+++ /dev/null
-
-/* @(#)e_asin.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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 "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-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 */
-
-#ifdef __STDC__
- double __ieee754_asin(double x)
-#else
- double __ieee754_asin(x)
- double x;
-#endif
-{
- double t,w,p,q,c,r,s;
- int32_t hx,ix;
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>= 0x3ff00000) { /* |x|>= 1 */
- uint32_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 = __ieee754_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;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
projects / msp430-gcc.git / blobdiff