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

1 files changed, 111 insertions, 0 deletions

diff --git a/libm/e_acos.c b/libm/e_acos.c
new file mode 100644
index 000000000..78bdae9f8
--- /dev/null
+++ b/libm/e_acos.c
@@ -0,0 +1,111 @@
+/* @(#)e_acos.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_acos.c,v 1.9 1995/05/12 04:57:13 jtc Exp $";
+#endif
+
+/* __ieee754_acos(x)
+ * Method :                  
+ *	acos(x)  = pi/2 - asin(x)
+ *	acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
+ * For x>0.5
+ * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ *		= 2asin(sqrt((1-x)/2))  
+ *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
+ *		= 2f + (2c + 2s*z*R(z))
+ *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ *     for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ *	if x is NaN, return x itself;
+ *	if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: __ieee754_sqrt
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+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_acos(double x)
+#else
+	double __ieee754_acos(x)
+	double x;
+#endif
+{
+	double z,p,q,r,w,s,c,df;
+	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) {	/* |x|==1 */
+		if(hx>0) return 0.0;		/* acos(1) = 0  */
+		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
+	    }
+	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
+	}
+	if(ix<0x3fe00000) {	/* |x| < 0.5 */
+	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+	    z = x*x;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    return pio2_hi - (x - (pio2_lo-x*r));
+	} else  if (hx<0) {		/* x < -0.5 */
+	    z = (one+x)*0.5;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    s = __ieee754_sqrt(z);
+	    r = p/q;
+	    w = r*s-pio2_lo;
+	    return pi - 2.0*(s+w);
+	} else {			/* x > 0.5 */
+	    z = (one-x)*0.5;
+	    s = __ieee754_sqrt(z);
+	    df = s;
+	    SET_LOW_WORD(df,0);
+	    c  = (z-df*df)/(s+df);
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    w = r*s+c;
+	    return 2.0*(df+w);
+	}
+}