/*
* 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 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __powf = powf
#include "libm.h"
#include "xpg6.h" /* __xpg6 */
#define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int
#if defined(__i386) && !defined(__amd64)
extern int __swapRP(int);
#endif
/* INDENT OFF */
static const double
ln2 = 6.93147180559945286227e-01, /* 0x3fe62e42, 0xfefa39ef */
invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
dtwo = 2.0,
done = 1.0,
dhalf = 0.5,
d32 = 32.0,
d1_32 = 0.03125,
A0 = 1.999999999813723303647511146995966439250e+0000,
A1 = 6.666910817935858533770138657139665608610e-0001,
t0 = 2.000000000004777489262405315073203746943e+0000,
t1 = 1.666663408349926379873111932994250726307e-0001;
static const double S[] = {
1.00000000000000000000e+00, /* 3FF0000000000000 */
1.02189714865411662714e+00, /* 3FF059B0D3158574 */
1.04427378242741375480e+00, /* 3FF0B5586CF9890F */
1.06714040067682369717e+00, /* 3FF11301D0125B51 */
1.09050773266525768967e+00, /* 3FF172B83C7D517B */
1.11438674259589243221e+00, /* 3FF1D4873168B9AA */
1.13878863475669156458e+00, /* 3FF2387A6E756238 */
1.16372485877757747552e+00, /* 3FF29E9DF51FDEE1 */
1.18920711500272102690e+00, /* 3FF306FE0A31B715 */
1.21524735998046895524e+00, /* 3FF371A7373AA9CB */
1.24185781207348400201e+00, /* 3FF3DEA64C123422 */
1.26905095719173321989e+00, /* 3FF44E086061892D */
1.29683955465100964055e+00, /* 3FF4BFDAD5362A27 */
1.32523664315974132322e+00, /* 3FF5342B569D4F82 */
1.35425554693689265129e+00, /* 3FF5AB07DD485429 */
1.38390988196383202258e+00, /* 3FF6247EB03A5585 */
1.41421356237309514547e+00, /* 3FF6A09E667F3BCD */
1.44518080697704665027e+00, /* 3FF71F75E8EC5F74 */
1.47682614593949934623e+00, /* 3FF7A11473EB0187 */
1.50916442759342284141e+00, /* 3FF82589994CCE13 */
1.54221082540794074411e+00, /* 3FF8ACE5422AA0DB */
1.57598084510788649659e+00, /* 3FF93737B0CDC5E5 */
1.61049033194925428347e+00, /* 3FF9C49182A3F090 */
1.64575547815396494578e+00, /* 3FFA5503B23E255D */
1.68179283050742900407e+00, /* 3FFAE89F995AD3AD */
1.71861929812247793414e+00, /* 3FFB7F76F2FB5E47 */
1.75625216037329945351e+00, /* 3FFC199BDD85529C */
1.79470907500310716820e+00, /* 3FFCB720DCEF9069 */
1.83400808640934243066e+00, /* 3FFD5818DCFBA487 */
1.87416763411029996256e+00, /* 3FFDFC97337B9B5F */
1.91520656139714740007e+00, /* 3FFEA4AFA2A490DA */
1.95714412417540017941e+00, /* 3FFF50765B6E4540 */
};
static const double TBL[] = {
0.00000000000000000e+00,
3.07716586667536873e-02,
6.06246218164348399e-02,
8.96121586896871380e-02,
1.17783035656383456e-01,
1.45182009844497889e-01,
1.71850256926659228e-01,
1.97825743329919868e-01,
2.23143551314209765e-01,
2.47836163904581269e-01,
2.71933715483641758e-01,
2.95464212893835898e-01,
3.18453731118534589e-01,
3.40926586970593193e-01,
3.62905493689368475e-01,
3.84411698910332056e-01,
4.05465108108164385e-01,
4.26084395310900088e-01,
4.46287102628419530e-01,
4.66089729924599239e-01,
4.85507815781700824e-01,
5.04556010752395312e-01,
5.23248143764547868e-01,
5.41597282432744409e-01,
5.59615787935422659e-01,
5.77315365034823613e-01,
5.94707107746692776e-01,
6.11801541105992941e-01,
6.28608659422374094e-01,
6.45137961373584701e-01,
6.61398482245365016e-01,
6.77398823591806143e-01,
};
static const float zero = 0.0F, one = 1.0F, huge = 1.0e25f, tiny = 1.0e-25f;
/* INDENT ON */
