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authorEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
committerEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
commit7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 (patch)
tree3a7e8476e868ae15f4da1b7ce26b2db6f434468c /libm/ldouble/igamil.c
parentc117dd5fb183afb1a4790a6f6110d88704be6bf8 (diff)
Totally rework the math library, this time based on the MacOs X
math library (which is itself based on the math lib from FreeBSD). -Erik
Diffstat (limited to 'libm/ldouble/igamil.c')
-rw-r--r--libm/ldouble/igamil.c193
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diff --git a/libm/ldouble/igamil.c b/libm/ldouble/igamil.c
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-/* igamil()
- *
- * Inverse of complemented imcomplete gamma integral
- *
- *
- *
- * SYNOPSIS:
- *
- * long double a, x, y, igamil();
- *
- * x = igamil( a, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * igamc( a, x ) = y.
- *
- * Starting with the approximate value
- *
- * 3
- * x = a t
- *
- * where
- *
- * t = 1 - d - ndtri(y) sqrt(d)
- *
- * and
- *
- * d = 1/9a,
- *
- * the routine performs up to 10 Newton iterations to find the
- * root of igamc(a,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0,0.5 3400 8.8e-16 1.3e-16
- * IEEE 0,0.5 10000 1.1e-14 1.0e-15
- *
- */
-
-/*
-Cephes Math Library Release 2.3: March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
-#ifdef ANSIPROT
-extern long double ndtril ( long double );
-extern long double expl ( long double );
-extern long double fabsl ( long double );
-extern long double logl ( long double );
-extern long double sqrtl ( long double );
-extern long double lgaml ( long double );
-extern long double igamcl ( long double, long double );
-#else
-long double ndtril(), expl(), fabsl(), logl(), sqrtl(), lgaml();
-long double igamcl();
-#endif
-
-long double igamil( a, y0 )
-long double a, y0;
-{
-long double x0, x1, x, yl, yh, y, d, lgm, dithresh;
-int i, dir;
-
-/* bound the solution */
-x0 = MAXNUML;
-yl = 0.0L;
-x1 = 0.0L;
-yh = 1.0L;
-dithresh = 4.0 * MACHEPL;
-
-/* approximation to inverse function */
-d = 1.0L/(9.0L*a);
-y = ( 1.0L - d - ndtril(y0) * sqrtl(d) );
-x = a * y * y * y;
-
-lgm = lgaml(a);
-
-for( i=0; i<10; i++ )
- {
- if( x > x0 || x < x1 )
- goto ihalve;
- y = igamcl(a,x);
- if( y < yl || y > yh )
- goto ihalve;
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
-/* compute the derivative of the function at this point */
- d = (a - 1.0L) * logl(x0) - x0 - lgm;
- if( d < -MAXLOGL )
- goto ihalve;
- d = -expl(d);
-/* compute the step to the next approximation of x */
- d = (y - y0)/d;
- x = x - d;
- if( i < 3 )
- continue;
- if( fabsl(d/x) < dithresh )
- goto done;
- }
-
-/* Resort to interval halving if Newton iteration did not converge. */
-ihalve:
-
-d = 0.0625L;
-if( x0 == MAXNUML )
- {
- if( x <= 0.0L )
- x = 1.0L;
- while( x0 == MAXNUML )
- {
- x = (1.0L + d) * x;
- y = igamcl( a, x );
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- break;
- }
- d = d + d;
- }
- }
-d = 0.5L;
-dir = 0;
-
-for( i=0; i<400; i++ )
- {
- x = x1 + d * (x0 - x1);
- y = igamcl( a, x );
- lgm = (x0 - x1)/(x1 + x0);
- if( fabsl(lgm) < dithresh )
- break;
- lgm = (y - y0)/y0;
- if( fabsl(lgm) < dithresh )
- break;
- if( x <= 0.0L )
- break;
- if( y > y0 )
- {
- x1 = x;
- yh = y;
- if( dir < 0 )
- {
- dir = 0;
- d = 0.5L;
- }
- else if( dir > 1 )
- d = 0.5L * d + 0.5L;
- else
- d = (y0 - yl)/(yh - yl);
- dir += 1;
- }
- else
- {
- x0 = x;
- yl = y;
- if( dir > 0 )
- {
- dir = 0;
- d = 0.5L;
- }
- else if( dir < -1 )
- d = 0.5L * d;
- else
- d = (y0 - yl)/(yh - yl);
- dir -= 1;
- }
- }
-if( x == 0.0L )
- mtherr( "igamil", UNDERFLOW );
-
-done:
-return( x );
-}