1 2 /* @(#)e_acos.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* __ieee754_acos(x) 15 * Method : 16 * acos(x) = pi/2 - ieee_asin(x) 17 * acos(-x) = pi/2 + ieee_asin(x) 18 * For |x|<=0.5 19 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 20 * For x>0.5 21 * acos(x) = pi/2 - (pi/2 - 2asin(ieee_sqrt((1-x)/2))) 22 * = 2asin(ieee_sqrt((1-x)/2)) 23 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=ieee_sqrt(z) 24 * = 2f + (2c + 2s*z*R(z)) 25 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 26 * for f so that f+c ~ ieee_sqrt(z). 27 * For x<-0.5 28 * acos(x) = pi - 2asin(ieee_sqrt((1-|x|)/2)) 29 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=ieee_sqrt(z) 30 * 31 * Special cases: 32 * if x is NaN, return x itself; 33 * if |x|>1, return NaN with invalid signal. 34 * 35 * Function needed: sqrt 36 */ 37 38 #include "fdlibm.h" 39 40 #ifdef __STDC__ 41 static const double 42 #else 43 static double 44 #endif 45 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 46 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 47 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ 48 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ 49 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 50 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 51 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 52 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 53 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 54 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 55 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 56 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 57 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 58 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 59 60 #ifdef __STDC__ __ieee754_acos(double x)61 double __ieee754_acos(double x) 62 #else 63 double __ieee754_acos(x) 64 double x; 65 #endif 66 { 67 double z,p,q,r,w,s,c,df; 68 int hx,ix; 69 hx = __HI(x); 70 ix = hx&0x7fffffff; 71 if(ix>=0x3ff00000) { /* |x| >= 1 */ 72 if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */ 73 if(hx>0) return 0.0; /* ieee_acos(1) = 0 */ 74 else return pi+2.0*pio2_lo; /* ieee_acos(-1)= pi */ 75 } 76 return (x-x)/(x-x); /* ieee_acos(|x|>1) is NaN */ 77 } 78 if(ix<0x3fe00000) { /* |x| < 0.5 */ 79 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 80 z = x*x; 81 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 82 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 83 r = p/q; 84 return pio2_hi - (x - (pio2_lo-x*r)); 85 } else if (hx<0) { /* x < -0.5 */ 86 z = (one+x)*0.5; 87 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 88 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 89 s = ieee_sqrt(z); 90 r = p/q; 91 w = r*s-pio2_lo; 92 return pi - 2.0*(s+w); 93 } else { /* x > 0.5 */ 94 z = (one-x)*0.5; 95 s = ieee_sqrt(z); 96 df = s; 97 __LO(df) = 0; 98 c = (z-df*df)/(s+df); 99 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 100 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 101 r = p/q; 102 w = r*s+c; 103 return 2.0*(df+w); 104 } 105 } 106