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 /* acos(x) 14 * Method : 15 * acos(x) = pi/2 - asin(x) 16 * acos(-x) = pi/2 + asin(x) 17 * For |x|<=0.5 18 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 19 * For x>0.5 20 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 21 * = 2asin(sqrt((1-x)/2)) 22 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 23 * = 2f + (2c + 2s*z*R(z)) 24 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 25 * for f so that f+c ~ sqrt(z). 26 * For x<-0.5 27 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 28 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 29 * 30 * Special cases: 31 * if x is NaN, return x itself; 32 * if |x|>1, return NaN with invalid signal. 33 * 34 * Function needed: sqrt 35 */ 36 37 #include <float.h> 38 #include <math.h> 39 40 #include "math_private.h" 41 42 static const double 43 one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 44 pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 45 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ 46 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ 47 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 48 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 49 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 50 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 51 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 52 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 53 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 54 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 55 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 56 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 57 58 double 59 acos(double x) 60 { 61 double z,p,q,r,w,s,c,df; 62 int32_t hx,ix; 63 GET_HIGH_WORD(hx,x); 64 ix = hx&0x7fffffff; 65 if(ix>=0x3ff00000) { /* |x| >= 1 */ 66 u_int32_t lx; 67 GET_LOW_WORD(lx,x); 68 if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 69 if(hx>0) return 0.0; /* acos(1) = 0 */ 70 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 71 } 72 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 73 } 74 if(ix<0x3fe00000) { /* |x| < 0.5 */ 75 if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 76 z = x*x; 77 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 78 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 79 r = p/q; 80 return pio2_hi - (x - (pio2_lo-x*r)); 81 } else if (hx<0) { /* x < -0.5 */ 82 z = (one+x)*0.5; 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 s = sqrt(z); 86 r = p/q; 87 w = r*s-pio2_lo; 88 return pi - 2.0*(s+w); 89 } else { /* x > 0.5 */ 90 z = (one-x)*0.5; 91 s = sqrt(z); 92 df = s; 93 SET_LOW_WORD(df,0); 94 c = (z-df*df)/(s+df); 95 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 96 q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 97 r = p/q; 98 w = r*s+c; 99 return 2.0*(df+w); 100 } 101 } 102 103 #if LDBL_MANT_DIG == DBL_MANT_DIG 104 __strong_alias(acosl, acos); 105 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 106