PIC Microcontoller Math Method

Divide 16 bit int by 8 bit int to 8 bit int and remainder

#define bf_carry 3, 0
#define bf_zero 3, 2

#define same 1
#define wreg 0

#define stc bsf bf_carry
#define clc bcf bf_carry

;-[ Div ]--------------------------------------------------------------
; Call w/: Number in f_divhi:f_divlo, divisor in W.
; Returns: Quotient in f_divlo, remainder in f_divhi. W preserved.
;          Carry set if error. Z if divide by zero, NZ if divide overflow.
; Notes:   Works by left shifted subtraction.
;          Size = 29, Speed(w/ call&ret) = 7 cycles if div by zero
;          Speed = 94 minimum, 129 maximum cycles

Div;
    addlw 0          ; w+=0 (to test for div by zero)
    stc              ; set carry in case of error
    btfsc bf_zero    ; if zero
     return          ;   return (error C,Z)

    call DivSkipHiShift
iDivRepeat = 8
while iDivRepeat

    call DivCode

iDivRepeat--
endw

    rlf f_divlo, same ; C << lo << C

    ; If the first subtract didn't underflow, and the carry was shifted
    ; into the quotient, then it will be shifted back off the end by this
    ; last RLF. This will automatically raise carry to indicate an error.
    ; The divide will be accurate to quotients of 9-bits, but past that
    ; the quotient and remainder will be bogus and carry will be set.

    bcf bf_zero  ; NZ (in case of overflow error)
    return       ; we are done!

DivCode
    rlf f_divlo, same    ; C << lo << C
    rlf f_divhi, same    ; C << hi << C
    btfss bf_carry       ; if Carry
     goto DivSkipHiShift ;
    subwf f_divhi, same  ;   hi-=w
    stc                  ;   ignore carry
    return               ;   done
                         ; endif
DivSkipHiShift
    subwf f_divhi, same  ; hi-=w
    btfsc bf_carry       ; if carry set
     return              ;   done
    addwf f_divhi, same  ; hi+=w
    clc                  ; clear carry
    return               ; done

Questions:

• norak.van at KILLspamgmail.com asks:

  hi,
  only one comment i suppose i don´t understand
  
  this instruction:
  bcf bf_zero ; NZ (in case of overflow error)
  
  Always clear FLAG Z --> so always indicates an overflow error ?

  James Newton of Massmind replies: At that point in the code, we know we are not dividing by zero; we already tested for that withbtfsc bf_zero ; if zero. Clearing bf_zero after we detect an overflow, just makes sure the routine does not send an ambiguous error message. At this point, we might have an overflow (see the previous lines) but we certainly do not have a divide by zero error.+

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• pic at KILLspamcanadaspeaks.com asks: " what language is this? it looks like mostly asm, but x = y and while loops are not assembly instructions." James Newton replies: That is pseudo code that should be translated into the equvilent ASM code before the code is used. Please consider posting a complete version if you get the code to work.+

  +

Very Good logic..I had been searching for a this type of division algorithm for a long time Thanks a Ton :), -Sid +

Comments:

• norak.van at KILLspamgmail.com " Thanks James,
  
  You are right, I now understand.
  thanks" +

Code:

• mark_jeronimus-gmail- shares this code:

  The next function divides a 16-bit number in MODREG1:MODREG0 by any N<=16 bit
  number in TEMP1:TEMP0. The quotient will be stored in DIVREG1:DIVREG:0 and the
  modulo in MODREG1:MODREG0.
  
  (in this notation, MODREG1 is th HI byte, etc.)
  
  It is optimized for dividing numbers by a constant.
  
