163 lines
3.0 KiB
C
163 lines
3.0 KiB
C
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/* cbrt.c
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*
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* Cube root
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, cbrt();
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*
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* y = cbrt( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the cube root of the argument, which may be negative.
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*
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* Range reduction involves determining the power of 2 of
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* the argument. A polynomial of degree 2 applied to the
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* mantissa, and multiplication by the cube root of 1, 2, or 4
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* approximates the root to within about 0.1%. Then Newton's
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* iteration is used three times to converge to an accurate
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* result.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -10,10 200000 1.8e-17 6.2e-18
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* IEEE 0,1e308 30000 1.5e-16 5.0e-17
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*
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*/
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/* cbrt.c */
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/*
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Cephes Math Library Release 2.2: January, 1991
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Copyright 1984, 1991 by Stephen L. Moshier
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Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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/*
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Modified for mingwex.a
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2002-07-01 Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifdef __MINGW32__
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#include <math.h>
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#include "cephes_mconf.h"
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#else
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#include "mconf.h"
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#endif
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static const double CBRT2 = 1.2599210498948731647672;
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static const double CBRT4 = 1.5874010519681994747517;
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static const double CBRT2I = 0.79370052598409973737585;
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static const double CBRT4I = 0.62996052494743658238361;
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#ifndef __MINGW32__
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#ifdef ANSIPROT
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extern double frexp ( double, int * );
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extern double ldexp ( double, int );
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extern int isnan ( double );
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extern int isfinite ( double );
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#else
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double frexp(), ldexp();
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int isnan(), isfinite();
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#endif
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#endif
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double cbrt(x)
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double x;
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{
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int e, rem, sign;
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double z;
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#ifdef __MINGW32__
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if (!isfinite (x) || x == 0 )
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return x;
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#else
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#ifdef NANS
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if( isnan(x) )
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return x;
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#endif
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#ifdef INFINITIES
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if( !isfinite(x) )
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return x;
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#endif
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if( x == 0 )
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return( x );
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#endif /* __MINGW32__ */
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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 = frexp( x, &e );
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/* Approximate cube root of number between .5 and 1,
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* peak relative error = 9.2e-6
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*/
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x = (((-1.3466110473359520655053e-1 * x
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+ 5.4664601366395524503440e-1) * x
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- 9.5438224771509446525043e-1) * x
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+ 1.1399983354717293273738e0 ) * x
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+ 4.0238979564544752126924e-1;
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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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/* argument less than 1 */
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else
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{
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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 = ldexp( x, e );
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/* Newton iteration */
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x -= ( x - (z/(x*x)) )*0.33333333333333333333;
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#ifdef DEC
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x -= ( x - (z/(x*x)) )/3.0;
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#else
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x -= ( x - (z/(x*x)) )*0.33333333333333333333;
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#endif
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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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