Prepare a MATLAB/Octave script that sums n random, single-precision floating-poi

Question

Prepare a MATLAB/Octave script that sums n random, single-precision floating-point numbers 2 uniformly distributed in the interval [0, 1]. Sum the numbers in each of the following ways (using single-precision variables unless specifically indicated otherwise) (a) Sum the numbers in the order in which they were generated, using a double-precision variable to accumulate the sum. (b) Sum the numbers in the order in which they were generated, this time using a single-precision accumulator (c) Use the following compensated summation algorithm, again using only single precision, to sum the numbers in the order in which they were generated: for i=: 1 to n do c=(t-s)-y end for

Explanation / Answer

MATLAB code

close all
clear
clc

n = 10;
x = single(rand(1,n));

% Part (a)
sum_double = double(0);
for i=1:n
sum_double = sum_double + x(i);
end
fprintf('(a) Sum [double] = %f ', sum_double);

% Part (b)
sum_single = single(0);
for i=1:n
sum_single = sum_single + x(i);
end
fprintf('(b) Sum [single] = %f ', sum_single);

% Part (c)
s = x(1);
c = single(0);
for i=2:n
y = x(i) - c;
t = s + y;
c = (t - s) - y;
s = t;
end
fprintf('(c) Sum = %f ', s);

% Part (d)
x = sort(x);
sum_sort = single(0);
for i=1:n
sum_sort = sum_sort + x(i);
end
fprintf('(d) Sum = %f ', sum_sort);

output

(a) Sum [double] = 5.322150
(b) Sum [single] = 5.322150
(c) Sum = 5.322150
(d) Sum = 5.322150

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