Initial commit

README.md

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+# level-index-simulator
+
+# `sli` - A custom precision MATLAB symmetric level-index arithmetic simulator.
+
+## About
+
+`sli` is a MATLAB toolbox that provides sli objects and operations on them.
+
+* [sli.m](sli.m) - the main object file.
+* [tests](./tests) - various testing scripts that test the accuracy of representation and operations.
+* [experiments](./experiments) - scripts to reproduce the experiments with level-index arithmetic in [1].
+
+[![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=north-numerical-computing/level-index-simulator)
+
+## Quick start
+
+```
+x = sli(2,12);
+x = x.set_val(pi)
+x = 
+
+  sli with properties:
+
+    level_bits: 2
+    index_bits: 12
+          sign: 0
+    reciprocal: 1
+         level: 2
+         index: 0.135253906250000
+         value: 3.141899100868418
+```
+
+### Installation
+
+Clone the repository and add the root directory to the MATLAB search path.
+
+## Requirements
+
+The code was developed on MATLAB 2023b. Experiments make use of the [CPFloat](https://github.com/north-numerical-computing/cpfloat) package.
+
+## References
+
+[1] Mantas Mikaitis. [*MATLAB Simulator of Level-Index Arithmetic*](https://). In Prep., Feb. 2024.
+
+## Licence
+
+The code is distributed under the terms of the BSD 2-Clause License;
+see [license.txt](license.txt).
+BBB

experiments/matvec.m

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+% Compare matrix-vector product accuracy in floating-point and
+% level-index arithmetics.
+%
+% References
+%
+% M. Mikaitis, MATLAB Simulator of Level Index Arithmetic, In Prep., 2024.
+
+clear all;
+
+nlist = round(logspace(1,4,20));
+
+% Set up cpfloat options
+options.format = 'fp16';
+options.round = 1;
+options.explim = 1;
+cpfloat([], options);
+k = 0;
+
+for n = nlist
+    k = k + 1;
+    fprintf('k = %2d, n = %7d\n',k,n);
+    A = rand(10,n)*100;
+    x = rand(n,1);
+
+    % Set up SLI vectors
+    Asli = zeros(10, n, 2, 12, 'sli');
+    xsli = zeros(n, 1, 2, 12, 'sli');
+
+    % Convert vectors to SLI
+    for j = 1:numel(A)
+       Asli(j) = Asli(j).set_val(A(j));
+    end
+    for j = 1:numel(x)
+       xsli(j) = xsli(j).set_val(x(j));
+    end
+
+    % Double reference result
+    ye = A*x;
+    absAx = abs(A)*abs(x);
+
+    % Binary16 result
+    y1 = mtimesv(A,x,options);
+    berr1(k) = max(abs(ye-y1)./absAx);
+
+    % Level index 2.12
+    y2 = Asli*xsli;
+    berr2(k) = max(abs(ye-[y2.value]')./absAx);
+end
+
+filename = sprintf('matvec_binary16_1.dat');
+fid = fopen(filename, 'w');
+for i=1:length(nlist)
+    fprintf(fid, "%d %f %f\n", nlist(i), berr1(i), berr2(i));
+end
+fclose(fid);
+
+loglog(nlist, berr1, '-*', ...
+      nlist, berr2, '-o');
+legend('binary16', 'level index 2.12');
+
+function y = mtimesv(A,x,options)
+    [m,n] = size(A);
+    y = zeros(m,1);
+    for i=1:n
+        y = cpfloat(y + cpfloat(A(:,i)*x(i), options), options);
+    end
+end

license.txt

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+BSD 2-Clause License
+
+Copyright (c) 2024, Mantas Mikaitis
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this
+   list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice,
+   this list of conditions and the following disclaimer in the documentation
+   and/or other materials provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.