Why isn't `int pow(int base, int exponent)` in the standard C++ libraries?
As of C++11, special cases were added to the suite of power functions (and others). C++11 [c.math] /11 states, after listing all the float/double/long double overloads (my emphasis, and paraphrased):
Moreover, there shall be additional overloads sufficient to ensure that, if any argument corresponding to a
doubleparameter has typedoubleor an integer type, then all arguments corresponding todoubleparameters are effectively cast todouble.
So, basically, integer parameters will be upgraded to doubles to perform the operation.
Prior to C++11 (which was when your question was asked), no integer overloads existed.
Since I was neither closely associated with the creators of C nor C++ in the days of their creation (though I am rather old), nor part of the ANSI/ISO committees that created the standards, this is necessarily opinion on my part. I'd like to think it's informed opinion but, as my wife will tell you (frequently and without much encouragement needed), I've been wrong before :-)
Supposition, for what it's worth, follows.
I suspect that the reason the original pre-ANSI C didn't have this feature is because it was totally unnecessary. First, there was already a perfectly good way of doing integer powers (with doubles and then simply converting back to an integer, checking for integer overflow and underflow before converting).
Second, another thing you have to remember is that the original intent of C was as a systems programming language, and it's questionable whether floating point is desirable in that arena at all.
Since one of its initial use cases was to code up UNIX, the floating point would have been next to useless. BCPL, on which C was based, also had no use for powers (it didn't have floating point at all, from memory).
As an aside, an integral power operator would probably have been a binary operator rather than a library call. You don't add two integers with
x = add (y, z)but withx = y + z- part of the language proper rather than the library.
Third, since the implementation of integral power is relatively trivial, it's almost certain that the developers of the language would better use their time providing more useful stuff (see below comments on opportunity cost).
That's also relevant for the original C++. Since the original implementation was effectively just a translator which produced C code, it carried over many of the attributes of C. Its original intent was C-with-classes, not C-with-classes-plus-a-little-bit-of-extra-math-stuff.
As to why it was never added to the standards before C++11, you have to remember that the standards-setting bodies have specific guidelines to follow. For example, ANSI C was specifically tasked to codify existing practice, not to create a new language. Otherwise, they could have gone crazy and given us Ada :-)
Later iterations of that standard also have specific guidelines and can be found in the rationale documents (rationale as to why the committee made certain decisions, not rationale for the language itself).
For example the C99 rationale document specifically carries forward two of the C89 guiding principles which limit what can be added:
- Keep the language small and simple.
- Provide only one way to do an operation.
Guidelines (not necessarily those specific ones) are laid down for the individual working groups and hence limit the C++ committees (and all other ISO groups) as well.
In addition, the standards-setting bodies realise that there is an opportunity cost (an economic term meaning what you have to forego for a decision made) to every decision they make. For example, the opportunity cost of buying that $10,000 uber-gaming machine is cordial relations (or probably all relations) with your other half for about six months.
Eric Gunnerson explains this well with his -100 points explanation as to why things aren't always added to Microsoft products- basically a feature starts 100 points in the hole so it has to add quite a bit of value to be even considered.
In other words, would you rather have a integral power operator (which, honestly, any half-decent coder could whip up in ten minutes) or multi-threading added to the standard? For myself, I'd prefer to have the latter and not have to muck about with the differing implementations under UNIX and Windows.
I would like to also see thousands and thousands of collection the standard library (hashes, btrees, red-black trees, dictionary, arbitrary maps and so forth) as well but, as the rationale states:
A standard is a treaty between implementer and programmer.
And the number of implementers on the standards bodies far outweigh the number of programmers (or at least those programmers that don't understand opportunity cost). If all that stuff was added, the next standard C++ would be C++215x and would probably be fully implemented by compiler developers three hundred years after that.
Anyway, that's my (rather voluminous) thoughts on the matter. If only votes were handed out based on quantity rather than quality, I'd soon blow everyone else out of the water. Thanks for listening :-)
For any fixed-width integral type, nearly all of the possible input pairs overflow the type, anyway. What's the use of standardizing a function that doesn't give a useful result for vast majority of its possible inputs?
You pretty much need to have an big integer type in order to make the function useful, and most big integer libraries provide the function.
Edit: In a comment on the question, static_rtti writes "Most inputs cause it to overflow? The same is true for exp and double pow, I don't see anyone complaining." This is incorrect.
Let's leave aside exp, because that's beside the point (though it would actually make my case stronger), and focus on double pow(double x, double y). For what portion of (x,y) pairs does this function do something useful (i.e., not simply overflow or underflow)?
I'm actually going to focus only on a small portion of the input pairs for which pow makes sense, because that will be sufficient to prove my point: if x is positive and |y| <= 1, then pow does not overflow or underflow. This comprises nearly one-quarter of all floating-point pairs (exactly half of non-NaN floating-point numbers are positive, and just less than half of non-NaN floating-point numbers have magnitude less than 1). Obviously, there are a lot of other input pairs for which pow produces useful results, but we've ascertained that it's at least one-quarter of all inputs.
Now let's look at a fixed-width (i.e. non-bignum) integer power function. For what portion inputs does it not simply overflow? To maximize the number of meaningful input pairs, the base should be signed and the exponent unsigned. Suppose that the base and exponent are both n bits wide. We can easily get a bound on the portion of inputs that are meaningful:
- If the exponent 0 or 1, then any base is meaningful.
- If the exponent is 2 or greater, then no base larger than 2^(n/2) produces a meaningful result.
Thus, of the 2^(2n) input pairs, less than 2^(n+1) + 2^(3n/2) produce meaningful results. If we look at what is likely the most common usage, 32-bit integers, this means that something on the order of 1/1000th of one percent of input pairs do not simply overflow.
Because there's no way to represent all integer powers in an int anyways:
>>> print 2**-4
0.0625