Due to unfortunate scheduling, you will likely not be able to make much headway on the first weekly assignment before the lecture, which is after the lab. Hence you should spend the lab ensuring that you are able to compile, run, and benchmark Futhark programs, either on your own machine or on DIKUs GPU cluster.
The following exercises serve as a simple introduction to Futhark programming. They should be solvable using material from the Monday lecture and the Futhark book.
Implement the following Futhark utility functions:
let rotate [n] 't (r: i32) (xs: [n]t) : [n]t =
...
let transpose [n] [m] 't (xss: [n][m]t) : [m][n]t =
...
let concat [n] [m] 't (xs: [n]t) (ys: [m]t) : []t =
...
This is doable with maps (possibly nested) and explicit array
indexing. Make sure to also write
tests.
How fast do they run using the opencl backend compared to the c
backend?
Use loop to implement a function for counting how many 1 bits are
set in an i32 value. Test your results against the built-in
i32.popc.
A one-dimensional array xs can be smoothed by, for every index
xs[i], recomputing it as (x[i-1] + x[i] + x[i+1])/3. This
pattern, where we update a cell in a grid based on its neighbours, is
called a stencil. Implement this one-dimensional smoothing in
Futhark.
What should you do for elements at the edge?
Implement the following functions using map, map2, reduce, and
transpose.
-- Multiply every element of vector with a scalar.
let vec_scale [n] (s: f32) (xs: [n]f32) : [n]f32 =
...
-- Elementwise addition of vectors.
let vec_add [n] (xs: [n]f32) (xs: [n]f32) : [n]f32 =
...
-- Dot product.
let dotprod [n] (xs: [n]f32) (ys: [n]f32) : f32 =
...
-- Matrix multiplication (the dot product of the rows of 'xss'
-- with the columns of 'yss').
let matmul [n][m][p] (xss: [n][p]f32) (yss: [p][m]f32) : [n][m]f32 =
...
You can write all of these without any explicit indexing.
The Game of Life is a two-dimensional stencil. Implement it in Futhark.