uniform_01 improvement

[agribov_no_s_p_a_m@…]

The current code to simulate uniform random number in interval [0;1] contains verification to skip 1.

if (result < result_type(1))

return result;

It means that random generator can generate 0 but not 1. This is used in some other code, for example, generate Exponential random number:

return -result_type(1) /

_lambda * log(result_type(1)-uniform_01<RealType>()(eng));

Meaning (1 - random number) will never be 0.

If eng() returns integer number, then, with some limitations for result_type and generated range of random numbers (result_type has to be double for generated 32 bit random numbers):

result_type factor = result_type(1) / (result_type((eng.max)()-(eng.min)()) + result_type(1));

return (result_type(eng() - (eng.min)()) + result_type(0.5)) * factor;

In this case, the result will never contain 0 or 1 and will be unbiased. No more checking for 0 or 1 is necessary.

[Steven Watanabe]

The check for 1 is *already* unnecessary for 32-bit integers and double. It is needed when the mantissa has fewer bits than the integer, because values close to 1 can be rounded to 1.

[anonymous]

I see, however it would be better to simulate a random number not including 0 (and 1). For example, this simplify code to generate random numbers from exponential distribution.