/****************************************************************************
*
* cuda-rule30.cu - "Rule 30" Callular Automaton
*
* Copyright (C) 2017--2022 by Moreno Marzolla
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
****************************************************************************/
/***
% HPC - "Rule 30" Cellular Automaton
% Moreno Marzolla
% Last updated: 2022-11-23
The goal of this exercise is to implement the [Rule 30 Cellular
Automaton](https://en.wikipedia.org/wiki/Rule_30) in CUDA.
The Rule 30 CA is a 1D cellular aotmaton that consists of an array
`x[N]` of $N$ integers that can be either 0 or 1. The state of the CA
evolves at discrete time steps: the new state of a cell depends on its
current state, and on the current state of the two neighbors. We
assume cyclic boundary conditions, so that the neighbors of $x[0]$ are
$x[N-1]$ and $x[1]$ and the neighbors of $x[N-1]$ are $x[N-2]$ and
$x[0]$ (Figure 1).
![Figure 1: Rule 30 CA](mpi-rule30-fig1.svg)
Given the current values $pqr$ of three adjacent cells, the new value
$q'$ of the middle cell is computed according to Table 1.
:Table 1: Rule 30 (■ = 1, □ = 0):
---------------------------------------- ----- ----- ----- ----- ----- ----- ----- -----
Current configuration $pqr$ ■■■ ■■□ ■□■ ■□□ □■■ □■□ □□■ □□□
New state $q'$ of the central cell □ □ □ ■ ■ ■ ■ □
---------------------------------------- ----- ----- ----- ----- ----- ----- ----- -----
The sequence □□□■■■■□ = 00011110 on the second row is the binary
representation of decimal 30, from which the name ("Rule 30 CA"); more
details can be found [here](mpi-rule30.pdf).
The file [cuda-rule30.cu](cuda-rule30.cu) contains a serial program
that computes the evolution of the Rule 30 CA, assuming an initial
condition where all cells are 0 except the central one. The program
accepts two optional command line parameters: the domain size $N$ and
the number of steps _nsteps_ to simulate. At the end, the program
produces the image `rule30.pbm` shown in Figure 2 of size $N \times
\textit{nsteps}$.
![Figure 2: Evolution of Rule 30 CA](rule30.png)
Each row of the image represents the state of the automaton at a
specific time step (1 = black, 0 = white). Time moves from top to
bottom: the first line is the initial state (time 0), the second line
is the state at time 1, and so on.
Interestingly, the pattern shown in Figure 2 is similar to the pattern
on the [Conus textile](https://en.wikipedia.org/wiki/Conus_textile)
shell, a highly poisonous marine mollusk which can be found in
tropical seas (Figure 3).
![Figure 3: Conus Textile by Richard Ling - Own work; Location: Cod
Hole, Great Barrier Reef, Australia, CC BY-SA 3.0,
](conus-textile.jpg)
The goal of this exercise is to write a parallel version where the
computation of the new states are performed by CUDA threads. In
particular, the `rule30()` function should be turned into a kernel.
Assume that the domain size $N$ is a multiple of the number of threads
per block (_BLKDIM_).
I suggest that you start with a version that does not use shared
memory; this first version should be easily derived from the provided
serial code.
Since each domain cell is read three times by three different threads
within the same block, the computation _might_ benefit from the use of
shared memory.
> **Note:** The use shared memory could produce minor improvements on
> modern GPUs, or even make the program _slower_. The reason is that
> there is little data reuse, and modern GPUs are equipped with caches
> that work reasonably well in these kind of
> computations. Nevertheless, it is useful to practice with shared
> memory, so this exercise should be considered as it is: an exercise.
To use shared memory, refer to the simple example of 1D stencil
computation that we have seen during the class; in this case, the
radius of the stencil is one, i.e., the new state of each cell depends
on the state of a cell and the state of the two neighbors. Be careful,
since in this exercise we are assuming a cyclic domain, whereas in the
stencil computation discussed in the class we did not.
![Figure 3: Using shared memory](cuda-rule30.svg)
Looking at Figure 2, you might proceed as follows:
- `d_cur[]` is the current state on GPU memory.
