# LLVM for numerical computations

Hello there,

I am considering to use LLVM as part of a numerical software. I have never used LLVM, but I have tried to thoroughly read the material available on llvm.org. I would appreciate some early pointers. Please bare with me as I explained the matter as concisely as possible! And you can already see this is not going to be that concise…

The part of our project LLVM could be relevant to has to do with automatic numerical differentiation. Basically we have a computational tree whose leaves are independent variables whereas any other node is a dependent variable, i.e. its value depends on the value of its children through some function. Finally the head of the tree is the final result we are interested in. One of the requirement is that the set of those functions is open-ended. The tree can have from 50 to a few thousands nodes and it is typically evaluated several 1000 times for different values of the leaves (i.e. a forward sweep to compute the values followed by a reverse sweep to compute the derivatives, c.f. [*]).

Here is where I was thinking to use LLVM. Instead of actually computing its value and derivatives, each node could feature two member functions value_by_LLVM and derivatives_by_LLVM which would produce the LLVM code necessary to respectively compute the value and the derivatives, each packaged as a function I guess. A visitor marching through the computational tree would then assemble the calls to those LLVM functions to compute the head (forward sweep), then another visitor would assemble the function calls to compute the derivatives (reverse sweep) -- it should be noted that the values computed during the forward sweep may be needed during the reverse sweep but it is not always the case. The LLVM JIT would then optimise the code and compile it to native code and execute it.

As I wrote, the function is evaluated 1000 times, and it seems to me that the overhead of assembling the LLVM code, optimising and compiling it during the first execution would not be significant overhaul. It also seems to me that LLVM would generate very efficient code.

Am I correct? Does it make sense to use LLVM for such a purpose?

How would the functions defined in <cmath> be called from the LLVM code?

How would I best specify in LLVM where to find the values of the independent variables? That is to say the inputs for the whole computation LLVM will perform…

You may actually wonder why I do not kit each node with two member functions compute_value and compute_derivatives by the by. Virtual calls would be involved for each of them on each node every time and it turns out that those functions are typically not very complex, which makes the cost of a virtual call significant. I should also mention that our golden standard is some old fashion but extremely fast FORTRAN program (which has only a fixed hard-wired set of types of node but our potential users are not quite ready to sacrifice speed for flexibility, the eternal story in numerical computation…).

[*] This is not quite exact: in fact we use the so-called reverse mode and therefore we actually propagate the derivatives from head to leaves but this does not matter at the level of this discussion.

Am I correct? Does it make sense to use LLVM for such a purpose?

Yes, that is a standard "jit compile vs interpret" scenario. LLVM should work well for that.

How would the functions defined in <cmath> be called from the LLVM code?

Just use standard calls to external functions, the JIT will autoresolve them to the current process.

How would I best specify in LLVM where to find the values of the
independent variables? That is to say the inputs for the whole
computation LLVM will perform…

You probably want to make one LLVM function per computation tree, the inputs to this would naturally become arguments to the function.

-Chris