So, I'm familiar with the concept of packing a bunch of Boolean values using a single bit inside of an integer (bit masking I think its called), and thus you conserve memory because a Boolean is a byte and you fit more than one Boolean in an byte long integer. Thus, if you have enough Booleans, packing them together can make a big difference, and we see that in the native Unreal source code this particular optimization is used quite heavily. What I'm not clear on however, is what are the downsides of this? There are places where many regular Booleans are used instead. Also, why in some paces are uint32 used and some places unint8 are used? I've read there may be some read write related inefficiencies or something?
The biggest problem is that there is no pointer to "packed bool" - like you have an int32 that packs 32 booleans then you cannot make bool* or bool& that refers to any of them in a proper way. This is due to the fact that byte is a minimal memory unit.
In STL they made std::vector<bool> that saved space and had the same interface semantically as other vectors. To do so they had to make special proxy class that is returned from operator [] so one do stuff like boolVec[5] = true. Unfortunately, this over-complication resulted in many problems in performance and usage of std::vector<bool>.
Even simple instructions on packed booleans tend to be composite and thus heavier than if the booleans represented via bool and took a whole byte. Additionally, modifying values of packed boolean is could be causing data-racing in multi-threaded environment.
Basically, hardware simply doesn't support booleans too well.
Next, image POV of OS designer and you create common interface of shared libraries (aka dll). How to treat booleans now? Byte is a minimal memory unit so to pass a single boolean one would still need to use at least a single byte. So why not simply forget about existence of bool and simply pass it via a single byte? So we don't even need to implement this needless type of bool and it will save lots of time for all compiler writers of all languages.
uint8 vs uint32; Also, note that Windows' COM (component object model - not serial port) uses int16 for boolean. In general, it is inherently unimportant as when passing values to a shared library's function that does complex stuff will not make any noticeable difference in performance as you are already calling a much heavier function. Still why is it so? I imagine they had some reasons a long time ago when they designed it and everybody has already forgotten why and they simply keep it unchanged as changing it will result in complete disaster in terms of backwards compatibility.
In C99 _Bool was introduced for booleans but it is just a different name for an unsigned int. I imagine from this originated usage of uint32 for booleans. In general, int is supposedly the most efficient integer type in terms of performance (which it why its size is not strictly defined) - so the C committee chose the supposedly most efficient type to represent booleans.
I'm in the process of converting a program to C++ from Scilab (similar to Matlab) and I'm required to maintain the same level of precision that is kept by the previous code.
Note: Although maintaining the same level of precision would be ideal. It's acceptable if there is some error with the finished result. The problem I'm facing (as I'll show below) is due to looping, so the calculation error compounds rather quickly. But if the final result is only a thousandth or so off (e.g. 1/1000 vs 1/1001) it won't be a problem.
I've briefly looked into a number of different ways to do this including:
GMP (A Multiple Precision
Arithmetic Library)
Using integers instead of floats (see example below)
Int vs Float Example: Instead of using the float 12.45, store it as an integer being 124,500. Then simply convert everything back when appropriate to do so. Note: I'm not exactly sure how this will work with the code I'm working with (more detail below).
An example of how my program is producing incorrect results:
for (int i = 0; i <= 1000; i++)
{
for (int j = 0; j <= 10000; j++)
{
// This calculation will be computed with less precision than in Scilab
float1 = (1.0 / 100000.0);
// The above error of float2 will become significant by the end of the loop
float2 = (float1 + float2);
}
}
My question is:
Is there a generally accepted way to go about retaining accuracy in floating point arithmetic OR will one of the above methods suffice?
Maintaining precision when porting code like this is very difficult to do. Not because the languages have implicitly different perspectives on what a float is, but because of what the different algorithms or assumptions of accuracy limits are. For example, when performing numerical integration in Scilab, it may use a Gaussian quadrature method. Whereas you might try using a trapezoidal method. The two may both be working on identical IEEE754 single-precision floating point numbers, but you will get different answers due to the convergence characteristics of the two algorithms. So how do you get around this?
