diff options
Diffstat (limited to 'libm/ldouble/igamil.c')
-rw-r--r-- | libm/ldouble/igamil.c | 193 |
1 files changed, 0 insertions, 193 deletions
diff --git a/libm/ldouble/igamil.c b/libm/ldouble/igamil.c deleted file mode 100644 index 1abe503e9..000000000 --- a/libm/ldouble/igamil.c +++ /dev/null @@ -1,193 +0,0 @@ -/* 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 ); -} |