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sub fmt{
    my $bin = unpack 'Q', pack 'd', $_[0];
...
    my $mant = ( $bin & 0x000FFFFFFFFFFFFF );
    sprintf "%s0x1.%xp%d", ( $sign ? '-' : '' ), $mant, $exp;
}

C:\test>fmt -- -1/9
-0x1.c71c71c71c71cp-4
...

C:\test>fmt -- "( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
+ + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/
+65536 + 1/131072 + 1/262144 + 1/524288 )"
0x1.ffffc00000000p-1