1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak __acos = acos 31 32 /* INDENT OFF */ 33 /* 34 * acos(x) 35 * Method : 36 * acos(x) = pi/2 - asin(x) 37 * acos(-x) = pi/2 + asin(x) 38 * For |x|<=0.5 39 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 40 * For x>0.5 41 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 42 * = 2asin(sqrt((1-x)/2)) 43 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 44 * = 2f + (2c + 2s*z*R(z)) 45 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 46 * for f so that f+c ~ sqrt(z). 47 * For x<-0.5 48 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 49 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 50 * 51 * Special cases: 52 * if x is NaN, return x itself; 53 * if |x|>1, return NaN with invalid signal. 54 * 55 * Function needed: sqrt 56 */ 57 /* INDENT ON */ 58 59 #include "libm_protos.h" /* _SVID_libm_error */ 60 #include "libm_macros.h" 61 #include <math.h> 62 63 /* INDENT OFF */ 64 static const double xxx[] = { 65 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ 66 /* pi */ 3.14159265358979311600e+00, /* 400921FB, 54442D18 */ 67 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */ 68 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */ 69 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */ 70 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */ 71 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */ 72 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */ 73 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */ 74 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */ 75 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */ 76 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */ 77 /* qS3 */ -6.88283971605453293030e-01, /* BFE6066C, 1B8D0159 */ 78 /* qS4 */ 7.70381505559019352791e-02 /* 3FB3B8C5, B12E9282 */ 79 }; 80 #define one xxx[0] 81 #define pi xxx[1] 82 #define pio2_hi xxx[2] 83 #define pio2_lo xxx[3] 84 #define pS0 xxx[4] 85 #define pS1 xxx[5] 86 #define pS2 xxx[6] 87 #define pS3 xxx[7] 88 #define pS4 xxx[8] 89 #define pS5 xxx[9] 90 #define qS1 xxx[10] 91 #define qS2 xxx[11] 92 #define qS3 xxx[12] 93 #define qS4 xxx[13] 94 /* INDENT ON */ 95 96 double 97 acos(double x) { 98 double z, p, q, r, w, s, c, df; 99 int hx, ix; 100 101 hx = ((int *) &x)[HIWORD]; 102 ix = hx & 0x7fffffff; 103 if (ix >= 0x3ff00000) { /* |x| >= 1 */ 104 if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) { 105 /* |x| == 1 */ 106 if (hx > 0) /* acos(1) = 0 */ 107 return (0.0); 108 else /* acos(-1) = pi */ 109 return (pi + 2.0 * pio2_lo); 110 } else if (isnan(x)) 111 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 112 return (ix >= 0x7ff80000 ? x : (x - x) / (x - x)); 113 /* assumes sparc-like QNaN */ 114 #else 115 return (x - x) / (x - x); /* acos(|x|>1) is NaN */ 116 #endif 117 else 118 return (_SVID_libm_err(x, x, 1)); 119 } 120 if (ix < 0x3fe00000) { /* |x| < 0.5 */ 121 if (ix <= 0x3c600000) 122 return (pio2_hi + pio2_lo); /* if |x| < 2**-57 */ 123 z = x * x; 124 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + 125 z * (pS4 + z * pS5))))); 126 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 127 r = p / q; 128 return (pio2_hi - (x - (pio2_lo - x * r))); 129 } else if (hx < 0) { 130 /* x < -0.5 */ 131 z = (one + x) * 0.5; 132 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + 133 z * (pS4 + z * pS5))))); 134 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 135 s = sqrt(z); 136 r = p / q; 137 w = r * s - pio2_lo; 138 return (pi - 2.0 * (s + w)); 139 } else { 140 /* x > 0.5 */ 141 z = (one - x) * 0.5; 142 s = sqrt(z); 143 df = s; 144 ((int *) &df)[LOWORD] = 0; 145 c = (z - df * df) / (s + df); 146 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + 147 z * (pS4 + z * pS5))))); 148 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 149 r = p / q; 150 w = r * s + c; 151 return (2.0 * (df + w)); 152 } 153 } 154