sub bit_vec {
  my ( $template, @rest ) = @_;  # to conform to pack's proto
  my $p = pack $template, @rest;
  return map vec( $p, $_, 1 ), 0..( ( length $p ) * 8 ) - 1;
}

sub ieee_fp_bit_string {
  my $f = shift;
  my $template = shift || 'd';
  die q(Template must be 'f' or 'd')
    unless $template eq 'f' || $template eq 'd';

  my @bits = reverse bit_vec( $template, $f );
  my ( $e, $m ) = $template eq 'f' ? ( 8, 32 ) : ( 11, 64 );
  return join ' ',
    $bits[ 0 ],
    join( '', @bits[ 1..$e ] ),
    join( '', @bits[ $e+1..$m-1 ] );
}

sub show {
  my $f = shift;
  my $fs = sprintf( '%g', $f );
  printf "%-12s: %s\n", $fs, ieee_fp_bit_string( $f, 'f' );
}

show( $_ ) for 4 * atan2( 1, 1 ),       # pi
               1,
               1 + 2**-23,              # 1 + POSIX::FLT_EPSILON
               4,                  
               4 - 2**-22,
               2**126 * ( 4 - 2**-22 ), # largest IEEE float
               2**-126,                 # smallest normalized IEEE float
               2**-149;                 # smallest unnormalized IEEE float

__END__
3.14159     : 0 10000000 10010010000111111011011
1           : 0 01111111 00000000000000000000000
1           : 0 01111111 00000000000000000000001
4           : 0 10000001 00000000000000000000000
4           : 0 10000000 11111111111111111111111
3.40282e+38 : 0 11111110 11111111111111111111111
1.17549e-38 : 0 00000001 00000000000000000000000
1.4013e-45  : 0 00000000 00000000000000000000001