OpenSolaris_b135/lib/libc/sparc/fp/_Q_sqrt.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,
0.5,
1.0,
68719476736.0,
536870912.0,
48.0,
16.0,
1.52587890625000000000e-05,
2.86102294921875000000e-06,
5.96046447753906250000e-08,
3.72529029846191406250e-09,
1.70530256582424044609e-13,
7.10542735760100185871e-15,
8.67361737988403547206e-19,
2.16840434497100886801e-19,
1.27054942088145050860e-21,
1.21169035041947413311e-27,
9.62964972193617926528e-35,
4.70197740328915003187e-38
};
#define zero C[0]
#define half C[1]
#define one C[2]
#define two36 C[3]
#define two29 C[4]
#define three2p4 C[5]
#define two4 C[6]
#define twom16 C[7]
#define three2m20 C[8]
#define twom24 C[9]
#define twom28 C[10]
#define three2m44 C[11]
#define twom47 C[12]
#define twom60 C[13]
#define twom62 C[14]
#define three2m71 C[15]
#define three2m91 C[16]
#define twom113 C[17]
#define twom124 C[18]
static const unsigned
fsr_re = 0x00000000u,
fsr_rn = 0xc0000000u;
#ifdef __sparcv9
/*
* _Qp_sqrt(pz, x) sets *pz = sqrt(*x).
*/
void
_Qp_sqrt(union longdouble *pz, const union longdouble *x)
#else
/*
* _Q_sqrt(x) returns sqrt(*x).
*/
union longdouble
_Q_sqrt(const union longdouble *x)
#endif /* __sparcv9 */
{
union longdouble z;
union xdouble u;
double c, d, rr, r[2], tt[3], xx[4], zz[5];
unsigned int xm, fsr, lx, wx[3];
unsigned int msw, frac2, frac3, frac4, rm;
int ex, ez;
if (QUAD_ISZERO(*x)) {
Z = *x;
QUAD_RETURN(Z);
}
xm = x->l.msw;
__quad_getfsrp(&fsr);
/* handle nan and inf cases */
if ((xm & 0x7fffffff) >= 0x7fff0000) {
if ((x->l.msw & 0xffff) | x->l.frac2 | x->l.frac3 |
x->l.frac4) {
if (!(x->l.msw & 0x8000)) {
/* snan, signal invalid */
if (fsr & FSR_NVM) {
__quad_fsqrtq(x, &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 (x->l.msw & 0x80000000) {
/* sqrt(-inf), signal invalid */
if (fsr & FSR_NVM) {
__quad_fsqrtq(x, &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);
}
/* sqrt(inf), return inf */
Z = *x;
QUAD_RETURN(Z);
}
/* handle negative numbers */
if (xm & 0x80000000) {
if (fsr & FSR_NVM) {
__quad_fsqrtq(x, &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);
}
/* now x is finite, positive */
__quad_setfsrp((unsigned *)&fsr_re);
/* get the normalized significand and exponent */
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 - 0x3fff;
if (ez & 1) {
/* make exponent even */
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;
ez--;
}
/* extract the significands into doubles */
c = twom16;
xx[0] = (double)((int)lx) * c;
c *= twom24;
xx[0] += (double)((int)(wx[0] >> 8)) * c;
c *= twom24;
xx[1] = (double)((int)(((wx[0] << 16) | (wx[1] >> 16)) &
0xffffff)) * c;
c *= twom24;
xx[2] = (double)((int)(((wx[1] << 8) | (wx[2] >> 24)) &
0xffffff)) * c;
c *= twom24;
xx[3] = (double)((int)(wx[2] & 0xffffff)) * c;
/* approximate the divisor for the Newton iteration */
c = xx[0] + xx[1];
c = __quad_dp_sqrt(&c);
rr = half / c;
/* compute the first five "digits" of the square root */
zz[0] = (c + two29) - two29;
tt[0] = zz[0] + zz[0];
r[0] = (xx[0] - zz[0] * zz[0]) + xx[1];
zz[1] = (rr * (r[0] + xx[2]) + three2p4) - three2p4;
tt[1] = zz[1] + zz[1];
r[0] -= tt[0] * zz[1];
r[1] = xx[2] - zz[1] * zz[1];
c = (r[1] + three2m20) - three2m20;
r[0] += c;
r[1] = (r[1] - c) + xx[3];
zz[2] = (rr * (r[0] + r[1]) + three2m20) - three2m20;
tt[2] = zz[2] + zz[2];
r[0] -= tt[0] * zz[2];
r[1] -= tt[1] * zz[2];
c = (r[1] + three2m44) - three2m44;
r[0] += c;
r[1] = (r[1] - c) - zz[2] * zz[2];
zz[3] = (rr * (r[0] + r[1]) + three2m44) - three2m44;
r[0] = ((r[0] - tt[0] * zz[3]) + r[1]) - tt[1] * zz[3];
r[1] = -tt[2] * zz[3];
c = (r[1] + three2m91) - three2m91;
r[0] += c;
r[1] = (r[1] - c) - zz[3] * zz[3];
zz[4] = (rr * (r[0] + r[1]) + three2m71) - three2m71;
/* reduce to three doubles, making sure zz[1] is positive */
zz[0] += zz[1] - twom47;
zz[1] = twom47 + 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 = (((((r[0] - tt[0] * zz[4]) - tt[1] * zz[4]) + r[1])
- tt[2] * zz[4]) - (zz[3] + zz[3]) * zz[4]) - zz[4] * zz[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;
/* adjust exponent and strip off integer bit */
ez = (ez >> 1) + 0x3fff;
zz[0] -= one;
/* 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 */
rm = fsr >> 30;
/* 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++;
}
}
}
/* stow the result */
z.l.msw = (ez << 16) | msw;
z.l.frac2 = frac2;
z.l.frac3 = frac3;
z.l.frac4 = frac4;
if ((fsr & FSR_CEXC) & (fsr >> 23)) {
__quad_setfsrp(&fsr);
__quad_fsqrtq(x, &Z);
} else {
Z = z;
fsr |= (fsr & 0x1f) << 5;
__quad_setfsrp(&fsr);
}
QUAD_RETURN(Z);
}