(* 
 * Barrett reduction algorithm (Mathematica)
 * 
 * Copyright (c) 2019 Project Nayuki
 * All rights reserved. Contact Nayuki for licensing.
 * https://www.nayuki.io/page/barrett-reduction-algorithm
 *)


(*---- User inputs ----*)

n = 8315;  (* The modulus *)
x = 28298572;  (* Number to reduce *)


(*---- The computation ----*)

BarrettReduce[x_, n_] := Block[{k, r, t},
    If[!IntegerQ[n] || n < 3, Abort[]];
    If[!IntegerQ[x] || !(0 <= x < n^2), Abort[]];
    
    k = Ceiling[Log[2, n]];
    r = Floor[4^k / n];
    t = x - Floor[x * r / 4^k] * n;
    If[t < n, t, t - n]]

(* Self-check *)
Print[BarrettReduce[x, n]]
Print[Mod[x, n]]
Print[BarrettReduce[x, n] == Mod[x, n]]  (* Must be true *)