CORDIC help!

Hello lovely people
I'm just getting my head around CORDIC multiplication and division. It sort of makes sense in a fuzzy kind of way.
What I actually want to do is 2 extra levels of complication:
1) 32 bit maths on an 8 bit pic, so I need 4 bytes for everything
2) the actual calculation is word = fout * 2^32 / clkin so I'm thinking is it ought to be possible to do a combined multiply and divide instead of 2 operations
3) I want to do this in assembler
(ok so I can't count!)

It's actually to generate the tuning word for an AD9850 I got ages ago pre-assembled into a module.

It doesn't have to be massively accurate, just better than the tempco of the cheap tcxo that gives clkin (and I've not idea what it's tempco actually is).

I think I can implement the algorithms individually, but don't understand enough to combine them. Any suggestions?
I also want to include a round up or down at the end.

Well, thanks in advance

 

Have you considered what is sometimes called Kenyan division (a misnomer as the algorithm was not developed in Kenya and a similar algorithm also works for both multiplication)?

I compared integer division using that algorithm with a more classical algorithm, and it was considerably faster particularly if the divisor and dividend were not vastly different, e.g., 3 and a four-byte number. I was looking at duty cycles of 20% to 80%, so the added efficiency was appreciable. The analogous multiplication algorithm exists, but I have not tried it.

There are lots of examples on the Internet, including PICList. If you go that way and are using a PIC, I suggest using an enhanced mid-range device as the new math instructions will save many steps of checking STATUS and carry/borrow. In fact, on a PIC24F with multiple WREG's, it should really fly, but I have not made that jump yet.

John

 

Thanks John.
I hadn't heard of it, and until a few days ago hadn't heard of any of these methods at all. So it turns out the multiplication method I've found is already the one you suggest, I just didn't know it. It looks like it may be more adaptable to what I want to do if I can get the division to work.
Late now. Will have to try and play with it at the weekend

 

Here is the crux of my other post:

For the standard method I chose Peter Hemsley's from Piclist (http://www.piclist.com/techref/microchip/math/div/32by16ph.htm). I have used it many times and simply adapted it to 24-bit X 16-bit for this experiment.

For the Kenyan method, I simply followed the algorithm developed by G. Reichborn-Kjennerud and presented here: http://www.piclist.com/techref/method/math/muldiv.htm The code is written for 24-bit X 24-bit. I will refer to it as the R-K algorithm .

Both methods were simulated on MPLab 8.92 using MPLab SIM at 4 MHz. The pseudo-Kenyan method uses the instruction set from an enhanced mid-range PIC 16F1829, namely the subwfb instruction. My code is still pretty crude. The common subwf(b) method destroys the number being subtracted from (minuend) and my current code uses a shadow register to reconstruct those registers when needed. I don't like doing that, if it can be avoided. It can be done other ways, but the added loop time for doing that may be self-defeating. For example, this destroys the minuend, which ends up with the result:

Code (MPASM):

     movf      T2L,w     ;
     subwf     T1L,f     ;
     movf      T2H,w     ;
     subwfb    T1H,f     ;
     nop
 

This preserves the minuend, but takes more time:
Code (Microchip Assembler):

Code (MPASM):

     movf      T2L,w     ;
     subwf     T1L,w
     movwf     T3L     ;
     movf      T2H,w     ;
     subwfb    T1H,w   ;
     movwf     T3H
     nop
 

Cutting to the chase, here are my timing results:



The Hemsley method uses rotations and has a relatively fixed time. The alternative method depends on the number of subtractions needed. It can be quite short when a number is divided by itself or long when the divisor is 1. My code does not check (yet) for a zero divisor.

Here's a complete, hopefully working version (trial subtraction method) that I used for simulation:

Code (mpasm):

;Author: ©JPANHALT
;Date: May 22,2016

    list        p=16f1829      ; list directive to define processor
    #include    <p16f1829.inc> ; processor specific variable definitions
     errorlevel -302,-305
     RADIX     DEC
     
