/* * 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); }