Probability Distribution and Statistical Functions -- Uniform Distribution Module #272
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changed the object name from stdlib_stats_distribution_implementation.o to stdlib_stats_distribution_imp.o
Jim-215-Fisher
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Jim-215-Fisher
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| ! Based on the paper by Frederic Goualard, "Generating Random Floating- | ||
| ! Point Numbers By Dividing Integers: a Case Study", Proceedings of | ||
| ! ICCS 2020, June 20202, Amsterdam, Netherlands | ||
| ! |
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Note that Goualard mentions dividing integers by a Mersenne number to make a floating-point number to make a point that doing so can lead to non-uniformity issues, and not necessarily to show that libraries should generate random floating-point numbers this way. He makes the same point with dividing integers by a power of 2.
Also, there are ways to implement uniform floating-point number generation that covers all numbers the real type covers in [0, 1], but in general they are far from trivial which is why I don't demand it here. Examples include the Rademacher Floating-Point Library by @christophe-conrads as well as an algorithm I give.
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Not quite understand your point. Yes, dividing Mersenne integer leads to non-uniformity. Multiplying the inverse of the same number reduces the issue significantly.
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My point is indeed to reduce non-uniformity, especially since this code is intended to form part of the standard library and thus be used by thousands of applications with different requirements, and while some of them may not care about the statistical quality of pseudorandom numbers, others may. In this sense, of the methods that involve multiplying or dividing an integer by a constant to create a binary64, the "best" one is to multiply a binary64 integer in [1, 2^53) (which is representable in binary64) by the binary64 constant 1/2^53. This is "better" than multiplying an integer by a Mersenne number or its inverse, because it "better" ensures the binary64 values are evenly spaced in [0, 1] as the result of the multiplication is representable in binary64. This difference is illustrated if we multiply 5201 by either 1/2^53 or 1/2^53-1 (in exact rational arithmetic), then convert the result to binary64 and back. (Notice that I put "best" and "better" in quotes here, in part because, in my opinion, floating-point random numbers should be avoided whenever random integers or random rational numbers suffice.)
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Based on Goualard paper, the best one is a binary64 integer in [1, 2^53) multiplying a float of 1/(2^53-1) as shown in Fig 7. in the paper. This is exactly what I implemented in the module. Dividing binary64 integer by 2^53 leads to more non-uniformity as GNU Fortran 9.2.0 does.
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@jvdp1 @Jim-215-Fisher Can this PR go forward or are there still some changes needed? |
Links for FORD should be checked before merging. I'll try to check ASAP |
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All corrections have been applied except links for FORD.
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@Jim-215-Fisher I opened a PR with some changes regarding links, meta-info, and specs in your Github directory Jim-215-Fisher#25 . When this is merged I will approve this PR. |
Proposed changes regarding links, meta-info and specs
@jvdp1 The PR has been applied and merged. All checks have passed. |
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Thank you @Jim-215-Fisher for this PR. LGTM.
@milancurcic @awvwgk @ivan-pi Could you have a last look at this PR, and merge it if OK?
@gareth-nx @epagone Could you approve this PR, please, if you are happy with it as is?
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Thank you @Jim-215-Fisher . It seems that all comments and requests were answered. If no other comments before tomorrow, then I will merge it. |
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Thank you @Jim-215-Fisher for this PR. I'll merge it. |
This is part of probability distribution and statistical functions for uniform distribution. In addition to original real variable functions, integer and complex variables related functions were added. The files uploaded are:
src/stdlib_stats_distribution_uniform.fypp
src/CMakeLists.txt
src/Makefile.manual
src/tests/stats/test_distribution_uniform.f90
src/tests/CMakeLists.txt
src/tests/Makefile.manual
doc/specs/index.md
doc/specs/stdlib_stats_distribution_uniform.md