Fourier Division Algorithm Explained

  • Thread starter Thread starter expert_vision
  • Start date Start date
  • Tags Tags
    Division Fourier
AI Thread Summary
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.
expert_vision
Messages
6
Reaction score
0
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
 
Last edited by a moderator:
Mathematics news on Phys.org
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.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top