Add kernel implementation of Binomial() #1921
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fingolfin
added
kind: enhancement
markuspf
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Nov 17, 2017
Codecov Report
@@ Coverage Diff @@
## master #1921 +/- ##
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+ Coverage 63.71% 63.77% +0.05%
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Files 947 947
Lines 284484 284539 +55
Branches 12744 12757 +13
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+ Hits 181264 181457 +193
+ Misses 100436 100284 -152
- Partials 2784 2798 +14
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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.
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Not really, I just forgot to remove it. Now fixed. Also tweaked the commit message a bit. |
ChrisJefferson
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Nov 20, 2017
olexandr-konovalov
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This example illustrates the speedup:
Note that on 32bit systems, some previously "supported" combinations (n,k) are no longer supported. But those values are effectively out of reach for the old code, too: if I extrapolate the results above in various ways, I get an estimate of about 30 days to compute the smallest binomial coefficient (for n=2^28) not supported. Granted, this is on my laptop, and your super computer might get to it quicker. But at that point you might also just use the 64 bit version of GAP, which gets the result on my laptop in less than 30 seconds: