A c++-20 template based short vector library with faithfully rounded vectorized elementary functions.
Cftal is a c++-20 template based short vector library with specializations using intrinsic functions. The library contains vectorized elementary and some special functions (erf, erfc, tgamma, lgamma, j0, y0, j1 and y1) which are part of the standard c++ math library for
- double (binary64),
- single (binary32),
- half (binary16) and
- bfloat16 (brain floating point)
precision arguments and results. The functions are probably faithfully rounded for double, single and half precision and bfloat16. The elementary functions for half precision and bfloat16 with one argument are faithfully rounded (if mpfr rounds correctly). Tests for a subset of the numbers for single and double precision show faithfully rounding compared to mpfr. The implemented special functions are fully tabulated for half and bfloat16 precision.
Specializations for x86 processors with instructions set extensions up to AVX2 are implemented and tested. The specializations for processors with AVX512 extensions are not much tested yet. AArch64 code is not tested.
The library also contains vectors with variable sizes. These use the short vectors of the library for their implementation.
- the reproduction of the used constants in the code requires sollya (https://www.sollya.org), libsollya-dev to build extensions to sollya and the maxima (https://maxima.sourceforge.io) computer algebra system
- the test code uses mpfr (https://www.mpfr.org) and requires libmpfr-dev to compile the programs testing the precision (and speed) of the vectorized elementary and special functions
- the documentation in the doc directory requires pdflatex
- cmake ist the used build system
- only linux as host and target system was tested and
- gcc or clang are the only compilers used to date
create a build directory in the root directory of the project, configure and build
mkdir buildcd buildCC=clang-18 CXX=clang++-18 cmake -DCMAKE_BUILD_TYPE=release ..
You may also use gcc instead of clang:
CC=gcc-14 CXX=g++-14 cmake -DCMAKE_BUILD_TYPE=release ..
If you want to use vectors of double's for the calculation of some elementary and special functions for single precision, use
-DCFTAL_CONFIG_USE_VF64_FOR_VF32=1
as additional cmake argument.
If you want to use vectors of float16's for the calculation of all elementary for half precision, use
-DCFTAL_CONFIG_USE_VF32_FOR_VF16=0
as additional cmake argument. The default is to calculate half precision functions using vectors of float's-
The compilation to a specific ABI is requested by configuring the library with
cmake -DCMAKE_BUILD_TYPE=release -DCFTAL_GCC_ARCH=x86-64-v3 ..
where x64-64-v3 is one of the possible arguments to gcc -march=.
The variable CFTAL_GCC_ARCH defaults to native.
To enable the experimental AVX512 support configure the library with
cmake -DCMAKE_BUILD_TYPE=release -DCFTAL_GCC_ARCH=x86-64-v4 -DCFTAL_CONFIG_ENABLE_AVX512=1 ..
or use
cmake -DCMAKE_BUILD_TYPE=release -DCFTAL_CONFIG_ENABLE_AVX512=1 ..
if your processors are avx512 capable.
During the build a number of test programs are built in ./test and a pdf is created in ./doc containing some documentation.
This project is licensed under the LGPL v2.1License.