    __CONFIG _CONFIG1, _FOSC_INTOSC & _WDTE_OFF & _PWRTE_OFF & _MCLRE_ON & _CP_OFF & _CPD_OFF & _BOREN_OFF & _CLKOUTEN_ON & _IESO_OFF & _FCMEN_OFF
    __CONFIG _CONFIG2, _WRT_OFF & _PLLEN_OFF & _STVREN_OFF & _BORV_19 & _LVP_OFF

     cblock    0x20
     T1U
     T1H
     T1L
     T2U
     T2H
     T2L
     count
     resultL
     resultH
     endc

    org 0x0000

     goto      Start
Start
;T1(24bit)/T2(16bit)
     movlw     high(881)  
     movwf     T2H
     movlw     low(881)    
     movwf     T2L
     call      Refresh
     clrf      count
     clrf      T2U
     clrf      resultL
     clrf      resultH
     nop
Kenyan
     incf      count,f
     movf      T2L,w
     subwf     T1L,f
     movf      T2H,w
     subwfb    T1H,f
     movf      T2U,w
     subwfb    T1U,f
     btfss     STATUS,0
     goto      Calculate
     lslf      T2L
     rlf       T2H
     rlf       T2U
     goto      Kenyan

Calculate
     call      Refresh
   
Cycle                        
;T1 registers are destroyed during subtraction.  When the subtrahend is too
;big, which results in a zero being rotated into the result, those registers
;must be recovered.  Back-up registers can be used; however, several steps are
;required to restore them.  Doing a trial subtraction and preserving the
;minuend registers was slightly faster.
     movf      T2L,w
     subwf     T1L,w
     movf      T2H,w
     subwfb    T1H,w
     movf      T2U,w
     subwfb    T1U,w
     btfss     STATUS,0       ;subtrahend too big divide by 2 and repeat
     goto      Result
     movf      T2L,w          ;subtractand OK, repeat subtraction w/saves in f
     subwf     T1L,f
     movf      T2H,w
     subwfb    T1H,f
     movf      T2U,w
     subwfb    T1U,f          ;carry will be set  
Result      
     rlf       resultL,f      ;carry bit is set or clear correctly from above
     rlf       resultH,f
     decfsz    count,f
     goto      DivideT2
     goto      Finish
DivideT2
     lsrf      T2U
     rrf       T2H
     rrf       T2L
     goto      Cycle

Finish
     nop                      ;answer in resultH and resultL

;Subroutine

Refresh  
     movlw     upper(55536)   ;(673312)
     movwf     T1U
     movlw     high(55536)    ;(673312)
     movwf     T1H
     movlw     low(55536)     ;(673312)
     movwf     T1L
     return    

     end
 

None of the code is really polished. I did it just out of curiosity to get something that worked. "Individual results may vary. "

Regards, John

 

I have PIC assembly code for generating the control word for an AD9850/51 to 1 Hz resolution. It uses a combination of math operations and lookup tables. I can either post it or email it to you.

 

Please post it to be consistent with ETO guidelines. I keep a file of Assembly routines, since that is all I know.

Admittedly, I enjoy Assembly, but feel like John (the other one) crying into the wilderness.

John

 

My only concern was that the source code includes a lot of other stuff making it rather large. It's a complete sweep generator application. But I will post it here (I may clean out the extraneous bits first). Won't be able to get to it until later tonight though.

 

Hi Bob,

Either way is OK with me. I am used to stripping what I need for my subroutines file.

I enjoy just diddling with Assembly from time to time with no immediate purpose in mind.

John

 

Here is my assembly code:

Code (MPASM):

; Code for generating Frequency Control Word for AD9850 and AD9851
;
; R. Weaver, 2017-08-01
;
; Assembler directives to allow for different reference frequencies
;    #define RefOsc180MHz ;Comment out this line for 125MHz reference osc (AD9850)
    #define LeftShifts 1 ; Set this value according to the following table:
; Ref Osc Freq       LeftShifts
; ------------       ----------
;   19-37 MHz           3
;   38-75 MHz           2
;  76-150 MHz           1
; 151-200 MHz           0
;
;  ****
;  Note that for a reference frequency other than 125 or 180 MHz
;  Changes must be made to the lookup table code.
;  ****


