Good practices: power and log functions

The processor doesn't have native functions for pow and log so it ends up calculating it with some sort of Taylor approximation which is rather expensive.

The processor doesn't have native functions for pow and log so it ends up calculating it with some sort of Taylor approximation which is rather expensive.

so is the log() to be avoided just as much as the pow()?

Meh. Write what's clearest and most natural and only rewrite things if a profiler tells you something's a bottleneck.

What SiCrane says. Also, the idea that powf is slow probably comes from times when compilers did something very naive with it. These days, a compiler will probably issue the same code for powf(x,2) as for x*x.

Optimisation needs to include the optimisation of the programmer's time. If log or pow makes most sense to write, then write it until the profiler tells you not do.

Basically what everyone else said. Don't try to second-guess the compiler; it will only end in tears.

thanks for all the responses. I will approach it that way. Will make my life so much easier:)

What SiCrane says. Also, the idea that powf is slow probably comes from times when compilers did something very naive with it. These days, a compiler will probably issue the same code for powf(x,2) as for x*x.

Actually they very probably don't. We went through this recently on a different forum.
To back that statement I just tried it in VS2008 Express with full optimisations on in release build and with code written such that it cannot be optimised out. There was a 14x speed difference between using powf(x, 2) and x*x.

That way of thinking works for a lot of things, but the math library routines are not one of them. Avoid using overly flexible functions when the simpler one will do. E.g. use sqrt(x) instead of pow(x, 0.5) because the former is specific and the later has to cater for the general case which means extra work.

The bottom line is, avoid log, pow, or other math library routines etc only where there is a clear, simple, and obvious alternative that doesn't require as much generality as those methods provide.

[quote name='alvaro' timestamp='1319313688' post='4875421']
What SiCrane says. Also, the idea that powf is slow probably comes from times when compilers did something very naive with it. These days, a compiler will probably issue the same code for powf(x,2) as for x*x.

Actually they very probably don't. We went through this recently on a different forum.
To back that statement I just tried it in VS2008 Express with full optimisations on in release build and with code written such that it cannot be optimised out. There was a 14x speed difference between using powf(x, 2) and x*x.[/quote]

I checked shortly after I posted that comment, just to make sure that I am not spreading false information. gcc 4.6.1 seems to be smarter about this.

In C:
#include <math.h>

float f(float x) {
return powf(x, 2);
}

The assembly produced is:
.file "kk.c"
.text
.p2align 4,,15
.globl f
.type f, @function
f:
.LFB3:
.cfi_startproc
mulss %xmm0, %xmm0 // Hard to optimize beyond this
ret
.cfi_endproc
.LFE3:
.size f, .-f
.ident "GCC: (Ubuntu/Linaro 4.6.1-9ubuntu3) 4.6.1"
.section .note.GNU-stack,"",@progbits


To back that statement I just tried it in VS2008 Express with full optimisations on in release build and with code written such that it cannot be optimised out.

Out of interest, did that include using the fast floating point model and SSE instruction sets?

VS2010, SSE2, FP:Fast

float x;
cin >> x;
cout << pow(x,2);

012D1014 movss xmm0,dword ptr [x]
012D1019 movss xmm1,dword ptr [__real@3f800000 (12D2104h)]
012D1021 mov eax,2
012D1026 test al,1
012D1028 je main+2Eh (12D102Eh)
012D102A mulss xmm1,xmm0
012D102E shr eax,1
012D1030 je main+38h (12D1038h)
012D1032 mulss xmm0,xmm0
012D1036 jmp main+26h (12D1026h)

It doesn't optimise out to x * x, however it is applying a very useful optimisation which becomes apparent for higher integral powers of x.

float x;
cin >> x;
cout << pow(x,241);

00AF1014 movss xmm0,dword ptr [x]
00AF1019 movss xmm1,dword ptr [__real@3f800000 (0AF2104h)]
00AF1021 mov eax,0F1h
00AF1026 test al,1
00AF1028 je main+2Eh (0AF102Eh)
00AF102A mulss xmm1,xmm0
00AF102E shr eax,1
00AF1030 je main+38h (0AF1038h)
00AF1032 mulss xmm0,xmm0
00AF1036 jmp main+26h (0AF1026h)

I'm not entirely sure how this works actually, but I think it's expanding x^n out to x*x*x*x... and then finding an optimum grouping. E.g. x^20 can be calculated quickly as:
x1 = x*x
x2 = x1*x1
x3 = x2 * x2
x4 = x3 * x3
result = x4 * x2


The branching incurs a performance cost, however the method is utilised even when the power is not a constant.

VS2010 seems to be using exponentiation by squaring. My gcc 4.6.1 (the C compiler) seems to only know the trick for powf(x,2), and it makes a function call for all other cases. g++ 4.6.1 (the C++ compiler) optimizes any constant positive integer power. The resulting code is very amusing. For std::pow(x,241):
movaps %xmm0, %xmm1
mulss %xmm0, %xmm1 // 1 + 1 = 2
mulss %xmm0, %xmm1 // 1 + 2 = 3
movaps %xmm1, %xmm2
mulss %xmm1, %xmm2 // 3 + 3 = 6
mulss %xmm2, %xmm1 // 6 + 3 = 9
mulss %xmm2, %xmm1 // 6 + 9 = 15
mulss %xmm1, %xmm1 // 15 + 15 = 30
mulss %xmm1, %xmm1 // 30 + 30 = 60
mulss %xmm1, %xmm1 // 60 + 60 = 120
mulss %xmm1, %xmm1 // 120 + 120 = 240
mulss %xmm0, %xmm1 // 1 + 240 = 241
movaps %xmm1, %xmm0
ret

[quote name='iMalc' timestamp='1319396655' post='4876035']To back that statement I just tried it in VS2008 Express with full optimisations on in release build and with code written such that it cannot be optimised out.

Out of interest, did that include using the fast floating point model and SSE instruction sets?
[/quote]I don't think it did, but I've deleted that now so never mind.

I would point out though that it isn't necessarily practical to change the floating point model when working on an existing codebase because you may needlessly introduce a bug somewhere.
Of course not everything is even about release build with full optimisations either. It's kinda nice when your debug version isn't 20 times slower than release as it makes for a much nicer debugging experience when the speed difference is minimal.

That's great to see that some compilers are smarter about this. Regardless, it's not going to change that I'm an advocate of just using x*x instead.

The debug version of MSVC's STL is so inefficient that my debug builds are closer to 100x slower than release. I once stepped through the assembly and counted 5 critical sections just to create an iterator. I know people keep saying not to write your own implementation of the STL, but debugging is getting to be a serious problem.

There are additional preprocessor flags you can turn off, even in debug mode. Look into HAS_ITERATOR_DEBUGGING and _SECURE_SCL. That said, your comment seems a little off topic.