In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. Automatic differentiation is an alternative technique to Symbolic differentiation and Numerical differentiation (the method of finite differences). Clad is based on Clang which provides the necessary facilities for code transformation. The AD library is able to differentiate non-trivial functions, to find a partial derivative for trivial cases and has good unit test coverage.
Clad also possesses the capabilities of annotating given source code with floating-point error estimation code. This allows Clad to compute any floating-point related errors in the given function on the fly. This allows Clad to reason about the numerical stability of the given function and also analyze the sensitivity of the variables involved.
The idea behind this project is to develop benchmarks and improve the floating-point error estimation framework as necessary. Moreover, find compelling real-world use-cases of the tool and investigate the possibility of performing lossy compression with it.
The project consists of the following tasks:
C/C++, Clang, LLVM
On successful completion of the project, the framework should have a sufficiently large set of benchmarks and example usages. Moreover, the framework should be able to run the following code as expected:
#include <iostream>
#include "clad/Differentiator/Differentiator.h"
// Some complicated function made up of doubles.
double someFunc(double F1[], double F2[], double V3[], double COUP1, double COUP2) {
double cI = 1;
double TMP3;
double TMP4;
TMP3 = (F1[2] * (F2[4] * (V3[2] + V3[5]) + F2[5] * (V3[3] + cI * (V3[4]))) +
F1[3] * (F2[4] * (V3[3] - cI * (V3[4])) + F2[5] * (V3[2] - V3[5])));
TMP4 = (F1[4] * (F2[2] * (V3[2] - V3[5]) - F2[3] * (V3[3] + cI * (V3[4]))) +
F1[5] * (F2[2] * (-V3[3] + cI * (V3[4])) + F2[3] * (V3[2] + V3[5])));
return (-1.) * (COUP2 * (+cI * (TMP3) + 2. * cI * (TMP4)) + cI * (TMP3 *
COUP1));
}
int main() {
auto df = clad::estimate_error(someFunc);
// This call should generate a report to decide
// which variables can be downcast to a float.
df.execute(args...);
}
If you have interest in working on the project there is a list of things to do in order to maximize your chances to get selected:
The mentors are interested in working with all candidates but unfortunately the rules allow only one to be selected. There are a few tasks which give bonus points to candidate’s application:
Compiler-Research clad clang-repl llvm clang