Logarithm with SSE, or switch to FPU?

Question

I'm doing some statistics calculations. I need them to be fast, so I rewrote most of it to use SSE. I'm pretty much new to it, so I was wondering what the right approach here is:

To my knowledge, there is no log2 or ln function in SSE, at least not up to 4.1, which is the latest version supported by the hardware I use.

Is it better to:

1. extract 4 floats, and do FPU calculations on them to determine enthropy - I won't need to load any of those values back into SSE registers, just sum them up to another float
2. find a function for SSE that does log2

Marcello

What kind of range and accuracy do you need for your log2 ? – Argumentation

Same accuracy I get from the FPU would be desirable – Marcello

There seem to be a few SSE log2 implementations around, e.g. jrfonseca.blogspot.com/2008/09/… – Argumentation

Neat, thanks! I'll try that and benchmark it. Extracting the floats to an array and then doing 4 consecutive log2's on that via FPU was disappointingly slow. Instruments said it's wasting 95% of its time there. – Marcello

There is also the Intel Approximate Maths Library - it's old (2000) but it's SSE2 and it should still work reasonably well: intel.com/design/pentiumiii/devtools/AMaths.zip – Argumentation

Woah... I'd tried the implementation from the blog you linked, the one I can approximate as close as I'd like. It's FAST. Cut down processing time down to about 10%. Thanks a LOT! – Marcello

OK - I'll put those two links in an answer for future reference. – Argumentation

Here is another link: http://gruntthepeon.free.fr/ssemath. Implements only the log function with SSE, but with with one more instruction you'll get the log2 – Anu

Answer 1

There seem to be a few SSE log2 implementations around, e.g. this one.

There is also the Intel Approximate Maths Library which has a log2 function among others - it's old (2000) but it's SSE2 and it should still work reasonably well.

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See also:

• sse_mathfun - SSE vector math library
• avx_mathfun - AVX vector math library
• libmvec - vector math library added in glibc 2.22

Argumentation

Due to the method used on the blog, the function is now memory bound, instead of CPU bound. I unrolled the loop a little to make use of some _mm_prefetch love, and it still is memory bound. Thanks for that awesome pointer! – Marcello

Glad it worked for you. You probably already know this, but if you're hitting a memory bandwidth bottleneck then try to combine other operations with your log2 so that you make more use of data while it's in cache. – Argumentation

If you are updating your answer, you might want to mention libmvec, which is shipped with recent glibc. – Custodial

Answer 2

There is no SSE instruction that implements a logarithm function. However, there's also no single x86 instruction that performs a generic logarithm either. If you're thinking about using a logarithm function like log or log10 from the C standard library, it's worth taking a look at the implementation that is used in an open-source library like libc. You can easily roll your own logarithm approximation that operates across all elements in an SSE register.

Such a function is often implemented using a polynomial approximation that is valid within some accuracy specification over a certain region of input arguments, such as a Taylor series. You can then take advantage of logarithm properties to wrap a generic input argument into the acceptable input range for your logarithm routine. In addition, you can parameterize the base of the logarithm by taking advantage of the property:

log_y(x) = log_a(x) / log_a(y)

Where a is the base of the logarithm routine that you created.

Exhalation