A primal S-matrix bootstrap framework parameterizes imaginary parts of partial waves, uses dispersion relations to enforce consistency, computes coupling bounds, and handles Regge behavior plus spinning states like glueballs.
Nakata, MPLAPACK version 1.0.0 user manual , CoRR abs/2109.13406 (2021) , [2109.13406]
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abstract
The MPLAPACK (formerly MPACK) is a multiple-precision version of LAPACK (https://www.netlib.org/lapack/). MPLAPACK version 2.0.1 is based on LAPACK version 3.9.1 and translated from Fortran 90 to C++ using FABLE, a Fortran to C++ source-to-source conversion tool (https://github.com/cctbx/cctbx_project/tree/master/fable/). MPLAPACK version 2.0.1 provides the real and complex version of MPBLAS, and the real and complex versions of MPLAPACK support all LAPACK features: solvers for systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems, and related matrix factorizations except for mixed-precision routines. The MPLAPACK defines an API for numerical linear algebra, similar to LAPACK. It is easy to port legacy C/C++ numerical codes using MPLAPACK. MPLAPACK supports binary64, binary128, FP80 (extended double), MPFR, GMP, and QD libraries (double-double and quad-double). Users can choose MPFR or GMP for arbitrary accurate calculations, double-double or quad-double for fast 32 or 64-decimal calculations. We can consider the binary64 version as the C++ version of LAPACK. Moreover, it comes with an OpenMP accelerated version of MPBLAS for some routines and CUDA (A100 and V100 support) for double-double versions of Rgemm and Rsyrk. The peak performances of the OpenMP version are almost proportional to the number of cores, and the performances of the CUDA version are impressive, and approximately 400-600 GFlops. MPLAPACK is available at GitHub (https://github.com/nakatamaho/mplapack/) under the 2-clause BSD license.
representative citing papers
Multiple double matrix multiplication on FP64 tensor cores is achieved by splitting doubles into 13-bit quarters with trailing zeros, enabling error-free inner products without branching renormalization.
citing papers explorer
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Primal S-matrix bootstrap with dispersion relations
A primal S-matrix bootstrap framework parameterizes imaginary parts of partial waves, uses dispersion relations to enforce consistency, computes coupling bounds, and handles Regge behavior plus spinning states like glueballs.
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Multiple Double Arithmetic on NVIDIA Tensor Cores
Multiple double matrix multiplication on FP64 tensor cores is achieved by splitting doubles into 13-bit quarters with trailing zeros, enabling error-free inner products without branching renormalization.