--- Scott Dattalo <scott@dattalo.com> wrote:

> Clay,
> 
> I looked at your MatLab code and I assume this is
> similar to what you 
> wish to implement in PIC assembly. If so, then it
> appears that all 
> divisions can be replaced with multiplications. For
> example, you write:
> dr = 2^20/seed
> Fref_act = FGHz/dr
> Which can obviously be written as:
> Fref_act = (FGHz * seed) / 2^20
> And division by 2^20 is the same thing as shifting
> right 20 bit positions.
> In another place you show a division by a constant.
> This one can be 
> replaced with a multiplication of 1/constant.

Yes, there is some mathematical simplification that
has been done already in C.  I posted the original
equations to more clearly represent the goal.

> Having said this, I don't have any routines to
> perform 64bit 
> multiplication. However, if I were to write one I'd
> either start from 
> first principles and implement a shift/add routine,
> or I'd use 
> pre-existing 32-bit routines. E.g. you may've
> already noticed that if N 
> and M are 64-bit numbers, they can be written as:
> 
>    N = a*2^32 + b
>    M = c*2^32 + d
> 
> and N*M can be written as
> 
>   N*M = ac*2^64 + (ad+bc)*2^32 + bd
> 
> A 64-bit multiplication has been replaced with 4
> 32-bit multiplications. 
>   This can actually be replaced with 3 32-bit
> multiplications:
> 
>   N*M = ac*2^64 + (ac + bd - (a - b)(c - d)) *2^32 +
> bd
> 
> However, the middle term is now signed.
> 
> Scott

Thanks for the tips on the fundamentals of binary
math.  I'll try and implement them.

Clay


		
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