Thread overview  


March 01, 2015 std.math unittests  accuracy of floating point results  

 
Hi all, I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.). I've hit on a problem that I do not know how to handle: floating point comparison. There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80bit reals, and I am converting them to 64bit reals (Win64). The problem is that the checks are bitprecise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests: std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450 exp(1.0L) = 0x4005bf0a8b145769 = 2.7182818284590450 [1] Wolfram Alpha = 2.718281828459045235... E*E*E = 0x403415e5bf6fb105 = 20.085536923187664 exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668 Wolfram Alpha = 20.08553692318766774... I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp. dmd 2.066.1 passes these unittests with values corresponding Wolfram Alpha. (Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly) How should I go about fixing these unittests for us? Thanks, Johan [1] The correct result for exp(1.0L) I was able to obtain by enabling the LLVM intrinsic for exp, although there is a comment saying that that actually causes unittest failure. Without the LLVM intrinsic, exp(1.0L) is 1 ulp off. 
March 02, 2015 Re: std.math unittests  accuracy of floating point results  

 
Posted in reply to Johan Engelen  On Sunday, 1 March 2015 at 23:08:54 UTC, Johan Engelen wrote: > Hi all, > I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.). Guess what I'm doing. :) > I've hit on a problem that I do not know how to handle: floating point comparison. > > There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80bit reals, and I am converting them to 64bit reals (Win64). The problem is that the checks are bitprecise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests: > > std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450 > exp(1.0L) = 0x4005bf0a8b145769 = 2.7182818284590450 [1] > Wolfram Alpha = 2.718281828459045235... > > E*E*E = 0x403415e5bf6fb105 = 20.085536923187664 > exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668 > Wolfram Alpha = 20.08553692318766774... > > I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp. They are too strict. floating point math is not exact between different architectures, or even compilation flags. You can get a different result just because the compiler reordered two operations. > dmd 2.066.1 passes these unittests with values corresponding Wolfram Alpha. > > (Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly) > > How should I go about fixing these unittests for us? > > Thanks, > Johan > > [1] The correct result for exp(1.0L) I was able to obtain by enabling the LLVM intrinsic for exp, although there is a comment saying that that actually causes unittest failure. Without the LLVM intrinsic, exp(1.0L) is 1 ulp off. Take a look at bool approxEqual in std.math. A lot of unit tests use it already, but some of them don't. Every floating point comparison should be using them, in my opinion. 
March 02, 2015 Re: std.math unittests  accuracy of floating point results  

 
Posted in reply to Johan Engelen  "Johan Engelen" <j@j.nl> writes: > Hi all, > I am working on making more of the std.math unittests pass (I'm new > to the project, and it is a nice niche thing to tinker on, learning > the codebase, workflow, etc.). > I've hit on a problem that I do not know how to handle: floating point > comparison. Hi Johan. I think you are running into similar problems I ran into with 64bit reals on ARM. Hopefully there is a common solution for all 64bit real architectures. > > (Incidentally, an inaccuracy of 1 ulp also haunts a std.csv unittest, but I do not yet know why exactly) I encountered this too. I found that std.conv.parse!double with 64bit real is often off by 1 ulp compared to strod(). For 80bit reals, they match. I think the fix for this problem is a change to std.conv.parse. > How should I go about fixing these unittests for us? You could look in https://github.com/smolt/phobos/blob/ios/std/math.d and see if any changes I made for iOS may help you. I have all remaining problems marked with D versions that are prefixed with "WIP_", like WIP_FloatPrecIssue. Here are the phobos files possibly of interest: std/csv.d std/internal/math/errorfunction.d std/internal/math/gammafunction.d std/math.d Hope this helps, Dan 
March 02, 2015 Re: std.math unittests  accuracy of floating point results  

 
Posted in reply to Kevin Brogan  Hi Kevin! Hi Johan!
On Monday, 2 March 2015 at 00:30:28 UTC, Kevin Brogan wrote:
> On Sunday, 1 March 2015 at 23:08:54 UTC, Johan Engelen wrote:
>> Hi all,
>> I am working on making more of the std.math unittests pass (I'm new to the project, and it is a nice niche thing to tinker on, learning the codebase, workflow, etc.).
>
> Guess what I'm doing. :)
>
>> I've hit on a problem that I do not know how to handle: floating point comparison.
>>
>> There are some tests that check whether exp(x) works well, including overflow checks for different x. See phobos/std/math.d line 2083. The checks are defined for 80bit reals, and I am converting them to 64bit reals (Win64). The problem is that the checks are bitprecise (i.e. assert(x == y)), but the calculation results are sometimes 1 ulp off. For example, the results of two tests:
>>
>> std.math.E = 0x4005bf0a8b145769 = 2.7182818284590450
>> exp(1.0L) = 0x4005bf0a8b145769 = 2.7182818284590450 [1]
>> Wolfram Alpha = 2.718281828459045235...
>>
>> E*E*E = 0x403415e5bf6fb105 = 20.085536923187664
>> exp(3.0L) = 0x403415e5bf6fb106 = 20.085536923187668
>> Wolfram Alpha = 20.08553692318766774...
>>
>> I do not know how I can make the second test pass, without breaking the first one. I feel the tests are too strict and should allow an error of 1 ulp.
>
> They are too strict. floating point math is not exact between different architectures, or even compilation flags. You can get a different result just because the compiler reordered two operations.
I agree, too. Bitwise comparison is worse if you are working with floating points.
BTW: These fixes should go upstream. Please create Phobos PRs for them. I am happy to cherrypick these changes as soon as they committed.
Regards,
Kai

March 08, 2015 Re: std.math unittests  accuracy of floating point results  

 
Posted in reply to Kai Nacke  Thanks for the link to your branch Dan. A few 64bit fixes for gammafunction.d : https://github.com/DProgrammingLanguage/phobos/pull/3045 
March 10, 2015 Re: std.math unittests  accuracy of floating point results  

 
Posted in reply to Johan Engelen  "Johan Engelen" <j@j.nl> writes:
> Thanks for the link to your branch Dan.
>
> A few 64bit fixes for gammafunction.d : https://github.com/DProgrammingLanguage/phobos/pull/3045
Thanks back. I'll have to try it out on ARM.

Copyright © 19992018 by the D Language Foundation