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, 131 insertions, 0 deletions

diff --git a/lib/msun/src/k_tan.c b/lib/msun/src/k_tan.c
new file mode 100644
index 0000000..27abc1c
--- /dev/null
+++ b/lib/msun/src/k_tan.c
@@ -0,0 +1,131 @@
+/* @(#)k_tan.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: k_tan.c,v 1.6 1994/08/18 23:06:16 jtc Exp $";
+#endif
+
+/* __kernel_tan( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or 
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ *	1. Since tan(-x) = -tan(x), we need only to consider positive x. 
+ *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
+ *	3. tan(x) is approximated by a odd polynomial of degree 27 on
+ *	   [0,0.67434]
+ *		  	         3             27
+ *	   	tan(x) ~ x + T1*x + ... + T13*x
+ *	   where
+ *	
+ * 	        |tan(x)         2     4            26   |     -59.2
+ * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
+ * 	        |  x 					| 
+ * 
+ *	   Note: tan(x+y) = tan(x) + tan'(x)*y
+ *		          ~ tan(x) + (1+x*x)*y
+ *	   Therefore, for better accuracy in computing tan(x+y), let 
+ *		     3      2      2       2       2
+ *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+ *	   then
+ *		 		    3    2
+ *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
+ *
+ *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
+ *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include "math.h"
+#include "math_private.h"
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
+T[] =  {
+  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
+  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
+  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
+  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
+  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
+  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
+  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
+  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
+  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
+  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
+  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
+ -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
+  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
+};
+
+#ifdef __STDC__
+	double __kernel_tan(double x, double y, int iy)
+#else
+	double __kernel_tan(x, y, iy)
+	double x,y; int iy;
+#endif
+{
+	double z,r,v,w,s;
+	int32_t ix,hx;
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;	/* high word of |x| */
+	if(ix<0x3e300000)			/* x < 2**-28 */
+	    {if((int)x==0) {			/* generate inexact */
+	        u_int32_t low;
+		GET_LOW_WORD(low,x);
+		if(((ix|low)|(iy+1))==0) return one/fabs(x);
+		else return (iy==1)? x: -one/x;
+	    }
+	    }
+	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */
+	    if(hx<0) {x = -x; y = -y;}
+	    z = pio4-x;
+	    w = pio4lo-y;
+	    x = z+w; y = 0.0;
+	}
+	z	=  x*x;
+	w 	=  z*z;
+    /* Break x^5*(T[1]+x^2*T[2]+...) into
+     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+     */
+	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
+	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
+	s = z*x;
+	r = y + z*(s*(r+v)+y);
+	r += T[0]*s;
+	w = x+r;
+	if(ix>=0x3FE59428) {
+	    v = (double)iy;
+	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
+	}
+	if(iy==1) return w;
+	else {		/* if allow error up to 2 ulp, 
+			   simply return -1.0/(x+r) here */
+     /*  compute -1.0/(x+r) accurately */
+	    double a,t;
+	    z  = w;
+	    SET_LOW_WORD(z,0);
+	    v  = r-(z - x); 	/* z+v = r+x */
+	    t = a  = -1.0/w;	/* a = -1.0/w */
+	    SET_LOW_WORD(t,0);
+	    s  = 1.0+t*z;
+	    return t+a*(s+t*v);
+	}
+}