  Restraints:
  - The divisor in TEMP1:TEMP0 should be left-aligned (eg, padded with zeroes on
    the LSB side). This is easy if you divide by 8-bits.
  - The high bit of the divisor (TEMP1.7) should be 1. If the high bit of the
    divisor is not 1 then the result may overflow. This will cause the (17-N)-bit
    quotient in DIVREG1:DIVREG0 to contain all ones and can be further detected by
    comparing MODREG1:MODREG0 by the used divisor (which was btw destroyed by this
    function). Bottomline, it is better to avoid this.
  - No detection for a divisor of zero (which would mean a divisor of 0 bits long
    which is nonsense)
  
  Worst case timing: 6+(17-N)*23 (where N is the number of bits in the divisor)
  N=4: T=305
  N=8: T=213
  N=12: T=121
  
  Here's the universal version:
  
  ;;DIVIDE A 16-BIT NUMBER BY AN N-BIT NUMBER
  ;;IN:
  ;;    MODREG1:MODREG0 = 16-BIT DIVIDEND
  ;;    TEMP1:TEMP0     = N-BIT DIVISOR, LEFT ALIGNED, WITH TEMP1.7 = 1
  ;;OUT:
  ;;    DIVREG1:DIVREG0 = (17-N)-BIT WIDE QUOTIENT
  ;;    MODREG1:MODREG0 = N-BIT REMAINDER
  ;;DESTROYED:
  ;;    COUNT = 0
  ;;    TEMO1:TEMP0 = ORIGINAL TEMO1:TEMP0 << (17-N)
  ;;        THAT MEANS TEMO1:TEMP0 = 0 IF INPUT IS CORRECT
  DIV16
      MOVLW   17-N
      MOVWF   COUNT
      CLRF    DIVREG0
      CLRF    DIVREG1
  DIV16_LOOP
      MOVF    TEMP0,W     ;W=MOD-DIVISOR
      SUBWF   MODREG0,W
      MOVF    TEMP1,W
      BTFSS   STATUS,C    ;PROCESS BORROW
      ADDLW   1
      SUBWF   MODREG1,W
  
      BTFSS   STATUS,C    ;IF W<0
      GOTO    DIV16_NOSUB
  
      MOVF    TEMP0,W     ;MOD=MOD-DIVISOR
      SUBWF   MODREG0,F
      BTFSS   STATUS,C
      DECF    MODREG1,F
      MOVF    TEMP1,W
      SUBWF   MODREG1,F
  
      BSF     STATUS,C
  DIV16_NOSUB
      RLF     DIVREG0,F   ;DIV << 1 + CARRY
      RLF     DIVREG1,F
  
      BCF     STATUS,C    ;DIVISOR>>=1
      RRF     TEMP1,F
      RRF     TEMP0,F
  
      DECFSZ  COUNT,F
      GOTO    DIV16_LOOP
      RETURN
  
  
  
  In the next example, it has been configured to divide a 16-bit number by a
  6-bit number in WREG. It will put it in TEMP1 (and clear TEMP0) and shift it
  to the left by 2 bits to align it left. The result is 11-bits wide in
  DIVREG1:DIVREG0 and the remainder is of course 6-bits wide (same width as the
  divisor) and still occupies MODREG1:MODREG0.
  
  
  ;;DIVIDE A 16-BIT NUMBER BY A 6-BIT WREG. RESULT IS 11-BIT WIDE
  DIV16_6
      ;SHIFT LEFT BY 10 BITS
      MOVWF   TEMP1
      CLRF    TEMP0
      BCF     STATUS,C
      RLF     TEMP1,F
      RLF     TEMP1,F
  
      MOVLW   11
      MOVWF   COUNT
      CLRF    DIVREG0
      CLRF    DIVREG1
  DIV16_6_LOOP
      MOVF    TEMP0,W     ;W=MOD-DIVISOR
      SUBWF   MODREG0,W
      MOVF    TEMP1,W
      BTFSS   STATUS,C    ;PROCESS BORROW
      ADDLW   1
      SUBWF   MODREG1,W
  
      BTFSS   STATUS,C    ;IF W<0
      GOTO    DIV16_6_NOSUB
  
      MOVF    TEMP0,W     ;MOD=MOD-DIVISOR
      SUBWF   MODREG0,F
      BTFSS   STATUS,C
      DECF    MODREG1,F
      MOVF    TEMP1,W
      SUBWF   MODREG1,F
  
      BSF     STATUS,C
  DIV16_6_NOSUB
      RLF     DIVREG0,F   ;DIV << 1 + CARRY
      RLF     DIVREG1,F
  
      BCF     STATUS,C    ;DIVISOR>>=1
      RRF     TEMP1,F
      RRF     TEMP0,F
  
      DECFSZ  COUNT,F
      GOTO    DIV16_6_LOOP
      RETURN

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