Re: adding numbers and floating point errors

[Anonymous Monk]

I htink this looks horrible, but is not :-)
You noticed the first time the error gets less than zero! If you calculate the error, you'll see it's around 10E-15 at this point (at last on my pc).

#!/usr/bin/perl
my $x=0.0;
my $y=0;
my $e_min=1.0;
my $e_max=0.0;
my $n=0;
my $e;
for ( 1 .. 999 ) {
    $x += 0.05;
    $y += 5;
    $e = abs($x - $y / 100);
    $n++ if $e == 0.0;
    $e_min = $e if $e > 0.0 && $e < $e_min;
    $e_max = $e if $e > $e_max;

    printf "%4d x = %.30f e = %E\n", $_, $x, $e;
}

printf "min %E max %E exact %d\n", $e_min, $e_max, $n;

result

 998 x = 49.899999999999302247033483581617 e = 6.963319E-13
 999 x = 49.949999999999299404862540541217 e = 7.034373E-13
min 2.775558E-17 max 7.034373E-13 exact 16

You'll find the lines arround 190 interesting:

 189 x = 9.449999999999999289457264239900 e = 0.000000E+00
 190 x = 9.500000000000000000000000000000 e = 0.000000E+00
 191 x = 9.550000000000000710542735760100 e = 0.000000E+00