- Introduction
- Compiling and installing the library
- Math library reference
- DFT library reference
- Other tools included in the package
- Benchmark results
- Additional notes

SLEEF has two kinds of testers, and each kind of testers has its own role.

The first kind of testers is separated into tester and iut (which stands for Implementation Under Test.) Those two are built as separate executables, and communicate with each other using a pipe. The role for this tester is to perform a perfunctory set of tests to check if the build is correct. It is also performs regression tests. Since the tester executable and the iut executable are separated, the iut can be implemented with an exotic languages. It is also possible to perform a test over the network.

The second kind of testers are designed to run continuously. It repeats randomly generating arguments for each function, and comparing the results of each function to the results calculated with the corresponding function in libmpfr. This tester is expected to find bugs if it is run for sufficiently long time.

The DFT has its own tester. This tester compares the results computed by SLEEF DFT with a naive implementation.

Gencoef is a small tool for generating the coefficients for polynomial approximation used in the kernels.

In order to change the configurations, please edit gencoefdp.c. In the beginning of the file, specifications of the parameters for generating coefficients are listed. Enable one of them by changing #if. Then, run make to compile the source code. Run the gencoef, and it will show the generated coefficients in a few minutes. It may take longer time depending on the settings.

There are two phases of the program. The first phase is the regression for minimizing the maximum relative error. This problem can be reduced to a linear programming problem, and the Simplex method is used in this implementation. This requires multi-precision calculation, and the implementation uses the MPFR library to do this. In this phase, it uses only a small number of values (specified by macro S, usually less than 100) within the input domain of the kernel function to approximate the function. The function to approximate is given by FRFUNC function. Specifying higher values for S does not always give better results.

The second phase is to optimize the coefficients so that it gives good accuracy with double precision calculation. In this phase, it checks 10000 points (specified by macro Q) within the specified argument range to see if the polynomial gives good error bounds. In some cases, the last few terms have to be calculated in higher precision in order to achieve 1 ULP or less overall accuracy, and this implementation can take care of that. The L parameter specifies the number of high precision coefficients.

In some cases, it is desirable to fix the last few coefficients to values like 1 or 0.5. This can be specified if you define FIXCOEF0 macro.

Finding a set of good parameters is not a straightforward process.