Just a quick calculation in a one-liner: 
$  time  perl -E 'my $c = log(2) * 1024000; my $d = $c / log(1e100);
> $d = int $d;  say $d; $c = $c - log(1e100) for 1..$d;
> say $c; say "Value is: ",  exp $c,  " x 1e${d}00";'
3082
125.987232628425
Value is: 5.19469341155068e+54 x 1e308200

real    0m0.039s
user    0m0.030s
sys     0m0.000s

[download]
The last decimals are certainly wrong, but it seems that we can say that 5.194693e+308254 is a fair approximation, obtained in 39 milliseconds.

Update (at 16:36 UTC): A better version of more or less the same: 

$ time  perl -E 'my $c = log(2) * 1024000; my $d = int ( $c / log(1e10
+0));
>  say $d; $c = $c - $d *  log(1e100);
> say $c; say "Value is: ",  exp $c,  " x 1e${d}00";'
3082
125.987232618965
Value is: 5.19469336241126e+54 x 1e308200

real    0m0.036s
user    0m0.000s
sys     0m0.046s

[download]
Update 2: fixed a wrong print out of the value.

Je suis Charlie.

In reply to Re: Efficiently working with huge exponents by Laurent_R
in thread Efficiently working with huge exponents by wanna_code_perl

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