On Wed, 1 Jun 2022 22:53:14 GMT, Chris Hennick <d...@openjdk.java.net> wrote:
>> Repeatedly adding DoubleZigguratTables.exponentialX0 to extra causes a >> rounding error to accumulate at the tail of the distribution (probably >> starting around 2*exponentialX0 == 0x1.e46eff20739afp3 ~ 15.1); this fixes >> that by tracking the multiple of exponentialX0 as a long. (This changes the >> maximum possible output to `1.0p63 * DoubleZigguratTables.exponentialX0 == >> 0x1.e46eff20739afp65`; previously it would have been `0x1.0p56` because once >> `extra` reaches that amount, `x + extra == extra` due to the rounding error. >> This lowers the probability of reaching the maximum with an ideal PRNG from >> about `1.3877787807814488E-17` to about `1.4323726067488646E-20` (calculated >> using the identity `ln(x) == Math.log10(x)/Math.log10(Math.exp(1))`). > > Chris Hennick has refreshed the contents of this pull request, and previous > commits have been removed. The incremental views will show differences > compared to the previous content of the PR. The pull request contains one new > commit since the last revision: > > Fix rounding error in computeNextExponential; use FMA > > Repeatedly adding DoubleZigguratTables.exponentialX0 to extra causes a > rounding error to accumulate at the tail of the distribution; this fixes that > by tracking the multiple of exponentialX0 as a long. > > Add computeWinsorizedNextExponential for testability In addition to the changes discussed heretofore, I've also changed line 1382 to eliminate unneeded tail exploration; this should make `nextGaussian` faster at high percentiles (probably measurable at 99%ile; should definitely be measurable at at 99.99%ile). ------------- PR: https://git.openjdk.java.net/jdk/pull/8131
