81 lines
1.6 KiB
C
81 lines
1.6 KiB
C
/**
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* This file has no copyright assigned and is placed in the Public Domain.
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* This file is part of the mingw-w64 runtime package.
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* No warranty is given; refer to the file DISCLAIMER.PD within this package.
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*/
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#include <math.h>
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static const long double CBRT2 = 1.2599210498948731647672L;
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static const long double CBRT4 = 1.5874010519681994747517L;
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static const long double CBRT2I = 0.79370052598409973737585L;
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static const long double CBRT4I = 0.62996052494743658238361L;
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long double cbrtl(long double x)
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{
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int e, rem, sign;
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long double z;
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if (!isfinite (x) || x == 0.0L)
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return (x);
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if (x > 0)
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sign = 1;
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else
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{
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sign = -1;
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x = -x;
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}
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z = x;
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/* extract power of 2, leaving
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* mantissa between 0.5 and 1
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*/
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x = frexpl(x, &e);
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/* Approximate cube root of number between .5 and 1,
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* peak relative error = 1.2e-6
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*/
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x = (((( 1.3584464340920900529734e-1L * x
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- 6.3986917220457538402318e-1L) * x
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+ 1.2875551670318751538055e0L) * x
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- 1.4897083391357284957891e0L) * x
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+ 1.3304961236013647092521e0L) * x
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+ 3.7568280825958912391243e-1L;
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/* exponent divided by 3 */
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if (e >= 0)
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{
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rem = e;
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e /= 3;
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rem -= 3*e;
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if (rem == 1)
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x *= CBRT2;
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else if (rem == 2)
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x *= CBRT4;
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}
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else
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{ /* argument less than 1 */
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e = -e;
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rem = e;
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e /= 3;
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rem -= 3*e;
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if (rem == 1)
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x *= CBRT2I;
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else if (rem == 2)
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x *= CBRT4I;
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e = -e;
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}
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/* multiply by power of 2 */
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x = ldexpl(x, e);
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/* Newton iteration */
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x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
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x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
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if (sign < 0)
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x = -x;
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return (x);
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}
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