From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 22 Nov 2001 14:04:29 +0000
Subject: Totally rework the math library, this time based on the MacOs X math
 library (which is itself based on the math lib from FreeBSD).  -Erik

---
 libm/e_asin.c | 120 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 120 insertions(+)
 create mode 100644 libm/e_asin.c

(limited to 'libm/e_asin.c')

diff --git a/libm/e_asin.c b/libm/e_asin.c
new file mode 100644
index 000000000..b62a1c991
--- /dev/null
+++ b/libm/e_asin.c
@@ -0,0 +1,120 @@
+/* @(#)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.
+ * ====================================================
+ */
+
+#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"
+
+#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 */
+	    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 = __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;    
+}
-- 
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