JuliaRandom / JuliaRandom/RandomNumbers.jl

Conversion to Float

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Julia
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Description

The "obvious" approach of converting to a float, then multiplying by a scale factor is slow, and has the potential to give an answer of `1.0`.

The easiest option is:

``` julia
import Base: significand_mask, exponent_one
f1(u::UInt64) = reinterpret(Float64, exponent_one(Float64) | significand_mask(Float64) & u) - 1.0
```

unfortunately this has the downside that the last bit will always be zero, so you only get 52 bits of randomness per float: see https://github.com/JuliaLang/julia/issues/16344.

A slightly more advanced option (based on [this proposal](http://stackoverflow.com/a/35351145/392585)) is:

``` julia
import Base: significand_mask, significand_bits, exponent_half
function f2(u::UInt64)
f = reinterpret(Float64, exponent_half(Float64) | 0x001f_ffff_ffff_ffff & u)
if (u >> significand_bits(Float64)) &1 == 1
f-= 0.5
end
f
end
```

This gets us 53 bits, but introduces a branch. There might be some clever stuff we can do here though.

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