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1. zimmermann6 commented on Jun 2, 2021

   

   zimmermann6

   on Jun 2, 2021

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   maybe you should mention the version of glibc you are comparing to, since starting from 2.28, the slow paths have been removed from some functions, improving their speed at the expense of less accurate results. In the next release (2.34) the slow path will be removed for tan, asin, acos, atan, and atan2 (all for double precision).

   #include <gnu/libc-version.h>
         printf("GNU libc version: %s\n", gnu_get_libc_version ());
         printf("GNU libc release: %s\n", gnu_get_libc_release ());
   
2. jessymilare commented on Jun 2, 2021

   

   jessymilare

   on Jun 2, 2021

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   maybe you should mention the version of glibc you are comparing to, since starting from 2.28, the slow paths have been removed from some functions, improving their speed at the expense of less accurate results. In the next release (2.34) the slow path will be removed for tan, asin, acos, atan, and atan2 (all for double precision).

   #include <gnu/libc-version.h>
         printf("GNU libc version: %s\n", gnu_get_libc_version ());
         printf("GNU libc release: %s\n", gnu_get_libc_release ());
   

   Got this:
   GNU libc version: 2.33
   GNU libc release: release
3. jessymilare commented on Jun 2, 2021

   

   jessymilare

   on Jun 2, 2021

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   What does MPS mean? I usually see speed comparisons reported as microsecond per call or cycles per call. Also, what are the compiler options used in building system libm and openlibm with both compilers?

   The benchmark code is test/libm-bench.cpp. MPS means millions (calls) per second (see #36).
4. jessymilare commented on Jun 3, 2021

   

   jessymilare

   on Jun 3, 2021

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   What does MPS mean? I usually see speed comparisons reported as microsecond per call or cycles per call. Also, what are the compiler options used in building system libm and openlibm with both compilers?

   The benchmark code is test/libm-bench.cpp. MPS means millions (calls) per second (see #36).

   Thanks for pointing to the benchmark. What I'm curious about is the compilation options for the libraries and when building the benchmark. For example, the system libm may have been compiled for the lowest common denominator for an X86_64 system while openlibm is compiled with -march=native. In addition, it is important at least with GCC to use the -fno-builtins option when linking against libm to ensure the math library functions are actually called.

   Openlibm was built with flags -fno-gnu89-inline -fno-builtin -O3 -fPIC -m64 -std=c99 -Wall and the output of make bench was:

   jessica@jessica-Kubuntu-ROG-Strix-G531GT:~/Dev/openlibm-0.7.5$ cd test/
   jessica@jessica-Kubuntu-ROG-Strix-G531GT:~/Dev/openlibm-0.7.5/test$ make bench
   cc   -fno-gnu89-inline -fno-builtin -O3 -fPIC -m64 -std=c99 -Wall -I/home/jessica/Dev/openlibm-0.7.5 -I/home/jessica/Dev/openlibm-0.7.5/include -I/home/jessica/Dev/openlibm-0.7.5/amd64 -I/home/jessica/Dev/openlibm-0.7.5/src -DASSEMBLER -D__BSD_VISIBLE -Wno-implicit-function-declaration -I/home/jessica/Dev/openlibm-0.7.5/ld80  -m64 libm-bench.cpp -lm -o bench-syslibm
   cc1plus: warning: command-line option ‘-Wno-implicit-function-declaration’ is valid for C/ObjC but not for C++
   cc1plus: warning: command-line option ‘-std=c99’ is valid for C/ObjC but not for C++
   cc1plus: warning: command-line option ‘-fno-gnu89-inline’ is valid for C/ObjC but not for C++
   cc   -fno-gnu89-inline -fno-builtin -O3 -fPIC -m64 -std=c99 -Wall -I/home/jessica/Dev/openlibm-0.7.5 -I/home/jessica/Dev/openlibm-0.7.5/include -I/home/jessica/Dev/openlibm-0.7.5/amd64 -I/home/jessica/Dev/openlibm-0.7.5/src -DASSEMBLER -D__BSD_VISIBLE -Wno-implicit-function-declaration -I/home/jessica/Dev/openlibm-0.7.5/ld80  -m64 libm-bench.cpp -L.. -lopenlibm -Wl,-rpath=/home/jessica/Dev/openlibm-0.7.5 -o bench-openlibm
   cc1plus: warning: command-line option ‘-Wno-implicit-function-declaration’ is valid for C/ObjC but not for C++
   cc1plus: warning: command-line option ‘-std=c99’ is valid for C/ObjC but not for C++
   cc1plus: warning: command-line option ‘-fno-gnu89-inline’ is valid for C/ObjC but not for C++
   
