algorithm - efficient way to divide a very large number stored in 2 registers by a constant

Question

Let's say I want to calculate the following:

A/Z

Where A is of length 128 bit and Z is 64 bit long. A is stored in 2 64 bit registers since the registers of the system can store up to 64 bits. What would be an efficient way to calculate the result?

P.S: I've solved similar multiplication problems by using CSD representations. However, this would require calculating 1/Z first.

Answer 1

The right way to solve such a problem, is by returning to the basics:

• divide the most significant register by the denominator
• calculate the quotient Q and the rest R
• define a new temporary register preferrably with the same length as the other 2
• the rest should occupy the most significant bits in the temporary register
• shift the lesser significant register to the right by the same amount of bits contained iR and add to the result to the temporary register.
• go back to step 1

after the division, the resulting rest must be casted to double, divided by the denominator then added to the quotient.