162 lines
3.0 KiB
C
162 lines
3.0 KiB
C
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/* cbrtl.c
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*
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* Cube root, long double precision
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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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* long double x, y, cbrtl();
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*
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* y = cbrtl( 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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* IEEE .125,8 80000 7.0e-20 2.2e-20
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* IEEE exp(+-707) 100000 7.0e-20 2.4e-20
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*
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*/
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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 "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 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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#ifndef __MINGW32__
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#ifdef ANSIPROT
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extern long double frexpl ( long double, int * );
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extern long double ldexpl ( long double, int );
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extern int isnanl ( long double );
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#else
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long double frexpl(), ldexpl();
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extern int isnanl();
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#endif
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#ifdef INFINITIES
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extern long double INFINITYL;
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#endif
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#endif /* __MINGW32__ */
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long double cbrtl(x)
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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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#ifdef __MINGW32__
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if (!isfinite (x) || x == 0.0L)
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return(x);
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#else
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#ifdef NANS
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if(isnanl(x))
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return(x);
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#endif
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#ifdef INFINITIES
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if( x == INFINITYL)
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return(x);
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if( x == -INFINITYL)
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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 = 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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