# sums

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Fast sumation functions.

# Imports

math

# Funcs

    func sumKbn[T](x: openArray[T]): T

  Kahan (compensated) summation: O(1) error growth, at the expense of a considerable increase in computational expense. Source Edit

    func sumPairs[T](x: openArray[T]): T

  Pairwise (cascade) summation of `x[i0:i0+n-1]`, with O(log n) error growth (vs O(n) for a simple loop) with negligible performance cost if the base case is large enough.

  See, e.g.:

  - http://en.wikipedia.org/wiki/Pairwise_summation Higham, Nicholas J. (1993), "The accuracy of floating point summation", SIAM Journal on Scientific Computing 14 (4): 783–799.

  In fact, the root-mean-square error growth, assuming random roundoff errors, is only O(sqrt(log n)), which is nearly indistinguishable from O(1) in practice. See:

  - Manfred Tasche and Hansmartin Zeuner, Handbook of Analytic-Computational Methods in Applied Mathematics (2000).
  Source Edit