;Macro definitions
bank0 macro
    bcf STATUS,RP0
    endm
bank1 macro
    bsf STATUS,RP0
    endm
;More intuitive skip definitions
skpeq macro
    btfss status,z
    endm
skpneq macro
    btfsc status,z
    endm
skpneg macro
    btfsc status,c
    endm
skppos macro
    btfss status,c
    endm
SaveAccHi macro rName ;Store 4 high bytes of acc to spec'd register set
    movlw rName
    call SaveAccHiInd
    endm
SaveAccLo macro rName ;Store 4 low bytes of acc to spec'd register set
    movlw rName
    call SaveAccLoInd
    endm
LoadAccHi macro rName ;Load 4 high bytes of acc from spec'd register set
    movlw rName
    call LoadAccHiInd
    endm
LoadAccLo macro rName ;Load 4 low bytes of acc from spec'd register set
    movlw rName
    call LoadAccLoInd
    endm
LoadRLo macro rName ;Load 4 low bytes of aux reg from spec'd register set
    movlw rName
    call LoadRxLoInd
    endm
LoadRHi macro rName ;Load 4 high bytes of aux reg from spec'd register set
    movlw rName
    call LoadRxHiInd
    endm
ClearNregisters macro nReg, rName ;Clear nReg registers starting at rName
    movlw nReg
    movwf xfrCount
    movlw rName
    call ClearNregistersInd
    endm
ShiftUpNregisters macro nReg, rName ;Shift nReg registers starting at rName
    movlw nReg
    movwf xfrCount
    movlw rName
    call ShiftUpNregistersInd
    endm

;
;variable memory area
    cblock 0x20
;   DDS variables:
    freqDigits:8 ;8 digit (decimal) frequency in Hz, F(0) is LSB, F(7) is MSB
;   Math Library variables
    acc0,acc1,acc2,acc3,acc4,acc5,acc6,acc7 ;accumulator for 32/64 bit math
    R0,R1,R2,R3,R4,R5,R6,R7 ; 32/64 bit math aux. registers
;   misc temporary registers
    count,temp
    xfrCount ;used to count registers moved by the load, save & clear routines
    endc

;Lookup tables for DDS frequency ctrl word
    #ifdef RefOsc180MHz ;Lookup tables for 180MHz ref frequency
Mpy_B0 ;Least significant byte
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0xE1
   retlw 0xC1
   retlw 0xA2
   retlw 0x82
   retlw 0x63
   retlw 0x44
   retlw 0x24
   retlw 0x05
   retlw 0xE5
Mpy_B1
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0xDE
   retlw 0xBD
   retlw 0x9C
   retlw 0x7B
   retlw 0x5A
   retlw 0x39
   retlw 0x18
   retlw 0xF7
   retlw 0xD5
Mpy_B2
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x65
   retlw 0xCB
   retlw 0x31
   retlw 0x97
   retlw 0xFD
   retlw 0x63
   retlw 0xC9
   retlw 0x2E
   retlw 0x94
Mpy_B3
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0xDC
   retlw 0xB8
   retlw 0x95
   retlw 0x71
   retlw 0x4D
   retlw 0x2A
   retlw 0x06
   retlw 0xE3
   retlw 0xBF
Mpy_B4 ;Most significant byte
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x17
   retlw 0x2F
   retlw 0x47
   retlw 0x5F
   retlw 0x77
   retlw 0x8F
   retlw 0xA7
   retlw 0xBE
   retlw 0xD6
    #else ;Lookup tables for 125 MHz reference oscillator
Mpy_B0 ;Least significant byte
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x27
   retlw 0x4E
   retlw 0x75
   retlw 0x9B
   retlw 0xC2
   retlw 0xE9
   retlw 0x10
   retlw 0x37
   retlw 0x5E
Mpy_B1
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0xE8
   retlw 0xD0
   retlw 0xB8
   retlw 0xA0
   retlw 0x88
   retlw 0x70
   retlw 0x59
   retlw 0x41
   retlw 0x29
Mpy_B2
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x0B
   retlw 0x17
   retlw 0x23
   retlw 0x2F
   retlw 0x3B
   retlw 0x47
   retlw 0x53
   retlw 0x5F
   retlw 0x6B
Mpy_B3
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x2E
   retlw 0x5C
   retlw 0x8A
   retlw 0xB8
   retlw 0xE6
   retlw 0x14
   retlw 0x42
   retlw 0x70
   retlw 0x9E
Mpy_B4 ;Most significant byte
   andlw 0x0F
   addwf pcl,f
   retlw 0x00
   retlw 0x11
   retlw 0x22
   retlw 0x33
   retlw 0x44
   retlw 0x55
   retlw 0x67
   retlw 0x78
   retlw 0x89
   retlw 0x9A
    #endif
;
;
;
MakeCtlWd   ;Generate DDS frequency control word
    call clrAcc64 ; Init the acc to zero
    movlw freqDigits+7    ;load addr of frequency digits array
MakeWdEntry
    movwf FSR    ; and store in indirect ptr reg
    movlw 0x08  ; load count of digits
    movwf count
;    call clrAcc64 ; Init the acc to zero
    goto LoopMCWenter ;skip the x10 for the 1st digit
LoopMCW
    call AccTimes10
LoopMCWenter
    movf indf,w
    call AddDigit
    decf fsr,f
    decfsz count,f
    goto LoopMCW
;
;All digits have been processed.
;If Ref freq is 150MHz or lower then do left shift here
;
    if LeftShifts != 0
      movlw LeftShifts
      call AccLShiftN
    endif
    btfsc acc3,7    ; Check fractional part to see if round up is req'd
    incfsz acc4,f   ;Yes, so increment integer part, and propagate carries.
    goto MCWshiftWord
    incfsz acc5,f
    goto MCWshiftWord
    incfsz acc6,f
    goto MCWshiftWord
    incf acc7,f
MCWshiftWord    ;move the result from acc4..acc7 to acc0..acc3
    LoadAccLo acc4
    return  ;Frequency/sweep Control Word is in acc0..acc3
AddDigit    ; Add next frequency digit to acc and mpy by 10
    movwf temp
    call mpy_B0
    movwf R0
    movf temp,w
    call mpy_B1
    movwf R1
    movf temp,w
    call mpy_B2
    movwf R2
    movf temp,w
    call mpy_B3
    movwf R3
    movf temp,w
    call mpy_B4
    movwf R4
    clrf R5
    clrf R6
    clrf R7
    call Add64
    return
AccTimes10    ;Multiply acc x 10
    ;copy acc to aux reg.
    call AccToR ;move acc contents to aux reg
    movlw 0x02
    call accLShiftN ;Shift left twice to get x4
    call Add64    ; add the saved value back to the acc to get x5
    movlw 0x01
    call accLShiftN ;shift left once more to get x10
    return
AccLShiftN ;Shift acc left N times where N is in Wreg
    movwf count1
LoopALSN
    bcf status,c
    rlf acc0,f
    rlf acc1,f
    rlf acc2,f
    rlf acc3,f
    rlf acc4,f
    rlf acc5,f
    rlf acc6,f
    rlf acc7,f
    decfsz count1,f
    goto LoopALSN
    return
;
;Start of general purpose multi-byte math routines
;
clrAcc64 ;clear 64 bit accumulator registers acc and r
    ClearNregisters d'16',acc0
    return


