60 citations · 131 across the 21 of their papers we have counts for
27 papers
Computing elementary functions using multi-prime argument reduction
Fredrik Johansson
We describe an algorithm for arbitrary-precision computation of the elementary functions (exp, log, sin, atan, etc.) which, after a cheap precomputation, gives roughly a factor-two…
Rapid computation of special values of Dirichlet -functions
Fredrik Johansson
We consider computing the Riemann zeta function and Dirichlet -functions to -bit accuracy for large . Using the approximate functional equation together wi…
Arbitrary-precision computation of the gamma function
Fredrik Johansson
We discuss the best methods available for computing the gamma function in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, al…
Computing isolated coefficients of the -function
Fredrik Johansson
We consider the problem of efficiently computing isolated coefficients in the Fourier series of the elliptic modular function . We show that a hybrid numerical-modular…
On a fast and nearly division-free algorithm for the characteristic polynomial
Fredrik Johansson
We review the Preparata-Sarwate algorithm, a simple method for computing the characteristic polynomial, determinant and adjugate of an matrix using only r…
Calcium: computing in exact real and complex fields
Fredrik Johansson
Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\…