Ben Cartwright wrote: > Russ wrote: > > Does "pow(x,2)" simply square x, or does it first compute logarithms > > (as would be necessary if the exponent were not an integer)? > > > The former, using binary exponentiation (quite fast), assuming x is an > int or long. > > If x is a float, Python coerces the 2 to 2.0, and CPython's float_pow() > function is called. This function calls libm's pow(), which in turn > uses logarithms.
I just did a little time test (which I should have done *before* my original post!), and 2.0**2 seems to be about twice as fast as pow(2.0,2). That seems consistent with your claim above. I'm a bit surprised that pow() would use logarithms even if the exponent is an integer. I suppose that just checking for an integer exponent could blow away the gain that would be achieved by avoiding logarithms. On the other hand, I would think that using logarithms could introduce a tiny error (e.g., pow(2.0,2) = 3.9999999996 <- made up result) that wouldn't occur with multiplication. > > > Does "x**0.5" use the same algorithm as "sqrt(x)", or does it use some > > other (perhaps less efficient) algorithm based on logarithms? > > The latter, and that algorithm is libm's pow(). Except for a few > special cases that Python handles, all floating point exponentation is > left to libm. Checking to see if the exponent is 0.5 is not one of > those special cases. I just did another little time test comparing 2.0**0.5 with sqrt(2.0). Surprisingly, 2.0**0.5 seems to take around a third less time. None of these differences are really significant unless one is doing super-heavy-duty number crunching, of course, but I was just curious. Thanks for the information. -- http://mail.python.org/mailman/listinfo/python-list
