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fnfeBarrettReduce(x: i16) i16 {
// This is standard Barrett reduction.
//
// For any x we have x mod q = x - ⌊x/q⌋ q. We will use 20159/2²⁶ as
// an approximation of 1/q. Note that 0 ≤ 20159/2²⁶ - 1/q ≤ 0.135/2²⁶
// and so | x 20156/2²⁶ - x/q | ≤ 2⁻¹⁰ for |x| ≤ 2¹⁶. For all x
// not a multiple of q, the number x/q is further than 1/q from any integer
// and so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋. If x is a multiple of q and x is positive,
// then x 20156/2²⁶ is larger than x/q so ⌊x 20156/2²⁶⌋ = ⌊x/q⌋ as well.
// Finally, if x is negative multiple of q, then ⌊x 20156/2²⁶⌋ = ⌊x/q⌋-1.
// Thus
// [ q if x=-nq for pos. integer n
// x - ⌊x 20156/2²⁶⌋ q = [
// [ x mod q otherwise
//
// To actually compute this, note that
//
// ⌊x 20156/2²⁶⌋ = (20159 x) >> 26.
returnx -% @as(i16, @intCast((@as(i32, x) * 20159) >> 26)) *% Q;
}