SaveAccHiInd ; Save high 4 bytes of acc to reg indirect
    movwf fsr ;start address is in w
    movf acc4,w
    movwf indf
    movf acc5,w
    incf fsr,f
    movwf indf
    movf acc6,w
    incf fsr,f
    movwf indf
    movf acc7,w
    incf fsr,f
    movwf indf
    return
SaveAccLoInd ; Save low 4 bytes of acc to reg indirect
    movwf fsr ;start address is in w
    movf acc0,w
    movwf indf
    movf acc1,w
    incf fsr,f
    movwf indf
    movf acc2,w
    incf fsr,f
    movwf indf
    movf acc3,w
    incf fsr,f
    movwf indf
    return
LoadAccHiInd ; Load high 4 bytes of acc from reg indirect
    movwf fsr ;start address is in w
    movf indf,w
    movwf acc4
    incf fsr,f
    movf indf,w
    movwf acc5
    incf fsr,f
    movf indf,w
    movwf acc6
    incf fsr,f
    movf indf,w
    movwf acc7
    return
LoadAccLoInd ; Load low 4 bytes of acc from reg indirect
    movwf fsr ;start address is in w
    movf indf,w
    movwf acc0
    incf fsr,f
    movf indf,w
    movwf acc1
    incf fsr,f
    movf indf,w
    movwf acc2
    incf fsr,f
    movf indf,w
    movwf acc3
    return
LoadRxLoInd ; Load low 4 bytes of aux reg r0 from reg indirect
    movwf fsr ;start address is in w
    movf indf,w
    movwf r0
    incf fsr,f
    movf indf,w
    movwf r1
    incf fsr,f
    movf indf,w
    movwf r2
    incf fsr,f
    movf indf,w
    movwf r3
    return
LoadRxHiInd ; Load low 4 bytes of aux reg r0 from reg indirect
    movwf fsr ;start address is in w
    movf indf,w
    movwf r4
    incf fsr,f
    movf indf,w
    movwf r5
    incf fsr,f
    movf indf,w
    movwf r6
    incf fsr,f
    movf indf,w
    movwf r7
    return
ClearNregistersInd
    ;Clear specified number of contiguous registers where number is in xfrCount
    ;and start register address is in w
    movwf fsr
LoopCNRI
    clrf indf
    incf fsr
    decfsz xfrCount,f
    goto LoopCNRI
    return
ShiftUpNregistersInd
    ;Shift bytes up across N registers
    ;highest register is in w
    movwf fsr
LoopSUNRI
    decf fsr,f
    movf indf,w
    incf fsr,f
    movwf indf
    decf fsr,f
    decfsz xfrCount,f
    goto LoopSUNRI
    return


