For curiosity and as i have a new license i asked ChatGPT:

#!/usr/bin/env perl                                                   
+                                                                     
+                                                                     
+                                                                for m
+y $val (qw(1 -1 2 -2 1/3 -1/3)) {
    my ($s, $e, $m) = double_to_bin_parts(eval $val);
    printf "%5s: sign=%s exp=%s mantissa=%s\n", $val, $s, $e, $m;
  }

for my $expr (qw(1 -1 2 -2 1/3 -1/3)) {
    my $val = eval $expr;
    my ($s, $e, $m) = double_to_bin_parts($val);
    printf "%5s %.13a\n      %s %s %s\n", $expr, $val, $s, $e, $m;
}

sub double_to_bin_parts {
    my $n = shift;
    my $bits = unpack "B64", pack "d>", $n;
    my $sign     = substr $bits, 0, 1;
    my $exp      = substr $bits, 1, 11;
    my $mantissa = substr $bits, 12, 52;
    return ($sign, $exp, $mantissa);
}

__END__

1: sign=0 exp=01111111111 mantissa=00000000000000000000000000000000000
+00000000000000000
-1: sign=1 exp=01111111111 mantissa=0000000000000000000000000000000000
+000000000000000000
 2: sign=0 exp=10000000000 mantissa=0000000000000000000000000000000000
+000000000000000000
-2: sign=1 exp=10000000000 mantissa=0000000000000000000000000000000000
+000000000000000000
1/3: sign=0 exp=01111111101 mantissa=010101010101010101010101010101010
+1010101010101010101
-1/3: sign=1 exp=01111111101 mantissa=01010101010101010101010101010101
+01010101010101010101
 1 0x1.0000000000000p+0
   0 01111111111 0000000000000000000000000000000000000000000000000000
-1 -0x1.0000000000000p+0
   1 01111111111 0000000000000000000000000000000000000000000000000000
 2 0x1.0000000000000p+1
   0 10000000000 0000000000000000000000000000000000000000000000000000
-2 -0x1.0000000000000p+1
   1 10000000000 0000000000000000000000000000000000000000000000000000
1/3 0x1.5555555555555p-2
   0 01111111101 0101010101010101010101010101010101010101010101010101
-1/3 -0x1.5555555555555p-2
   1 01111111101 0101010101010101010101010101010101010101010101010101
[download]

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