[Python-ideas] What math.floor(inf) should return? Was: Make `float('inf') //1 == float('inf')`

[Stefan Krah]

Alexander Belopolsky <alexander.belopolsky at gmail.com> wrote:
> > I accept that having math.floor() return an integer (and raise an exception
> > for +-Inf) may be useful in many cases but it is different from the standard.
> > Other floating-point libraries still return a floating-point value.
> 
> The standards are influenced by the limitation inherent in many languages where
> ints have finite range and cannot represent floor() of many finite floating
> point values.  Python does not have this limitation.  (Granted - PEP 3141 could
> do a better job explaining why floor, ceil, round, //, etc. should return
> Integer rather than Real.)  

Scheme (which IIRC infuenced PEP-3141) has arbitrary precision ints, but guile
at least returns floats:

scheme@(guile-user)> (floor 2e308)
$3 = +inf.0


[I'm mentioning Decimal now since the standard is *very* close to
 IEEE 754-2008.]

Decimal's divide_int function returns "integers" (Decimals with exponent 0),
but only if they don't overflow the context precision:

c = getcontext()
>>> c.prec
28
>>> c.divide_int(Decimal("333e25"), 1)
Decimal('3330000000000000000000000000')

>>> c.divide_int(Decimal("333e250"), 1)
decimal.InvalidOperation: quotient too large in //, % or divmod


Despite this fact, Decimal still returns inf in the disputed case:

>>> c.divide_int(Decimal("inf"), 1)
Decimal('Infinity')


Also, even when the Overflow trap is set, Decimal only raises Overflow
when an operation actually overflows:

>>> c.traps[Overflow] = True
>>> Decimal("1e999999999") * 10
decimal.Overflow: above Emax


>>> Decimal("inf") * 10
Decimal('Infinity')


>>> c.divide_int(Decimal("inf"), 1)
Decimal('Infinity')



Stefan Krah