You could also create the bit pattern yourself and unpack it. It's system dependant, but it will allow you to generate every possible special value.

For example, Windows uses little-endian IEEE

sub double_from_hex { unpack 'd', scalar reverse pack 'H*', $_[0] }

use constant POS_INF => double_from_hex '7FF0000000000000';
use constant NEG_INF => double_from_hex 'FFF0000000000000';

use constant qNaN    => double_from_hex '7FF8000000000000';
use constant NaN     => qNaN;

print(POS_INF, "\n");  # 1.#INF
print(NEG_INF, "\n");  # -1.#INF
print(qNaN,    "\n");  # 1.#QNAN
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x86 doesn't seem to have signaled NaNs or they're not recognized when stringified. On the other hand, "FFF8000000000000" is recognized as being "-1.#IND".