Subtract with carry

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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".


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

where .

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

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


  1. ^ a b A New Class of Random Number Generators, George Marsaglia and Arif Zaman, The Annals of Applied Probability, Vol. 1, No. 3, 1991
  2. ^ subtract_with_carry_engine Class, Microsoft Visual Studio 2015
  3. ^ std::subtract_with_carry_engine,