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Diffstat (limited to 'libm/double/igami.c')
| -rw-r--r-- | libm/double/igami.c | 187 |
1 files changed, 187 insertions, 0 deletions
diff --git a/libm/double/igami.c b/libm/double/igami.c new file mode 100644 index 000000000..e93ba2a14 --- /dev/null +++ b/libm/double/igami.c @@ -0,0 +1,187 @@ +/* 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 ); +} |