GEMV Tutorial 0: Basic CSL Syntax¶

This tutorial is the first in a series of successive tutorials aimed at teaching CSL and the SDK by implementing a general matrix-vector product, or GEMV.

We start by illustrating the syntax of some of the core language constructs. The code in this example is not a complete program, but it shows some of the most commonly-used features of the language.

Before you start¶

These tutorials are intended for a beginner CSL programmer using the Cerebras SDK. Before you proceed, make sure you installed the Cerebras SDK successfully. See Installation and Setup.

Learning objectives¶

After completing this tutorial, you should know:

Basic syntax of the CSL language
How to write for and while loops
How to declare constants and variables
CSL’s function syntax

Introduction¶

CSL is a language for writing programs that run on the Cerebras Wafer Scale Engine (WSE). The WSE consists of hundreds of thousands of independent processing elements (PEs). Each PE has room for a small program and some data. CSL is designed to help you handle the multi-PE nature of the WSE and the specific challenges of writing dataflow programs for the Cerebras hardware.

The language syntax is similar, although not identical, to Zig. However, despite the similarity in the language constructs, both the purpose as well as the implementation of the CSL compiler are substantially different from that of the Zig compiler.

Types¶

CSL includes some basic types such as:

bool for boolean values
i16 and i32 for 16- and 32-bit signed integers
u16 and u32 for 16- and 32-bit unsigned integers
f16 and f32 for 16- and 32-bit IEEE-754 floating point numbers

In addition to the above, CSL also supports array types and pointer types.

Functions¶

Functions are declared using the fn keyword. The compiler provides special functions called Builtins, whose names start with @ and whose implementation is provided by the compiler. All CSL builtins are described in Builtins.

Conditional Statements and Loops¶

CSL includes support for if statements and while and for loops.

Example overview¶

This simple code computes the general matrix-vector product y = Ax + b, where A has dimensions M x N, x is N x 1, and b and y are M x 1.

Our code will store A in a one-dimensional array of size M*N, using a row-major ordering. This computation will be performed with 32-bit arithmetic.

Writing the CSL¶

What does our code need to do?

Define the dimensions of our matrix
Define arrays for holding A, x, b, and y
Define a function that initialize the arrays
Define a function to compute A*x + b and store the result in y

We explain the sections of our code.csl file containing this code below. This code file, along with all tutorials and examples, are available in the csl-extras directory contained within the SDK tarball.

// Not a complete program; we include it here for illustrating some syntax

// Every variable must be declared either "const" or "var"
// Const cannot be modified after declaration, but var can

// Constants defining dimensions of our matrix
const M: i16 = 4;
const N: i16 = 6;

// 48 kB of global memory contain A, x, b, y
var A: [M*N]f32; // A is stored in row-major order
var x: [N]f32;
var b: [M]f32;
var y: [M]f32;

// Initialize matrix and vectors
fn initialize() void {
  // for loop with range syntax
  // loops over 0, 1, ...., M*N-1
  // idx stores the loop index
  for (@range(i16, M*N)) |idx| {
    // @as casts idx from i16 to f32
    A[idx] = @as(f32, idx);
  }

  for (@range(i16, N)) |j| {
    x[j] = 1.0;
  }

  // while loop with iterator syntax
  var i: i16 = 0;
  while (i < M) : (i += 1) {
    b[i] = 2.0;
    y[i] = 0.0;
  }
}

// Compute gemv
fn gemv() void {
  for (@range(i16, M)) |i| {
    var tmp: f32 = 0.0;
    for (@range(i16, N)) |j| {
      tmp += A[i*N + j] * x[j];
    }
    y[i] = tmp + b[i];
  }
}

// Call initialize and gemv functions
fn init_and_compute() void {
  initialize();
  gemv();
}

Reading the above CSL code, we can see the following:

Defining our variables and constants¶

We first define two constants, N and M, that give our matrix and vector dimensions. For the purposes of this and the next few tutorials, we’ll use M = 4 and N = 6.

We then declare the arrays A, x, b, and y, which hold our matrix and vectors. A stores N*M single-precision floating point elements. We will store the matrix in A in a row-major fashion. These constants and arrays are declared in global scope: they will be visible to all functions in this code file.

Note that all data items must explicitly be declared as variables or constants, with the var or const keywords.

Defining our initialize function¶

Next, we define a function named initialize that we will call to initialize the values stored in A, x, b, and y. A will be initialized such that each element i holds the value i, all values of x will be initialized to 1.0, and all values of b will be initialized to 2.0. y will be zero-initialized.

To initialize A, we use a for loop with the range syntax. @range(i16, M*N) returns the sequence of integers 0, 1, 2, ..., M*N-1, in i16, or half-precision signed, format. The for loop iterates over this sequence of integers, and the variable idx stores the index of the current loop iteration. On each loop iteration, @as(f32, idx) casts the integer value idx to type f32, or single precision float, and assigns this value to the element A[idx].

We also use a range-for loop to initialize all elements of x to the value 1.0.

To initialize y and b, we demonstrate the syntax of a while loop with an assignment expression that acts as a loop index. At each loop iteration, the variable i is incremented by 1. This assignment expression is executed at the end of each loop iteration.

Defining our gemv function¶

The function gemv actually computes y = A*x + b. The outer loop iterates over M, i.e., over the rows of the matrix. For each row i in the matrix, the inner loop over N computes the dot product of that row with the vector x by incrementing the variable tmp. After completing the inner loop, the final value of y[i] is computed from tmp and b[i].

This code sample ends with a function named init_and_compute, which simply calls initialize followed by gemv.

Next¶

In the next tutorial, we’ll expand this code to a full program.

SDK Documentation (0.9.0)

GEMV Tutorial 0: Basic CSL Syntax

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