Adding upstream version 115.8.0esr.upstream/115.8.0esr

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 78 insertions, 0 deletions

diff --git a/modules/fdlibm/src/k_cos.cpp b/modules/fdlibm/src/k_cos.cpp
new file mode 100644
index 0000000000..5bee28daf3
--- /dev/null
+++ b/modules/fdlibm/src/k_cos.cpp
@@ -0,0 +1,78 @@
+
+/* @(#)k_cos.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+//#include <sys/cdefs.h>
+//__FBSDID("$FreeBSD$");
+
+/*
+ * __kernel_cos( x,  y )
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x. 
+ *
+ * Algorithm
+ *	1. Since cos(-x) = cos(x), we need only to consider positive x.
+ *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ *	3. cos(x) is approximated by a polynomial of degree 14 on
+ *	   [0,pi/4]
+ *		  	                 4            14
+ *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ *	   where the remez error is
+ *	
+ * 	|              2     4     6     8     10    12     14 |     -58
+ * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
+ * 	|    					               | 
+ * 
+ * 	               4     6     8     10    12     14 
+ *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
+ *	       cos(x) ~ 1 - x*x/2 + r
+ *	   since cos(x+y) ~ cos(x) - sin(x)*y 
+ *			  ~ cos(x) - x*y,
+ *	   a correction term is necessary in cos(x) and hence
+ *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ *	   For better accuracy, rearrange to
+ *		cos(x+y) ~ w + (tmp + (r-x*y))
+ *	   where w = 1 - x*x/2 and tmp is a tiny correction term
+ *	   (1 - x*x/2 == w + tmp exactly in infinite precision).
+ *	   The exactness of w + tmp in infinite precision depends on w
+ *	   and tmp having the same precision as x.  If they have extra
+ *	   precision due to compiler bugs, then the extra precision is
+ *	   only good provided it is retained in all terms of the final
+ *	   expression for cos().  Retention happens in all cases tested
+ *	   under FreeBSD, so don't pessimize things by forcibly clipping
+ *	   any extra precision in w.
+ */
+
+#include "math_private.h"
+
+static const double
+one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
+C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
+C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
+C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
+C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
+C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+double
+__kernel_cos(double x, double y)
+{
+	double hz,z,r,w;
+
+	z  = x*x;
+	w  = z*z;
+	r  = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
+	hz = 0.5*z;
+	w  = one-hz;
+	return w + (((one-w)-hz) + (z*r-x*y));
+}