RFR: 8284493: Fix rounding error in computeNextExponential [v16]

[Chris Hennick]

On Tue, 4 Oct 2022 17:36:56 GMT, Chris Hennick <duke at openjdk.org> wrote:

>> This PR improves both the performance of `nextExponential` and `nextGaussian` and the distribution of output at the tails. It fixes the following imperfections:
>> 
>> * 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 PR fixes that by tracking the multiple of exponentialX0 as a long. (This distortion is worst when `x > 0x1.0p56` since in that case, a rounding error means `extra + x == extra`.
>> * Reduces several equations using `Math.fma`. (This will almost certainly improve performance, and may or may not improve output distribution.)
>> * Uses the newly-extracted `computeWinsorizedNextExponential` function to greatly reduce the probability that `nextGaussian` suffers from *two* tail cases of `nextExponential`.
>
> Chris Hennick has updated the pull request incrementally with one additional commit since the last revision:
> 
>   Add parameter to enable/disable fixed PRNG seed

JMH benchmark results (`make test TEST="micro:java.util.random"`) with `fixedSeed = true` on EC2 are below. Average time improves only for nextExponential() and only on non-Intel CPUs, but p100 improved more consistently (7 of the 12 tests improved by at least 1000ns, only 2 deteriorated by that amount.)
# c6i.metal
L64X128MixRandom.nextExponential() average ns/op: 26.984 ± 0.015 before, 34.914 ± 0.021 after
L64X128MixRandom.nextExponential() p100 ns/op: 8224 before, 5624 after
L64X1024MixRandom.nextExponential() average ns/op: 30.026 ± 0.020 before, 36.730 ± 0.024 after
L64X1024MixRandom.nextExponential() p100 ns/op: 8736 before, 7464 after
L64X128MixRandom.nextGaussian() average ns/op: 29.995 ± 0.017 before, 30.016 ± 0.019 after
L64X128MixRandom.nextGaussian() p100 ns/op: 5392 before, 3024 after
L64X1024MixRandom.nextGaussian() average ns/op: 31.394 ± 0.020 before, 31.660 ± 0.021 after
L64X1024MixRandom.nextGaussian() p100 ns/op: 5984 before, 6072 after
# c7g.16xlarge
L64X128MixRandom.nextExponential() average ns/op: 41.006 ± 0.056 before, 40.288 ± 0.055 after
L64X128MixRandom.nextExponential() p100 ns/op: 6384 before, 6416 after
L64X1024MixRandom.nextExponential() average ns/op: 45.218 ± 0.071 before, 40.549 ± 0.062 after
L64X1024MixRandom.nextExponential() p100 ns/op: 560 before, 3760 after
L64X128MixRandom.nextGaussian() average ns/op: 39.643 ± 0.052 before, 40.473 ± 0.070 after
L64X128MixRandom.nextGaussian() p100 ns/op: 7728 before, 1264 after
L64X1024MixRandom.nextGaussian() average ns/op: 40.393 ± 0.061 before, 40.274 ± 0.061 after
L64X1024MixRandom.nextGaussian() p100 ns/op: 9184 before, 1280 after
# m6a.metal
L64X128MixRandom.nextExponential() average ns/op: 31.241 ± 0.039 before, 29.004 ± 0.018 after
L64X128MixRandom.nextExponential() p100 ns/op: 4224 before, 7224 after
L64X1024MixRandom.nextExponential() average ns/op: 31.903 ± 0.017 before, 31.146 | ± | 0.021 | ns/op |
L64X1024MixRandom.nextExponential() p100 ns/op: 9744 before, 8688 after
L64X128MixRandom.nextGaussian() average ns/op: 29.164 ± 0.017 before, 29.073 ± 0.021 after
L64X128MixRandom.nextGaussian() p100 ns/op: 5920 before, 1504 after
L64X1024MixRandom.nextGaussian() average ns/op: 29.503 ± 0.022 before, 29.639 ± 0.018 after
L64X1024MixRandom.nextGaussian() p100 ns/op: 4256 before, 4288 after

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PR: https://git.openjdk.org/jdk/pull/8131