Kahan summation

Raku does not offer a fixed precision decimal. It does have IEEE 754 floating point numbers so let's try implementing the floating point option as shown in Python. Need to explicitly specify scientific notation numbers to force floating point Nums.

constant ε = (1e0, */2e0 … *+1e0==1e0)[*-1];

sub kahan (*@nums) {
    my $summ = my $c = 0e0;
    for @nums -> $num {
        my $y = $num - $c;
        my $t = $summ + $y;
        $c = ($t - $summ) - $y;
        $summ = $t;
    }
    $summ
}

say 'Epsilon:    ', ε;

say 'Simple sum: ', ((1e0 + ε) - ε).fmt: "%.16f";

say 'Kahan sum:  ', kahan(1e0, ε, -ε).fmt: "%.16f";

Output:

Epsilon:    1.1102230246251565e-16
Simple sum: 0.9999999999999999
Kahan sum:  1.0000000000000000