float
powf(float x, float y) {
float fx = x, fy = y;
float fz;
int ix, iy, jx, jy, k, iw, yisint;
ix = *(int *)&x;
iy = *(int *)&y;
jx = ix & ~0x80000000;
jy = iy & ~0x80000000;
if (jy == 0)
return (one); /* x**+-0 = 1 */
else if (ix == 0x3f800000 && (__xpg6 & _C99SUSv3_pow) != 0)
return (one); /* C99: 1**anything = 1 */
else if (((0x7f800000 - jx) | (0x7f800000 - jy)) < 0)
return (fx * fy); /* at least one of x or y is NaN */
/* includes Sun: 1**NaN = NaN */
/* INDENT OFF */
/*
* determine if y is an odd int
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
/* INDENT ON */
yisint = 0;
if (ix < 0) {
if (jy >= 0x4b800000) {
yisint = 2; /* |y|>=2**24: y must be even */
} else if (jy >= 0x3f800000) {
k = (jy >> 23) - 0x7f; /* exponent */
iw = jy >> (23 - k);
if ((iw << (23 - k)) == jy)
yisint = 2 - (iw & 1);
}
}
/* special value of y */
if ((jy & ~0x7f800000) == 0) {
if (jy == 0x7f800000) { /* y is +-inf */
if (jx == 0x3f800000) {
if ((__xpg6 & _C99SUSv3_pow) != 0)
fz = one;
/* C99: (-1)**+-inf is 1 */
else
fz = fy - fy;
/* Sun: (+-1)**+-inf = NaN */
} else if (jx > 0x3f800000) {
/* (|x|>1)**+,-inf = inf,0 */
if (iy > 0)
fz = fy;
else
fz = zero;
} else { /* (|x|<1)**-,+inf = inf,0 */
if (iy < 0)
fz = -fy;
else
fz = zero;
}
return (fz);
} else if (jy == 0x3f800000) { /* y is +-1 */
if (iy < 0)
fx = one / fx; /* y is -1 */
return (fx);
} else if (iy == 0x40000000) { /* y is 2 */
return (fx * fx);
} else if (iy == 0x3f000000) { /* y is 0.5 */
if (jx != 0 && jx != 0x7f800000)
return (sqrtf(x));
}
}
/* special value of x */
if ((jx & ~0x7f800000) == 0) {
if (jx == 0x7f800000 || jx == 0 || jx == 0x3f800000) {
/* x is +-0,+-inf,-1; set fz = |x|**y */
*(int *)&fz = jx;
if (iy < 0)
fz = one / fz;
if (ix < 0) {
if (jx == 0x3f800000 && yisint == 0) {
/* (-1)**non-int is NaN */
fz = zero;
fz /= fz;
} else if (yisint == 1) {
/* (x<0)**odd = -(|x|**odd) */
fz = -fz;
}
}
return (fz);
}
}
/* (x<0)**(non-int) is NaN */
if (ix < 0 && yisint == 0) {
fz = zero;
return (fz / fz);
}
/*
* compute exp(y*log(|x|))
* fx = *(float *) &jx;
* fz = (float) exp(((double) fy) * log((double) fx));
*/
{
double dx, dy, dz, ds;
int *px = (int *)&dx, *pz = (int *)&dz, i, n, m;
#if defined(__i386) && !defined(__amd64)
int rp = __swapRP(fp_extended);
#endif
fx = *(float *)&jx;
dx = (double)fx;
/* compute log(x)/ln2 */
i = px[HIWORD] + 0x4000;
n = (i >> 20) - 0x3ff;
pz[HIWORD] = i & 0xffff8000;
pz[LOWORD] = 0;
ds = (dx - dz) / (dx + dz);
i = (i >> 15) & 0x1f;
dz = ds * ds;
dy = invln2 * (TBL[i] + ds * (A0 + dz * A1));
if (n == 0)
dz = (double)fy * dy;
else
dz = (double)fy * (dy + (double)n);
/* compute exp2(dz=y*ln(x)) */
i = pz[HIWORD];
if ((i & ~0x80000000) >= 0x40640000) { /* |z| >= 160.0 */
fz = (i > 0)? huge : tiny;
if (ix < 0 && yisint == 1)
fz *= -fz; /* (-ve)**(odd int) */
else
fz *= fz;
#if defined(__i386) && !defined(__amd64)
if (rp != fp_extended)
(void) __swapRP(rp);
#endif
return (fz);
}
n = (int)(d32 * dz + (i > 0 ? dhalf : -dhalf));
i = n & 0x1f;
m = n >> 5;
dy = ln2 * (dz - d1_32 * (double)n);
dx = S[i] * (done - (dtwo * dy) / (dy * (done - dy * t1) - t0));
if (m != 0)
px[HIWORD] += m << 20;
fz = (float)dx;
#if defined(__i386) && !defined(__amd64)
if (rp != fp_extended)
(void) __swapRP(rp);
#endif
}
/* end of computing exp(y*log(x)) */
if (ix < 0 && yisint == 1)
fz = -fz; /* (-ve)**(odd int) */
return (fz);
}