diff --git a/heat_equation/Makefile b/heat_equation/Makefile new file mode 100644 index 0000000000000000000000000000000000000000..076842546b1aa6e7aba5029ba9b71c3503616273 --- /dev/null +++ b/heat_equation/Makefile @@ -0,0 +1,20 @@ +# Makefile that builds each src/*.chpl file into a binary in bin/* + +CC=chpl +CFLAGS=-g +LDFLAGS= + +SRC=$(wildcard src/*.chpl) +PROGRAM=$(addprefix bin/, $(subst .chpl,, $(subst src/,,$(SRC)))) + +all: mkdir $(PROGRAM) + +bin/% : src/%.chpl + $(CC) $(CFLAGS) -o $@ $< + +.PHONY: clean mkdir + +mkdir: + mkdir -p bin +clean: + rm -R bin diff --git a/heat_equation/README.md b/heat_equation/README.md new file mode 100644 index 0000000000000000000000000000000000000000..980bc3d0d5db7d47f0bd308056d445eec781cc97 --- /dev/null +++ b/heat_equation/README.md @@ -0,0 +1,85 @@ +Heat Equation +============= + +In this example, we solve the heat equation. The idea is to apply a 5-point stencil on a domain iteratively until equilibrium. + +Sequential +---------- + +[sequential.chpl](src/sequential.chpl) is a sequential implementation of the heat equation written in Chapel. The stencil computation is the most time consuming part of the code and look like: + +``` + for (i,j) in Interior do//Iterate over all non-border cells + { + //Assign each cell in 'T' the mean of its neighboring cells in 'A' + T[i,j] = (A[i,j] + A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1]) / 5; + } +``` + +Basically, each *interior* element in `T` gets the mean of the corresponding element in `A` as well as the neighboring elements. Since `for` is a sequential language construct in Chapel, a single CPU-core will execute this code. + +Now, let's run it: + +``` + ./bin/heat_equation -nl 1 --size=5000*10 + Heat Equation (sequential) - n: 5000, iterations: 10, elapsed-time: 381.5 seconds +``` + +Multi-core +---------- + +In order to improve the performance, we can tell Chapel to use threads to execute the stencil operations in parallel ([single_machine.chpl](src/single_machine.chpl)). We do that by replacing `for` with `forall`, which tells Chapel to execute each iteration in `Interior` parallel. +It is our responsibility to make sure that each iteration in the `forall` loop is independent in order not to introduce race conditions. + +Clearly in this case iteration is clearly independent since we do not read `T`: + +``` + forall (i,j) in Interior do//Iterate over all non-border cells + { + //Assign each cell in 'T' the mean of its neighboring cells in 'A' + T[i,j] = (A[i,j] + A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1]) / 5; + } +``` + +Now, let's run it (note that `CHPL_RT_NUM_THREADS_PER_LOCALE` tells Chapel the number of threads to use):: + +``` + export CHPL_RT_NUM_THREADS_PER_LOCALE=16 + ./bin/heat_equation -nl 1 --size=5000*10 + Heat Equation (single machine) - n: 5000, iterations: 10, elapsed-time: 25.7052 seconds +``` + +Multiple Machines +----------------- + +In order to improve the performance even further, we can tell Chapel to execute the stencil operation in parallel on multiple machines ([multiple_machines.chpl](src/multiple_machines.chpl)). +We still use the `forall` loop construct, be we have to tell Chapel how to distributes `A` and `T` between the multiple machines. For that, we use the `dmapped` language construct when defining the `Grid` and `Interior` domain: + +``` + //A n+2 by n+2 domain. + const Grid = {0..n+1, 0..n+1} dmapped Block({1..n, 1..n}); + + //A n by n domain that represents the interior of 'Grid' + const Interior = {1..n, 1..n} dmapped Block({1..n, 1..n}); + + var A, T : [Grid] real;//Zero initialized as default +``` + +We tell Chapel to use the same *block* distribution of the `Grid` and `Interior` domain such that each index in `Grid` has the same location as the corresponding index in `Interior`. Because they use the same distribution, no communication is needed when accessing the same index. For example, the operations `A[2,4] + T[2,4]` can be done locally on the machine that *owns* index `[2,4]`. However, it also means that a operations such as `A[2,4] + T[3,4]` will generally require