B100 Binomial Coefficient

Function subprograms BINOM and DBINOM calculate the binomial coefficient

$x\; k\; =$

$x(x-1)...(x-k+1)/k!$	$(k>0)$
$1$	$(k=0)$
$0$

$.$

for real x and integer k. Function subprogram KBINOM calculates the binomial coefficient only for integer x=n.

On CDC and Cray computers, the double-precision version DBINOM is not available.

Structure:

FUNCTION subprograms
User Entry Names: BINOM, DBINOM, KBINOM
Files Referenced: Unit 6

Usage:

In any arithmetic expression, BINOM(X,K), DBINOM(X,K) or KBINOM(N,K)

has the value of the binomial coefficient. BINOM is of type REAL, DBINOM is of type DOUBLE PRECISION and X has the same type as the function name. KBINOM, N and K are of type INTEGER.

Restrictions:

Function subprogram KBINOM can compute only binomial coefficients which lie in the integer range of the machine.

Accuracy:

Full machine accuracy.

Error handling:

If the result of KBINOM would lie outside the integer range of the machine, KBINOM is set equal to zero and an error message is printed.
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B101