AccToR ;move acc contents to aux reg.
    ;No indirects here, so that calling code can use FSR without it
    ;getting corrupted here.
    movf acc0,w
    movwf R0
    movf acc1,w
    movwf R1
    movf acc2,w
    movwf R2
    movf acc3,w
    movwf R3
    movf acc4,w
    movwf R4
    movf acc5,w
    movwf R5
    movf acc6,w
    movwf R6
    movf acc7,w
    movwf R7
    return


add32 ;32 bit add routine
    movf R0,w
    addwf acc0,f
    btfsc status,c
    call carry1
    movf R1,w
    addwf acc1,f
    btfsc status,c
    call carry2
    movf R2,w
    addwf acc2,f
    btfsc status,c
    incf acc3,f
    movf R3,w
    addwf acc3,f
    return
neg32    ;Negate the accumulator
    comf acc0,f
    comf acc1,f
    comf acc2,f
    comf acc3,f
    incfsz acc0,f ;increment and check for carry
    return ;no carry, so return
carry1
    incfsz acc1,f
    return
carry2
    incfsz acc2,f
    return
    incf acc3,f
    return
add64 ;64 bit add routine
    movf R0,w
    addwf acc0,f
    btfsc status,c
    call carry64_1
    movf R1,w
    addwf acc1,f
    btfsc status,c
    call carry64_2
    movf R2,w
    addwf acc2,f
    btfsc status,c
    call carry64_3
add40 ;Entry point for 40 bit add
    movf R3,w
    addwf acc3,f
    btfsc status,c
    call carry64_4
    movf R4,w
    addwf acc4,f
    btfsc status,c
    call carry64_5
    movf R5,w
    addwf acc5,f
    btfsc status,c
    call carry64_6
    movf R6,w
    addwf acc6,f
    btfsc status,c
    incf acc7,f
    movf R7,w
    addwf acc7,f
    return
carry64_1   ;Chained skips to propagate carries
    incfsz acc1,f
    return
carry64_2
    incfsz acc2,f
    return
carry64_3
    incfsz acc3,f
    return
carry64_4
    incfsz acc4,f
    return
carry64_5
    incfsz acc5,f
    return
carry64_6
    incfsz acc6,f
    return
    incf acc7,f
    return
NegDecimal ; Negate 8-digit unpacked decimal number in acc0..7
    movlw 0x08
    movwf count
    movlw acc0
    movwf fsr
LoopND
    movf indf,w
    sublw 0x09
    movwf indf
    incf fsr,f
    decfsz count
    goto LoopND
    ;Acc now contains nines complement. Now increment to get tens complement
    ClearNregisters 8,r0
    incf r0,f
    ;continue to AddDecimal to
AddDecimal ; Eight digit unpacked BCD add; operands in acc0..7 and r0..7
    call Add64 ; add the two 8-digit numbers
;fsr indf
;Now adjust digits for carry
LoopAD2
    movlw 0xF6
    movwf r0
    movwf r1
    movwf r2
    movwf r3
    movwf r4
    movwf r5
    movwf r6
    movwf r7
;new code
    movlw acc0
    movwf fsr
    movlw 0x08
    movwf count
LoopAD1
    movf indf,w
    sublw 0x09
    rrf temp,f ; save carry bit
    incf fsr,f
    decfsz count,f
    goto LoopAD1
    comf temp,f ;
    btfsc status,z
    return ;no adjustment required
    movlw r0
    movwf fsr
    movlw 0x08
    movwf count
LoopAD3
    rrf temp,f
    btfss status,c
    clrf indf
    incf fsr
    decfsz count,f
    goto LoopAD3
    call Add64
    goto LoopAD2
 

The desired frequency in decimal Hz should be entered in the register array freqdigits. Then call subroutine MakeCtlWd to generate the frequency control word. The result is in registers acc0..acc3.

