148 lines
2.4 KiB
C
148 lines
2.4 KiB
C
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/* cbrtf.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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* float x, y, cbrtf();
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*
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* y = cbrtf( 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 to converge to an accurate 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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* IEEE 0,1e38 100000 7.6e-8 2.7e-8
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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: June, 1992
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Copyright 1984, 1987, 1988, 1992 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 float CBRT2 = 1.25992104989487316477;
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static const float CBRT4 = 1.58740105196819947475;
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#ifndef __MINGW32__
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#ifdef ANSIC
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float frexpf(float, int *), ldexpf(float, int);
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float cbrtf( float xx )
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#else
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float frexpf(), ldexpf();
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float cbrtf(xx)
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double xx;
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#endif
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{
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int e, rem, sign;
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float x, z;
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x = xx;
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#else /* __MINGW32__ */
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float cbrtf (float x)
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{
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int e, rem, sign;
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float z;
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#endif /* __MINGW32__ */
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#ifdef __MINGW32__
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if (!isfinite (x) || x == 0.0F )
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return x;
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#else
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if( x == 0 )
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return( 0.0 );
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#endif
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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 = frexpf( 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 = (((-0.13466110473359520655053 * x
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+ 0.54664601366395524503440 ) * x
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- 0.95438224771509446525043 ) * x
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+ 1.1399983354717293273738 ) * x
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+ 0.40238979564544752126924;
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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 /= CBRT2;
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else if( rem == 2 )
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x /= CBRT4;
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e = -e;
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}
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/* multiply by power of 2 */
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x = ldexpf( x, e );
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/* Newton iteration */
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x -= ( x - (z/(x*x)) ) * 0.333333333333;
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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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