root/usr/src/lib/libm/common/R/powf.c
/*
 * 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);
}