The calculation is done digit by digit. The 5 byte constant is looked up for the current digit and added to the accumulated result. This is then multiplied by 10. This is repeated until all 8 digits have been processed. The lookup table has 5 byte precision to prevent round off error.

I trimmed this out of a much larger program, so there are probably one or two small subroutines here that aren't used.

 

Thank you, Bob,

I will definitely be playing with it. My method (http://www.electro-tech-online.com/articles/demo-assembly-code-ad9850-dds-signal-generator.755/ ) used brute force and the math part took a little more than 1.3 ms.

Right now, though, I am kept busy dealing with rodent damage to my vehicles* and downed ash trees. Bad weather helps, but we have had a very dry Summer so far. Beautiful weather, but the ground is like cinder block.

Regards, John

*Chewed through ABS in multiple places on my F-150, vacuum control of the front locking axle hubs, and the electronic shift on fly (ESOF) for FWD. About $260 in non-Ford dealer parts (twice that at dealer prices) plus the time to diagnose and fix. I think the rascals are trained at Ford to eat where a repair is not practical, like right where the wire enters a casting on the FWD shift motor.

 

A bit of additional info:

1. The way I arranged this, nothing more complicated than multiply by 10 is required.
2. I realized after writing the code, that it could be done without the lookup tables, by storing just a single constant based on the reference oscillator frequency, but I have all of this (and much more code) programmed into a 16F630 and started to run low on register memory. Eliminating the lookup tables would have required more registers which I didn't have enough of. On the other hand, using a single constant would allow for easier fine tuning in case the reference oscillator is slightly off frequency.
3. The code has provision for both 180 MHz ref oscillator (AD9851) and 125 MHz ref oscillator (AD9850). There is a set of lookup tables for each one, and the correct one is chosen by setting an assembler directive (see code comments). If a different ref oscillator frequency is needed then a new set of lookup table data needs to be generated. I created a spreadsheet that does this. See attached.
4. The calculation principle may be a bit obscure. So, if there is any confusion about how it works, let me know and I'll provide more detail.

Sorry to hear about your rodent problem. Ford should learn not to use flavor ingredients in their parts that appeal to rodents. It's been hot and dry here too.

 

I have heard that peanut oil is used in its PVC insulation. Not sure exactly how that happens (proteins?), but that is what they attack. Peanuts are like sex to rodents. By comparison, have yet to have a rodent attack regular household wiring. What I have learned to do is a good scan (Autel, not HF scanner) of my system, then investigate for broken wires.

Ford dealer was clueless on an A/C problem with my Fusion, which usually means replacing parts until the fault is located. A several hundred $ repair of the A/C on my Fusion ended up costing me a piece of wire, some heat-shrink tubing, and the Autel scanner that has more than paid for itself.

Today, the hardest part of working under a car for me is getting on the crawler at my age. My new dog is great company, except he does get a little close at times. His breath is enough to keep you awake.

John

 

Wow. When I eventually have enough time off work without a load of other things to do and I'm not actually knackered, (which is a big one, I seem to be permanently knackered) I'll study these!
Thanks guys, big help
Bob, is the lookup table working the same way it does when you do trig using the cordic method? Going to take me a while to understand what's gonig on there!
Sounds like you need a pit, John!
Feed the dog raw, he'll thank you for it and his breath won't smell (well, hardly anyway). You just have to make sure it's balanced.

 

No. Actually in the simplest version of the algorithm, the lookup table is simply the values of 2^32/FREF multiplied by the digits 0-9. If we refer to the value 2^32/FREF as constant k, and the tuning control word as W, then:

W = k * FOUT

Eight decimal digits allow us to represent frequencies from 0 to 99,999,999 Hz with 1 Hz resolution. We can represent FOUT as the sum of its eight decimal digits (D0..D7) multiplied by the appropriate powers of 10. Hence:

FOUT = D7*10^7 + D6*10^6 + D5*10^5 + D4*10^4 + D3*10^3 + D2*10^2 + D1*10^1 + D0*10^0

D0 is the least significant digit and D7 is the most significant.
And then the tuning word will be:

W = k*(D7*10^7 + D6*10^6 + D5*10^5 + D4*10^4 + D3*10^3 + D2*10^2 + D1*10^1 + D0*10^0)

