How parentheses effects multiplication with pi ?

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Emre Doruk 2020-8-4

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编辑： Bruno Luong 2020-8-5

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Hi,

I am trying to generate sine wave. I am usning following two code lines. But they are slightly different (about e-15). Why is it happenning ? What is the differences of two lines;

f0=5e2;
fs=500e2;
len=3e3;
dt=1/fs;
t=0:dt:(len-1);
sing1= sin (2*pi*f0*t);
sing2= sin(2*pi*(f0*t));
isequal(sing1,sing2)

Thanks for your help,

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Bruno Luong 2020-8-5

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https://ww2.mathworks.cn/matlabcentral/answers/574954-how-parentheses-effects-multiplication-with-pi#answer_475288

编辑：Bruno Luong 2020-8-5

From wikipedia

"While floating-point addition and multiplication are both commutative (a + b = b + a and a × b = b × a), they are not necessarily associative. That is, (a + b) + c is not necessarily equal to a + (b + c). ... "

"(2*pi*f0*t)" interpreted by MATLAB as ((2*pi)*f0)*t
"2*pi*(f0*t)" interpreted by MATLAB as (2*pi)*(f0*t)

As floating-point multiplication is NOT ASSOCIATIVE, both results might be different.

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Bruno Luong 2020-8-5

Sometime this non-associativity is a real headeach, such as finding a limits of a sign- alternate series by partial sum, or integral of an oscillated signal (any wave propagation SW might encounters this). There is a real challenge to know what really the limits and the order of the sum can make the result change widely.

Emre Doruk 2020-8-5

Actually I realized it recently, I thougth this problem is about pi. Because it is irrational and maybe MATLAB coverge it sth. I asked for this reason but I see that it is more common from this. I should check all of my old codes which needs exact values. Genereally it can be accept like precision mistake but sometimes I really need exact value.

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