On Saturday, 18 October 2014 at 10:44:59 UTC, Ola Fosheim Grøstad
wrote:
On Saturday, 18 October 2014 at 08:21:47 UTC, eles wrote:
On Saturday, 18 October 2014 at 05:54:01 UTC, Ola Fosheim
Grøstad wrote:
On Saturday, 18 October 2014 at 04:35:07 UTC, Walter Bright
wrote:
Larger mantissa can help a little bit, but only a little bit.
https://en.wikipedia.org/wiki/Kahan_summation_algorithm
Kahan helps a little bit:
a = [math.pi*(n**9) for n in range(0,101)]
+[-math.pi*(n**9) for n in range(100,0,-1)]
print sum(a), kahan(a), fsum(a)
-1389.4713685 239.156561184 0.0
but not a lot:
a = [1e16,math.pi,-1e16]
print sum(a), kahan(a), fsum(a)
4.0 4.0 3.14159265359
a = [1e17,math.pi,-1e17]
print sum(a), kahan(a), fsum(a)
0.0 0.0 3.14159265359
auto kahanSum(R)(R input)
{
double sum = 0.0;
double c = 0.0;
foreach(double el; input)
{
double y = el - c;
double t = sum + y;
c = (t - sum) - y;
sum = t;
}
return sum;
}
import std.math;
import std.range;
import std.algorithm;
import std.stdio;
double pi = PI;
void main()
{
auto a = chain(
iota(101L).map!((x) => pi * x^^9),
iota(101L).map!((x) => -pi * x^^9)
);
writeln(kahanSum(a));
writeln(a.sum);
}
$ rdmd kahantest.d
0
-980
