add fdlibm

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

external/fdlibm/s_cbrt.c

@@ -0,0 +1,72 @@
+
+/* @(#)s_cbrt.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 "math.h"
+
+/* cbrt(x)
+ * Return cube root of x
+ */
+static const unsigned
+    B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
+    B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
+
+static const double
+    C = 5.42857142857142815906e-01,  /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
+    D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
+    E = 1.41428571428571436819e+00,  /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
+    F = 1.60714285714285720630e+00,  /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
+    G = 3.57142857142857150787e-01;  /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */
+
+double cbrt(double x) {
+	int	 hx;
+	double	 r, s, t = 0.0, w;
+	unsigned sign;
+
+	hx   = __HI(x);		/* high word of x */
+	sign = hx & 0x80000000; /* sign= sign(x) */
+	hx ^= sign;
+	if(hx >= 0x7ff00000) return (x + x); /* cbrt(NaN,INF) is itself */
+	if((hx | __LO(x)) == 0)
+		return (x); /* cbrt(0) is itself */
+
+	__HI(x) = hx;	    /* x <- |x| */
+			    /* rough cbrt to 5 bits */
+	if(hx < 0x00100000) /* subnormal number */
+	{
+		__HI(t) = 0x43500000; /* set t= 2**54 */
+		t *= x;
+		__HI(t) = __HI(t) / 3 + B2;
+	} else
+		__HI(t) = hx / 3 + B1;
+
+	/* new cbrt to 23 bits, may be implemented in single precision */
+	r = t * t / x;
+	s = C + r * t;
+	t *= G + F / (s + E + D / s);
+
+	/* chopped to 20 bits and make it larger than cbrt(x) */
+	__LO(t) = 0;
+	__HI(t) += 0x00000001;
+
+	/* one step newton iteration to 53 bits with error less than 0.667 ulps */
+	s = t * t; /* t*t is exact */
+	r = x / s;
+	w = t + t;
+	r = (r - t) / (w + r); /* r-s is exact */
+	t = t + t * r;
+
+	/* retore the sign bit */
+	__HI(t) |= sign;
+	return (t);
+}