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-rw-r--r--libm/src/s_cbrt.c92
1 files changed, 0 insertions, 92 deletions
diff --git a/libm/src/s_cbrt.c b/libm/src/s_cbrt.c
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--- a/libm/src/s_cbrt.c
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-/* @(#)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.
- * ====================================================
- *
- * Optimized by Bruce D. Evans.
- */
-
-#ifndef lint
-static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cbrt.c,v 1.10 2005/12/13 20:17:23 bde Exp $";
-#endif
-
-#include "math.h"
-#include "math_private.h"
-
-/* cbrt(x)
- * Return cube root of x
- */
-static const u_int32_t
- B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */
- B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*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;
- 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 */
-
- /*
- * Rough cbrt to 5 bits:
- * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3)
- * where e is integral and >= 0, m is real and in [0, 1), and "/" and
- * "%" are integer division and modulus with rounding towards minus
- * infinity. The RHS is always >= the LHS and has a maximum relative
- * error of about 1 in 16. Adding a bias of -0.03306235651 to the
- * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE
- * floating point representation, for finite positive normal values,
- * ordinary integer divison of the value in bits magically gives
- * almost exactly the RHS of the above provided we first subtract the
- * exponent bias (1023 for doubles) and later add it back. We do the
- * subtraction virtually to keep e >= 0 so that ordinary integer
- * division rounds towards minus infinity; this is also efficient.
- */
- 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,sign|((high&0x7fffffff)/3+B2));
- } else
- SET_HIGH_WORD(t,sign|(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);
-
- /* chop t to 20 bits and make it larger in magnitude 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-t is exact */
- t=t+t*r;
-
- return(t);
-}