Why is floor() so slow?

Question

I wrote some code recently (ISO/ANSI C), and was surprised at the poor performance it achieved. Long story short, it turned out that the culprit was the floor() function. Not only it was slow, but it did not vectorize (with Intel compiler, aka ICL).

Here are some benchmarks for performing floor for all cells in a 2D matrix:

VC:  0.10
ICL: 0.20

Compare that to a simple cast:

VC:  0.04
ICL: 0.04

How can floor() be that much slower than a simple cast?! It does essentially the same thing (apart for negative numbers). 2nd question: Does someone know of a super-fast floor() implementation?

PS: Here is the loop that I was benchmarking:

void Floor(float *matA, int *intA, const int height, const int width, const int width_aligned)
{
    float *rowA=NULL;
    int   *intRowA=NULL;
    int   row, col;

    for(row=0 ; row<height ; ++row){
        rowA = matA + row*width_aligned;
        intRowA = intA + row*width_aligned;
#pragma ivdep
        for(col=0 ; col<width; ++col){
            /*intRowA[col] = floor(rowA[col]);*/
            intRowA[col] = (int)(rowA[col]);
        }
    }
}

Answer 1

A couple of things make floor slower than a cast and prevent vectorization.

The most important one:

floor can modify the global state. If you pass a value that is too huge to be represented as an integer in float format, the errno variable gets set to EDOM. Special handling for NaNs is done as well. All this behavior is for applications that want to detect the overflow case and handle the situation somehow (don't ask me how).

Detecting these problematic conditions is not simple and makes up more than 90% of the execution time of floor. The actual rounding is cheap and could be inlined/vectorized. Also It's a lot of code, so inlining the whole floor-function would make your program run slower.

Some compilers have special compiler flags that allow the compiler to optimize away some of the rarely used c-standard rules. For example GCC can be told that you're not interested in errno at all. To do so pass -fno-math-errno or -ffast-math. ICC and VC may have similar compiler flags.

Btw - You can roll your own floor-function using simple casts. You just have to handle the negative and positive cases differently. That may be a lot faster if you don't need the special handling of overflows and NaNs.