Well, you can go through the Scilab source code and look at all of the algorithms it uses for each thing you need. You can then replicate these algorithms taking care of any pre- or post-conditioning of the data that Scilab implicitly does (if any at all). That's a lot of work. And, frankly, probably not the best way to spend your time. Rather, I would look into using the Interfacing with Other Languages section from the developer's documentation to see how you can call the Scilab functions directly from your C, C++, Java, or Fortran code.
Of course, with the second option, you have to consider how you are going to distribute your code (if you need to).Scilab has a GPL-compatible license, so you can just bundle it with your code. However, it is quite big (~180MB) and you may want to just bundle the pieces you need (e.g., you don't need the whole interpreter system). This is more work in a different way, but guarantees numerical-compatibility with your current Scilab solutions.
Is there a generally accepted way to go about retaining accuracy in floating
point arithmetic
"Generally accepted" is too broad, so no.
will one of the above methods suffice?
Yes. Particularly gmp seems to be a standard choice. I would also have a look at the Boost Multiprecision library.
A hand-coded integer approach can work as well, but is surely not the method of choice: it requires much more coding, and more severe a means to store and process aritrarily precise integers.
If your compiler supports it use BCD (Binary-coded decimal)
Sam
Well, another alternative if you use GCC compilers is to go with quadmath/__float128 types.
I am new to Fortran 2008 and am trying to implement a Sieve of Atkin. In C++ I implemented this using a std::bitset but was unable to find anything in Fortran 2008 that serves this purpose.
Can anyone point me at any example code or explain an implementation strategy for one?
Standard Fortran doesn't have a precise analogue of what I understand std:bitset to be -- though I grant you my understanding may be defective. Generally, and if you want to stick to standard Fortran, you would use integers as sets of bits. If one integer doesn't have enough bits for your purposes, use arrays of integers. This does mean, though, that the responsibility for tracking where, say, the 307-th bit of your bitset is falls on you
Prior to the 2008 standard you have functions such as bit_size, iand, ibset, btest and others (see your compiler documentation or Google for language references, or try the Intel Fortran documentation) for bit manipulation.
If you are unfamiliar with Fortran's boz literals then familiarise yourself with them. You can, for example, set the bits of an integer using a statement such as this
integer :: mybits
...
mybits = b'00000011000000100000000000001111'
With the b edit descriptor you can read and write binary literals too. For example the statements
write(*,*) mybits
write(*,'(b32.32)') mybits
will produce the output
50462735
00000011000000100000000000001111
If you can lay your hands on a modern-enough compiler then you will find that the 2008 standard added new bit-twiddling functions such as bge, bgt, dshiftl, iall and a whole lot more. These are defined for input arguments which are integer arrays or integers, but I don't have any experience of using them to pass on.
This should be enough to get you started.
Fortran has bit intrinsics for manipulating the bits of default integers. Bit arrays are straightforward to build off that...
Determine how many bits you need, divide by number of bits in default integer, allocate an integer array of default kind of the size you computed +1 if the modulo of the division was non-zero, and you're essentially done. The bit intrinsics are well covered in Metcalf and Reid.
What you may want could look like:
program test
logical,allocatable:: flips(:)
...
allocate(flips(ntris),status=err)
call tris(ntris,...,flips)
...
end
subroutine tris(nnewtris, ...,flips)
logical flips(nnewtris)
...
if(flips(i)) then
...
end if
return
end
I know that you can get the digits of a number using modulus and division. The following is how I've done it in the past: (Psuedocode so as to make students reading this do some work for their homework assignment):
int pointer getDigits(int number)
initialize int pointer to array of some size
initialize int i to zero
while number is greater than zero
store result of number mod 10 in array at index i
divide number by 10 and store result in number
increment i
return int pointer
Anyway, I was wondering if there is a better, more efficient way to accomplish this task? If not, is there any alternative methods for this task, avoiding the use of strings? C-style or otherwise?
Thanks. I ask because I'm going to be wanting to do this in a personal project of mine, and I would like to do it as efficiently as possible.
Any help and/or insight is greatly appreciated.
The time it takes to extract the digits will be dwarfed by the time required to dynamically allocate the array. Consider returning the result in a struct:
struct extracted_digits
{
int number_of_digits;
char digits[12];
};
You'll want to pick a suitable value for the maximum number of digits (12 here, which is enough for a 32-bit integer). Alternatively, you could return a std::array<char, 12> and encode the terminal by using an invalid value (so, after the last value, store a 10 or something else that isn't a digit).