- We create a kernel, say `fill_ghost(...)` that fills the ghost area
of `d_cur[]`. The kernel will be executed by a single thread only,
since just two values need to be copied, and therefore will be
executed as `fill_ghost<<<1, 1>>>(...)`
- We create another kernel that computes the new state of the domain,
given the current state. To this aim, we use 1D blocks and grid.
Each block defined a `__shared__` array `buf[BLKDIM+2]`; we need
`BLKDIM+2` elements since we need to include ghost cells in each
partition in order to be able to compute the new states of all
cells.
- Each thread computes the "local" index `lindex` in the `buf[]`
array, and a "global" index `gindex` in the `d_cur[]` array, of the
element it is associated with. Care should be taken, since both the
local and global domains have ghost cells. Therefore, indices should
be computed as:
```C
const int lindex = 1 + threadIdx.x;
const int gindex = 1 + threadIdx.x + blockIdx.x * blockDim.x;
```
- Each thread copies one element from global to shared memory:
```C
buf[lindex] = cur[gindex];
```
- The first thread of each block also fills the ghost area
of the shared array `buf[]`:
```C
if (0 == threadIdx.x) {
buf[0] = cur[gindex-1];
buf[BLKDIM + 1] = cur[gindex + BLKDIM];
}
```
To generate the output image, the new domain should be transferred
back to host memory after each iteration. Then, `d_cur` and `d_next`
must be exchanged before starting the next iteration.
To compile:
nvcc cuda-rule30.cu -o cuda-rule30
To execute:
./cuda-rule30 [width [steps]]
Example:
./cuda-rule30 1024 1024
The output is stored to the file `cuda-rule30.pbm`
## Files
- [cuda-rule30.cu](cuda-rule30.cu)
- [hpc.h](hpc.h)
***/
#include "hpc.h"
#include
#include
#include
typedef unsigned char cell_t;
/**
* Given the current state of the CA, compute the next state. This
* version requires that the `cur` and `next` arrays are extended with
* ghost cells; therefore, `ext_n` is the length of `cur` and `next`
* _including_ ghost cells.
*
* +----- ext_n-2
* | +- ext_n-1
* 0 1 V V
* +---+-------------------------+---+
* |///| |///|
* +---+-------------------------+---+
*
*/
void step( cell_t *cur, cell_t *next, int ext_n )
{
const int LEFT = 1;
const int RIGHT = ext_n - 2;
int i;
for (i=LEFT; i<=RIGHT; i++) {
const cell_t left = cur[i-1];
const cell_t center = cur[i ];
const cell_t right = cur[i+1];
next[i] =
( left && !center && !right) ||
(!left && !center && right) ||
(!left && center && !right) ||
(!left && center && right);
}
}
/**
* Initialize the domain; all cells are 0, with the exception of a
* single cell in the middle of the domain. `cur` points to an array
* of length `ext_n`; the length includes two ghost cells.
*/
void init_domain( cell_t *cur, int ext_n )
{
int i;
for (i=0; i 3 ) {
fprintf(stderr, "Usage: %s [width [steps]]\n", argv[0]);
return EXIT_FAILURE;
}
if ( argc > 1 ) {
width = atoi(argv[1]);
}
if ( argc > 2 ) {
steps = atoi(argv[2]);
}
const int ext_width = width + 2;
const size_t ext_size = ext_width * sizeof(*cur); /* includes ghost cells */
const int LEFT_GHOST = 0;
const int LEFT = 1;
const int RIGHT_GHOST = ext_width - 1;
const int RIGHT = RIGHT_GHOST - 1;
/* Create the output file */
out = fopen(outname, "w");
if ( !out ) {
fprintf(stderr, "FATAL: cannot create file \"%s\"\n", outname);
return EXIT_FAILURE;
}
fprintf(out, "P1\n");
fprintf(out, "# produced by cuda-rule30.cu\n");
fprintf(out, "%d %d\n", width, steps);
/* Allocate space for the `cur[]` and `next[]` arrays */
cur = (cell_t*)malloc(ext_size); assert(cur != NULL);
next = (cell_t*)malloc(ext_size); assert(next != NULL);
/* Initialize the domain */
init_domain(cur, ext_width);
/* Evolve the CA */
for (s=0; s