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