Kahan summation: Difference between revisions
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{{out}}<pre>Simple: 1.00000E +4 + 3.14159E +0 + 2.71828E +0 = 1.00058E +4
Kahan : 1.00000E +4 + 3.14159E +0 + 2.71828E +0 = 1.00059E +4</pre>
=={{header|AWK}}==
<lang AWK>
# syntax: GAWK -f KAHAN_SUMMATION.AWK
# converted from C
BEGIN {
epsilon = 1
while (1 + epsilon != 1) {
epsilon /= 2
}
arr[1] = a = 1.0
arr[2] = b = epsilon
arr[3] = c = -b
printf("Epsilon = %18.16g\n",b)
printf("(a+b)+c = %18.16f\n",(a+b)+c)
printf("Kahan sum = %18.16f\n",kahan_sum(arr))
exit(0)
}
function kahan_sum(nums, c,i,sum,t,y) {
for (i=1; i<=length(nums); i++) {
y = nums[i] - c
t = sum + y
c = (t - sum) - y
sum = t
}
return(sum)
}
</lang>
{{out}}
<pre>
Epsilon = 1.110223024625157e-016
(a+b)+c = 0.9999999999999999
Kahan sum = 1.0000000000000000
</pre>
=={{header|C}}==
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