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| Commit | Line | Data |
|---|---|---|
| 4acf9396 GCI |
1 | /* @(#)e_acos.c 5.1 93/09/24 */ |
| 2 | /* | |
| 3 | * ==================================================== | |
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
| 5 | * | |
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
| 7 | * Permission to use, copy, modify, and distribute this | |
| 8 | * software is freely granted, provided that this notice | |
| 9 | * is preserved. | |
| 10 | * ==================================================== | |
| 11 | */ | |
| 12 | ||
| 13 | #ifndef lint | |
| 14 | static char rcsid[] = "$Id: e_acos.c,v 1.4 1994/03/03 17:04:03 jtc Exp $"; | |
| 15 | #endif | |
| 16 | ||
| 17 | /* __ieee754_acos(x) | |
| 18 | * Method : | |
| 19 | * acos(x) = pi/2 - asin(x) | |
| 20 | * acos(-x) = pi/2 + asin(x) | |
| 21 | * For |x|<=0.5 | |
| 22 | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) | |
| 23 | * For x>0.5 | |
| 24 | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) | |
| 25 | * = 2asin(sqrt((1-x)/2)) | |
| 26 | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) | |
| 27 | * = 2f + (2c + 2s*z*R(z)) | |
| 28 | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term | |
| 29 | * for f so that f+c ~ sqrt(z). | |
| 30 | * For x<-0.5 | |
| 31 | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) | |
| 32 | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) | |
| 33 | * | |
| 34 | * Special cases: | |
| 35 | * if x is NaN, return x itself; | |
| 36 | * if |x|>1, return NaN with invalid signal. | |
| 37 | * | |
| 38 | * Function needed: sqrt | |
| 39 | */ | |
| 40 | ||
| 41 | #include "math.h" | |
| 42 | #include <machine/endian.h> | |
| 43 | ||
| 44 | #if BYTE_ORDER == LITTLE_ENDIAN | |
| 45 | #define n0 1 | |
| 46 | #else | |
| 47 | #define n0 0 | |
| 48 | #endif | |
| 49 | ||
| 50 | #ifdef __STDC__ | |
| 51 | static const double | |
| 52 | #else | |
| 53 | static double | |
| 54 | #endif | |
| 55 | one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ | |
| 56 | pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ | |
| 57 | pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ | |
| 58 | pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ | |
| 59 | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ | |
| 60 | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ | |
| 61 | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ | |
| 62 | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ | |
| 63 | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ | |
| 64 | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ | |
| 65 | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ | |
| 66 | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ | |
| 67 | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ | |
| 68 | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ | |
| 69 | ||
| 70 | #ifdef __STDC__ | |
| 71 | double __ieee754_acos(double x) | |
| 72 | #else | |
| 73 | double __ieee754_acos(x) | |
| 74 | double x; | |
| 75 | #endif | |
| 76 | { | |
| 77 | double z,p,q,r,w,s,c,df; | |
| 78 | int hx,ix; | |
| 79 | ||
| 80 | hx = *(n0+(int*)&x); | |
| 81 | ix = hx&0x7fffffff; | |
| 82 | if(ix>=0x3ff00000) { /* |x| >= 1 */ | |
| 83 | if(((ix-0x3ff00000)|*(1-n0+(int*)&x))==0) { /* |x|==1 */ | |
| 84 | if(hx>0) return 0.0; /* acos(1) = 0 */ | |
| 85 | else return pi+2.0*pio2_lo; /* acos(-1)= pi */ | |
| 86 | } | |
| 87 | return (x-x)/(x-x); /* acos(|x|>1) is NaN */ | |
| 88 | } | |
| 89 | if(ix<0x3fe00000) { /* |x| < 0.5 */ | |
| 90 | if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ | |
| 91 | z = x*x; | |
| 92 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
| 93 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
| 94 | r = p/q; | |
| 95 | return pio2_hi - (x - (pio2_lo-x*r)); | |
| 96 | } else if (hx<0) { /* x < -0.5 */ | |
| 97 | z = (one+x)*0.5; | |
| 98 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
| 99 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
| 100 | s = sqrt(z); | |
| 101 | r = p/q; | |
| 102 | w = r*s-pio2_lo; | |
| 103 | return pi - 2.0*(s+w); | |
| 104 | } else { /* x > 0.5 */ | |
| 105 | z = (one-x)*0.5; | |
| 106 | s = sqrt(z); | |
| 107 | df = s; | |
| 108 | *(1-n0+(int*)&df) = 0; | |
| 109 | c = (z-df*df)/(s+df); | |
| 110 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); | |
| 111 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); | |
| 112 | r = p/q; | |
| 113 | w = r*s+c; | |
| 114 | return 2.0*(df+w); | |
| 115 | } | |
| 116 | } |