www.piclist.com/techref/method/math.htm?key=divide

>I can save 600bytes in a lookup table if I can figure out a good way to

>divide a 16 bit number by 10.

>

>I have the app notes with the general 16 math, but I need a smaller and

>faster routine.

>

>

As everybody was probably expecting, I have to put in my two cents worth and

drop in some code...

Here is a 16 bit unsigned division algorithm that I have used in the past.

Initially, it shifts the Divisor until bit 14 is set and then begins

shifting down. If the divisor can be taken from the dividend, it is. Next,

the divisor is shifted down until you get the initial divisor. The results

(quotient and remainder) are all 16 bits long and an additional 8 bit

register is used in the example code below.

Here is the psuedo-code:

Count = 0 - Count keeps track of where the Divisor is

Quotient = 0 - Quotient is actually a 16 bit sum

while ( Divisor & 0x04000 ) != 0 - Find where to shift the Divisor up to

Count = Count + 1 - Record How Many Bits Shifted

Divisor = Divisor << 1 - Shift up the Divisor

while Count != 0 - Now, do the Shifting Subtraction (Division)

if Dividend >= Divisor - Can Subtract from the Result

Quotient = Quotient + ( 2 ^ Count )

Divident = Divident - Divisor

Count = Count - 1

Divisor = Divisor >> 1

That's it. Divident contains the remainder and Quotient contains the

quotient of the value. Note that this algorithm will go into an endless

loop if the divisor is equal to zero. I stop the shifting up with bit 14 of

the Divisor so that signed values can be supported (even though this

algorithm won't work with negative values).

The PIC code for doing this is below. Note, that I have changed the code in

two places. The first is with regards to Count. Rather than using a

counter, I shift a "1" up and down (ending the division when the "1" ends up

in the Carry Flag). This means that I can add Count to the Quotient

directly. The second area that I have changed is in regard to the

comparison of the Dividend to the Divisor, note that I save the contents of

the subtraction (compare) and use it later, rather than subtracting twice.

clrf Quotient ; Initialize the Variables

clrf Quotient + 1

movlw 1 ; Instead of a Counter, Count is a shifted

movwf Count ; Value for adding to the Quotient

clrf Count + 1

StartLoop ; Find the Top Value for the Divisor

btfsc Dividend, 6 ; If Bit 14 Set, then we have the value

goto DivLoop

bcf STATUS, C ; Shift over the Carry and the Divisor

rlf Count

rlf Count + 1

rlf Divisor ; Note, Carry will be Zero from Count

rlf Divisor + 1

goto StartLoop ; Now, see if we can shift again

DivLoop ; Do the Shifted Subtraction

movf Divisor + 1, w ; Compare Values, High First

subwf Dividend + 1, w

movwf Temp ; Save Result for later (just in case)

movf Divisor, w

subwf Dividend

btfss STATUS, C ; Make Sure Carry is accounted for

decf Temp

btfsc Temp, 7 ; Do we have a Negative Number from Subtract?

goto DivSkip ; Yes, Don't Subtract this value

movwf Dividend ; Else, save the result for the Next

movf Temp, w ; Subtract

movwf Dividend

movf Count + 1, w ; Add the Bit Offset to the Quotient

addwf Quotient + 1

movf Count, w

addwf Quotient ; Don't have to worry about Carry

DivSkip ; Now, Shift the Values Down

bcf STATUS, C ; Shift down the Divisor

rrf Divisor + 1

rrf Divisor

rrf Count + 1 ; Now see if the Count is finished

rrf Count

btfss STATUS, C ; Finished if Carry is Set

goto DivLoop

Note that with this code, "Dividend" now contains the Remainder and

"Divisor" is the original "Divisor" >> 1.

In terms of space and execution speed, I think you'll find this to be a

pretty good improvement from the code in the ECBK (although not as good as

some of the algorithms other people have put in for a direct divide by 10).

Myke

Myke

"We're Starfleet officers, weird is part of the job."

Capt. Catherine Janeway

See also: www.piclist.com/techref/method/math.htm?key=divide