IEEE_UNIFORM_SAMPLE is a FORTRAN90 program which samples uniformly from the IEEE numbers.
Unlike usual random number generators, which attempt to sample uniformly over a range of real numbers, this library treats the set of IEEE numbers as a discrete set, and randomly samples them. The results are very different from a uniform random number sample.
There are as many IEEE values in the interval (A,B) and the interval (1/B,1/A). This seems fine, and we need this to be so in order to have multiplicative inverses. But it also means that there are as many numbers between 1/1,000,000 and 1 as there are between 1 and 1,000,000. Since the IEEE values are naturally weighted by 2, a better way to think of this is that if there are N values between 1 and 2, then there are also N values between 2 and 4, 4 and 8, 1024 and 2048, one million and 2 million, 2 millionths and 1 millionth, and so on. The density function for the IEEE values looks like a power function 2^(-x).
Let's ignore the "bizarre" IEEE numbers, which include Inf, NaN and the denormalized numbers (very very small values). For 32 bit real numbers, this leaves us with numbers that can be described by a 1 bit sign, an 8 bit exponent biased by 127, and a 23 bit mantissa with an implicit leading 1 and an implicit divisor of 2^23.
Except when a "bizarre" creature would be created, every random sequence of 32 0's and 1's creates a legal IEEE value. So to sample from the IEEE set of values, we can simply create random strings of 0's and 1's.
The current routines are very preliminary, and even so aren't working all that well. However, the idea makes sense, and once some details are worked out, it should be easy to extend this approach to double precision values, or to allow the user to specify a "model" IEEE implementation in which the exponent and mantissa range have been modified.
I am not aware of any serious purpose to which this library could be put, but it does, I think, help in trying to understand that strange structure of the discrete set of numbers that underly almost all of our computations, and that do a reasonably good job of mimicking a continuous range of real values.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
IEEE_UNIFORM_SAMPLE is available in a FORTRAN90 version.
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You can go up one level to the FORTRAN90 source codes.