Kahan summation: Difference between revisions
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With "down" and "floor" rounding, the Kahan sum is too low (10005.8), but any other rounding makes it correct (10005.9).
The Associative largest-to-smallest sum is never correct: "up" and "ceiling" rounding make it too high, while the rest make it low.
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<lang vbnet>Module Module1
Function KahanSum(ParamArray fa As Single()) As Single
Dim sum = 0.0F
Dim c = 0.0F
For Each f In fa
Dim y = f - c
Dim t = sum + y
c = (t - sum) - y
sum = t
Next
Return sum
End Function
Function Epsilon() As Single
Dim eps = 1.0F
While 1.0F + eps <> 1.0F
eps /= 2.0F
End While
Return eps
End Function
Sub Main()
Dim a = 1.0F
Dim b = Epsilon()
Dim c = -b
Console.WriteLine("Epsilon = {0}", b)
Console.WriteLine("(a + b) + c = {0}", (a + b) + c)
Console.WriteLine("Kahan sum = {0}", KahanSum(a, b, c))
End Sub
End Module</lang>
{{out}}
<pre>Epsilon = 1.110223E-16
(a + b) + c = 1
Kahan sum = 1</pre>
=={{header|zkl}}==
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