Depending on whether you want to handle negative values, you'll also have to decide how to report the unary minus (-).
Unless you want the representation of the number in a base that's a power of 2, that's about the only way to do it.
Smacks of premature optimisation. If profiling proves it matters, then be sure to compare your algo to itoa - internally it may use some CPU instructions that you don't have explicit access to from C++, and which your compiler's optimiser may not be clever enough to employ (e.g. AAM, which divs while saving the mod result). Experiment (and benchmark) coding the assembler yourself. You might dig around for assembly implementations of ITOA (which isn't identical to what you're asking for, but might suggest the optimal CPU instructions).
By "avoiding the use of strings", I'm going to assume you're doing this because a string-only representation is pretty inefficient if you want an integer value.
To that end, I'm going to suggest a slightly unorthodox approach which may be suitable. Don't store them in one form, store them in both. The code below is in C - it will work in C++ but you may want to consider using c++ equivalents - the idea behind it doesn't change however.
By "storing both forms", I mean you can have a structure like:
typedef struct {
int ival;
char sval[sizeof("-2147483648")]; // enough for 32-bits
int dirtyS;
} tIntStr;
and pass around this structure (or its address) rather than the integer itself.
By having macros or inline functions like:
inline void intstrSetI (tIntStr *is, int ival) {
is->ival = i;
is->dirtyS = 1;
}
inline char *intstrGetS (tIntStr *is) {
if (is->dirtyS) {
sprintf (is->sval, "%d", is->ival);
is->dirtyS = 0;
}
return is->sval;
}
Then, to set the value, you would use:
tIntStr is;
intstrSetI (&is, 42);
And whenever you wanted the string representation:
printf ("%s\n" intstrGetS(&is));
fprintf (logFile, "%s\n" intstrGetS(&is));
This has the advantage of calculating the string representation only when needed (the fprintf above would not have to recalculate the string representation and the printf only if it was dirty).
This is a similar trick I use in SQL with using precomputed columns and triggers. The idea there is that you only perform calculations when needed. So an extra column to hold the indexed lowercased last name along with an insert/update trigger to calculate it, is usually a lot more efficient than select lower(non_lowercased_last_name). That's because it amortises the cost of the calculation (done at write time) across all reads.
In that sense, there's little advantage if your code profile is set-int/use-string/set-int/use-string.... But, if it's set-int/use-string/use-string/use-string/use-string..., you'll get a performance boost.
Granted this has a cost, at the bare minimum extra storage required, but most performance issues boil down to a space/time trade-off.
And, if you really want to avoid strings, you can still use the same method (calculate only when needed), it's just that the calculation (and structure) will be different.
As an aside: you may well want to use the library functions to do this rather than handcrafting your own code. Library functions will normally be heavily optimised, possibly more so than your compiler can make from your code (although that's not guaranteed of course).
It's also likely that an itoa, if you have one, will probably outperform sprintf("%d") as well, given its limited use case. You should, however, measure, not guess! Not just in terms of the library functions, but also this entire solution (and the others).
It's fairly trivial to see that a base-100 solution could work as well, using the "digits" 00-99. In each iteration, you'd do a %100 to produce such a digit pair, thus halving the number of steps. The tradeoff is that your digit table is now 200 bytes instead of 10. Still, it easily fits in L1 cache (obviously, this only applies if you're converting a lot of numbers, but otherwise efficientcy is moot anyway). Also, you might end up with a leading zero, as in "0128".
Yes, there is a more efficient way, but not portable, though. Intel's FPU has a special BCD format numbers. So, all you have to do is just to call the correspondent assembler instruction that converts ST(0) to BCD format and stores the result in memory. The instruction name is FBSTP.
Mathematically speaking, the number of decimal digits of an integer is 1+int(log10(abs(a)+1))+(a<0);.
You will not use strings but go through floating points and the log functions. If your platform has whatever type of FP accelerator (every PC or similar has) that will not be a big deal ,and will beat whatever "sting based" algorithm (that is noting more than an iterative divide by ten and count)
I feel like I must just be unable to find it. Is there any reason that the C++ pow function does not implement the "power" function for anything except floats and doubles?
