1 /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 /* acos(x) 13 * Method : 14 * acos(x) = pi/2 - asin(x) 15 * acos(-x) = pi/2 + asin(x) 16 * For |x|<=0.5 17 * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 18 * For x>0.5 19 * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 20 * = 2asin(sqrt((1-x)/2)) 21 * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 22 * = 2f + (2c + 2s*z*R(z)) 23 * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 24 * for f so that f+c ~ sqrt(z). 25 * For x<-0.5 26 * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 27 * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 28 * 29 * Special cases: 30 * if x is NaN, return x itself; 31 * if |x|>1, return NaN with invalid signal. 32 * 33 * Function needed: sqrt 34 */ 35 36 #include "libm.h" 37 38 static const double 39 pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ 40 pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ 41 pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 42 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 43 pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 44 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 45 pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 46 pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 47 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 48 qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 49 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 50 qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 51 52 static double R(double z) 53 { 54 double_t p, q; 55 p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 56 q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 57 return p/q; 58 } 59 60 double acos(double x) 61 { 62 double z,w,s,c,df; 63 uint32_t hx,ix; 64 65 GET_HIGH_WORD(hx, x); 66 ix = hx & 0x7fffffff; 67 /* |x| >= 1 or nan */ 68 if (ix >= 0x3ff00000) { 69 uint32_t lx; 70 71 GET_LOW_WORD(lx,x); 72 if ((ix-0x3ff00000 | lx) == 0) { 73 /* acos(1)=0, acos(-1)=pi */ 74 if (hx >> 31) 75 return 2*pio2_hi + 0x1p-120f; 76 return 0; 77 } 78 return 0/(x-x); 79 } 80 /* |x| < 0.5 */ 81 if (ix < 0x3fe00000) { 82 if (ix <= 0x3c600000) /* |x| < 2**-57 */ 83 return pio2_hi + 0x1p-120f; 84 return pio2_hi - (x - (pio2_lo-x*R(x*x))); 85 } 86 /* x < -0.5 */ 87 if (hx >> 31) { 88 z = (1.0+x)*0.5; 89 s = sqrt(z); 90 w = R(z)*s-pio2_lo; 91 return 2*(pio2_hi - (s+w)); 92 } 93 /* x > 0.5 */ 94 z = (1.0-x)*0.5; 95 s = sqrt(z); 96 df = s; 97 SET_LOW_WORD(df,0); 98 c = (z-df*df)/(s+df); 99 w = R(z)*s+c; 100 return 2*(df+w); 101 } 102