use Math::Random::MT qw[ srand rand ];
use POSIX qw[ frexp ];

sub bigRand {
    my $max = shift;
    my $exp = scalar frexp( $max );
    ++$exp if $exp &1;             ## Update: Didn't work if exponent was odd.
    my $halfbits = $exp / 2;

    my @rand = map{ rand 2**$halfbits } 1 .. 2;
    my $rand = ( $rand[ 0 ] * 2**$halfbits ) + $rand[ 1 ]; 
                             ## Updated: Use * not << for floats!
    my $rv = int( $rand * ( $max / 2**$exp ) ); ## Update: Less roundoff

}