Fourier Division Algorithm Explained

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The discussion revolves around the Fourier division algorithm and its computation of "b terms." It highlights the confusion around calculating quotient (q) and remainder (r) using three different methods based on the sign of x. The first method uses standard integer division, while the second and third methods adjust the calculations when x is positive or negative, respectively. The user clarifies that when a b term is negative, the remainder must be adjusted to be positive, leading to further adjustments in subsequent calculations. Overall, the thread seeks deeper understanding and clarification of the Fourier division algorithm's nuances.
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There is an article on wikipedia (http://en.wikipedia.org/wiki/Fourier_division" ) about Fourier division algorithm, but there is something that confuses me.
When they compute the so called "b terms" they have to divide 2 numbers. Let's call them x and y, and x/y=q+r. To compute q and r they use 3 methods:

1. q=x/y (integer division) and r=x%y
2. q=x/y+1 and r=x%y-b (when x is positive)
3. q=x/y-1 and r=b+x%y (when x is negative)Does anyone know more about Fourier division or where can I find some details about it?

Thx
 
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I think I got it. I don't know why but when a b term gets negative the remainder has to be made positive using 3th method. Then the next remainder has to be made negative using 2th method if x is positive or 1th method if x is negative.
 

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