For a program I wrote to find Euler bricks (rectangular solids where all 3 edges and all three face diagonals are integers), the run time for longest edge < 2^32 and shortest edge < 2^15.5 = 46341 was 10.8s without bigint and 549.4s with bigint. That's a 51X slowdown. However, I believe the problem is mainly in multiplication rather than addition. I noticed that the largest multiplier in my program was 3, so I tried replacing 2*a with a+a and 3*a with a+a+a. The runtime was then 24.8s, only a 2.3X slowdown. I can live with that, even if it gets somewhat worse for larger numbers, in order to guarantee correctness.

Specifically, I rewrote:

        # Now recursively generate the ternary tree.
        # (Note that the terms are the same in each branch except for 
+sign.)

        # Branch 1 (+-+):
        $i =   $a - 2*$b + 2*$h;
        $j = 2*$a -   $b + 2*$h;
        $k = 2*$a - 2*$b + 3*$h;
        &generate($i,$j,$k);

        # Branch 2 (+++):
        $i =   $a + 2*$b + 2*$h;
        $j = 2*$a +   $b + 2*$h;
        $k = 2*$a + 2*$b + 3*$h;
        &generate($i,$j,$k);

        # Branch 3 (-++):
        $i =   -$a + 2*$b + 2*$h;
        $j = -2*$a +   $b + 2*$h;
        $k = -2*$a + 2*$b + 3*$h;
        &generate($i,$j,$k);
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        # Now recursively generate the ternary tree.
        # (Note that the terms are the same in each branch except for 
+sign.)

        # Code to test whether bigint is mainly slowed by multiplies.
        $a2 = $a + $a;
        $b2 = $b + $b;
        $h2 = $h + $h;
        $h3 = $h + $h2;

        # Branch 1 (+-+):
        $i = $a  - $b2 + $h2;
        $j = $a2 - $b  + $h2;
        $k = $a2 - $b2 + $h3;
        &generate($i,$j,$k);

        # Branch 2 (+++):
        $i = $a  + $b2 + $h2;
        $j = $a2 + $b  + $h2;
        $k = $a2 + $b2 + $h3;
        &generate($i,$j,$k);

        # Branch 3 (-++):
        $i = -$a  + $b2 + $h2;
        $j = -$a2 + $b  + $h2;
        $k = -$a2 + $b2 + $h3;
        &generate($i,$j,$k);
[download]