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/s_cbrt.c | 77 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 src/math/s_cbrt.c

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

diff --git a/src/math/s_cbrt.c b/src/math/s_cbrt.c
new file mode 100644
index 00000000..8adcb191
--- /dev/null
+++ b/src/math/s_cbrt.c
@@ -0,0 +1,77 @@
+/* @(#)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.
+ * ====================================================
+ */
+
+#include <math.h>
+#include "math_private.h"
+
+/* cbrt(x)
+ * Return cube root of x
+ */
+static const uint32_t
+        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)
+{
+        int32_t hx;
+        double r,s,t=0.0,w;
+        uint32_t sign;
+        uint32_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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