Hi all,
According to the GMP website, GMP 6 was apparently released 3 days ago.
They seem to have made some improvements for large operands, so I was of
course keen to compare with the upcoming MPIR 2.7 release (should be only a
few more days away now).
So here are the results from a circa 2008 AMD K10-2 Opteron machine with
the mpir_bench_two program.
The first two columns represent operand sizes, in bits.
The third column is GMP 6.0.0a. The fourth column is MPIR 2.7.0.
***HIGHER*** numbers are better:
Squaring
128 128 => 50422927 51153639
512 512 => 12892203 13781556
8192 8192 => 151686 159689
131072 131072 => 2650 2773
2097152 2097152 => 83.7 104
Balanced Multiplication
128 128 => 50345548 51153639
512 512 => 8655112 11410535
8192 8192 => 101107 110689
131072 131072 => 1787 1948
2097152 2097152 => 51.2 69.2
Unbalanced Multiplication
15000 10000 => 51197 53835
20000 10000 => 39069 42495
30000 10000 => 24891 25082
16777216 512 => 414 392
16777216 262144 => 13.2 13.4
Divide
8192 32 => 1337305 1414864
8192 64 => 1329811 1323797
8192 128 => 932384 799122
8192 4096 => 249044 265375
131072 65536 => 2595 3036
8388608 4194304 => 11.8 9.80
8192 8064 => 8097331 8071930
16777216 262144 => 6.99 6.99
[Note: much of our implementation of mul and div is distinct from GMP, but
for example we use their toom8 implementation and make heavy use of their
division code, even though the main underlying division algorithms are
different.]
The figures show we need to improve our divrem_2 and asymptotically fast
(fft based) division. But overall I think we are looking good.
GMP 6 will of course totally thrash us on very modern chips due to new
instruction support that we don't yet have (avx, etc). It's very sad that
our assembly language expert Jason Moxham passed away in 2012. He will be
hard to replace and is sorely missed!
Bill.
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