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Barrett reduction
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Barrett reduction : ウィキペディア英語版
Barrett reduction
In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett. A naive way of computing
:c = a \,\bmod\, n. \,
would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming n is constant, and a, replacing divisions by multiplications.
== General idea ==

Let m=1/n be the inverse of n as a floating point number. Then
:a \,\bmod\, n = a-\lfloor a m\rfloor n
where \lfloor x \rfloor denotes the floor function. The result is exact, as long as m is computed with sufficient accuracy.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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