RFR: 8320759: Creation of random BigIntegers can be made faster [v2]

[Brian Burkhalter]

On Tue, 28 Nov 2023 11:46:10 GMT, fabioromano1 <duke at openjdk.org> wrote:

>> Indeed it looks as if that is correct.
>
> As specified in https://docs.oracle.com/javase/specs/jls/se21/html/jls-15.html#jls-15.19:
> "If the promoted type of the left-hand operand is int, then only the five lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & ([§15.22.1](https://docs.oracle.com/javase/specs/jls/se21/html/jls-15.html#jls-15.22.1)) with the mask value 0x1f (0b11111). The shift distance actually used is therefore always in the range 0 to 31, inclusive.
> The value of n >>> s is n right-shifted s bit positions with zero-extension, where If n is negative and the type of the left-hand operand is int, then the result is equal to that of the expression (n >> s) + (2 << ~s). The added term (2 << ~s) cancels out the propagated sign bit."
> Since (excessBits == 32 * numInts - numBits), then (excessBits == (32 - (numBits & 0x1f)) & 0x1f), because (n & 0x1f == n mod 32). Since the five lowest-order bits of 32 are 0, then the five lowest-order bits of (32 - (numBits & 0x1f)) are the same of (-numBits), and so (excessBits == (-numBits) & 0x1f), therefore (-1 >>> excessBits == -1 >>> -numBits).

Thanks for the proof.

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PR Review Comment: https://git.openjdk.org/jdk/pull/16817#discussion_r1408164544