fraction_floats.jl

function fraction_floats(float_type, int_type)
    # Size in bits of the integer type
    int_size = sizeof(int_type) * 8
    # Number of bits of the mantissa of the floating point type
    mantissa_size = Base.significand_bits(float_type)
    s = BigInt(2) ^ (mantissa_size + 1)
    # Make sure this is the maximum integer of type `int_type` representable
    # with the floating point type
    @assert s == maxintfloat(float_type, int_type)
    for n in (mantissa_size + 2):int_size
        s += BigInt((BigInt(2) ^ n - BigInt(2) ^ (n - 1)) / BigInt(2) ^ (n - (mantissa_size + 1)))
    end
    # Return the fraction of the `int_type` numbers `x` for which `float_type(x) == float_type(x + 1)`
    return (1 - s / BigInt(2) ^ int_size)
end