Trying to save the idea by reusing the non-P0952 post-processed generate_canonical with subnormal numbers in the case of -log(generate_canonical()): Internally -log(generate_canonical()) is used The case of 0 could be mapped to a number slightly lower or higher than 1 to keep statistical properties (like expected value)? Numbers around 1 cannot be represented with high accuracy, but -log(1) = -0 can.   The overall problem with statistical properties is: Having a discrete distribution with expected value and variance and putting it through a non-linear function like log changes the resulting expected value and variance slightly compared to a continuous distribution. That effect is there, even when using the fixed-point random numbers of P0952. If the discreteness is known, the distributions can apply correction factors.   -----Ursprüngliche Nachricht----- Von:Lénárd Szolnoki <cpp_at_[hidden]> Gesendet:Mo 08.12.2025 01:00 Betreff:Re: [std-proposals] solution proposal for Issue 2524: generate_canonical can occasionally return 1.0 An:std-proposals_at_[hidden]; CC:Sebastian Wittmeier <wittmeier_at_[hidden]>; On 07/12/2025 14:50, Sebastian Wittmeier via Std-Proposals wrote: > I meant something like > > val = generate_canonical(); > > if (val==0) val=1; > > Or would the remaining subnormal numbers violate the lower b bound of the interval as they > sometimes are rounded to 0? If I used 32 bit IEEE float and made a uniform distribution where every representable value was possible on the selected range, then for a uniform distribution on (0, 1] rolls 1 with probability 2^-24 or 2^-25, depending on rounding strategy. For a uniform distribution on [0, 1), 0 is rolled with probability 2^-149 or 2^-150, depending on rounding strategy and assuming that subnormals are also rolled with uniform probabilities and no representable value is skipped. The set of representable values are much more dense near 0 than near 1, hence the different probabilities. I don't think that changing such a distribution by adjusting 0 to 1 has the desired effect, at least the resulting distribution doesn't resemble a uniform distribution on (0, 1] that one would write from scratch. Having said that, if I read it right, generate_canonical as specified P0952 effectively treats float as a fixed-point number with 24 bit of mantissa, and never accesses the extra precision that is available on [0, 0.5), always skipping over subnormals and more. So there adjusting 0 to 1 works as intended, as it always produces a distribution where each possible value has the same probability. But 1-x works here as well, as there is no more precision to lose.