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authorUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
committerUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
commitabfbdde177c3a7155070dda1b2cdc8292054cc26 (patch)
treee021306b596381fbf8311d2b7eb294e918ff17c8 /sysdeps/libm-ieee754/e_asin.c
parent86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff)
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Update.
Diffstat (limited to 'sysdeps/libm-ieee754/e_asin.c')
-rw-r--r--sysdeps/libm-ieee754/e_asin.c143
1 files changed, 0 insertions, 143 deletions
diff --git a/sysdeps/libm-ieee754/e_asin.c b/sysdeps/libm-ieee754/e_asin.c
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--- a/sysdeps/libm-ieee754/e_asin.c
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@@ -1,143 +0,0 @@
-/* @(#)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.
- * ====================================================
- */
-/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
-   for performance improvement on pipelined processors.
-*/
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: e_asin.c,v 1.9 1995/05/12 04:57:22 jtc 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"
-#define one qS[0]
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-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) */
-pS[] =  {1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
- -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
-  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
- -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
-  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
-  3.47933107596021167570e-05}, /* 0x3F023DE1, 0x0DFDF709 */
-qS[] = {1.0, -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
-  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
- -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
-  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,p1,p2,p3,q1,q2,z2,z4,z6;
-	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;
-#ifdef DO_NOT_USE_THIS
-		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
-#else
-		p1 = t*pS[0]; z2=t*t;
-		p2 = pS[1]+t*pS[2]; z4=z2*z2;
-		p3 = pS[3]+t*pS[4]; z6=z4*z2;
-		q1 = one+t*qS[1];
-		q2 = qS[2]+t*qS[3];
-		p = p1 + z2*p2 + z4*p3 + z6*pS[5];
-		q = q1 + z2*q2 + z4*qS[4];
-#endif
-		w = p/q;
-		return x+x*w;
-	    }
-	}
-	/* 1> |x|>= 0.5 */
-	w = one-fabs(x);
-	t = w*0.5;
-#ifdef DO_NOT_USE_THIS
-	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
-	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
-#else
-	p1 = t*pS[0]; z2=t*t;
-	p2 = pS[1]+t*pS[2]; z4=z2*z2;
-	p3 = pS[3]+t*pS[4]; z6=z4*z2;
-	q1 = one+t*qS[1];
-	q2 = qS[2]+t*qS[3];
-	p = p1 + z2*p2 + z4*p3 + z6*pS[5];
-	q = q1 + z2*q2 + z4*qS[4];
-#endif
-	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;
-}