RFR: 8284493: Fix rounding error in computeNextExponential

[Raffaello Giulietti]

On Sun, 22 May 2022 20:19:38 GMT, Andrey Turbanov <aturbanov at openjdk.org> 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))`).
>
> src/java.base/share/classes/jdk/internal/util/random/RandomSupport.java line 1411:
> 
>> 1409:                 long U2 = (rng.nextLong() >>> 1);
>> 1410:                 // Compute the actual x-coordinate of the randomly chosen point.
>> 1411:                 x = Math.fma(X[j-1] - X[j], (double)U1, X[j] * 0x1.0p63));
> 
> Code is not compilable

@Pr0methean As @turbanoff observes, I think there's a closing parentheses too much on L.1411 and one on L.1421.
Which compiler are you using ;-)  ?

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PR: https://git.openjdk.java.net/jdk/pull/8131