communication. + +Now, let's run it (note that `-nl 8` tells Chapel to use eight locations): + +``` + export CHPL_RT_NUM_THREADS_PER_LOCALE=16 + ./bin/heat_equation -nl 8 --size=5000*10 + Heat Equation (multiple machines) - n: 5000, iterations: 10, elapsed-time: 5.13 seconds +``` + +It is very importation that all arrays in the calculation uses similar `dmapped` layouts. For example, if we do not use `dmapped` when defines `Interior` we get horrible performance: + +``` + export CHPL_RT_NUM_THREADS_PER_LOCALE=16 + ./bin/heat_equation -nl 8 --size=5000*10 + Heat Equation (multiple machines) - n: 5000, iterations: 10, elapsed-time: 1823.23 seconds +``` + diff --git a/heat_equation/src/multiple_machines.chpl b/heat_equation/src/multiple_machines.chpl new file mode 100644 index 0000000000000000000000000000000000000000..0aa625fde492d5a99d812ce0a89a73f521117024 --- /dev/null +++ b/heat_equation/src/multiple_machines.chpl @@ -0,0 +1,77 @@ +//The format of 'size' is two integers separated with a '*'. +//The first integer is the domain size squired and the second integer is +//the number of iterations. +config const size = "100*10";//Default, 100 by 100 domain and 10 iterations + +//Stop condition in amount of change (ignored when 'iterations' are non-zero). +config const epsilon = 1.0e-10; + +//Parse the --size argument into 'n' and 'iterations' +use Regexp; +const arg = size.matches(compile("(\\d+)*(\\d+)")); +const arg_n = arg[1][1]; +const arg_i = arg[2][1]; +const n = size[arg_n.offset+1..arg_n.offset+arg_n.length] : int; +const iterations = size[arg_i.offset+1..arg_i.offset+arg_i.length]: int; + +//Initiate a Timer object +use Time; +var timer : Timer; + +//Now, let's implement the heat equation! + +//We will use the Block distribution +use BlockDist; + +//A n+2 by n+2 domain. +const Grid = {0..n+1, 0..n+1} dmapped Block({1..n, 1..n}); + +//A n by n domain that represents the interior of 'Grid' +const Interior = {1..n, 1..n} dmapped Block({1..n, 1..n}); + +var A, T : [Grid] real;//Zero initialized as default + +A[..,0] = -273.15; //Left column +A[..,n+1] = -273.15; //Right column +A[n+1,..] = -273.15; //Bottom row +A[0,..] = 40.0; //Top row + +timer.start(); +var iter_count = 0; +do{ + //Since all iterations are independent, we can use 'forall', which allows + //the Chapel runtime system to calculate the iterations in parallel + forall (i,j) in Interior do//Iterate over all non-border cells + { + //Assign each cell in 'T' the mean of its neighboring cells in 'A' + T[i,j] = (A[i,j] + A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1]) / 5; + } + + //Delta is the total amount of change done in this iteration + const delta = + reduce abs(A[Interior] - T[Interior]); + + //Copy back the non-border cells + A[Interior] = T[Interior]; + + //if 'iterations' is non-zero we stop after a fixed number of iterations + //otherwise we stop when the calculation has converged, i.e. 'delta' is smaller than 'epsilon'. + var stop = false; + if(iterations > 0) + { + if iter_count >= iterations then + stop = true; + } + else + { + if delta < epsilon then + stop = true; + } + +} while (!stop); + +timer.stop(); +writeln("Heat Equation (multiple machines) - n: ",n, + ", iterations: ", iterations, + ", elapsed: ", timer.elapsed(), " seconds"); + + diff --git a/heat_equation/src/sequential.chpl b/heat_equation/src/sequential.chpl new file mode 100644 index 0000000000000000000000000000000000000000..5d110b6ac020b94bab586525bfdea511bd7956bb --- /dev/null +++ b/heat_equation/src/sequential.chpl @@ -0,0 +1,74 @@ +//The format of 'size' is two integers separated with a '*'. +//The first integer is the domain size squired and the second integer is +//the number of iterations. +config const size = "100*10";//Default, 100 by 100 domain and 10 iterations + +//Stop condition in amount of change (ignored when 'iterations' are non-zero). +config const epsilon = 1.0e-10; + +//Parse the --size argument into 'n' and 'iterations' +use Regexp; +const arg = size.matches(compile("(\\d+)*(\\d+)")); +const arg_n = arg[1][1]; +const arg_i = arg[2][1]; +const n = size[arg_n.offset+1..arg_n.offset+arg_n.length] : int; +const