64 bit binary floating point (what Python uses as Float) as 1 sign bit,
11 exponent bits, as 52 mantissa bits.
NaNs are numbers with the exponent bits being all ones, with the
exception that exponent bits all ones and mantissa bits all zeros is
infinity.
Within NaNs, the MSB of the mantissa indicates if the NaN is signalling
or quiet, so we have 51 mantissa bits, and the sign bit (52 total) to
make different NaNs with.
On 12/30/19 12:09 AM, David Mertz wrote:
What is it, 2**48-2 signaling NaNs and 2**48 quiet NaNs? Is my quick
count correct (in 64-bit)? Great opportunity for steganography, I reckon.
On Sun, Dec 29, 2019 at 11:51 PM Tim Peters <tim.pet...@gmail.com
<mailto:tim.pet...@gmail.com>> wrote:
[David]
> Has anyone actually ever used those available bits for the
zillions of NaNs for
> anything good?
Yes: in Python, many sample programs I've posted cleverly use NaN
bits to hide ASCII encodings of delightful puns ;-)
Seriously? Not that I've seen. The _intent_ was that, e.g., quiet
NaNs could encode diagnostic information, such as the source code line
number of the operation that produced a qNaN. But I don't know that
anyone ever exploited that.
Signaling NaNs were even more quixotic. For example, in theory, an
implementation _could_ reserve some range of sNaN bit patterns to mean
"the lower 20 bits are an index into a table of extended precision
values", and a trap handler could catch the signal when the sNaN was
used, and do extended-precision calculation in software, store the
result in the table, and return an sNaN containing the result's index
(or a regular double if the result fit in the format).
In short, the kinds of things hardware designers think software
would love ;-)
--
Richard Damon
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