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| Rev | Author | Line No. | Line |
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| 2 | pj | 1 | /* @(#)e_acos.c 5.1 93/09/24 */ |
| 2 | /* |
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| 3 | * ==================================================== |
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 5 | * |
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 7 | * Permission to use, copy, modify, and distribute this |
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| 8 | * software is freely granted, provided that this notice |
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| 9 | * is preserved. |
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| 10 | * ==================================================== |
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| 11 | */ |
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| 12 | |||
| 13 | #ifndef lint |
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| 14 | static char rcsid[] = "$\Id: e_acos.c,v 1.2.6.1 1997/02/23 11:02:58 joerg Exp $"; |
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| 15 | #endif |
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| 16 | |||
| 17 | /* __ieee754_acos(x) |
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| 18 | * Method : |
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| 19 | * acos(x) = pi/2 - asin(x) |
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| 20 | * acos(-x) = pi/2 + asin(x) |
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| 21 | * For |x|<=0.5 |
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| 22 | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
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| 23 | * For x>0.5 |
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| 24 | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
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| 25 | * = 2asin(sqrt((1-x)/2)) |
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| 26 | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
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| 27 | * = 2f + (2c + 2s*z*R(z)) |
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| 28 | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
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| 29 | * for f so that f+c ~ sqrt(z). |
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| 30 | * For x<-0.5 |
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| 31 | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
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| 32 | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
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| 33 | * |
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| 34 | * Special cases: |
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| 35 | * if x is NaN, return x itself; |
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| 36 | * if |x|>1, return NaN with invalid signal. |
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| 37 | * |
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| 38 | * Function needed: sqrt |
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| 39 | */ |
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| 40 | |||
| 41 | #include "math.h" |
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| 42 | #include "math_private.h" |
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| 43 | |||
| 44 | #ifdef __STDC__ |
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| 45 | static const double |
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| 46 | #else |
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| 47 | static double |
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| 48 | #endif |
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| 49 | one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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| 50 | pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
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| 51 | pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ |
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| 52 | pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ |
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| 53 | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
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| 54 | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
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| 55 | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
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| 56 | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
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| 57 | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
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| 58 | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
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| 59 | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
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| 60 | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
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| 61 | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
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| 62 | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
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| 63 | |||
| 64 | #ifdef __STDC__ |
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| 65 | double __generic___ieee754_acos(double x) |
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| 66 | #else |
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| 67 | double __generic___ieee754_acos(x) |
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| 68 | double x; |
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| 69 | #endif |
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| 70 | { |
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| 71 | double z,p,q,r,w,s,c,df; |
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| 72 | int32_t hx,ix; |
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| 73 | GET_HIGH_WORD(hx,x); |
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| 74 | ix = hx&0x7fffffff; |
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| 75 | if(ix>=0x3ff00000) { /* |x| >= 1 */ |
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| 76 | u_int32_t lx; |
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| 77 | GET_LOW_WORD(lx,x); |
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| 78 | if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ |
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| 79 | if(hx>0) return 0.0; /* acos(1) = 0 */ |
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| 80 | else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
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| 81 | } |
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| 82 | return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
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| 83 | } |
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| 84 | if(ix<0x3fe00000) { /* |x| < 0.5 */ |
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| 85 | if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
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| 86 | z = x*x; |
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| 87 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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| 88 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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| 89 | r = p/q; |
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| 90 | return pio2_hi - (x - (pio2_lo-x*r)); |
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| 91 | } else if (hx<0) { /* x < -0.5 */ |
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| 92 | z = (one+x)*0.5; |
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| 93 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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| 94 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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| 95 | s = sqrt(z); |
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| 96 | r = p/q; |
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| 97 | w = r*s-pio2_lo; |
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| 98 | return pi - 2.0*(s+w); |
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| 99 | } else { /* x > 0.5 */ |
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| 100 | z = (one-x)*0.5; |
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| 101 | s = sqrt(z); |
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| 102 | df = s; |
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| 103 | SET_LOW_WORD(df,0); |
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| 104 | c = (z-df*df)/(s+df); |
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| 105 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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| 106 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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| 107 | r = p/q; |
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| 108 | w = r*s+c; |
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| 109 | return 2.0*(df+w); |
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| 110 | } |
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| 111 | } |