about summary refs log tree commit diff
path: root/sysdeps/libm-ieee754/k_tan.c
diff options
context:
space:
mode:
authorRoland McGrath <roland@gnu.org>1996-03-05 21:41:30 +0000
committerRoland McGrath <roland@gnu.org>1996-03-05 21:41:30 +0000
commitf7eac6eb504f4baf13dbb4d26717942df050ebe6 (patch)
tree95ff129c06c7f6f246a5e2bfa489ba6382659d19 /sysdeps/libm-ieee754/k_tan.c
parent1521668f2afae1dc2ef5d7ffaeb84353b36874dd (diff)
downloadglibc-f7eac6eb504f4baf13dbb4d26717942df050ebe6.tar.gz
glibc-f7eac6eb504f4baf13dbb4d26717942df050ebe6.tar.xz
glibc-f7eac6eb504f4baf13dbb4d26717942df050ebe6.zip
Mon Mar 4 20:54:40 1996 Andreas Schwab <schwab@issan.informatik.uni-dortmund.de>
	* Makeconfig ($(common-objpfx)config.make): Depend on config.h.in.


Mon Mar  4 17:35:09 1996  Roland McGrath  <roland@charlie-brown.gnu.ai.mit.edu>

	* hurd/catch-signal.c (hurd_safe_memmove): New function.
	(hurd_safe_copyin, hurd_safe_copyout): New functions.
	* hurd/hurd/sigpreempt.h: Declare them.

Sun Mar  3 08:43:44 1996  Roland McGrath  <roland@charlie-brown.gnu.ai.mit.edu>

	Replace math code with fdlibm from Sun as modified for netbsd by
	JT Conklin and Ian Taylor, including x86 FPU support.
	* sysdeps/libm-ieee754, sysdeps/libm-i387: New directories.
	* math/math_private.h: New file.
	* sysdeps/i386/fpu/Implies: New file.
	* sysdeps/ieee754/Implies: New file.
	* math/machine/asm.h, math/machine/endian.h: New files.
	* math/Makefile, math/math.h: Rewritten.
	* mathcalls.h, math/mathcalls.h: New file, broken out of math.h.
	* math/finite.c: File removed.
	* sysdeps/generic/Makefile [$(subdir)=math]: Frobnication removed.

	* math/test-math.c: Include errno.h and string.h.

	* sysdeps/unix/bsd/dirstream.h: File removed.
	* sysdeps/unix/bsd/readdir.c: File removed.
Diffstat (limited to 'sysdeps/libm-ieee754/k_tan.c')
-rw-r--r--sysdeps/libm-ieee754/k_tan.c131
1 files changed, 131 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/k_tan.c b/sysdeps/libm-ieee754/k_tan.c
new file mode 100644
index 0000000000..aa9c67c9d0
--- /dev/null
+++ b/sysdeps/libm-ieee754/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.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: k_tan.c,v 1.8 1995/05/10 20:46:37 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);
+	}
+}