Creating Inf/NaN:

use Devel::Peek;
$inf = (~@~)**(~@~);
$nan = $inf / $inf;
Dump $_ for $inf, $nan;
__END__
SV = NV(0x9e15f84) at 0x9dfc11c
  REFCNT = 2
  FLAGS = (NOK,pNOK)
  NV = inf
SV = NV(0x9e15f9c) at 0x9dfc59c
  REFCNT = 2
  FLAGS = (NOK,pNOK)
  NV = nan
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Detecting Inf/NaN: since they are numeric values, Inf and NaN can be tested for with the numeric equality/inequality operators == and !=. For Inf, greater and less also work.

Handling: not useful ;-)

Devel::Peek