1 /** @file 2 Compute acos(x) using ieee FP math. 3 4 Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR> 5 This program and the accompanying materials are licensed and made available under 6 the terms and conditions of the BSD License that accompanies this distribution. 7 The full text of the license may be found at 8 http://opensource.org/licenses/bsd-license. 9 10 THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS, 11 WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED. 12 13 * ==================================================== 14 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 15 * 16 * Developed at SunPro, a Sun Microsystems, Inc. business. 17 * Permission to use, copy, modify, and distribute this 18 * software is freely granted, provided that this notice 19 * is preserved. 20 * ==================================================== 21 22 e_acos.c 5.1 93/09/24 23 NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp 24 */ 25 #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ 26 // Keep older compilers quiet about floating-point divide-by-zero 27 #pragma warning ( disable : 4723 ) 28 #endif 29 30 #include <LibConfig.h> 31 #include <sys/EfiCdefs.h> 32 33 /* __ieee754_acos(x) 34 * Method : 35 * acos(x) = pi/2 - asin(x) 36 * acos(-x) = pi/2 + asin(x) 37 * For |x|<=0.5 38 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 39 * For x>0.5 40 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 41 * = 2asin(sqrt((1-x)/2)) 42 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 43 * = 2f + (2c + 2s*z*R(z)) 44 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 45 * for f so that f+c ~ sqrt(z). 46 * For x<-0.5 47 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 48 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 49 * 50 * Special cases: 51 * if x is NaN, return x itself; 52 * if |x|>1, return NaN with invalid signal. 53 * 54 * Function needed: __ieee754_sqrt 55 */ 56 57 #include "math.h" 58 #include "math_private.h" 59 60 static const double 61 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 62 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 63 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ 64 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ 65 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 66 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 67 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 68 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 69 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 70 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 71 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 72 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 73 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 74 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 75 76 double 77 __ieee754_acos(double x) 78 { 79 double z,p,q,r,w,s,c,df; 80 int32_t hx,ix; 81 GET_HIGH_WORD(hx,x); 82 ix = hx&0x7fffffff; 83 if(ix>=0x3ff00000) { /* |x| >= 1 */ 84 u_int32_t lx; 85 86 GET_LOW_WORD(lx,x); 87 if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 88 if(hx>0) return 0.0; /* acos(1) = 0 */ 89 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 90 } 91 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 92 } 93 if(ix<0x3fe00000) { /* |x| < 0.5 */ 94 if(ix<=0x3c600000) return pio2_hi+pio2_lo; /*if|x|<2**-57*/ 95 z = x*x; 96 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 97 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 98 r = p/q; 99 return pio2_hi - (x - (pio2_lo-x*r)); 100 } 101 else if (hx<0) { /* x < -0.5 */ 102 z = (one+x)*0.5; 103 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 104 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 105 s = __ieee754_sqrt(z); 106 r = p/q; 107 w = r*s-pio2_lo; 108 return pi - 2.0*(s+w); 109 } 110 else { /* x > 0.5 */ 111 z = (one-x)*0.5; 112 s = __ieee754_sqrt(z); 113 df = s; 114 SET_LOW_WORD(df,0); 115 c = (z-df*df)/(s+df); 116 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 117 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 118 r = p/q; 119 w = r*s+c; 120 return 2.0*(df+w); 121 } 122 } 123
