Logarithm of Binomial Coefficient

Compute the natural logarithm of the binomial coefficient.

The natural logarithm of the binomial coefficient is

The binomial coefficient of two nonnegative integers n and k is defined as

The binomial coefficient can be generalized to negative integers n as follows:

Usage

var binomcoefln = require( '@stdlib/math/base/special/binomcoefln' );

binomcoefln( n, k )

Evaluates the natural logarithm of the binomial coefficient of two integers n and k.

var v = binomcoefln( 8, 2 );
// returns ~3.332

v = binomcoefln( 0, 0 );
// returns 0.0

v = binomcoefln( -4, 2 );
// returns ~2.303

v = binomcoefln( 88, 3 );
// returns ~11.606

v = binomcoefln( NaN, 3 );
// returns NaN

v = binomcoefln( 5, NaN );
// returns NaN

v = binomcoefln( NaN, NaN );
// returns NaN

For negative k, the function returns -Infinity.

var v = binomcoefln( 2, -1 );
// returns -Infinity

v = binomcoefln( -3, -1 );
// returns -Infinity

The function returns NaN for non-integer n or k.

var v = binomcoefln( 2, 1.5 );
// returns NaN

v = binomcoefln( 5.5, 2 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var binomcoefln = require( '@stdlib/math/base/special/binomcoefln' );

var n;
var k;
var i;

for ( i = 0; i < 100; i++ ) {
    n = round( (randu()*40.0) - 10.0 );
    k = round( randu()*20.0 );
    console.log( 'ln( %d choose %d ) = %d', n, k, binomcoefln( n, k ) );
}

C APIs

Usage

#include "stdlib/math/base/special/binomcoefln.h"

stdlib_base_binomcoefln( n, k )

Evaluates the natural logarithm of the binomial coefficient of two integers n and k.

double v = stdlib_base_binomcoefln( 8, 2 );
// returns ~3.332

The function accepts the following arguments:

n: [in] int64_t input value.
k: [in] int64_t input value.

double stdlib_base_binomcoefln( const int64_t n, const int64_t k );

Examples

#include "stdlib/math/base/special/binomcoefln.h"
#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>

int main( void ) {
    const int64_t a[] = { 24, 32, 48, 116, 33 };
    const int64_t b[] = { 12, 6, 15, 52, 22 };

    double out;
    int i;
    for ( i = 0; i < 5; i++ ) {
        out = stdlib_base_binomcoef( a[ i ], b[ i ] );
        printf( "binomcoefln(%" PRId64 ", %" PRId64 ") = %lf\n", a[ i ], b[ i ], out );
    }
}