SIMD, Single Instruction Multiple Data

Abstract

The single instruction, multiple data (SIMD) mode is the simplest method of parallelism and now becoming the most common. In most cases this SIMD mode means the same as vectorization. Ten years ago, ve ctor computers were expensive but reasonably simple to program. Today, encouraged by multimedia applications, vector hardware is now commonly available in Intel Pentium III and Pentium 4 PCs, and Apple/Motorola G-4 machines. In this chapter, we will cover both old and new and find that the old paradigms for programming were simpler because CMOS or ECL memories permitted easy non-unit stride memory access. Most of the ideas are the same, so the simpler programming methodology makes it easy to understand the concepts. As PC and Mac compilers improve, perhaps automatic vectorization will become as effective as on the older non-cache machines. In the meantime, on PCs and Macs we will often need to use intrinsics ([23, 22, 51]). It seems at first that the intrinsics keep a programmer close to the hardware, which is not a bad thing, but this is somewhat misleading. Hardware control in this method of programming is only indirect. Actual register assignments are made by the compiler and may not be quite what the programmer wants. The SSE2 or Altivec programming serves to illustrate a form of instruction level parallelism we wish to emphasize. This form, SIMD or vectorization, has single instructions which operate on multiple data. There are variants on this theme which use templates or macros which consist of multiple instructions carefully scheduled to accomplish the same objective, but are not strictly speaking SIMD, for example see Section 1.2.2.1. Intrinsics are C macros which contain one or more SIMD instructions to execute certain operations on multiple data, usually 4-words/time in our case. Data are explicitly declared mm128 datatypes in the Intel SSE case and vector variables using the G-4 Altivec. Our examples will show you how this works. Four basic concepts are important: Consistent with our notion that examples are the best way to learn, several will be illustrated: • from linear algebra, the Level 1 basic linear algebra subprograms (BLAS) — vector updates (-axpy) — reduction operations and linear searches • recurrence formulae and polynomial evaluations • uniform random number generation.