Cpanel web hosting - 98 RANDOM NUMBERS 3.3.4 be quite small in
98 RANDOM NUMBERS 3.3.4 be quite small in most cases. Occasionally these bounds (21) will be poor, and another type of transformation will usually get the algorithm unstuck again and reduce the bounds (see exercise 18). However, transformation (23) by itself has proved to be quite adequate for the spectral test; in fact, it has proved to be amazingly powerful when the computations are arranged as in the algorithm discussed below. *D. How to perform the spectral test. Here now is an efficient computational procedure that follows from our considerations. R. W. Gosper and U. Dieter have observed that it is possible to use the results of lower dimensions to make the spectral test significantly faster in higher dimensions. This refinement has been incorporated into the following algorithm, together with a significant simp- lification of the two-dimensional case. Algorithm S (The spectral test). This algorithm determines the value of v,=rnin{fi+…+xz ).~+.~~+…+at- s~O(modulorn) } (27) for 2 2 t < T, given a, m, and T, where 0 < a < m and a is relatively prime to m. (The number vt measures the t-dimensional accuracy of random number generators, as discussed in the text above.) All arithmetic within this algorithm is done on integers whose magnitudes rarely if ever exceed m2, except in step S8; in fact, nearly all of the integer variables will be less than m in absolute value during the computation. When vt is being calculated for t 2 3, the algorithm works with two t x t matrices U and V, whose row vectors are denoted by Vi = (uir, . . . , uit) and vi = (Wil,…, vit) for 1 5 i 5 t. These vectors satisfy the conditions uil + uuis + 1.. + ut-ruit = 0 (modulo m), 1