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Add kernel implementation of Binomial() #1921

Merged
merged 1 commit into from
Nov 21, 2017
Merged

Add kernel implementation of Binomial() #1921

merged 1 commit into from
Nov 21, 2017

Commits on Nov 17, 2017

  1. Add kernel implementation of Binomial() 

    This uses the GMP functions mpz_bin_ui and mpz_bin_uiui. The following timings
for certain central binomial coefficients illustrates the speedup:

gap> n:=2^14;; a:=BINOMIAL_INT(2*n,n);; time; b:=Binomial_GAP(2*n,n);; time;
0
51

gap> n:=2^16;; a:=BINOMIAL_INT(2*n,n);; time; b:=Binomial_GAP(2*n,n);; time;
2
719

gap> n:=2^18;; a:=BINOMIAL_INT(2*n,n);; time; b:=Binomial_GAP(2*n,n);; time;
8
11470

gap> n:=2^19;; a:=BINOMIAL_INT(2*n,n);; time; b:=Binomial_GAP(2*n,n);; time;
14
51386

gap> n:=2^20;; a:=BINOMIAL_INT(2*n,n);; time; b:=Binomial_GAP(2*n,n);; time;
33
190444

The main reason the C version is so much faster is that it can accumulate the
result in-place, whereas GAP creates tons and tons of temporary integer
objects which then need to be garbage collected. Of course some other tricks
employed by GMP help, too.
    @fingolfin
    fingolfin committed Nov 17, 2017
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