Homework 1

Part 1: Calculating PI using Monte Carlo In BRIL

After looking at the example benchmarks and the BRIL documentation, I noticed that the example benchmarks had a pseudo random number generator, and BRIL had a floating point extension. Inspired by the other scientific-based floating-point benchmarks, I decided on writing a benchmark to calculate PI using Monte Carlo (explained here). What could possibly go wrong?

Problem 1: BRIL Doesn’t Seem to Convert float to int, Or Vice Versa

Probably the main issue I encountered was that there was no way to convert floats to ints, meaning no matter how many random integers I was generating, I couldn’t use them to generate numbers inside a unit square (1x1). To get around this issue, I tried sampling integers inside a non-unit square instead (e.g. square is 10x10, and points come from an interval of [-10, 10] on both x and y). All I had to do was make sure the pseudo random number generator outputs had a lower bound that I specified instead of zero. Again, what could possibly go wrong?

Problem 2: The Number Generator Didn’t Have a Lower-bound, Or Plain Just Didn’t Work As Advertised.

After some debugging, I noticed that either the random number generator didn’t work as advertised (I put print statements in other benchmarks, and the values certainly weren’t greater than zero), or I was using it wrong.

To get around both of these issues, instead I opted in to discretize the unit square into a set of grid points, and then query whether they are inside the unit circle or not. Increasing the number of points leads to the output of the BRIL program converging to PI, so it seems to work. The benchmark and its test files are added under the benchmarks folder.

Part 2: Writing A Tool That Converts All int values to floats, Changing Any Instructions Operating On them To Their Floating Point Counterparts

To continue the trend of studying floats in BRIL, I decided to write a tool that would change any usage of int values to float. This would also mean that any opcode that operated on an int must be changed to its float variant.

I decided to test the tool on the following test cases: - argwrite: The tool must detect if an argument to the function is an int or not, and change it to float. - loop: The tool must detect all ints and their operations, and change them to their float variants. This involves the arithmetic (add, sub, etc.) and logical operations (le, ge, etc). - all-float: The tool must keep a program that already only uses floats intact.

The tool and the tests can be found under the examples/ folder.