/* * 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 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ #pragma weak __acos = acos /* INDENT OFF */ /* * acos(x) * Method : * acos(x) = pi/2 - asin(x) * acos(-x) = pi/2 + asin(x) * For |x|<=0.5 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) * For x>0.5 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) * = 2asin(sqrt((1-x)/2)) * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) * = 2f + (2c + 2s*z*R(z)) * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term * for f so that f+c ~ sqrt(z). * For x<-0.5 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) * * Special cases: * if x is NaN, return x itself; * if |x|>1, return NaN with invalid signal. * * Function needed: sqrt */ /* INDENT ON */ #include "libm_protos.h" /* _SVID_libm_error */ #include "libm_macros.h" #include /* INDENT OFF */ static const double xxx[] = { /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ /* pi */ 3.14159265358979311600e+00, /* 400921FB, 54442D18 */ /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */ /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */ /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */ /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */ /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */ /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */ /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */ /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */ /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */ /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */ /* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */ /* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */ }; #define one xxx[0] #define pi xxx[1] #define pio2_hi xxx[2] #define pio2_lo xxx[3] #define pS0 xxx[4] #define pS1 xxx[5] #define pS2 xxx[6] #define pS3 xxx[7] #define pS4 xxx[8] #define pS5 xxx[9] #define qS1 xxx[10] #define qS2 xxx[11] #define qS3 xxx[12] #define qS4 xxx[13] /* INDENT ON */ double acos(double x) { double z, p, q, r, w, s, c, df; int hx, ix; hx = ((int *) &x)[HIWORD]; ix = hx & 0x7fffffff; if (ix >= 0x3ff00000) { /* |x| >= 1 */ if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) { /* |x| == 1 */ if (hx > 0) /* acos(1) = 0 */ return (0.0); else /* acos(-1) = pi */ return (pi + 2.0 * pio2_lo); } else if (isnan(x)) #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) return (ix >= 0x7ff80000 ? x : (x - x) / (x - x)); /* assumes sparc-like QNaN */ #else return (x - x) / (x - x); /* acos(|x|>1) is NaN */ #endif else return (_SVID_libm_err(x, x, 1)); } if (ix < 0x3fe00000) { /* |x| < 0.5 */ if (ix <= 0x3c600000) return (pio2_hi + pio2_lo); /* if |x| < 2**-57 */ z = x * x; p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); r = p / q; return (pio2_hi - (x - (pio2_lo - x * r))); } else if (hx < 0) { /* x < -0.5 */ z = (one + x) * 0.5; p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); s = sqrt(z); r = p / q; w = r * s - pio2_lo; return (pi - 2.0 * (s + w)); } else { /* x > 0.5 */ z = (one - x) * 0.5; s = sqrt(z); df = s; ((int *) &df)[LOWORD] = 0; c = (z - df * df) / (s + df); p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); r = p / q; w = r * s + c; return (2.0 * (df + w)); } }