From 0b44a0315b47dd8eced9f3b7f31580cf14bbfc01 Mon Sep 17 00:00:00 2001
From: Rich Felker <dalias@aerifal.cx>
Date: Sat, 12 Feb 2011 00:22:29 -0500
Subject: initial check-in, version 0.5.0

---
 src/math/k_cos.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 src/math/k_cos.c

(limited to 'src/math/k_cos.c')

diff --git a/src/math/k_cos.c b/src/math/k_cos.c
new file mode 100644
index 00000000..22e9841e
--- /dev/null
+++ b/src/math/k_cos.c
@@ -0,0 +1,85 @@
+
+/* @(#)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.
+ * ====================================================
+ */
+
+/*
+ * __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 when x > 0.3, let qx = |x|/4 with
+ *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
+ *         Then
+ *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
+ *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
+ *         magnitude of the latter is at least a quarter of x*x/2,
+ *         thus, reducing the rounding error in the subtraction.
+ */
+
+#include <math.h>
+#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 a,hz,z,r,qx;
+        int32_t ix;
+        GET_HIGH_WORD(ix,x);
+        ix &= 0x7fffffff;                       /* ix = |x|'s high word*/
+        if(ix<0x3e400000) {                     /* if x < 2**27 */
+            if(((int)x)==0) return one;         /* generate inexact */
+        }
+        z  = x*x;
+        r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
+        if(ix < 0x3FD33333)                     /* if |x| < 0.3 */ 
+            return one - (0.5*z - (z*r - x*y));
+        else {
+            if(ix > 0x3fe90000) {               /* x > 0.78125 */
+                qx = 0.28125;
+            } else {
+                INSERT_WORDS(qx,ix-0x00200000,0);       /* x/4 */
+            }
+            hz = 0.5*z-qx;
+            a  = one-qx;
+            return a - (hz - (z*r-x*y));
+        }
+}
-- 
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