From be22b15ae2ff8d7fe06b6e14fddf0c5b444a95da Mon Sep 17 00:00:00 2001
From: rgrimes <rgrimes@FreeBSD.org>
Date: Fri, 27 May 1994 05:00:24 +0000
Subject: BSD 4.4 Lite Lib Sources

---
 lib/libm/ieee/cbrt.c | 120 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 120 insertions(+)
 create mode 100644 lib/libm/ieee/cbrt.c

(limited to 'lib/libm/ieee/cbrt.c')

diff --git a/lib/libm/ieee/cbrt.c b/lib/libm/ieee/cbrt.c
new file mode 100644
index 0000000..fe5fb95
--- /dev/null
+++ b/lib/libm/ieee/cbrt.c
@@ -0,0 +1,120 @@
+/*
+ * Copyright (c) 1985, 1993
+ *	The Regents of the University of California.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *	This product includes software developed by the University of
+ *	California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ *    may be used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#ifndef lint
+static char sccsid[] = "@(#)cbrt.c	8.1 (Berkeley) 6/4/93";
+#endif /* not lint */
+
+#include <sys/cdefs.h>
+
+/* kahan's cube root (53 bits IEEE double precision)
+ * for IEEE machines only
+ * coded in C by K.C. Ng, 4/30/85
+ *
+ * Accuracy:
+ *	better than 0.667 ulps according to an error analysis. Maximum
+ * error observed was 0.666 ulps in an 1,000,000 random arguments test.
+ *
+ * Warning: this code is semi machine dependent; the ordering of words in
+ * a floating point number must be known in advance. I assume that the
+ * long interger at the address of a floating point number will be the
+ * leading 32 bits of that floating point number (i.e., sign, exponent,
+ * and the 20 most significant bits).
+ * On a National machine, it has different ordering; therefore, this code 
+ * must be compiled with flag -DNATIONAL. 
+ */
+#if !defined(vax)&&!defined(tahoe)
+
+static const unsigned long
+		     B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
+	             B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
+static const double
+	    C= 19./35.,
+	    D= -864./1225.,
+	    E= 99./70.,
+	    F= 45./28.,
+	    G= 5./14.;
+
+double cbrt(x) 
+double x;
+{
+	double r,s,t=0.0,w;
+	unsigned long *px = (unsigned long *) &x,
+	              *pt = (unsigned long *) &t,
+		      mexp,sign;
+
+#ifdef national /* ordering of words in a floating points number */
+	const int n0=1,n1=0;
+#else	/* national */
+	const int n0=0,n1=1;
+#endif	/* national */
+
+	mexp=px[n0]&0x7ff00000;
+	if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */
+	if(x==0.0) return(x);		/* cbrt(0) is itself */
+
+	sign=px[n0]&0x80000000; /* sign= sign(x) */
+	px[n0] ^= sign;		/* x=|x| */
+
+
+    /* rough cbrt to 5 bits */
+	if(mexp==0) 		/* subnormal number */
+	  {pt[n0]=0x43500000; 	/* set t= 2**54 */
+	   t*=x; pt[n0]=pt[n0]/3+B2;
+	  }
+	else
+	  pt[n0]=px[n0]/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) */ 
+	pt[n1]=0; pt[n0]+=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-t is exact */
+	t=t+t*r;
+
+
+    /* retore the sign bit */
+	pt[n0] |= sign;
+	return(t);
+}
+#endif
-- 
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