| The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 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 | #ifndef lint |
| 15 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_acos.c,v 1.10 2005/02/04 18:26:05 das Exp $"; |
| 16 | #endif |
| 17 | |
| 18 | /* __ieee754_acos(x) |
| 19 | * Method : |
| 20 | * acos(x) = pi/2 - asin(x) |
| 21 | * acos(-x) = pi/2 + asin(x) |
| 22 | * For |x|<=0.5 |
| 23 | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
| 24 | * For x>0.5 |
| 25 | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
| 26 | * = 2asin(sqrt((1-x)/2)) |
| 27 | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
| 28 | * = 2f + (2c + 2s*z*R(z)) |
| 29 | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
| 30 | * for f so that f+c ~ sqrt(z). |
| 31 | * For x<-0.5 |
| 32 | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
| 33 | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
| 34 | * |
| 35 | * Special cases: |
| 36 | * if x is NaN, return x itself; |
| 37 | * if |x|>1, return NaN with invalid signal. |
| 38 | * |
| 39 | * Function needed: sqrt |
| 40 | */ |
| 41 | |
| 42 | #include "math.h" |
| 43 | #include "math_private.h" |
| 44 | |
| 45 | static const double |
| 46 | one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| 47 | pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
| 48 | pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ |
| 49 | pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ |
| 50 | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
| 51 | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
| 52 | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
| 53 | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
| 54 | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
| 55 | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
| 56 | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
| 57 | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
| 58 | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
| 59 | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
| 60 | |
| 61 | double |
| 62 | __ieee754_acos(double x) |
| 63 | { |
| 64 | double z,p,q,r,w,s,c,df; |
| 65 | int32_t hx,ix; |
| 66 | GET_HIGH_WORD(hx,x); |
| 67 | ix = hx&0x7fffffff; |
| 68 | if(ix>=0x3ff00000) { /* |x| >= 1 */ |
| 69 | u_int32_t lx; |
| 70 | GET_LOW_WORD(lx,x); |
| 71 | if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ |
| 72 | if(hx>0) return 0.0; /* acos(1) = 0 */ |
| 73 | else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
| 74 | } |
| 75 | return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
| 76 | } |
| 77 | if(ix<0x3fe00000) { /* |x| < 0.5 */ |
| 78 | if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
| 79 | z = x*x; |
| 80 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
| 81 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
| 82 | r = p/q; |
| 83 | return pio2_hi - (x - (pio2_lo-x*r)); |
| 84 | } else if (hx<0) { /* x < -0.5 */ |
| 85 | z = (one+x)*0.5; |
| 86 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
| 87 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
| 88 | s = sqrt(z); |
| 89 | r = p/q; |
| 90 | w = r*s-pio2_lo; |
| 91 | return pi - 2.0*(s+w); |
| 92 | } else { /* x > 0.5 */ |
| 93 | z = (one-x)*0.5; |
| 94 | s = sqrt(z); |
| 95 | df = s; |
| 96 | SET_LOW_WORD(df,0); |
| 97 | c = (z-df*df)/(s+df); |
| 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 | r = p/q; |
| 101 | w = r*s+c; |
| 102 | return 2.0*(df+w); |
| 103 | } |
| 104 | } |