I've used this:

sub double_to_bin {
   my $n = shift;

   my ( $s, $e, $m ) =
      unpack "a1 a11 a52",
         unpack "B64",
            pack "d>", $n;

   $e = oct( "0b$e" );
   if ( $e == 0x7FF ) {
      if ( $m =~ /^0+\z/ ) {
         return $s ? "-inf" : "+inf" ;
      } else {
         return "nan";
      }
   }

   my $n_bin = ( $e ? "1" : "" ) . $m;

   $e -= 1023;
   if ( $e < 0 ) {
      $n_bin = "0." . ( "0" x ( -$e - 1 ) ) . $n_bin;
   } else {
      my $z = ( $e + 1 ) - length( $n_bin );
      if ( $z >= 0 ) {
         $n_bin .= "0" x $z;
      } else {
         substr( $n_bin, $e+1, 0, "." );
      }
   }

   $n_bin =~ s/^0+(?=[01])//;
   if ( $n_bin =~ /\./ ) {
      #$n_bin =~ s/0+\z//;
      $n_bin =~ s/\.\z//;
   }

   $n_bin = ( $s ? "-" : "" ) . $n_bin;

   return $n_bin;
}
[download]

Handles subnormals, infinities and NaNs. [Updated to handle the latter two.]

To print the exact value in decimal, you need up to 1074 decimal places (%.1074f) or 751 in scientific notation (%.751g) for IEEE doubles.

$ perl -e'printf "%.751g\n", unpack "d", pack "Q", 1'
4.94065645841246544176568792868221372365059802614324764425585682500675
+507270208751865299836361635992379796564695445717730926656710355939796
+398774796010781878126300713190311404527845817167848982103688718636056
+998730723050006387409153564984387312473397273169615140031715385398074
+126238565591171026658556686768187039560310624931945271591492455329305
+456544401127480129709999541931989409080416563324524757147869014726780
+159355238611550134803526493472019379026810710749170333222684475333572
+083243193609238289345836806010601150616980975307834227731832924790498
+252473077637592724787465608477820373446969953364701797267771758512566
+055119913150489110145103786273816725095583738973359899366480994116420
+5702637090279242767544565229087538682506419718265533447265625e-324
[download]