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, 139 insertions, 0 deletions

diff --git a/lib/msun/src/s_atan.c b/lib/msun/src/s_atan.c
new file mode 100644
index 0000000..dd79665
--- /dev/null
+++ b/lib/msun/src/s_atan.c
@@ -0,0 +1,139 @@
+/* @(#)s_atan.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: s_atan.c,v 1.6 1994/08/18 23:06:23 jtc Exp $";
+#endif
+
+/* atan(x)
+ * Method
+ *   1. Reduce x to positive by atan(x) = -atan(-x).
+ *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ *      is further reduced to one of the following intervals and the
+ *      arctangent of t is evaluated by the corresponding formula:
+ *
+ *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following 
+ * constants. The decimal values may be used, provided that the 
+ * compiler will convert from decimal to binary accurately enough 
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double atanhi[] = {
+#else
+static double atanhi[] = {
+#endif
+  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+};
+
+#ifdef __STDC__
+static const double atanlo[] = {
+#else
+static double atanlo[] = {
+#endif
+  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+};
+
+#ifdef __STDC__
+static const double aT[] = {
+#else
+static double aT[] = {
+#endif
+  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+};
+
+#ifdef __STDC__
+	static const double 
+#else
+	static double 
+#endif
+one   = 1.0,
+huge   = 1.0e300;
+
+#ifdef __STDC__
+	double atan(double x)
+#else
+	double atan(x)
+	double x;
+#endif
+{
+	double w,s1,s2,z;
+	int32_t ix,hx,id;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
+	    u_int32_t low;
+	    GET_LOW_WORD(low,x);
+	    if(ix>0x7ff00000||
+		(ix==0x7ff00000&&(low!=0)))
+		return x+x;		/* NaN */
+	    if(hx>0) return  atanhi[3]+atanlo[3];
+	    else     return -atanhi[3]-atanlo[3];
+	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
+	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
+		if(huge+x>one) return x;	/* raise inexact */
+	    }
+	    id = -1;
+	} else {
+	x = fabs(x);
+	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
+	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
+		id = 0; x = (2.0*x-one)/(2.0+x); 
+	    } else {			/* 11/16<=|x|< 19/16 */
+		id = 1; x  = (x-one)/(x+one); 
+	    }
+	} else {
+	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
+		id = 2; x  = (x-1.5)/(one+1.5*x);
+	    } else {			/* 2.4375 <= |x| < 2^66 */
+		id = 3; x  = -1.0/x;
+	    }
+	}}
+    /* end of argument reduction */
+	z = x*x;
+	w = z*z;
+    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+	if (id<0) return x - x*(s1+s2);
+	else {
+	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+	    return (hx<0)? -z:z;
+	}
+}