5. t-bltg commented on Sep 24, 2021

   

   t-bltg

   on Sep 24, 2021

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   Also reproduced with glibc 2.34, Intel(R) Xeon(R) CPU E5-2670 0 @ 2.60GHz:

   $ cd test; make bench
   $ diff -y <(echo bench-syslibm; ./bench-syslibm) <(echo bench-openlibm; ./bench-openlibm)
   bench-syslibm						      |	bench-openlibm
     pow     :  30.8371 MPS				      |	  pow     :  12.1320 MPS
     hypot   :  82.2698 MPS				      |	  hypot   :  56.0207 MPS
     exp     :  98.3850 MPS				      |	  exp     :  79.9451 MPS
     log     :  101.1390 MPS				      |	  log     :  71.0276 MPS
     log10   :  63.9289 MPS				      |	  log10   :  57.6193 MPS
     sin     :  80.4622 MPS				      |	  sin     :  103.3160 MPS
     cos     :  85.3477 MPS				      |	  cos     :  92.5908 MPS
     tan     :  65.5768 MPS				      |	  tan     :  53.8914 MPS
     asin    :  88.9095 MPS				      |	  asin    :  64.9857 MPS
     acos    :  81.0402 MPS				      |	  acos    :  70.5646 MPS
     atan    :  82.0650 MPS				      |	  atan    :  70.4644 MPS
     atan2   :  28.3463 MPS				      |	  atan2   :  34.4602 MPS
6. zimmermann6 commented on Mar 13, 2023

   

   zimmermann6

   on Mar 13, 2023

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   see https://members.loria.fr/PZimmermann/papers/accuracy.pdf (which uses Intel's compiler from 2023)
7. zimmermann6 commented on Mar 13, 2023

   

   zimmermann6

   on Mar 13, 2023

   Last edited by zimmermann6

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   Do standard functions use other standard functions internally?

   no, as far as I know.

   Also, should not it be possible to write a wrapper around the double precision worst cases? Will that descrease max error?

   I believe the answer is no, since worst cases are in regions where the algorithm used has a bad accuracy. If you add a special case for one input, another one near that input will also give a large error.

   Yes all CRlibm functions have maximal error 0.5 ulp, as do the functions from CORE-MATH (https://core-math.gitlabpages.inria.fr/)
8. zimmermann6 commented on Mar 15, 2023

   

   zimmermann6

   on Mar 15, 2023

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   Why possible? cannot you trace the memory in IDA pro/radare2 to say that for sure?

   I don't have the knowledge to do that.

   Also reading your paper I see there is no mention of complex numbers at all (why?)

   the paper is already quite long, feel free to do the same for complex numbers !

   and I see there is no speed comparisons

   we prefer to focus on accuracy

   which THIS issue is all about

   sorry I answered your question about worst cases
9. zimmermann6 commented on Mar 15, 2023

   

   zimmermann6

   on Mar 15, 2023

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   Are you aware of any evidence of Windows vs Linux issues?

   yes, the next update of https://members.loria.fr/PZimmermann/papers/accuracy.pdf will include the Microsoft math library

   BTW, is it possible to fix fdlibm with regards to pow(10, -5) printing 0.000009999999999999999 instead of just 0.0001?

   1/10^5 is not exactly representable in binary. I prefer 0.000009999999999999999 which recalls you this fact.
   But OpenJDK has now a new algorithm for printing floating-point numbers.
10. zimmermann6 commented on Mar 16, 2023

    

    zimmermann6

    on Mar 16, 2023

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    Microsoft just uses AMD

    I'm not sure, since for the binary64 pow function, the largest error I get with AMD Libm 4.0 is 0.762 ulp (for x=0x1.00a000205d461p+1 and y=-0x1.fd35c41fc20bbp+9), whereas with Visual Studio 2022 I get 91.3 ulps (with x=0x1.fffff9c61ce40p-1 and y=0x1.c4e304ed4c734p+31).