[gambit-list] New fft bignum multiplication
Bradley Lucier
lucier at math.purdue.edu
Wed May 23 10:27:30 EDT 2007
I ran the tests on my opteron server (2.2 GHz, RHEL 4, gcc-4.1.2)
after compiling mzscheme 370 on the box. Previously I used the
prebuilt (presumably 32-bit) mzscheme binaries and native 64-bit
gambit binaries on MacOS, but this build uses 64-bit operations in
both the mzscheme and gambit libraries, and mzscheme looks better
here. If mzscheme were to use the fft multiply routines in gmp it
would look better still; with the current binaries of gsi/gsc and
mzscheme, mzscheme would look worse for larger numbers.
Anyway, here are the results:
370 b22
(expt 3 1000000) ; a 124 89
(expt 3 1000001) ; b 126 89
(* a a) ; c 221 106
(* a b) ; 221 150
(quotient c a) ; 560 687
(sqrt c) ; 402 667
(gcd a b) ; note 1 1959 2708
(* a b) 62 62
(expt1 3 1000000) ; note 2 124 85
(expt2 3 1000000) ; note 3 362 370
(* a a) ; a=3^1000000 221 105
(expt 10 10000000); a 228 193
(fib 10000) ; note 4 33 29
(factorial 10000) ; note 5 137 158
(partial-factorial 0 10000) ; note 6 9 13
(binary-splitting-compute-e 10000) ; note 7 539 968
(binary-splitting-compute-pi 10000) ; note 9 716 1220
(pi-brent-salamin) ; n. 10, beta^k=10^100000 2646 3939
(pi-brent-salamin) ; beta^k=2^332193 1486 2889
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