This is a little program designed to understand the perormance characteristics of libm math functions. It is designed to answer questions like:
- Does the input deck have suitable coverage?
- How many performance steps does this implementation have?
Ultimately, this tool is intended to compare different implementations of functions. so that the various implementations of the math libraries can be compared in terms of things like:
- What are the absolute times to compute the value using this implementation
- What is the probability of hitting the various performance steps.
- How well does this implementation perform in selected targeted ranges.
Math functions tend to have very specific performance characteristics where different input parameters take different amounts of time than others. Plotted along a graph these numbers fall into a step function with gently sloping lines. This program gathers the time needed to calculate the sum of some number of calls to a particular math function and then tries to identify ranges of times which represent those various steps.
The general idea is:
./time_math2 -t -d input-decks/exp-inputs-hard
The general idea is it will take the list of numbers fed into it via the input deck and then it runs something like your time_math1.c and then it groups the numbers into ranges based upon time.
9 Ranges: 2-101 c:100 m:1445 r:1357:1495 102-117 c:16 m:2014 r:1981:2105 118-213 c:96 m:2647 r:2473:2736 215-357 c:143 m:3332 r:3220:3501 361-538 c:178 m:275710 r:231875:366838 539-554 c:16 m:444913 r:382567:481886 557-746 c:190 m:2404787 r:2280278:2866830 748-750 c:3 m:3270449 r:3227605:3327688 751-755 c:4 m:3955378 r:3927310:5240862
What you can see from this is glibc's libm really tends to fall into 9 ranges of time to compute. The first column is the range of numbers in the input-deck. The 'c' is the count of items that fall in that range. 'm' is the median of all the numbers that fall in that range and then 'r' is the actual range of times that the values that fall in that range.
-d is dump the numbers used to make the range
-t is target the numbers provided in the input deck. It looks at the numbers adjacent to the ones provided in the input deck and then tries those out. The idea with this is to see how likely we are to hit these worst case values. Is it just one particular number that is bad or is it a whole range of numbers. In that area which perform badly which can suggest a problem with the polynomial or function used to calculate in that vicinity.
I also have a -r mode which basically tries random numbers.This currently doesn't work really well. I think that I need to constrain it to a range so that it just checks something like 0.0-2.0 or something.
The rest are just tuning parameters.
- Ben Woodard [email protected]
This is a toy program. Giving it a license seems excessive. Never the less consider it under the GPLv3. If someone wants some other license contact me.