Random2

The Random2 class generates random real numbers in the range (0, 1). It implements, using 32-bit integers (Int's), the 'MRG31k3p' generator developed by L'Ecuyer and Touzin, described in "FAST COMBINED MULTIPLE RECURSIVE GENERATORS WITH MULTIPLIERS OF THE FORM a = 2^q +/- 2^r". MRG31k3p is a Combined Multiple Recursive Generator (CMRG) shown to have good performance and statistical properties for simulations. It has a period of about 2^185 and is considered to be a faster alternative to the popular 'MRG32k3' generator. MRG31k3p combines MRG1 and MRG2.

MRG1: x_i = (0          + a_12 x_i-2 + a_13 x_i-3) % M1
MRG2: x_i = (a_21 x_i-1 + 0          + a_23 x_i-3) % M2

where a_12 = 2^22, a_13 = 2^7+1, a_21 = 2^15 and a_23 = 2^15+1.