Fourier Division Algorithm Explained

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SUMMARY

The Fourier Division Algorithm involves calculating the quotient and remainder of two numbers, x and y, using three distinct methods. The methods include integer division for positive x, an adjustment for positive remainders, and a correction for negative x values. Specifically, when the b term is negative, the remainder must be adjusted to ensure positivity, impacting the subsequent calculations. Understanding these methods is crucial for accurately implementing the Fourier Division Algorithm.

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  • Understanding of integer division and modulus operations
  • Familiarity with the concept of quotients and remainders
  • Basic knowledge of algorithm design principles
  • Experience with mathematical notation and operations
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  • Explore integer division and modulus in programming languages like Python or C++
  • Study the implications of negative numbers in division algorithms
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expert_vision
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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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