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 #include <sys/cdefs.h> 15 __FBSDID("$FreeBSD$"); 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 <float.h> 42 43 #include "math.h" 44 #include "math_private.h" 45 46 static const double 47 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 48 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 49 pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ 50 static volatile double 51 pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ 52 static const double 53 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 54 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 55 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 56 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 57 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 58 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 59 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 60 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 61 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 62 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 63 64 double 65 __ieee754_acos(double x) 66 { 67 double z,p,q,r,w,s,c,df; 68 int32_t hx,ix; 69 GET_HIGH_WORD(hx,x); 70 ix = hx&0x7fffffff; 71 if(ix>=0x3ff00000) { /* |x| >= 1 */ 72 u_int32_t lx; 73 GET_LOW_WORD(lx,x); 74 if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 75 if(hx>0) return 0.0; /* acos(1) = 0 */ 76 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 77 } 78 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 79 } 80 if(ix<0x3fe00000) { /* |x| < 0.5 */ 81 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 82 z = x*x; 83 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 84 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 85 r = p/q; 86 return pio2_hi - (x - (pio2_lo-x*r)); 87 } else if (hx<0) { /* x < -0.5 */ 88 z = (one+x)*0.5; 89 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 90 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 91 s = sqrt(z); 92 r = p/q; 93 w = r*s-pio2_lo; 94 return pi - 2.0*(s+w); 95 } else { /* x > 0.5 */ 96 z = (one-x)*0.5; 97 s = sqrt(z); 98 df = s; 99 SET_LOW_WORD(df,0); 100 c = (z-df*df)/(s+df); 101 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 102 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 103 r = p/q; 104 w = r*s+c; 105 return 2.0*(df+w); 106 } 107 } 108 109 #if LDBL_MANT_DIG == 53 110 __weak_reference(acos, acosl); 111 #endif 112