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Diffstat (limited to 'libm/double/igami.c')
-rw-r--r-- | libm/double/igami.c | 187 |
1 files changed, 0 insertions, 187 deletions
diff --git a/libm/double/igami.c b/libm/double/igami.c deleted file mode 100644 index e93ba2a14..000000000 --- a/libm/double/igami.c +++ /dev/null @@ -1,187 +0,0 @@ -/* igami() - * - * Inverse of complemented imcomplete gamma integral - * - * - * - * SYNOPSIS: - * - * double a, x, p, igami(); - * - * x = igami( a, p ); - * - * DESCRIPTION: - * - * Given p, the function finds x such that - * - * igamc( a, x ) = p. - * - * Starting with the approximate value - * - * 3 - * x = a t - * - * where - * - * t = 1 - d - ndtri(p) sqrt(d) - * - * and - * - * d = 1/9a, - * - * the routine performs up to 10 Newton iterations to find the - * root of igamc(a,x) - p = 0. - * - * ACCURACY: - * - * Tested at random a, p in the intervals indicated. - * - * a p Relative error: - * arithmetic domain domain # trials peak rms - * IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15 - * IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15 - * IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14 - */ - -/* -Cephes Math Library Release 2.8: June, 2000 -Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier -*/ - -#include <math.h> - -extern double MACHEP, MAXNUM, MAXLOG, MINLOG; -#ifdef ANSIPROT -extern double igamc ( double, double ); -extern double ndtri ( double ); -extern double exp ( double ); -extern double fabs ( double ); -extern double log ( double ); -extern double sqrt ( double ); -extern double lgam ( double ); -#else -double igamc(), ndtri(), exp(), fabs(), log(), sqrt(), lgam(); -#endif - -double igami( a, y0 ) -double a, y0; -{ -double x0, x1, x, yl, yh, y, d, lgm, dithresh; -int i, dir; - -/* bound the solution */ -x0 = MAXNUM; -yl = 0; -x1 = 0; -yh = 1.0; -dithresh = 5.0 * MACHEP; - -/* approximation to inverse function */ -d = 1.0/(9.0*a); -y = ( 1.0 - d - ndtri(y0) * sqrt(d) ); -x = a * y * y * y; - -lgm = lgam(a); - -for( i=0; i<10; i++ ) - { - if( x > x0 || x < x1 ) - goto ihalve; - y = igamc(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 - 1.0) * log(x) - x - lgm; - if( d < -MAXLOG ) - goto ihalve; - d = -exp(d); -/* compute the step to the next approximation of x */ - d = (y - y0)/d; - if( fabs(d/x) < MACHEP ) - goto done; - x = x - d; - } - -/* Resort to interval halving if Newton iteration did not converge. */ -ihalve: - -d = 0.0625; -if( x0 == MAXNUM ) - { - if( x <= 0.0 ) - x = 1.0; - while( x0 == MAXNUM ) - { - x = (1.0 + d) * x; - y = igamc( a, x ); - if( y < y0 ) - { - x0 = x; - yl = y; - break; - } - d = d + d; - } - } -d = 0.5; -dir = 0; - -for( i=0; i<400; i++ ) - { - x = x1 + d * (x0 - x1); - y = igamc( a, x ); - lgm = (x0 - x1)/(x1 + x0); - if( fabs(lgm) < dithresh ) - break; - lgm = (y - y0)/y0; - if( fabs(lgm) < dithresh ) - break; - if( x <= 0.0 ) - break; - if( y >= y0 ) - { - x1 = x; - yh = y; - if( dir < 0 ) - { - dir = 0; - d = 0.5; - } - else if( dir > 1 ) - d = 0.5 * d + 0.5; - else - d = (y0 - yl)/(yh - yl); - dir += 1; - } - else - { - x0 = x; - yl = y; - if( dir > 0 ) - { - dir = 0; - d = 0.5; - } - else if( dir < -1 ) - d = 0.5 * d; - else - d = (y0 - yl)/(yh - yl); - dir -= 1; - } - } -if( x == 0.0 ) - mtherr( "igami", UNDERFLOW ); - -done: -return( x ); -} |