Kahan summation: Difference between revisions

==={{header|FreeBASIC}}===

<syntaxhighlight lang="vbnet">Dim Shared As Double a, b, c

Function KahanSum (a As Double, b As Double, c As Double) As Double

Dim As Double sum = 0.0, i, y, t

c = 0.0

For i = 1 To a

y = i - c

t = sum + y

c = (t - sum) - y

sum = t

Next i

Return sum

End Function

Function epsilon() As Double

Dim As Double eps = 1

While (1 + eps <> 1)

eps /= 2

Wend

Return eps

End Function

a = 1.0

b = epsilon()

c = -b

Dim As Double s = (a + b) + c

Dim As Double k = KahanSum(a, b, c)

Dim As Double d = k - s

Print "Epsilon ="; b

Print "(a + b) + c ="; s

Print "Kahan sum ="; k

Print "Delta ="; d

Sleep</syntaxhighlight>

{{out}}

<pre>

Epsilon = 1.110223024625157e-016

(a + b) + c = 0.9999999999999999

Kahan sum = 1

Delta = 1.110223024625157e-016

</pre>

==={{header|FutureBasic}}===

FB has proper decimal numbers supporting mantissas and exponents. But conversion to and from floating point numbers (or strings) makes it easier and more readable for this task to be completed with doubles as are many other examples here.

<syntaxhighlight lang="futurebasic">

_elements = 3

local fn Epsilon as double

double eps = 1.0

while ( 1.0 + eps != 1.0 )

eps = eps / 2.0

wend

end fn = eps

local fn KahanSum( nums(_elements) as double, count as long ) as double

double sum = 0.0

double c = 0.0

double t, y

long i

for i = 0 to count - 1

y = nums(i) - c

t = sum + y

c = (t - sum) - y

sum = t

next

end fn = sum

local fn DoKahan

double a = 1.0

double b = fn Epsilon

double c = -b

double fa[_elements]

fa(0) = a : fa(1) = b : fa(2) = c

printf @"Epsilon = %.9e", b

printF @"(a + b) + c = %.9e", (a + b) + c

printf @"Kahan sum = %.9e", fn KahanSum( fa(0), 3 )

printf @"Delta = %.9e", fn KahanSum( fa(0), 3 ) - ((a + b) + c)

end fn

fn DoKahan

HandleEvents</syntaxhighlight>

{{output}}

<pre>

Epsilon = 1.110223025e-16

(a + b) + c = 1.000000000e+00

Kahan sum = 1.000000000e+00

Delta = 1.110223025e-16

</pre>

==={{header|Visual Basic .NET}}===

{{trans|C#}}

<syntaxhighlight 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</syntaxhighlight>

{{out}}

<pre>Epsilon = 1.110223E-16

(a + b) + c = 1

Kahan sum = 1</pre>

==={{header|Yabasic}}===

{{trans|FreeBASIC}}

<syntaxhighlight lang="vbnet">a = 1.0

b = epsilon()

c = -b

s = (a + b) + c

k = KahanSum(a, b, c)

d = k - s

print "Epsilon = ", b

print "(a + b) + c = ", s

print "Kahan sum = ", k

print "Delta = ", d

end

sub KahanSum (a, b, c)

sum = 0.0

c = 0.0

for i = 1 to a

y = i - c

t = sum + y

c = (t - sum) - y

sum = t

next i

return sum

end sub

sub epsilon()

eps = 1

while (1 + eps <> 1)

eps = eps / 2.0

wend

return eps

end sub</syntaxhighlight>

{{out}}

<pre>

Epsilon = 1.11022e-16

(a + b) + c = 1

Kahan sum = 1

Delta = 1.11022e-16

</pre>