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use Benchmark qw(:all);
use  Math::BigInt;
...
        'iterate' => sub { iterate( 100) },
        'direct' =>  sub { direct(  100) },
    });

Benchmark: timing 1000 iterations of direct, iterate, recurse...
    direct:  1 wallclock secs ( 1.68 usr +  0.00 sys =  1.68 CPU) @ 59
+5.24/s (n=1000)
...
iterate 104/s      --     -0%    -82%
recurse 105/s      0%      --    -82%
direct  595/s    470%    468%      --

use Benchmark qw(:all);
use Math::GMP;
...
        'iterate' => sub { iterate( 25_000) },
        'direct' =>  sub { direct(  25_000) },
    });

Benchmark: timing 10 iterations of direct, iterate, recurse...
    direct:  0 wallclock secs ( 0.24 usr +  0.01 sys =  0.25 CPU) @ 40
+.00/s (n=10)
...
iterate 1.28/s      --     -1%    -97%
recurse 1.29/s      1%      --    -97%
direct  40.0/s   3024%   2992%      --