From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 22 Nov 2001 14:04:29 +0000
Subject: Totally rework the math library, this time based on the MacOs X math
 library (which is itself based on the math lib from FreeBSD).  -Erik

---
 libm/s_cbrt.c | 93 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 93 insertions(+)
 create mode 100644 libm/s_cbrt.c

(limited to 'libm/s_cbrt.c')

diff --git a/libm/s_cbrt.c b/libm/s_cbrt.c
new file mode 100644
index 000000000..ef8e2e209
--- /dev/null
+++ b/libm/s_cbrt.c
@@ -0,0 +1,93 @@
+/* @(#)s_cbrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: s_cbrt.c,v 1.8 1995/05/10 20:46:49 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* cbrt(x)
+ * Return cube root of x
+ */
+#ifdef __STDC__
+static const u_int32_t
+#else
+static u_int32_t
+#endif
+	B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
+	B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+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 */
+
+#ifdef __STDC__
+	double cbrt(double x) 
+#else
+	double cbrt(x) 
+	double x;
+#endif
+{
+	int32_t	hx;
+	double r,s,t=0.0,w;
+	u_int32_t sign;
+	u_int32_t high,low;
+
+	GET_HIGH_WORD(hx,x);
+	sign=hx&0x80000000; 		/* sign= sign(x) */
+	hx  ^=sign;
+	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
+	GET_LOW_WORD(low,x);
+	if((hx|low)==0) 
+	    return(x);		/* cbrt(0) is itself */
+
+	SET_HIGH_WORD(x,hx);	/* x <- |x| */
+    /* rough cbrt to 5 bits */
+	if(hx<0x00100000) 		/* subnormal number */
+	  {SET_HIGH_WORD(t,0x43500000);	/* set t= 2**54 */
+	   t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
+	  }
+	else
+	  SET_HIGH_WORD(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) */ 
+	GET_HIGH_WORD(high,t);
+	INSERT_WORDS(t,high+0x00000001,0);
+
+
+    /* 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 */
+	GET_HIGH_WORD(high,t);
+	SET_HIGH_WORD(t,high|sign);
+	return(t);
+}
-- 
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