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(* Kahan summation *)
signature KAHAN = sig
type t
val zero: t
val add: t * real -> t
val sum: t -> real
val sequence: real Sequence.t -> real
val list: real list -> real
val array: real array -> real
end
structure Kahan :> KAHAN = struct
type t = real * real
val zero = (0.0, 0.0)
fun add ((s, c), x) =
let
val y = x - c
val t = s + y
in
(t, t - s - y)
end
fun sum (s, c) = s
local
fun swappedAdd (a, b) = add (b, a)
in
fun sequence e = sum (Sequence.fold swappedAdd zero e)
fun list l = sum (foldl swappedAdd zero l)
fun array a = sum (Array.foldl swappedAdd zero a)
end
end
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