Fast and Accurate Evaluation of Wigner 3j, 6j, and 9j Symbols Using Prime Factorization and Multiword Integer Arithmetic
Artikel i vetenskaplig tidskrift, 2016

We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and square roots of ratios of integers. The integers can be very large due to factorials. We avoid numerical precision loss due to cancellation through the use of multiword integer arithmetic for exact accumulation of all sums. A fixed relative accuracy is maintained as the limited number of floating-point operations in the final step incur rounding errors only in the least significant bits. Time spent to evaluate large multiword integers is in turn reduced by using explicit prime factorization of the ingoing factorials, thereby improving execution speed. Comparison with existing routines shows the efficiency of our approach, and we therefore provide a computer code based on this work.

multiword integer arithmetic

quantum theory of angular

computational physics

prime factorization


Håkan T Johansson

Chalmers, Fysik, Subatomär fysik och plasmafysik

Christian Forssen

Chalmers, Fysik, Subatomär fysik och plasmafysik

SIAM Journal of Scientific Computing

1064-8275 (ISSN) 1095-7197 (eISSN)

Vol. 38 1 A376-A384

Ab initio approach to nuclear structure and reactions (++) (ANSR)

Europeiska kommissionen (EU) (EC/FP7/240603), 2009-12-01 -- 2014-11-30.



Annan fysik


Grundläggande vetenskaper


C3SE (Chalmers Centre for Computational Science and Engineering)



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