Commit 54f53840 authored by Lukas Trümper's avatar Lukas Trümper

Basic structure

parent c63882fd
## macOS
# POP2 Kernel
This repository systematically classifies parallel algorithms and kernels based on the idea of parallel patterns.
- *Julian Miller -*
- *Lukas Trümper -*.
### A Parallel Pattern based Model
The essential idea of our classification approach separates a kernel's structure from its function
parallel \; algorithm \; = \; structure \; + \; function.
Structure describes the kernel's high-level structure of parallelism, like the scheme of synchronization and dependencies. In short, which *parallel patterns* are observable. On the other side, function means the concrete operations, which are performed within the structure.
For better understanding consider two kernels:
1. The first kernel simply increments each entry of an array:
int[] array;
for (int i = 0; i < len(array); i++){
array[i] += 1
2. The second kernel computes a linear mapping of the logarithm of each entry of an array:
int[] array;
for (int i = 0; i < len(array); i++){
array[i] = math.log(array[i]) * 2 + 10
In our model, 1. and 2. have identical structure but different functions.
#### Classification of Structure
Structure is seen as a high-level property of a parallel algorithm. In particular, structure directly corresponds to the potential degree of parallelism. Hence,
> structure defines the *scalability* of an algorithm.
Since structure expressed by programming languages follows a hierarchical scheme, the classification is also based on hierarchical compositions of parallel patterns. A parallel pattern describes a certain kind of dependency and synchronization. Typically, these patterns describe rather small structures like
- a **map**,
- a **reduction**,
- or communication like a **broadcast**.
However, the hierarchical composition of them allows to describe every larger structure in a simple way. Moreover, previous example implies a crucial property:
> the structure spans *equivalence classes* on the set of parallel algorithms.
The members of the **equivalence classes** share all properties directly affected by the structure and the high-level parallelism. For instance, we would expect the two kernels of previous example expect to have similar scalability and parallelization effort.
#### Classification of Function
Functions are concrete computations performed within a structure. Thus, they actually define the algorithm as they define the output. Classification of computations can be detailed up to any desired degree. Typically, a classification might cover properties
- measuring the computational intensity (**compute-bound**),
- instruction counts (e.g. number of arithmetic expressions),
- measuring the memory intensity (**memory-bound**),
- caching behavior,
- load-to-store ratio,
- measuring the **instruction-level parallelism**,
- pipelining ability,
- vector operations,
- e.g. branching count.
- categorizing the **application**,
- matrix-vector,
- graphs.
> the functions define the serial (thread-wise) performance.
#### Runtime
The main advantage of the model is that it allows systematic reasoning about the runtime behavior of a parallel algorithm based on static properties. More particular, since
- the class of the structure defines the scalability,
- the properties of the function define the serial peformance,
the overall performance might be predicted by the combined investigation.
This means, a parallel algorithm scales with increasing core count according to the scaling behavior of its patterns; a map scales differently than a reduction. Together with the serial performance the overall performance can be estimated. Moreover, the serial performance indicates whether the scalability might saturate because of machine limitations. For instance, a memory-bound function limits the scalabiltiy of a map.
Therefore, the measurement of **runtime properties (performance metrics)** would be an essential part of the validiation of the model.
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