RFR: 8284493: Fix rounding error in computeNextExponential [v13]

Chris Hennick duke at openjdk.org
Sun Jun 19 23:30:32 UTC 2022


> 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:

  Simplify Javadoc description

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Changes:
  - all: https://git.openjdk.org/jdk/pull/8131/files
  - new: https://git.openjdk.org/jdk/pull/8131/files/5919faeb..e3f55542

Webrevs:
 - full: https://webrevs.openjdk.org/?repo=jdk&pr=8131&range=12
 - incr: https://webrevs.openjdk.org/?repo=jdk&pr=8131&range=11-12

  Stats: 4 lines in 1 file changed: 2 ins; 0 del; 2 mod
  Patch: https://git.openjdk.org/jdk/pull/8131.diff
  Fetch: git fetch https://git.openjdk.org/jdk pull/8131/head:pull/8131

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


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