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Diffstat (limited to 'libm/ldouble/fdtrl.c')
| -rw-r--r-- | libm/ldouble/fdtrl.c | 237 |
1 files changed, 0 insertions, 237 deletions
diff --git a/libm/ldouble/fdtrl.c b/libm/ldouble/fdtrl.c deleted file mode 100644 index da2f8910a..000000000 --- a/libm/ldouble/fdtrl.c +++ /dev/null @@ -1,237 +0,0 @@ -/* fdtrl.c - * - * F distribution, long double precision - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * long double x, y, fdtrl(); - * - * y = fdtrl( df1, df2, x ); - * - * - * - * DESCRIPTION: - * - * Returns the area from zero to x under the F density - * function (also known as Snedcor's density or the - * variance ratio density). This is the density - * of x = (u1/df1)/(u2/df2), where u1 and u2 are random - * variables having Chi square distributions with df1 - * and df2 degrees of freedom, respectively. - * - * The incomplete beta integral is used, according to the - * formula - * - * P(x) = incbetl( df1/2, df2/2, (df1*x/(df2 + df1*x) ). - * - * - * The arguments a and b are greater than zero, and x - * x is nonnegative. - * - * ACCURACY: - * - * Tested at random points (a,b,x) in the indicated intervals. - * x a,b Relative error: - * arithmetic domain domain # trials peak rms - * IEEE 0,1 1,100 10000 9.3e-18 2.9e-19 - * IEEE 0,1 1,10000 10000 1.9e-14 2.9e-15 - * IEEE 1,5 1,10000 10000 5.8e-15 1.4e-16 - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtrl domain a<0, b<0, x<0 0.0 - * - */ - /* fdtrcl() - * - * Complemented F distribution - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * long double x, y, fdtrcl(); - * - * y = fdtrcl( df1, df2, x ); - * - * - * - * DESCRIPTION: - * - * Returns the area from x to infinity under the F density - * function (also known as Snedcor's density or the - * variance ratio density). - * - * - * inf. - * - - * 1 | | a-1 b-1 - * 1-P(x) = ------ | t (1-t) dt - * B(a,b) | | - * - - * x - * - * (See fdtr.c.) - * - * The incomplete beta integral is used, according to the - * formula - * - * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ). - * - * - * ACCURACY: - * - * See incbet.c. - * Tested at random points (a,b,x). - * - * x a,b Relative error: - * arithmetic domain domain # trials peak rms - * IEEE 0,1 0,100 10000 4.2e-18 3.3e-19 - * IEEE 0,1 1,10000 10000 7.2e-15 2.6e-16 - * IEEE 1,5 1,10000 10000 1.7e-14 3.0e-15 - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtrcl domain a<0, b<0, x<0 0.0 - * - */ - /* fdtril() - * - * Inverse of complemented F distribution - * - * - * - * SYNOPSIS: - * - * int df1, df2; - * long double x, p, fdtril(); - * - * x = fdtril( df1, df2, p ); - * - * DESCRIPTION: - * - * Finds the F density argument x such that the integral - * from x to infinity of the F density is equal to the - * given probability p. - * - * This is accomplished using the inverse beta integral - * function and the relations - * - * z = incbi( df2/2, df1/2, p ) - * x = df2 (1-z) / (df1 z). - * - * Note: the following relations hold for the inverse of - * the uncomplemented F distribution: - * - * z = incbi( df1/2, df2/2, p ) - * x = df2 z / (df1 (1-z)). - * - * ACCURACY: - * - * See incbi.c. - * Tested at random points (a,b,p). - * - * a,b Relative error: - * arithmetic domain # trials peak rms - * For p between .001 and 1: - * IEEE 1,100 40000 4.6e-18 2.7e-19 - * IEEE 1,10000 30000 1.7e-14 1.4e-16 - * For p between 10^-6 and .001: - * IEEE 1,100 20000 1.9e-15 3.9e-17 - * IEEE 1,10000 30000 2.7e-15 4.0e-17 - * - * ERROR MESSAGES: - * - * message condition value returned - * fdtril domain p <= 0 or p > 1 0.0 - * v < 1 - */ - - -/* -Cephes Math Library Release 2.3: March, 1995 -Copyright 1984, 1995 by Stephen L. Moshier -*/ - - -#include <math.h> -#ifdef ANSIPROT -extern long double incbetl ( long double, long double, long double ); -extern long double incbil ( long double, long double, long double ); -#else -long double incbetl(), incbil(); -#endif - -long double fdtrcl( ia, ib, x ) -int ia, ib; -long double x; -{ -long double a, b, w; - -if( (ia < 1) || (ib < 1) || (x < 0.0L) ) - { - mtherr( "fdtrcl", DOMAIN ); - return( 0.0L ); - } -a = ia; -b = ib; -w = b / (b + a * x); -return( incbetl( 0.5L*b, 0.5L*a, w ) ); -} - - - -long double fdtrl( ia, ib, x ) -int ia, ib; -long double x; -{ -long double a, b, w; - -if( (ia < 1) || (ib < 1) || (x < 0.0L) ) - { - mtherr( "fdtrl", DOMAIN ); - return( 0.0L ); - } -a = ia; -b = ib; -w = a * x; -w = w / (b + w); -return( incbetl(0.5L*a, 0.5L*b, w) ); -} - - -long double fdtril( ia, ib, y ) -int ia, ib; -long double y; -{ -long double a, b, w, x; - -if( (ia < 1) || (ib < 1) || (y <= 0.0L) || (y > 1.0L) ) - { - mtherr( "fdtril", DOMAIN ); - return( 0.0L ); - } -a = ia; -b = ib; -/* Compute probability for x = 0.5. */ -w = incbetl( 0.5L*b, 0.5L*a, 0.5L ); -/* If that is greater than y, then the solution w < .5. - Otherwise, solve at 1-y to remove cancellation in (b - b*w). */ -if( w > y || y < 0.001L) - { - w = incbil( 0.5L*b, 0.5L*a, y ); - x = (b - b*w)/(a*w); - } -else - { - w = incbil( 0.5L*a, 0.5L*b, 1.0L - y ); - x = b*w/(a*(1.0L-w)); - } -return(x); -} |