Generating a random `float64` with `crypto/rand`

We went through a pen test recently, and one of the low priority items that fell out of it was the use of Go’s math/rand in a few places instead of the cryptographically secure crypto/rand. I shouldn’t have been surprised – security people hate the use of PRNGs, even when their use is deliberate and secure. In this case I’d been using a PRNG to check whether we should enable or disable random flags, and although it wasn’t a security problem, we’d recently introduced some rand helper utilities, so I switched them over anyway.

I ran into the problem that crypto/rand provides only a very minimal interface – not much more than a reader on top of the system’s version of /dev/urandom. I’d previously been using math/rand’s Float64 for flag checks and there was no equivalent.

It wasn’t too hard to put in, but doing so did make me learn a little bit about how floats are implemented. I’d previously written a helper to supplement the built-in Int by providing an easy way of generating a number between 1 an N that doesn’t require diving into math/big:

package randutil

import (
	"crypto/rand"
	"math/big"
)

// Intn is a shortcut for generating a random integer between 0 and
// max using crypto/rand.
func Intn(max int64) int64 {
	nBig, err := rand.Int(rand.Reader, big.NewInt(max))
	if err != nil {
		panic(err)
	}
	return nBig.Int64()
}

We then build on that to implement Float64:

// Float64 is a shortcut for generating a random float between 0 and
// 1 using crypto/rand.
func Float64() float64 {
	return float64(Intn(1<<53)) / (1 << 53)
}

Put simply: generate a number between 0 and 253, then divide that by 253 to get a float between 0 and 1.

Why 253? A float64 in Go consists of three parts:

  • 1 bit sign.
  • 53 bits “mantissa”, otherwise known as a coefficient or significand.
  • 10 bits signed integer exponent which modifies the magnitude of the mantissa.

So a float64’s primary value is within those 53 mantissa bits, which is why we use that number as the bound for our float calculation.

I stole the implementation from math/rand’s Float64 which notes that the float64(Intn(1<<53)) / (1 << 53) one-liner would be its implementation, if not for a concern around backwards compatibility dating back to Go 1, which ties it to a slightly more complicated version.

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Generating a random `float64` with `crypto/rand`

Published
June 2, 2022

Find me on Twitter at @brandur.

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