> If Python functions are inconsistent then I think they should either
be
> made consistent, or if that's not possible they should be clearly
> documented as being inconsistent.
I think 'inconsistent' is a bit strong for what happens here. In my
view, the expressions log10(x) and log(x, 10) behave consistently: they
both give (good) floatingpoint approximations to the base10 logarithm
of x. However, since they use slightly different methods to get those
approximations, the approximations are not identical.
Would you also say that atan2(y, x) is inconsistent with atan(y/x) (for
positive x, y, say), because they give minutely different results in
some cases?
> The docs for log10(x) could be improved to say:
> "this function gives the correct result for powers of 10,
> but breaks consistency with log(a,10) == log10(a)"
I find this unnecessarily negative. I propose instead to leave the log
documentation as it is, and add something like the following to the
log10 documentation, as an explanation of why log10 is still valuable in
the presence of the twoargument log function:
"""Since this function directly wraps the platform log10 function,
``log10(x)`` will usually (depending on the platform) be faster and more
accurate than the mathematically equivalent ``log(x, 10)``."""
Note that historically, the twoargument version of math.log appeared
long after math.log10 did; this might help explain the apparent
redundancy. (I'd actually argue that the twoargument log should not
have been added in the first place: it doesn't wrap a standard C math
function, and it's really no different from log(x)/log(y), except that
having it as a builtin library function gives the illusion that it
might be more accurate than it actually is. However, that's academic
now.)
One possible 'fix' for this situation does occur to me: instead of
computing log(x, y) internally as log(x)/log(y), compute it as
log10(x)/log10(y). This at least doesn't involve extensive changes or
additions to the code. I don't think it really makes any practical
difference, except perhaps in reducing the number of bug reports like
this one. And it won't help make log2(x) == log(x, 2) if/when the C99
log2 function is added to the math library, either. I'd be 0 on making
this change.