I know the implementation is trivial, I just feel like I'm doing work that should be in a standard library. A robust power function (i.e. handles overflow in some consistent, explicit way) is not fun to write.
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 double parameter has type double or an integer type, then all arguments corresponding to double parameters are effectively cast to double.
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 with x = 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
That's actually an interesting question. One argument I haven't found in the discussion is the simple lack of obvious return values for the arguments. Let's count the ways the hypthetical int pow_int(int, int) function could fail.
Overflow
Result undefined pow_int(0,0)
Result can't be represented pow_int(2,-1)
The function has at least 2 failure modes. Integers can't represent these values, the behaviour of the function in these cases would need to be defined by the standard - and programmers would need to be aware of how exactly the function handles these cases.
Overall leaving the function out seems like the only sensible option. The programmer can use the floating point version with all the error reporting available instead.
Short answer:
A specialisation of pow(x, n) to where n is a natural number is often useful for time performance. But the standard library's generic pow() still works pretty (surprisingly!) well for this purpose and it is absolutely critical to include as little as possible in the standard C library so it can be made as portable and as easy to implement as possible. On the other hand, that doesn't stop it at all from being in the C++ standard library or the STL, which I'm pretty sure nobody is planning on using in some kind of embedded platform.
Now, for the long answer.
pow(x, n) can be made much faster in many cases by specialising n to a natural number. I have had to use my own implementation of this function for almost every program I write (but I write a lot of mathematical programs in C). The specialised operation can be done in O(log(n)) time, but when n is small, a simpler linear version can be faster. Here are implementations of both:
// Computes x^n, where n is a natural number.
double pown(double x, unsigned n)
{
double y = 1;
// n = 2*d + r. x^n = (x^2)^d * x^r.
unsigned d = n >> 1;
unsigned r = n & 1;
double x_2_d = d == 0? 1 : pown(x*x, d);
double x_r = r == 0? 1 : x;
return x_2_d*x_r;
}
// The linear implementation.
double pown_l(double x, unsigned n)
{
double y = 1;
for (unsigned i = 0; i < n; i++)
y *= x;
return y;
}
(I left x and the return value as doubles because the result of pow(double x, unsigned n) will fit in a double about as often as pow(double, double) will.)
(Yes, pown is recursive, but breaking the stack is absolutely impossible since the maximum stack size will roughly equal log_2(n) and n is an integer. If n is a 64-bit integer, that gives you a maximum stack size of about 64. No hardware has such extreme memory limitations, except for some dodgy PICs with hardware stacks that only go 3 to 8 function calls deep.)
As for performance, you'll be surprised by what a garden variety pow(double, double) is capable of. I tested a hundred million iterations on my 5-year-old IBM Thinkpad with x equal to the iteration number and n equal to 10. In this scenario, pown_l won. glibc pow() took 12.0 user seconds, pown took 7.4 user seconds, and pown_l took only 6.5 user seconds. So that's not too surprising. We were more or less expecting this.
Then, I let x be constant (I set it to 2.5), and I looped n from 0 to 19 a hundred million times. This time, quite unexpectedly, glibc pow won, and by a landslide! It took only 2.0 user seconds. My pown took 9.6 seconds, and pown_l took 12.2 seconds. What happened here? I did another test to find out.
I did the same thing as above only with x equal to a million. This time, pown won at 9.6s. pown_l took 12.2s and glibc pow took 16.3s. Now, it's clear! glibc pow performs better than the three when x is low, but worst when x is high. When x is high, pown_l performs best when n is low, and pown performs best when x is high.
