guy.steele at oracle.com
Tue Jul 16 19:23:22 UTC 2013
On Jul 16, 2013, at 2:57 PM, Guy Steele <guy.steele at oracle.com> wrote:
> . . .
> So here's the punchline: this change makes my Monte Carlo calculation of pi run over 19% faster!
> Hard to believe. It's certainly avoiding most of the hard work in addGammaModGeorge,
> and perhaps also making branch prediction totally win, but 19% ??? Someone please verify this
I ran more tests.
Using 60-bit gamma values, the improvement is about 14-15%.
Using 56-bit gamma values, the improvement is about 19-20%, as already reported.
Using 52-bit gamma values, the improvement is about 19-20%.
So, as expected, there is a knee in the curve, and 56-bit values are about right.
But I should check 57, 58, and 59 bits.
> Still to be done: (a) verify avalanche behavior of mix56; (b) run more DieHarder tests.
And (c), look again at the mathematical proofs and see whether limiting the range
of gamma values adversely affects the likelihood of hitting a bad case (different
pedigrees producing duplicate values).
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