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Kahan summation: Difference between revisions
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Kahan : 1.00000E +4 + 3.14159E +0 + 2.71828E +0 = 1.00059E +4
</pre>
=={{header|EchoLisp}}==
EchoLisp floating point numbers are always stored as double precision floating point numbers, following the international IEEE 754 standard.
<lang scheme>
;; using floating point arithmetic
;; the maximum number of decimals is 17. Floating point arithmetic is not always 100% accurate
;; even with simple data :
(+ 0.2 0.1 0.3) → 0.6000000000000001 ;; (1)
;; 👀 Will Kahan method do better ??
;; Kahan procedure :
(define ( K+ nums ( sum 0.0) (c 0.0) (y) (t))
(while (!null? nums)
(set! y (- (first nums) c))
(set! t (+ sum y))
(set! c (- (- t sum) y))
(set! sum t)
(set! nums (rest nums)))
sum)
;; 👏 👏 Kahan improves on the above (1)
(K+ '( 0.2 0.1 0.3)) → 0.6
;; using epsilon such as (1.0 + epsilon) = 1.0
;; compute 1 + epsilon - epsilon :
(define eps 1.0)
(while (!= (+ 1.0 eps) 1.0) (set! eps (// eps 2.0)))
eps → 1.1102230246251565e-16
(define a 1.0 )
(define b eps)
(define c (- b))
(writeln 'standard-add= (+ a b c))
(writeln 'Kahan-add= (K+ (list a b c)))
→ standard-add= 0.9999999999999999
→ Kahan-add= 1
</lang>
=={{header|F sharp|F#}}==
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