9 citations · 30 across the 18 of their papers we have counts for
20 papers
A Branch-Free General Renormalization Scheme for Pair Arithmetic and Its Performance Evaluation
Tomonori Kouya
Pair arithmetic omits the renormalization stage performed at the end of each operation of multi-component multiple-precision arithmetic, reducing the operation count and, by elimin…
Performance Evaluation of an Adaptive Quadrature and a Double Exponential Formula Using Arbitrary-Precision Floating-Point Arithmetic
Tomonori Kouya
Using arbitrary-precision arithmetic provided by the GNU Multiple Precision Floating-Point Reliable Library, we implement AQE11D---that is, Ninomiya's adaptive 9-point Newton--Cote…
Accelerating Multiple-Precision LU Decomposition with Ozaki Scheme II
Tomonori Kouya
Solving ill-conditioned linear systems needs LU decomposition in precisions beyond binary64. The standard approaches -- GMP/MPFR, or multi-component arithmetic such as double-doubl…
Ozaki Scheme II Is Fast on CPUs Too: Multiple-Precision Matrix Multiplication on Intel AMX-INT8 and Arm SVE2-i8mm
Tomonori Kouya
We implement Ozaki Scheme II (residue number system + Chinese remainder theorem), which reduces multiple-precision dense matrix multiplication to a sequence of low-precision, high-…
Performance evaluation of branch-free fused multiply-add algorithms for multi-component-type multiple-precision floating-point arithmetic
Tomonori Kouya
Multicomponent multiple-precision arithmetic is constructed from existing floating-point operations using error-free transformations (EFTs). Its performance can be improved by empl…
Construction and Performance Evaluation of an Arbitrary-Precision Floating-Point Arithmetic Environment on CUDA
Tomonori Kouya
Arbitrary-precision floating-point arithmetic is used to solve ill-conditioned problems in scientific computing, and MPFR and MPC have become the de facto standard libraries for CP…
Acceleration of multi-component multiple-precision arithmetic with branch-free algorithms and SIMD vectorization
Tomonori Kouya
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, part…
Assessing the Performance of Mixed-Precision ILU(0)-Preconditioned Multiple-Precision Real and Complex Krylov Subspace Methods
Tomonori Kouya
Krylov subspace methods are linear solvers based on matrix-vector multiplications and vector operations. While easily parallelizable, they are sensitive to rounding errors and may…
Performance evaluation of accelerated real and complex multiple-precision sparse matrix-vector multiplication
Tomonori Kouya
Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on…
Performance evaluation of accelerated complex multiple-precision LU decomposition
Tomonori Kouya
The direct method is one of the most important algorithms for solving linear systems of equations, with LU decomposition comprising a significant portion of its computation time. T…
Acceleration of Multiple Precision Matrix Multiplication using Ozaki scheme
Taiga Utsugiri, Tomonori Kouya
Optimized multiple precision basic linear computation, especially matrix multiplication, is crucial for solving ill-conditioned problems. The recently proposed Ozaki scheme, which…
Acceleration of multiple precision solver for ill-conditioned algebraic equations with lower precision eigensolver
Tomonori Kouya
There are some types of ill-conditioned algebraic equations that have difficulty in obtaining accurate roots and coefficients that must be expressed with a multiple precision float…
Accelerated Multiple Precision Direct Method and Mixed Precision Iterative Refinement on Python Programming Environment
Tomonori Kouya
Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except ``mpmath" and ``gmpy2" packages based on G…
Acceleration of multiple precision matrix multiplication based on multi-component floating-point arithmetic using AVX2
Tomonori Kouya
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-…
Performance Evaluation of an Extrapolation Method for Ordinary Differential Equations with Error-free Transformation
Tomonori Kouya
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compar…
Tuning Technique for Multiple Precision Dense Matrix Multiplication using Prediction of Computational Time
Tomonori Kouya
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision…
Performance evaluation of multiple precision matrix multiplications using parallelized Strassen and Winograd algorithms
Tomonori Kouya
It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very…
A Highly Efficient Implementation of Multiple Precision Sparse Matrix-Vector Multiplication and Its Application to Product-type Krylov Subspace Methods
Tomonori Kouya
We evaluate the performance of the Krylov subspace method by using highly efficient multiple precision sparse matrix-vector multiplication (SpMV). BNCpack is our multiple precision…
Accelerated Multiple Precision Matrix Multiplication using Strassen's Algorithm and Winograd's Variant
Tomonori Kouya
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have b…
Practical Implementation of High-Order Multiple Precision Fully Implicit Runge-Kutta Methods with Step Size Control Using Embedded Formula
Tomonori Kouya
We propose a practical implementation of high-order fully implicit Runge-Kutta(IRK) methods in a multiple precision floating-point environment. Although implementations based on IR…