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-rw-r--r--libm/double/incbi.c313
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diff --git a/libm/double/incbi.c b/libm/double/incbi.c
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-/* incbi()
- *
- * Inverse of imcomplete beta integral
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, b, x, y, incbi();
- *
- * x = incbi( a, b, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Given y, the function finds x such that
- *
- * incbet( a, b, x ) = y .
- *
- * The routine performs interval halving or Newton iterations to find the
- * root of incbet(a,b,x) - y = 0.
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * x a,b
- * arithmetic domain domain # trials peak rms
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.3e-13
- * IEEE 0,1 .25,100 100000 1.8e-13 3.9e-15
- * IEEE 0,1 0,5 50000 1.1e-12 5.5e-15
- * VAX 0,1 .5,100 25000 3.5e-14 1.1e-15
- * With a and b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 50000 5.8e-12 1.1e-13
- * IEEE 0,1 .5,100 100000 1.7e-14 7.9e-16
- * With a = .5, b constrained to half-integer or integer values:
- * IEEE 0,1 .5,10000 10000 8.3e-11 1.0e-11
- */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1996, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-
-extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
-#ifdef ANSIPROT
-extern double ndtri ( double );
-extern double exp ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double sqrt ( double );
-extern double lgam ( double );
-extern double incbet ( double, double, double );
-#else
-double ndtri(), exp(), fabs(), log(), sqrt(), lgam(), incbet();
-#endif
-
-double incbi( aa, bb, yy0 )
-double aa, bb, yy0;
-{
-double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
-int i, rflg, dir, nflg;
-
-
-i = 0;
-if( yy0 <= 0 )
- return(0.0);
-if( yy0 >= 1.0 )
- return(1.0);
-x0 = 0.0;
-yl = 0.0;
-x1 = 1.0;
-yh = 1.0;
-nflg = 0;
-
-if( aa <= 1.0 || bb <= 1.0 )
- {
- dithresh = 1.0e-6;
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- x = a/(a+b);
- y = incbet( a, b, x );
- goto ihalve;
- }
-else
- {
- dithresh = 1.0e-4;
- }
-/* approximation to inverse function */
-
-yp = -ndtri(yy0);
-
-if( yy0 > 0.5 )
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- yp = -yp;
- }
-else
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
-
-lgm = (yp * yp - 3.0)/6.0;
-x = 2.0/( 1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0) );
-d = yp * sqrt( x + lgm ) / x
- - ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
- * (lgm + 5.0/6.0 - 2.0/(3.0*x));
-d = 2.0 * d;
-if( d < MINLOG )
- {
- x = 1.0;
- goto under;
- }
-x = a/( a + b * exp(d) );
-y = incbet( a, b, x );
-yp = (y - y0)/y0;
-if( fabs(yp) < 0.2 )
- goto newt;
-
-/* Resort to interval halving if not close enough. */
-ihalve:
-
-dir = 0;
-di = 0.5;
-for( i=0; i<100; i++ )
- {
- if( i != 0 )
- {
- x = x0 + di * (x1 - x0);
- if( x == 1.0 )
- x = 1.0 - MACHEP;
- if( x == 0.0 )
- {
- di = 0.5;
- x = x0 + di * (x1 - x0);
- if( x == 0.0 )
- goto under;
- }
- y = incbet( a, b, x );
- yp = (x1 - x0)/(x1 + x0);
- if( fabs(yp) < dithresh )
- goto newt;
- yp = (y-y0)/y0;
- if( fabs(yp) < dithresh )
- goto newt;
- }
- if( y < y0 )
- {
- x0 = x;
- yl = y;
- if( dir < 0 )
- {
- dir = 0;
- di = 0.5;
- }
- else if( dir > 3 )
- di = 1.0 - (1.0 - di) * (1.0 - di);
- else if( dir > 1 )
- di = 0.5 * di + 0.5;
- else
- di = (y0 - y)/(yh - yl);
- dir += 1;
- if( x0 > 0.75 )
- {
- if( rflg == 1 )
- {
- rflg = 0;
- a = aa;
- b = bb;
- y0 = yy0;
- }
- else
- {
- rflg = 1;
- a = bb;
- b = aa;
- y0 = 1.0 - yy0;
- }
- x = 1.0 - x;
- y = incbet( a, b, x );
- x0 = 0.0;
- yl = 0.0;
- x1 = 1.0;
- yh = 1.0;
- goto ihalve;
- }
- }
- else
- {
- x1 = x;
- if( rflg == 1 && x1 < MACHEP )
- {
- x = 0.0;
- goto done;
- }
- yh = y;
- if( dir > 0 )
- {
- dir = 0;
- di = 0.5;
- }
- else if( dir < -3 )
- di = di * di;
- else if( dir < -1 )
- di = 0.5 * di;
- else
- di = (y - y0)/(yh - yl);
- dir -= 1;
- }
- }
-mtherr( "incbi", PLOSS );
-if( x0 >= 1.0 )
- {
- x = 1.0 - MACHEP;
- goto done;
- }
-if( x <= 0.0 )
- {
-under:
- mtherr( "incbi", UNDERFLOW );
- x = 0.0;
- goto done;
- }
-
-newt:
-
-if( nflg )
- goto done;
-nflg = 1;
-lgm = lgam(a+b) - lgam(a) - lgam(b);
-
-for( i=0; i<8; i++ )
- {
- /* Compute the function at this point. */
- if( i != 0 )
- y = incbet(a,b,x);
- if( y < yl )
- {
- x = x0;
- y = yl;
- }
- else if( y > yh )
- {
- x = x1;
- y = yh;
- }
- else if( y < y0 )
- {
- x0 = x;
- yl = y;
- }
- else
- {
- x1 = x;
- yh = y;
- }
- if( x == 1.0 || x == 0.0 )
- break;
- /* Compute the derivative of the function at this point. */
- d = (a - 1.0) * log(x) + (b - 1.0) * log(1.0-x) + lgm;
- if( d < MINLOG )
- goto done;
- if( d > MAXLOG )
- break;
- d = exp(d);
- /* Compute the step to the next approximation of x. */
- d = (y - y0)/d;
- xt = x - d;
- if( xt <= x0 )
- {
- y = (x - x0) / (x1 - x0);
- xt = x0 + 0.5 * y * (x - x0);
- if( xt <= 0.0 )
- break;
- }
- if( xt >= x1 )
- {
- y = (x1 - x) / (x1 - x0);
- xt = x1 - 0.5 * y * (x1 - x);
- if( xt >= 1.0 )
- break;
- }
- x = xt;
- if( fabs(d/x) < 128.0 * MACHEP )
- goto done;
- }
-/* Did not converge. */
-dithresh = 256.0 * MACHEP;
-goto ihalve;
-
-done:
-
-if( rflg )
- {
- if( x <= MACHEP )
- x = 1.0 - MACHEP;
- else
- x = 1.0 - x;
- }
-return( x );
-}
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