iterations = size[arg_i.offset+1..arg_i.offset+arg_i.length]: int; + +//Initiate a Timer object +use Time; +var timer : Timer; + +//Now, let's implement the heat equation! + +//A n+2 by n+2 domain. +const Grid = {0..n+1, 0..n+1}; + +//A n by n domain that represents the interior of 'Grid' +const Interior = {1..n, 1..n}; + +var A, T : [Grid] real;//Zero initialized as default + +A[..,0] = -273.15; //Left column +A[..,n+1] = -273.15; //Right column +A[n+1,..] = -273.15; //Bottom row +A[0,..] = 40.0; //Top row + +timer.start(); +var iter_count = 0; +do{ + //Since all iterations are independent, we can use 'forall', which allows + //the Chapel runtime system to calculate the iterations in parallel + for (i,j) in Interior do//Iterate over all non-border cells + { + //Assign each cell in 'T' the mean of its neighboring cells in 'A' + T[i,j] = (A[i,j] + A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1]) / 5; + } + + //Delta is the total amount of change done in this iteration + const delta = + reduce abs(A[Interior] - T[Interior]); + + //Copy back the non-border cells + A[Interior] = T[Interior]; + + //if 'iterations' is non-zero we stop after a fixed number of iterations + //otherwise we stop when the calculation has converged, i.e. 'delta' is smaller than 'epsilon'. + var stop = false; + if(iterations > 0) + { + if iter_count >= iterations then + stop = true; + } + else + { + if delta < epsilon then + stop = true; + } + +} while (!stop); + +timer.stop(); +writeln("Heat Equation (sequential) - n: ",n, + ", iterations: ", iterations, + ", elapsed: ", timer.elapsed(), " seconds"); + + diff --git a/heat_equation/src/single_machine.chpl b/heat_equation/src/single_machine.chpl new file mode 100644 index 0000000000000000000000000000000000000000..54af20bb15cc374d000d2abfbe197489027d0be8 --- /dev/null +++ b/heat_equation/src/single_machine.chpl @@ -0,0 +1,74 @@ +//The format of 'size' is two integers separated with a '*'. +//The first integer is the domain size squired and the second integer is +//the number of iterations. +config const size = "100*10";//Default, 100 by 100 domain and 10 iterations + +//Stop condition in amount of change (ignored when 'iterations' are non-zero). +config const epsilon = 1.0e-10; + +//Parse the --size argument into 'n' and 'iterations' +use Regexp; +const arg = size.matches(compile("(\\d+)*(\\d+)")); +const arg_n = arg[1][1]; +const arg_i = arg[2][1]; +const n = size[arg_n.offset+1..arg_n.offset+arg_n.length] : int; +const iterations = size[arg_i.offset+1..arg_i.offset+arg_i.length]: int; + +//Initiate a Timer object +use Time; +var timer : Timer; + +//Now, let's implement the heat equation! + +//A n+2 by n+2 domain. +const Grid = {0..n+1, 0..n+1}; + +//A n by n domain that represents the interior of 'Grid' +const Interior = {1..n, 1..n}; + +var A, T : [Grid] real;//Zero initialized as default + +A[..,0] = -273.15; //Left column +A[..,n+1] = -273.15; //Right column +A[n+1,..] = -273.15; //Bottom row +A[0,..] = 40.0; //Top row + +timer.start(); +var iter_count = 0; +do{ + //Since all iterations are independent, we can use 'forall', which allows + //the Chapel runtime system to calculate the iterations in parallel + forall (i,j) in Interior do//Iterate over all non-border cells + { + //Assign each cell in 'T' the mean of its neighboring cells in 'A' + T[i,j] = (A[i,j] + A[i-1,j] + A[i+1,j] + A[i,j-1] + A[i,j+1]) / 5; + } + + //Delta is the total amount of change done in this iteration + const delta = + reduce abs(A[Interior] - T[Interior]); + + //Copy back the non-border cells + A[Interior] = T[Interior]; + + //if 'iterations' is non-zero we stop after a fixed number of iterations + //otherwise we stop when the calculation has converged, i.e. 'delta' is smaller than 'epsilon'. + var stop = false; + if(iterations > 0) + { + if iter_count >= iterations then + stop = true; + } + else + { + if delta < epsilon then + stop = true; + } + +} while (!stop); + +timer.stop(); +writeln("Heat Equation (single machine) - n: ",n, + ", iterations: ", iterations, + ", elapsed: ", timer.elapsed(), " seconds"); + +