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The Lehmer random number generator [1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
The CLCG provides an efficient way to calculate pseudo-random numbers. The LCG algorithm is computationally inexpensive to use. [3] The results of multiple LCG algorithms are combined through the CLCG algorithm to create pseudo-random numbers with a longer period than is achievable with the LCG method by itself. [3]
Visualisation of generation of pseudo-random 32-bit integers using a Mersenne Twister. The 'Extract number' section shows an example where integer 0 has already been output and the index is at integer 1. 'Generate numbers' is run when all integers have been output.
For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 21 random samples (a little over two million), etc ...
These approaches combine a pseudo-random number generator (often in the form of a block or stream cipher) with an external source of randomness (e.g., mouse movements, delay between keyboard presses etc.). /dev/random – Unix-like systems; CryptGenRandom – Microsoft Windows; Fortuna; RDRAND instructions (called Intel Secure Key by Intel ...
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ALGLIB is an open source / commercial numerical analysis library with C++ version; Armadillo is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use. [1] It employs template classes, and has optional links to BLAS and LAPACK. The syntax is similar to MATLAB.
Xorshift random number generators, also called shift-register generators, are a class of pseudorandom number generators that were invented by George Marsaglia. [1] They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation in software without the excessive use of sparse polynomials . [ 2 ]