Division with FV-1

[mrushg]

The problem is to synthesize a triangle or sawtooth waveform of constant amplitude from a variable-pitch incoming square wave. The ramp can be generated by incrementing or decrementing a register, resetting it at transitions. The pitch can be measured by counting the number of processor clocks between transitions, but to calculate the register increment value needs a division.
Is there a simple way to achieve this with the FV-1? The log and exp functions look frightening!
Any ideas gratefully appreciated

[DrAlx]

To evaluate

y = A / B

on the FV-1 you evaluate this

y = exp( log(A) - log(B) )

The problem is that the FV-1 log() only works on values in the range 0 to 1, and the exp() function only produces values in the range 0 to 1. This means that you need to make sure that the final answer lies in the range 0 to 1.

Example:

Lets say you want to evaluate

y = 1 / (1 + 9 * x) where x is between 0 and 1

This has an answer in the range 0 to 1, but to evaluate it on the FV-1 you need to scale the
numerator and denominator so that they are both in the range 0 to 1 so that log() works OK.
So you evaluate this instead...

y = 0.1 / (0.1 + 0.9*x)

which in terms of exp() and log() is

y = exp( log(0.1) - log(0.1 + 0.9x) )

The two quantites that log() operates on are both between 0 and 1 so the log() functions will work OK,
and since the final answer for y is known to be in the range 0 to 1, the exp() should work OK too.


EDIT: If you are calculating the duration of the "high" period of the square wave then you could increment a register "T" by some very small fractional value "D" with each clock tick (and choose "D" to try to keep the value in "T" below 1).

So T will be between D and 1

Therefore 1/T can be larger than 1.

Therefore evaluate (D/T) since this will be <= 1.