Fast Algorithm for Division w/ Remainder - Division Revision

[mtanti]

Guys I need a fast algorithm to perform division with a remainder. It has to be very fast though...

 

[gregmead]

Something like, x/y could be done like: (where x and y are numbers)

[Int(x/y)]

Then the remainder is: [y*Frac(x/y)]

That'll be pretty much instant (if you want to do it on a computer or something)


If you want to do it with a calculator then just do:

x/y but disregard the decimals

Then to work out the remainder just do:

x/y but disregard the integer before the decimals then multiply them by y


If you want to do it without a calculator then just do it the old fasioned way :)

 

[tacman]

There are several algorithms that can be used for fast division with remainder, but the most commonly used one is the "long division" algorithm. This algorithm involves dividing the dividend (the number being divided) by the divisor (the number dividing the dividend) and then using the remainder to continue dividing until there is no remainder left.

To make this algorithm faster, you can use a technique called "multiplication by reciprocals". This involves finding the reciprocal of the divisor and multiplying it by the dividend to get a quotient. Then, you can use this quotient to find the remainder by subtracting it from the dividend. This process can be repeated until there is no remainder left.

Another way to make the long division algorithm faster is by using binary division. This involves converting both the dividend and divisor into binary numbers and performing the division using binary operations such as shifting and bitwise subtraction. This method is particularly useful for larger numbers as it reduces the number of operations needed to find the remainder.

In summary, to perform fast division with remainder, you can use techniques such as multiplication by reciprocals or binary division. These methods can greatly improve the speed of the long division algorithm and provide a fast solution for your division needs.