[added 22...@debbugs.gnu.org to the CC list]
Leo Famulari <l...@famulari.name> writes:
> Greetings from Guix! [0]
>
> We're having trouble building ilmbase-2.2.0 for the i686 architecture on
> Linux, with gcc-4.9.3.
>
> The build process fails during testing. Specifically, it fails
> testBoxAlgo, like this:
>
> ImathTest: testBoxAlgo.cpp:892: void {anonymous}::boxMatrixTransform():
> Assertion `b21 == b2' failed.
> /gnu/store/isxqjfaglyfsbcv75y8qbqbph8v28ykr-bash-4.3.39/bin/bash: line 5:
> 4565 Aborted ${dir}$tst
>
> On our mailing list, this was suggested as the nature of the problem
> [1]:
> On Mon, Nov 30, 2015 at 10:14:49PM +0200, Ludovic Courtès wrote:
>> Right. This sounds very much like a rounding issue, whereby the
>> epsilon in floating-point number comparisons is to strict for 32-bit
>> machines.
Given that ilmbase builds successfully in Guix on x86_64, mips64el, and
armhf, and only fails on i686, I believe that Ludovic's suggestion is
right on the mark.
The issue is that the x87 instruction set (used on 32-bit Intel systems
without SSE) uses 80-bit double-extended precision internally. When
these 80-bit results are later converted to 64-bit doubles, they are
rounded a second time. This "double rounding" results in larger
round-off errors than would occur when rounding only once to 64-bit
doubles, as is done when using x86_64, SSE2, or other architectures.
For more on this, see:
https://en.wikipedia.org/wiki/Rounding#Double_rounding
Quoting from that page:
Some computer languages and the IEEE 754-2008 standard dictate that in
straightforward calculations the result should not be rounded twice.
This has been a particular problem with Java as it is designed to be
run identically on different machines, special programming tricks have
had to be used to achieve this with x87 floating point.[1][2]
[1] Samuel A. Figueroa (July 1995). "When is double rounding
innocuous?". ACM SIGNUM Newsletter (ACM) 30 (3):
21–25. doi:10.1145/221332.221334.
[2] Roger Golliver (October 1998). "Efficiently producing default
orthogonal IEEE double results using extended IEEE
hardware". Intel.
<http://www.open-std.org/JTC1/SC22/JSG/docs/m3/docs/jsgn326.pdf>
Hope this helps,
Mark
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