+ initial commit

readme.md

+<!--
+- SPDX-License-Identifier: Apache-2.0
+- Copyright (C) 2025 Jayesh Badwaik <j.badwaik@fz-juelich.de>
+-->
+
+# logmap - a microbenchmark with controllable arithmetic intensity
+
+A [logistic map](https://en.wikipedia.org/wiki/Logistic_map) is a simple
+mathematical model that exhibits chaotic behavior. This repository contains a
+microbenchmark that is based on the logistic map that can be controlled to have
+a desired arbitrary workload and desired arbitrary arithmetic intensity.
+
+The microbenchmark works by iterating each element of an array of floating-point
+numbers `x` of size `N` using the logistic map formula for a
+specified number of iterations `niter`. The logistic map formula is given by:
+
+
+```math
+x_{i, n+1} = r * x_{i,n} * (1 - x_{i,n})
+```
+
+where $i$ is the index of the element in the array and $n$ is the iteration
+number. The value of `r` is a constant that determines the behavior of the
+logistic map. The value of `r` is selected to be within the range [3.5, 4.0] to
+ensure that the logistic map exhibits chaotic behavior. The chaotic nature of
+the logistic map ensures that the benchmark hardware is not susceptible to
+effects of [input-dependent power
+consumption](https://arxiv.org/abs/2409.18324).
+
+The arithmetic intensity of the benchmark is directly proportional to the number
+of iterations `niter` and independent of the size of the array `N` and can be
+written as
+
+```math
+AI = k_i * niter
+```
+
+where `k_i` is the arithmetic intensity  for a single iteration of the logistic
+map for a single input. The workload of the benchmark is directly proportional
+to the size of the array `N` and directly proportional to the number of
+iterations `niter` and can be written as
+
+```math
+W = k_w * N * niter
+```
+
+where `k_w` is the floating-point operations per element of the array `x` for a
+single iteration of the logistic map.
+
+
+