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Diffstat (limited to 'libm/src/e_asin.c')
| -rw-r--r-- | libm/src/e_asin.c | 113 |
1 files changed, 0 insertions, 113 deletions
diff --git a/libm/src/e_asin.c b/libm/src/e_asin.c deleted file mode 100644 index 1ba7026..0000000 --- a/libm/src/e_asin.c +++ /dev/null @@ -1,113 +0,0 @@ - -/* @(#)e_asin.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#ifndef lint -static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_asin.c,v 1.11 2005/02/04 18:26:05 das Exp $"; -#endif - -/* __ieee754_asin(x) - * Method : - * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... - * we approximate asin(x) on [0,0.5] by - * asin(x) = x + x*x^2*R(x^2) - * where - * R(x^2) is a rational approximation of (asin(x)-x)/x^3 - * and its remez error is bounded by - * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) - * - * For x in [0.5,1] - * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) - * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; - * then for x>0.98 - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) - * For x<=0.98, let pio4_hi = pio2_hi/2, then - * f = hi part of s; - * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) - * and - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) - * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - */ - - -#include "math.h" -#include "math_private.h" - -static const double -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -huge = 1.000e+300, -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ - /* coefficient for R(x^2) */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ - -double -__ieee754_asin(double x) -{ - double t=0.0,w,p,q,c,r,s; - int32_t hx,ix; - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>= 0x3ff00000) { /* |x|>= 1 */ - u_int32_t lx; - GET_LOW_WORD(lx,x); - if(((ix-0x3ff00000)|lx)==0) - /* asin(1)=+-pi/2 with inexact */ - return x*pio2_hi+x*pio2_lo; - return (x-x)/(x-x); /* asin(|x|>1) is NaN */ - } else if (ix<0x3fe00000) { /* |x|<0.5 */ - if(ix<0x3e400000) { /* if |x| < 2**-27 */ - if(huge+x>one) return x;/* return x with inexact if x!=0*/ - } else - t = x*x; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - w = p/q; - return x+x*w; - } - /* 1> |x|>= 0.5 */ - w = one-fabs(x); - t = w*0.5; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - s = sqrt(t); - if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ - w = p/q; - t = pio2_hi-(2.0*(s+s*w)-pio2_lo); - } else { - w = s; - SET_LOW_WORD(w,0); - c = (t-w*w)/(s+w); - r = p/q; - p = 2.0*s*r-(pio2_lo-2.0*c); - q = pio4_hi-2.0*w; - t = pio4_hi-(p-q); - } - if(hx>0) return t; else return -t; -} |