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Re: Will Math.random return 0.0?

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On 7/16/2016 2:37 PM, Arne Vajhøj wrote:
> On 7/16/2016 11:24 AM, Stefan Ram wrote:
> The seed algorithm is:
>
> seed = (seed * 0x5DEECE66DL + 0xBL) & ((1L << 48) - 1)
>
> and given that:
>
> mod(0x5DEECE66D,4) is 1
> 0xB is odd
> & ((1L << 48) - 1) must be equivalent to mod pow(2,48)
>
> then the algorithm should have full cycle aka seed
> will have all values including zero.
>
> so if nextDouble() just returned seed/pow(2,48) then
> it will return 0.0 occasionally.
>
> But it does not. Instead it uses:
>
> return (((long)next(26) << 27) + next(27)) / (double)(1L << 53);
>
> So it will only return 0.0 if the high 26 bits of seed
> and after update the high 27 bits of seed are both zero.
>
> Now my math skills are not good enough to evaluate
> whether that is indeed the case or not.
>
> The above has pow(2,53) potential values but given the
> seed cycle of pow(2,48) and the need for 2 calls, then
> it will only be able to return pow(2,47) different values.

Hmm. Eric's post just got me thinking.

A given seed will only give pow(2,47) doubles in
a cycle.

But there must be two possible double cycles meaning
that the answer (0.0 possible) may depend on the initial
seed.

That may complicate the test a bit.

Arne

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Re: Will Math.random return 0.0? Arne Vajhøj <arne@vajhoej.dk> - 2016-07-16 14:37 -0400
  Re: Will Math.random return 0.0? Arne Vajhøj <arne@vajhoej.dk> - 2016-07-16 16:51 -0400

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