J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point.  This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code.  After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by:	jkh
Submitted by:	jtc

1 files changed, 111 insertions, 0 deletions

diff --git a/lib/msun/src/e_acos.c b/lib/msun/src/e_acos.c
new file mode 100644
index 0000000..0958a32
--- /dev/null
+++ b/lib/msun/src/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.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_acos.c,v 1.6 1994/08/18 23:04:51 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: 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 = 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 = 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);
+	}
+}