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_sin.c | 68 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 src/math/k_sin.c

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

diff --git a/src/math/k_sin.c b/src/math/k_sin.c
new file mode 100644
index 00000000..9def2589
--- /dev/null
+++ b/src/math/k_sin.c
@@ -0,0 +1,68 @@
+
+/* @(#)k_sin.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_sin( x, y, iy)
+ * kernel sin 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 iy indicates whether y is 0. (if iy=0, y assume to be 0). 
+ *
+ * Algorithm
+ *      1. Since sin(-x) = -sin(x), we need only to consider positive x. 
+ *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
+ *      3. sin(x) is approximated by a polynomial of degree 13 on
+ *         [0,pi/4]
+ *                               3            13
+ *              sin(x) ~ x + S1*x + ... + S6*x
+ *         where
+ *      
+ *      |sin(x)         2     4     6     8     10     12  |     -58
+ *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
+ *      |  x                                               | 
+ * 
+ *      4. sin(x+y) = sin(x) + sin'(x')*y
+ *                  ~ sin(x) + (1-x*x/2)*y
+ *         For better accuracy, let 
+ *                   3      2      2      2      2
+ *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
+ *         then                   3    2
+ *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
+ */
+
+#include <math.h>
+#include "math_private.h"
+
+static const double
+half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
+S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
+S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
+S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
+S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
+S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
+
+double
+__kernel_sin(double x, double y, int iy)
+{
+        double z,r,v;
+        int32_t ix;
+        GET_HIGH_WORD(ix,x);
+        ix &= 0x7fffffff;                       /* high word of x */
+        if(ix<0x3e400000)                       /* |x| < 2**-27 */
+           {if((int)x==0) return x;}            /* generate inexact */
+        z       =  x*x;
+        v       =  z*x;
+        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
+        if(iy==0) return x+v*(S1+z*r);
+        else      return x-((z*(half*y-v*r)-y)-v*S1);
+}
-- 
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