add fdlibm

git-svn-id: http://svn2.nishi.boats/svn/milsko/trunk@557 b9cfdab3-6d41-4d17-bbe4-086880011989

external/fdlibm/k_sin.c

@@ -0,0 +1,67 @@
+
+/* @(#)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.
+ * ====================================================
+ */
+
+/* __fdlibm_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"
+
+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 __fdlibm_kernel_sin(double x, double y, int iy) {
+	double z, r, v;
+	int    ix;
+	ix = __HI(x) & 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);
+}