Hank Childs, University of Oregon Jan. 30 th, 2014 CIS 610: Vector Models for Data-Parallel Computing

Class Organization Who will lecture next week? Alternate ideas for organizing lectures?

Material for Today’s Lecture A.K.A, “Data Parallel Bible” according to Chris Sewell Material & figures in this lecture almost uniformly come from this dissertation

History Lesson via Google Scholar

Machine Models Machine models you likely know about – Random access machine (RAM) model – Turing machine model This thesis defines a new model: parallel vector model – Defined in terms of machine architecture

Parallel Vector Models

Machine specifics V-RAM = S-RAM + vector memory & vector processor Each instruction of the vector processor operates on – Fixed number of vectors from the vector memory – Possibly scalars from scalar memory Example vector instruction: sum the elements of two vectors

Premise Claim: parallel vector models are the right abstraction to connect theory, languages, and architecture Specifically: – Can be mapped onto a broad variety of architectures – Can serve as algorithmic models to analyze complexity – Can serve as instruction sets for virtual machine for higher-level programming languages

Complexity Two main notions of complexity – Step complexity # of steps executed by a program – Element complexity Sum over all steps of the lengths of all vectors manipulated in each step Important: all data-parallel primitives considered have to finish in O(log N) time for N elements.

Complexity Example Step #1: – Sum two vectors of size 10 Step #2: – Square vector of length 100 What is Step Complexity? What is Element Complexity? What is Step Complexity? What is Element Complexity?

Some New Vector Instructions…

Scan Instruction

Segmented Instructions It is a little fuzzy to me how to do this in practice…

Quicksort

Quicksort pseudo-code OK, let’s try to do quicksort.

Rest of Book