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73 lines
2.0 KiB
C
73 lines
2.0 KiB
C
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/* @(#)s_cbrt.c 1.3 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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#include "math.h"
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/* cbrt(x)
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* Return cube root of x
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*/
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static const unsigned
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B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
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B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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static const double
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C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
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D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
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F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
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G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
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double cbrt(double x) {
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int hx;
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double r, s, t = 0.0, w;
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unsigned sign;
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hx = __HI(x); /* high word of x */
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sign = hx & 0x80000000; /* sign= sign(x) */
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hx ^= sign;
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if(hx >= 0x7ff00000) return (x + x); /* cbrt(NaN,INF) is itself */
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if((hx | __LO(x)) == 0)
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return (x); /* cbrt(0) is itself */
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__HI(x) = hx; /* x <- |x| */
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/* rough cbrt to 5 bits */
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if(hx < 0x00100000) /* subnormal number */
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{
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__HI(t) = 0x43500000; /* set t= 2**54 */
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t *= x;
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__HI(t) = __HI(t) / 3 + B2;
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} else
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__HI(t) = hx / 3 + B1;
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/* new cbrt to 23 bits, may be implemented in single precision */
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r = t * t / x;
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s = C + r * t;
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t *= G + F / (s + E + D / s);
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/* chopped to 20 bits and make it larger than cbrt(x) */
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__LO(t) = 0;
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__HI(t) += 0x00000001;
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/* one step newton iteration to 53 bits with error less than 0.667 ulps */
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s = t * t; /* t*t is exact */
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r = x / s;
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w = t + t;
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r = (r - t) / (w + r); /* r-s is exact */
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t = t + t * r;
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/* retore the sign bit */
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__HI(t) |= sign;
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return (t);
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}
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