C++ Ranges proposal for the Standard Library

[John Colvin via Digitalmars-d]

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