1/* Copyright JS Foundation and other contributors, http://js.foundation 2 * 3 * Licensed under the Apache License, Version 2.0 (the "License"); 4 * you may not use this file except in compliance with the License. 5 * You may obtain a copy of the License at 6 * 7 * http://www.apache.org/licenses/LICENSE-2.0 8 * 9 * Unless required by applicable law or agreed to in writing, software 10 * distributed under the License is distributed on an "AS IS" BASIS 11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 * See the License for the specific language governing permissions and 13 * limitations under the License. 14 * 15 * This file is based on work under the following copyright and permission 16 * notice: 17 * 18 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 19 * 20 * Developed at SunSoft, a Sun Microsystems, Inc. business. 21 * Permission to use, copy, modify, and distribute this 22 * software is freely granted, provided that this notice 23 * is preserved. 24 * 25 * @(#)e_acos.c 1.3 95/01/18 26 */ 27 28#include "jerry-libm-internal.h" 29 30/* acos(x) 31 * 32 * Method: 33 * acos(x) = pi/2 - asin(x) 34 * acos(-x) = pi/2 + asin(x) 35 * For |x|<=0.5 36 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 37 * For x>0.5 38 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 39 * = 2asin(sqrt((1-x)/2)) 40 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 41 * = 2f + (2c + 2s*z*R(z)) 42 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 43 * for f so that f+c ~ sqrt(z). 44 * For x<-0.5 45 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 46 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 47 * 48 * Special cases: 49 * if x is NaN, return x itself; 50 * if |x|>1, return NaN with invalid signal. 51 * 52 * Function needed: sqrt 53 */ 54 55#define one 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */ 56#define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */ 57#define pio2_hi 1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */ 58#define pio2_lo 6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */ 59#define pS0 1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */ 60#define pS1 -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */ 61#define pS2 2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */ 62#define pS3 -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */ 63#define pS4 7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */ 64#define pS5 3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */ 65#define qS1 -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */ 66#define qS2 2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */ 67#define qS3 -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */ 68#define qS4 7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */ 69 70double 71acos (double x) 72{ 73 double z, p, q, r, w, s, c; 74 int hx, ix; 75 76 hx = __HI (x); 77 ix = hx & 0x7fffffff; 78 if (ix >= 0x3ff00000) /* |x| >= 1 */ 79 { 80 if (((ix - 0x3ff00000) | __LO (x)) == 0) /* |x| == 1 */ 81 { 82 if (hx > 0) /* acos(1) = 0 */ 83 { 84 return 0.0; 85 } 86 else /* acos(-1) = pi */ 87 { 88 return pi + 2.0 * pio2_lo; 89 } 90 } 91 return NAN; /* acos(|x|>1) is NaN */ 92 } 93 if (ix < 0x3fe00000) /* |x| < 0.5 */ 94 { 95 if (ix <= 0x3c600000) /* if |x| < 2**-57 */ 96 { 97 return pio2_hi + pio2_lo; 98 } 99 z = x * x; 100 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); 101 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 102 r = p / q; 103 return pio2_hi - (x - (pio2_lo - x * r)); 104 } 105 else if (hx < 0) /* x < -0.5 */ 106 { 107 z = (one + x) * 0.5; 108 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); 109 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 110 s = sqrt (z); 111 r = p / q; 112 w = r * s - pio2_lo; 113 return pi - 2.0 * (s + w); 114 } 115 else /* x > 0.5 */ 116 { 117 double_accessor df; 118 z = (one - x) * 0.5; 119 s = sqrt (z); 120 df.dbl = s; 121 df.as_int.lo = 0; 122 c = (z - df.dbl * df.dbl) / (s + df.dbl); 123 p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); 124 q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); 125 r = p / q; 126 w = r * s + c; 127 return 2.0 * (df.dbl + w); 128 } 129} /* acos */ 130 131#undef one 132#undef pi 133#undef pio2_hi 134#undef pio2_lo 135#undef pS0 136#undef pS1 137#undef pS2 138#undef pS3 139#undef pS4 140#undef pS5 141#undef qS1 142#undef qS2 143#undef qS3 144#undef qS4 145