HEBench
Matrix Multiplication Workload

Table of Contents

Operation Description

Summary

This operation is defined as:

M = op(M0, M1)

where

op(M0, M1) = M0 x M1

is the standard matrix multiplication operation.

Operation Parameters

Input: 2 parameters

Parameter Description
0 M0 is a matrix with m rows and n columns (m x n).
1 M1 is a n x p matrix.

Result:

Output: 1 output

Output Description
0 M is a m x p matrix. It is the result of multiplying M0 and M1.

Details

If A[i][j] denotes the element at row i and column j in matrix A, then, the standard matrix multiplication operation is defined as:

M[i][j] = M0[i][1] * M1[1][j] + M0[i][2] * M1[2][j] + ... + M0[i][n] * M1[n][j]

Workloads

This document applies to the following workloads:

// From hebench/api_bridge/types.h
hebench:APIBridge::Workload::MatrixMultiply

Workload Parameters

Required workload parameters: 3

Index Name Type Description
0 m uint64_t Number of rows in matrix M0.
1 n uint64_t Number of columns in matrix M0.
2 p uint64_t Number of columns in matrix M1.

Number of rows in M1 is the same as number of columns in M0 as per definition of the operation.

Above parameters are required for the workload in the specified order. A backend must specify, at least, a set of default arguments for these parameters.

Backends can require extra parameters beyond the base requirements. If a backend requires extra parameters, these must have default values in every set of default arguments for the workload parameters.

Categories

This workload supports the following categories:

hebench:APIBridge::Category::Latency
hebench:APIBridge::Category::Offline

Category Parameters

Latency

See Latency Category .

Offline

See Offline Category .

Value ranges for elements in CategoryParams::offline::data_count. Default value is used when the backend implementation sets the data_count for the corresponding operand to 0, but user specified 0 or no value at run-time.

Parameter Lower bound Upper bound Default
0 1 none 100
1 1 none 100

Data Type

This workload is defined for the following data types:

hebench::APIBridge::DataType::Int32
hebench::APIBridge::DataType::Int64
hebench::APIBridge::DataType::Float32
hebench::APIBridge::DataType::Float64
hebench::APIBridge::WorkloadParamType::Float64
@ Float64
64 bits IEEE 754 standard floating point real numbers.
Definition: types.h:306
hebench::APIBridge::WorkloadParamType::Int64
@ Int64
64 bits signed integers.
Definition: types.h:304
hebench::APIBridge::Float32
@ Float32
32 bits IEEE 754 standard floating point real numbers.
Definition: types.h:382
hebench::APIBridge::Int32
@ Int32
32 bits signed integers.
Definition: types.h:380

Data Layout

Data layout in memory for a matrix with elements of type T (where T is any of the supported types), follows a row major ordering. All scalar elements in a matrix lie contiguous in memory, where consecutives elements in a row reside next to each other.

For example, given the following matrix A (2 x 3):

/ a00 a01 a02 \
A = | |
\ a10 a11 a12 /

The elements will be stored in memory as:

Offset: 0 1 2 3 4 5
A a00 a01 a02 a10 a11 a12

Backends should expect this layout for their raw, clear text inputs, and must generate this layout for their decoded outputs.

Notes

If several matrices will be pointed at by a single pointer, consecutive matrix will follow each other in memory.

Dataset

Supported modes:

Generate External
yes yes

Data generation for vectors used as input for this workload occurs during workload initialization by Test Harness. Ground truths are pre-computed during data generation. There is no standard dataset.

During data generation, all matrix elements are extracted from a pseudo-random normal distribution with mean 0 and standard deviation of 10: n(0, 10).