Subtract with carry explained

Subtract-with-carry is a pseudorandom number generator: one of many algorithms designed to produce a long series of random-looking numbers based on a small amount of starting data. It is of the lagged Fibonacci type introduced by George Marsaglia and Arif Zaman in 1991.^[1] "Lagged Fibonacci" refers to the fact that each random number is a function of two of the preceding numbers at some specified, fixed offsets, or "lags".

Algorithm

Sequence generated by the subtract-with-carry engine may be described by the recurrence relation:

x(i)=(x(i-S)-x(i-R)-cy(i-1)) \bmod M

where

cy(i)=\begin{cases} 1,&ifx(i-S)-x(i-R)-cy(i-1)<0\\ 0,&otherwise \end{cases}

Constants S and R are known as the short and long lags, respectively.^[2] Therefore, expressions

x(i-S)

and

x(i-R)

correspond to the S-th and R-th previous terms of the sequence.S and R satisfy the condition

0<S<R

.Modulus M has the value

M=2^W

, where W is the word size, in bits, of the state sequence and

W>0

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]

It is one of three random number generator engines included in the standard C++11 library.^[3]

Notes and References

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap/1177005878 A New Class of Random Number Generators
https://msdn.microsoft.com/en-us/library/ee462331.aspx subtract_with_carry_engine Class
http://en.cppreference.com/w/cpp/numeric/random/subtract_with_carry_engine std::subtract_with_carry_engine