Subtract with carry
Lua error in package.lua at line 80: module 'strict' not found. Subtract-with-carry is a pseudorandom number generator of the lagged Fibonacci type introduced by George Marsaglia and Arif Zaman in 1991.[1] It is one of three random number generator engines included in the standard C++11 library.[2]
Sequence generated by the subtract-with-carry engine may be described by the recurrence relation:
where Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): cy(i) = \begin{cases} 1, & \text{if } x(i-S) - x(i-R) - cy(i-1) < 0\\ 0, & \text{otherwise} \end{cases} .
Constants S and R are known as the short and long lags, respectively.[3] Therefore, expressions 
and 
correspond to the S-th and R-th previous terms of the sequence. S and R satisfy the condition 
. Modulus M has the value 
, where W is the word size, in bits, of the state sequence and 
.
The subtract-with-carry engine is one of the family of generators which includes as well add-with-carry and subtract-with-borrow engines.[1]
References
- ↑ 1.0 1.1 A New Class of Random Number Generators, George Marsaglia and Arif Zaman, The Annals of Applied Probability, Vol. 1, No. 3, 1991
- ↑ std::subtract_with_carry_engine, cppreference.com
- ↑ subtract_with_carry_engine Class, Microsoft Visual Studio 2015
