Differences calculating the sum of squares in single between sum() and a loop

Question

Jonathan Currie 2013-8-20

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Update: Please Visit the Following Simplified Version of This Question http://www.mathworks.com/matlabcentral/answers/85211-different-results-between-2013a-32bit-and-64bit-in-single-precision

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Hi, I'm calculating the sum of squares in C and MATLAB in single precision and noted some differences. I wondered if anyone can fill me in on the behaviour below. Suspect floating point associative problem, but still seems a little odd...

Numbers in my array a are 'reasonably' well scaled, from a column in a single precision matrix generated by MATLAB. Differences being seen here are common and leading to substantial differences between same algorithm in C and MATLAB.

Answer displayed from code below:

Code to reproduce:

clc
format long
a = single([-0.112033270,0.153425455,-0.751111090,-0.129932076,0.206365064,-0.871111095,0.000000000,...
            0.000000000,0.000000000,0.000662919,-0.000005372,0.004444445,0.002651675,-0.000085950,...
            0.017777778,0.005966269,-0.000435120,0.039999999,0.010606701,-0.001375194,0.071111113,...
            0.016572969,-0.003357407,0.111111112,0.023865076,-0.006961920,0.159999996,0.032483019,...
            -0.012897816,0.217777774,0.042426802,-0.022003105,0.284444451,0.053696420,-0.035244718,...
            0.360000014,0.066291876,-0.053718518,0.444444448,0.080213174,-0.078649282,0.537777781,...
            0.095460303,-0.111390717,0.639999986,0.112033270,-0.153425455,0.751111090,0.129932076,...
            -0.206365064,0.871111095]);
%Method one (matlab code)
r1 = sum(a.^2);
%Method two (as done in C)
r2=single(0);
for i = 1:length(a)
    r2 = r2 + a(i)^2;
end
%Method 3 (variation, correct answer (why?))
r3=single(0);
for i = 1:length(a)
    x = a(i)^2;
    r3 = r3 + x;
end
%Method 4 (why does double(0) change things - single takes precedence?)
r4 = double(0);
for i = 1:length(a)
    r4 = r4 + a(i)^2;
end
display([r1;r2;r3;r4])

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Roger Stafford 2013-8-20

编辑：Roger Stafford 2013-8-20

Those results could be different if in the first case the computer does the squaring and adding all in double precision before rounding back to single precision, while in the second case such a rounding might occur both after the squaring operation and after the addition.

These single precision results differ only in their` least bit. It takes only one rounding difference among the fifty-one steps to produce that.

Jonathan Currie 2013-8-20

OK I have simplified the problem to two elements. New simplified question posed: http://www.mathworks.com/matlabcentral/answers/85211-different-results-between-2013a-32bit-and-64bit-in-single-precision

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Answer 1

the cyclist 2013-8-20

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/85148-differences-calculating-the-sum-of-squares-in-single-between-sum-and-a-loop#answer_94654

在 MATLAB Online 中打开

What version of MATLAB are you using? I get

from your code, using R2013a on a OS X 10.8.4.

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Jonathan Currie 2013-8-20

编辑：Jonathan Currie 2013-8-20

Hi - yep just checked on another PC, I get the correct answer on Matlab 2013a 64bit, but the incorrect answer on 2013a 32bit (Win64)... Can anyone else repeat this result?

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Differences calculating the sum of squares in single between sum() and a loop

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Differences calculating the sum of squares in single between sum() and a loop

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