Fast and Accurate Evaluation of Wigner 3j, 6j, and 9j Symbols Using Prime Factorization and Multiword Integer Arithmetic
Fast and Accurate Evaluation of Wigner 3j, 6j, and 9j Symbols Using Prime Factorization and Multiword Integer Arithmetic
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使用质因数分解和多字整数算术快速准确地评估 Wigner 3j、6j 和 9j 符号
DOI：
10.1137/15m1021908
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. Forssén
中科院分区：
文献类型：
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作者：
H. Johansson;C. Forssén
我们提出了一种有效的Wigner$3J$、$6J$和$9J$符号求值的实现方法。它们表示角动量量子理论中使用的数值变换系数。它们可以表示为整数比率的和和平方根。由于阶乘的原因，整数可能非常大。通过使用多字整数算法对所有和进行精确累加，避免了因相消而造成的数值精度损失。当最后一步中的有限数量的浮点运算仅在最低有效位中引起舍入误差时，保持固定的相对精度。通过使用传入阶乘的显式素因式分解，进而减少了计算大型多字整数所花费的时间，从而提高了执行速度。与现有程序的比较表明，该方法是有效的，因此，我们提供了一个基于这项工作的计算机代码。
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.