= c;
xx[2] = xx[3] - (d - c);
d = zz[0] * yy[4];
c = (d + three2m61) - three2m61;
xx[2] -= c;
xx[3] = c - d;
zz[1] = (ry * (xx[0] + xx[1]) + three2p3) - three2p3;
xx[0] = ((xx[0] - zz[1] * yy[0]) - zz[1] * yy[1]) + xx[1];
d = zz[1] * yy[2];
c = (d + three2m37) - three2m37;
xx[0] -= c;
xx[1] = xx[2] - (d - c);
d = zz[1] * yy[3];
c = (d + three2m61) - three2m61;
xx[1] -= c;
xx[2] = xx[3] - (d - c);
d = zz[1] * yy[4];
c = (d + three2m85) - three2m85;
xx[2] -= c;
xx[3] = c - d;
zz[2] = (ry * (xx[0] + xx[1]) + three2m21) - three2m21;
xx[0] = ((xx[0] - zz[2] * yy[0]) - zz[2] * yy[1]) + xx[1];
d = zz[2] * yy[2];
c = (d + three2m61) - three2m61;
xx[0] -= c;
xx[1] = xx[2] - (d - c);
d = zz[2] * yy[3];
c = (d + three2m85) - three2m85;
xx[1] -= c;
xx[2] = xx[3] - (d - c);
d = zz[2] * yy[4];
c = (d + three2m109) - three2m109;
xx[2] -= c;
xx[3] = c - d;
zz[3] = (ry * (xx[0] + xx[1]) + three2m45) - three2m45;
xx[0] = ((xx[0] - zz[3] * yy[0]) - zz[3] * yy[1]) + xx[1];
d = zz[3] * yy[2];
c = (d + three2m85) - three2m85;
xx[0] -= c;
xx[1] = xx[2] - (d - c);
d = zz[3] * yy[3];
c = (d + three2m109) - three2m109;
xx[1] -= c;
xx[2] = xx[3] - (d - c);
d = zz[3] * yy[4];
c = (d + three2m133) - three2m133;
xx[2] -= c;
xx[3] = c - d;
zz[4] = (ry * (xx[0] + xx[1]) + three2m73) - three2m73;
/* reduce to three doubles, making sure zz[1] is positive */
zz[0] += zz[1] - twom48;
zz[1] = twom48 + zz[2] + zz[3];
zz[2] = zz[4];
/* if the third term might lie on a rounding boundary, perturb it */
if (zz[2] == (twom62 + zz[2]) - twom62) {
/* here we just need to get the sign of the remainder */
c = (((((xx[0] - zz[4] * yy[0]) - zz[4] * yy[1]) + xx[1]) +
(xx[2] - zz[4] * yy[2])) + (xx[3] - zz[4] * yy[3]))
- zz[4] * yy[4];
if (c < zero)
zz[2] -= twom124;
else if (c > zero)
zz[2] += twom124;
}
/*
* propagate carries/borrows, using round-to-negative-infinity mode
* to make all terms nonnegative (note that we can't encounter a
* borrow so large that the roundoff is unrepresentable because
* we took care to make zz[1] positive above)
*/
__quad_setfsrp(&fsr_rn);
c = zz[1] + zz[2];
zz[2] += (zz[1] - c);
zz[1] = c;
c = zz[0] + zz[1];
zz[1] += (zz[0] - c);
zz[0] = c;
/* check for borrow */
if (c < one) {
/* postnormalize */
zz[0] += zz[0];
zz[1] += zz[1];
zz[2] += zz[2];
ez--;
}
/* if exponent > 0 strip off integer bit, else denormalize */
if (ez > 0) {
ibit = 1;
zz[0] -= one;
} else {
ibit = 0;
if (ez > -128)
u.l.hi = (unsigned int)(0x3fe + ez) << 20;
else
u.l.hi = 0x37e00000;
u.l.lo = 0;
zz[0] *= u.d;
zz[1] *= u.d;
zz[2] *= u.d;
ez = 0;
}
/* the first 48 bits of fraction come from zz[0] */
u.d = d = two36 + zz[0];
msw = u.l.lo;
zz[0] -= (d - two36);
u.d = d = two4 + zz[0];
frac2 = u.l.lo;
zz[0] -= (d - two4);
/* the next 32 come from zz[0] and zz[1] */
u.d = d = twom28 + (zz[0] + zz[1]);
frac3 = u.l.lo;
zz[0] -= (d - twom28);
/* condense the remaining fraction; errors here won't matter */
c = zz[0] + zz[1];
zz[1] = ((zz[0] - c) + zz[1]) + zz[2];
zz[0] = c;
/* get the last word of fraction */
u.d = d = twom60 + (zz[0] + zz[1]);
frac4 = u.l.lo;
zz[0] -= (d - twom60);
/* keep track of what's left for rounding; note that the error */
/* in computing c will be non-negative due to rounding mode */
c = zz[0] + zz[1];
/* get the rounding mode, fudging directed rounding modes */
/* as though the result were positive */
rm = fsr >> 30;
if (sign)
rm ^= (rm >> 1);
/* round and raise exceptions */
fsr &= ~FSR_CEXC;
if (c != zero) {
fsr |= FSR_NXC;
/* decide whether to round the fraction up */
if (rm == FSR_RP || (rm == FSR_RN && (c > twom113 ||
(c == twom113 && ((frac4 & 1) || (c - zz[0] !=
zz[1])))))) {
/* round up and renormalize if necessary */
if (++frac4 == 0)
if (++frac3 == 0)
if (++frac2 == 0)
if (++msw == 0x10000) {
msw = 0;
ez++;
}
}
}
/* check for under/overflow */
if (ez >= 0x7fff) {
if (rm == FSR_RN || rm == FSR_RP) {
z.l.msw = sign | 0x7fff0000;
z.l.frac2 = z.l.frac3 = z.l.frac4 = 0;
} else {
z.l.msw = sign | 0x7ffeffff;
z.l.frac2 = z.l.frac3 = z.l.frac4 = 0xffffffff;
}
fsr |= FSR_OFC | FSR_NXC;
} else {
z.l.msw = sign | (ez << 16) | msw;
z.l.frac2 = frac2;
z.l.frac3 = frac3;
z.l.frac4 = frac4;
/* !ibit => exact result was tiny before rounding, */
/* t nonzero => result delivered is inexact */
if (!ibit) {
if (c != zero)
fsr |= FSR_UFC | FSR_NXC;
else if (fsr & FSR_UFM)
fsr |= FSR_UFC;
}
}
if ((fsr & FSR_CEXC) & (fsr >> 23)) {
__quad_setfsrp(&fsr);
__quad_fdivq(x, y, &Z);
} else {
Z = z;
fsr |= (fsr & 0x1f) << 5;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}