c++ - Convert "__m256 with random-bits" into float values of [0, 1] range

Question

I have a __m256 value that holds random bits.

I would like to to "interpret" it, to obtain another __m256 that holds float values in a uniform [0.0f, 1.0f] range.

Planning to do it using:

__m256 randomBits = /* generated random bits, uniformly distribution */;
__m256 invFloatRange =  _mm256_set1_ps( numeric_limits<float>::min() ); //min is a smallest increment of float precision

__m256 float01 =  _mm256_mul(randomBits, invFloatRange);
//float01 is now ready to be used

Question 1:

However, will this cause a problem in very rare cases where randomBits has all bits as 1 and is therefore NAN?

What can I do to protect myself from this?

I want the float01 to always be a usable number

Question 2:

Will the [0 to 1] range remain uniform after I obtain it using the above approach? I know float has varying precision at different magnitudes

Answer 1

Reinterpreting an int32_t as float, one can

 auto const one = _mm256_set1_epi32(0x7f800000);
 a = _mm256_and_si256(a, _mm256_set1_epi32(0x007fffff));
 a = _mm256_or_si256(a, one);
 return _mm256_sub_ps(_mm256_castsi256_ps(a), _mm256_castsi256_ps(one));

The and/or sequence will reuse the 23 LSBs of the input sequence to produce a uniform distribution of values between 1.0f <= a < 2.0f. And then the bias of 1.0f is removed.