Compiling using PILCOM
This document describes how Polynomial Identity Language programs are compiled by PILCOM.
Depending on the language used in implementation, every PIL code can be compiled into either a \(\texttt{JSON}\) file or a \(\texttt{C++}\) code by using a compiler called \(\bf{pilcom}\).
The \(\bf{pilcom}\) compiler package can be found at this Github repository here. Setup can be fired up at the command line with the usual \(\texttt{clone}\), \(\texttt{install}\) and \(\texttt{build}\) CLI commands.
Any PIL code can be compiled into a \(\texttt{JSON}\) file with the command,
node src/pil.js <input.pil> -o <output.pil.json>
which is a basic \(\texttt{JSON}\) representation of the PIL program (with some extra metadata) to be later consumed on by the pil-stark package in order to generate a STARK proof.
Similarly, any PIL code can be compiled into C++ code with this command,
node src/pil.js <input.pil> -c -n namespace
in which case the corresponding header files (.hpp) will be generated in the ./pols_generated folder.
Restriction on polynomial degrees¶
The current version of PIL can only handle quadratics. Simply put, given any set of polynomials; \(\texttt{a}\), \(\texttt{b}\) and \(\texttt{c}\); PIL can only handle products of two polynomials at a time,
but not higher degrees such as,
These higher degree products are handled via an \(\texttt{intermediate}\) polynomial, conveniently dubbed \(\texttt{carry}\). Consider again the constraint of the optimized Multiplier program:
which involves the trinomial,
A \(\texttt{carry}\) can be used in \(\text{Eqn. 6}\) as follows,
where in this case, \(\texttt{carry} = \texttt{freeIn} * \texttt{out}\).
In the same sense that keywords \(\texttt{commit}\) and \(\texttt{constant}\) can be thought of as \(\text{types}\) of polynomials, \(\texttt{intermediate}\) can also be regarded as a third type of polynomial in PIL.
PIL compilation¶
In order to compile the above PIL code to a JSON file, follow the following steps.
-
Create a subdirectory/folder for the Multiplier SM and call it
multiplier_sm. -
Switch directory to the new subdirectory
multiplier_sm, and open a new file. Name itmultiplier.pil, copy in it the text below and save;namespace Multiplier(2**10); // Constant Polynomials pol constant RESET; // Committed Polynomials pol commit freeIn; pol commit out; // Intermediate Polynomials pol carry = out*freeIn; // Constraints out' = RESET*freeIn + (1-RESET)*carry; -
Switch directory to \(\texttt{pilcom}/\) and run the below command,
node src/pil.js ~/multiplier_sm/multiplier.pil -o multiplier-1st.json
If compilation is successful, the following debug message will be printed on the command line,
Input Pol Commitments: 2
Q Pol Commitmets: 1
Constant Pols: 1
Im Pols: 1
plookupIdentities: 0
permutationIdentities: 0
connectionIdentities: 0
polIdentities: 1
The debug message reflects the numbers of;
- Input committed polynomials, denoted by \(\texttt{Input Pol Commitments}\),
- Quadratic polynomials, denoted by \(\texttt{Q Pol Commitmets}\),
- Constant polynomials, denoted by \(\texttt{Constant Pols}\),
- Intermediate polynomials, denoted by \(\texttt{Im Pols}\),
- The various identities that can be checked; the \(\texttt{Plookup}\), the \(\texttt{Permutation}\), the \(\texttt{connection}\) and the \(\texttt{Polynomial}\) identities.
The resulting \(\texttt{JSON}\) file into which the multiplier.pil code is compiled looks like this:
{
"name": "multiplier_sm",
"version": "1.0.0",
"description": "",
"main": "index.js",
"scripts": {
"test": "echo \"Error: no test specified\" && exit 1"
},
"keywords": [],
"author": "",
"license": "ISC"
}
This \(\texttt{JSON}\) file contains all the information needed by the proof/verification package called \(\texttt{pil-stark}\) for processing.