Python Infinity - Any caveats

Question

So Python has positive and negative infinity   float  inf    float  -inf     This just seems like the type of feature that has to have some caveat  Is there anything I should be aware of

User · Answer

So does C99   The IEEE 754 floating point representation used by all modern processors has several special bit patterns reserved for positive infinity  sign 0  exp  0  frac 0   negative infinity  sign 1  exp  0  frac 0   and many NaN  Not a Number  exp  0  frac 0    All you need to worry about  some arithmetic may cause floating point exceptions traps  but those aren t limited to only these  interesting  constants

User · Answer

I found a caveat that no one so far has mentioned  I don t know if it will come up often in practical situations  but here it is for the sake of completeness   Usually  calculating a number modulo infinity returns itself as a float  but a fraction modulo infinity returns nan  not a number   Here is an example    gt  gt  gt  from fractions import Fraction  gt  gt  gt  from math import inf  gt  gt  gt  3   inf 3 0  gt  gt  gt  3 5   inf 3 5  gt  gt  gt  Fraction  1 3     inf nan   I filed an issue on the Python bug tracker  It can be seen at https   bugs python org issue32968   Update  this will be fixed in Python 3 8

User · Answer

Python s implementation follows the IEEE-754 standard pretty well  which you can use as a guidance  but it relies on the underlying system it was compiled on  so platform differences may occur  Recently    a fix has been applied that allows  infinity  as well as  inf   but that s of minor importance here   The following sections equally well apply to any language that implements IEEE floating point arithmetic correctly  it is not specific to just Python   Comparison for inequality  When dealing with infinity and greater-than  gt  or less-than  lt  operators  the following counts    any number including  inf is higher than -inf any number including -inf is lower than  inf   inf is neither higher nor lower than  inf -inf is neither higher nor lower than -inf any comparison involving NaN is false  inf is neither higher  nor lower than NaN    Comparison for equality  When compared for equality   inf and  inf are equal  as are -inf and -inf  This is a much debated issue and may sound controversial to you  but it s in the IEEE standard and Python behaves just like that   Of course   inf is unequal to -inf and everything  including NaN itself  is unequal to NaN   Calculations with infinity  Most calculations with infinity will yield infinity  unless both operands are infinity  when the operation division or modulo  or with multiplication with zero  there are some special rules to keep in mind    when multiplied by zero  for which the result is undefined  it yields NaN when dividing any number  except infinity itself  by infinity  which yields 0 0 or -0 0    when dividing  including modulo  positive or negative infinity by positive or negative infinity  the result is undefined  so NaN  when subtracting  the results may be surprising  but follow common math sense    when doing inf - inf  the result is undefined  NaN  when doing inf - -inf  the result is inf  when doing -inf - inf  the result is -inf  when doing -inf - -inf  the result is undefined  NaN   when adding  it can be similarly surprising too    when doing inf   inf  the result is inf  when doing inf   -inf  the result is undefined  NaN  when doing -inf   inf  the result is undefined  NaN  when doing -inf   -inf  the result is -inf   using math pow  pow or    is tricky  as it doesn t behave as it should  It throws an overflow exception when the result with two real numbers is too high to fit a double precision float  it should return infinity   but when the input is inf or -inf  it behaves correctly and returns either inf or 0 0  When the second argument is NaN  it returns NaN  unless the first argument is 1 0  There are more issues  not all covered in the docs  math exp suffers the same issues as math pow  A solution to fix this for overflow is to use code similar to this   try      res   math exp 420000  except OverflowError      res   float  inf      Notes  Note 1  as an additional caveat  that as defined by the IEEE standard  if your calculation result under-or overflows  the result will not be an under- or overflow error  but positive or negative infinity  1e308   10 0 yields inf   Note 2  because any calculation with NaN returns NaN and any comparison to NaN  including NaN itself is false  you should use the math isnan function to determine if a number is indeed NaN   Note 3  though Python supports writing float  -NaN    the sign is ignored  because there exists no sign on NaN internally  If you divide -inf    inf  the result is NaN  not -NaN  there is no such thing    Note 4  be careful to rely on any of the above  as Python relies on the C or Java library it was compiled for and not all underlying systems implement all this behavior correctly  If you want to be sure  test for infinity prior to doing your calculations       Recently means since version 3 2      Floating points support positive and negative zero  so  x   float  inf   keeps its sign and -1   float  inf   yields -0 0  1   float -inf  yields -0 0  1   float  inf   yields 0 0 and -1  float -inf  yields 0 0  In addition  0 0    -0 0 is true  you have to manually check the sign if you don t want it to be true

User · Answer

You can still get not-a-number  NaN  values from simple arithmetic involving inf    gt  gt  gt  0   float  inf   nan   Note that you will normally not get an inf value through usual arithmetic calculations    gt  gt  gt  2 0  2 4 0  gt  gt  gt     2 16 0  gt  gt  gt     2 256 0  gt  gt  gt     2 65536 0  gt  gt  gt     2 4294967296 0  gt  gt  gt     2 1 8446744073709552e 19  gt  gt  gt     2 3 4028236692093846e 38  gt  gt  gt     2 1 157920892373162e 77  gt  gt  gt     2 1 3407807929942597e 154  gt  gt  gt     2 Traceback  most recent call last     File   lt stdin gt    line 1  in   OverflowError   34   Numerical result out of range     The inf value is considered a very special value with unusual semantics  so it s better to know about an OverflowError straight away through an exception  rather than having an inf value silently injected into your calculations

User · Answer

A VERY BAD CAVEAT     Division by Zero    in a 1 x fraction  up to x   1e-323 it is inf but when x   1e-324 or little it throws ZeroDivisionError   gt  gt  gt  1 1e-323 inf   gt  gt  gt  1 1e-324 Traceback  most recent call last     File   lt stdin gt    line 1  in  lt module gt  ZeroDivisionError  float division by zero   so be cautious

[python] Python Infinity - Any caveats?

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