So here are three different algorithms, each capable of performing better than the others under the right circumstances. So, ultimately, which to use most likely depends on how you're planning on using pow, but using the right version is worth it, and having all of the versions is nice. In fact, you could even automate the choice of algorithm with a function like this:
double pown_auto(double x, unsigned n, double x_expected, unsigned n_expected) {
if (x_expected < x_threshold)
return pow(x, n);
if (n_expected < n_threshold)
return pown_l(x, n);
return pown(x, n);
}
As long as x_expected and n_expected are constants decided at compile time, along with possibly some other caveats, an optimising compiler worth its salt will automatically remove the entire pown_auto function call and replace it with the appropriate choice of the three algorithms. (Now, if you are actually going to attempt to use this, you'll probably have to toy with it a little, because I didn't exactly try compiling what I'd written above. ;))
On the other hand, glibc pow does work and glibc is big enough already. The C standard is supposed to be portable, including to various embedded devices (in fact embedded developers everywhere generally agree that glibc is already too big for them), and it can't be portable if for every simple math function it needs to include every alternative algorithm that might be of use. So, that's why it isn't in the C standard.
footnote: In the time performance testing, I gave my functions relatively generous optimisation flags (-s -O2) that are likely to be comparable to, if not worse than, what was likely used to compile glibc on my system (archlinux), so the results are probably fair. For a more rigorous test, I'd have to compile glibc myself and I reeeally don't feel like doing that. I used to use Gentoo, so I remember how long it takes, even when the task is automated. The results are conclusive (or rather inconclusive) enough for me. You're of course welcome to do this yourself.
Bonus round: A specialisation of pow(x, n) to all integers is instrumental if an exact integer output is required, which does happen. Consider allocating memory for an N-dimensional array with p^N elements. Getting p^N off even by one will result in a possibly randomly occurring segfault.
One reason for C++ to not have additional overloads is to be compatible with C.
C++98 has functions like double pow(double, int), but these have been removed in C++11 with the argument that C99 didn't include them.
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2011/n3286.html#550
Getting a slightly more accurate result also means getting a slightly different result.
The World is constantly evolving and so are the programming languages. The fourth part of the C decimal TR¹ adds some more functions to <math.h>. Two families of these functions may be of interest for this question:
The pown functions, that takes a floating point number and an intmax_t exponent.
The powr functions, that takes two floating points numbers (x and y) and compute x to the power y with the formula exp(y*log(x)).
It seems that the standard guys eventually deemed these features useful enough to be integrated in the standard library. However, the rational is that these functions are recommended by the ISO/IEC/IEEE 60559:2011 standard for binary and decimal floating point numbers. I can't say for sure what "standard" was followed at the time of C89, but the future evolutions of <math.h> will probably be heavily influenced by the future evolutions of the ISO/IEC/IEEE 60559 standard.
Note that the fourth part of the decimal TR won't be included in C2x (the next major C revision), and will probably be included later as an optional feature. There hasn't been any intent I know of to include this part of the TR in a future C++ revision.
¹ You can find some work-in-progress documentation here.
Here's a really simple O(log(n)) implementation of pow() that works for any numeric types, including integers:
template<typename T>
static constexpr inline T pown(T x, unsigned p) {
T result = 1;
while (p) {
if (p & 0x1) {
result *= x;
}
x *= x;
p >>= 1;
}
return result;
}
It's better than enigmaticPhysicist's O(log(n)) implementation because it doesn't use recursion.
It's also almost always faster than his linear implementation (as long as p > ~3) because:
it doesn't require any extra memory
it only does ~1.5x more operations per loop
it only does ~1.25x more memory updates per loop
Perhaps because the processor's ALU didn't implement such a function for integers, but there is such an FPU instruction (as Stephen points out, it's actually a pair). So it was actually faster to cast to double, call pow with doubles, then test for overflow and cast back, than to implement it using integer arithmetic.
(for one thing, logarithms reduce powers to multiplication, but logarithms of integers lose a lot of accuracy for most inputs)
Stephen is right that on modern processors this is no longer true, but the C standard when the math functions were selected (C++ just used the C functions) is now what, 20 years old?
As a matter of fact, it does.
Since C++11 there is a templated implementation of pow(int, int) --- and even more general cases, see (7) in
http://en.cppreference.com/w/cpp/numeric/math/pow
EDIT: purists may argue this is not correct, as there is actually "promoted" typing used. One way or another, one gets a correct int result, or an error, on int parameters.
A very simple reason:
5^-2 = 1/25
Everything in the STL library is based on the most accurate, robust stuff imaginable. Sure, the int would return to a zero (from 1/25) but this would be an inaccurate answer.
I agree, it's weird in some cases.