We can rearrange this formula as follows:

W = k*D7*10^7 + k*D6*10^6 + k*D5*10^5 + k*D4*10^4 + k*D3*10^3 + k*D2*10^2 + k*D1*10^1 + k*D0*10^0

Since D0..D7 are decimal digits, they can only have the values 0..9, and so we can create a lookup table for the ten possible values of k*DN.
Now that we've done that, the only remaining operations are multiplication by powers of 10. Again rearranging the formula, we get:

W = ((((((k*D7*10 + k*D6)*10 + k*D5)*10 + k*D4)*10 + k*D3)*10 + k*D2)*10 + k*D1)*10 + k*D0

With this rearrangement, it is only necessary to use the lookup table to get the values k*DN and then to multiply by 10, which is very easy.

In order to minimize roundoff error, I used 5 byte precision rather than 4 bytes. That's the reason for 5 lookup tables. There's one for each byte in the table output value. That's basically how the algorithm works for a 180 MHz ref frequency as used by an AD9851. Since the AD9850 ref frequency is a maximum of 125 MHz, I made a slight change to the algorithm to maximize precision. Instead of making k = 2^32/FREF, I use the smallest power of two that won't overflow 5 bytes. For FREF = 125MHz, the value is 2^31. The algorithm proceeds exactly the same way with the only difference being that the final result needs to be shifted left one bit position.

I find that it's often possible to rearrange a calculation to make it much easier to do in assembly language, and that is the case here.

 

Ohhhhhhhhh I see now. Elegant.
But isn't all that multiplying by 10 messy?
I'd been wondering about the rounding error. I couldn't get past outright truncation.

 

The multiplication by 10 is in the same loop that sums the lookup table value. Seven lines of code (not counting comments).

Code (mpasm):

AccTimes10    ;Multiply acc x 10
    ;copy acc to aux reg.
    call AccToR ;move acc contents to aux reg
    movlw 0x02
    call accLShiftN ;Shift left twice to get x4
    call Add64    ; add the saved value back to the acc to get x5
    movlw 0x01
    call accLShiftN ;shift left once more to get x10
    return
 

 

Oh of course, x8 and add 2 more, only done a better way.
See if I can find time tomorrow for a bit of contrast and compare...
Thanks for this, saved me many hours (and wasted ticks/registers!) I think leaves some space in my brain to think about other functions...

 

Ok so it's been nearly a year...
I found your website, Bob and followed the explanation there since you'd made it easier to understand, so I'm writing my own implementation now.
I played some more with the "fast multiplication" I found at convict.lu but there's no gain in using it. Although it did get me to making a working "reverse double-dabble", which I'm now not using. So I'm just adding k onto the accumulator as many times as a bcd digit gives a count down for, then the x10, next digit, etc etc.
I'm using a vfd for my display. The controller chip also has outputs for led's and inputs for keys - more blinkenlampen!
I'd been wanting to include a sweep function too but kind of "knew what I wanted without really knowing what I wanted" with that - so you've helped there too!
I had another look at the spreadsheet you used to calculate the original LUT values. Still don't understand the maths there - particularly how you're using MOD to generate the values and LOG to get the bit width.

 

You got there just in the nick of time. I think I only had that page up for a couple of weeks before I rewrote the PIC program so that it no longer needed lookup tables. Since the tables were gone, I removed the link to the spreadsheet file. Maybe I should put it back again.

As for the MOD function, it simply returns the remainder of an integer division. To convert a number into individual bytes, you divide by 256. The remainder is the low order byte, the integer quotient is the high byte. If the number takes more than two bytes, the process is repeated with the integer quotient until it's less than 256. So for a number like 1234567, which would require 3 bytes, you divide by 256 giving a quotient of 4822 and a remainder of 135.
MOD(1234567,256)=135 <-- this is byte 0 (least significant)
INT(1234567/256)=4822
Repeat:
MOD(4822,256)=214 <-- this is byte 1
INT(4822/256)=18 <-- this quotient is now less than 256, so this is byte 2 (most significant), and we're done.

As for the LOG function, it will inherently give you the number of digits (minus 1) required to represent the number in whatever base you're working in. In base 10 (decimal), use the base 10 log to tell how many decimal digits a number has. For example, the number 1234567 has 7 digits,
LOG(1234567,10)=6.09151
Take the integer part, 6, and add 1, giving 7, which is the number of digits in the number.
For calculating the number of bits required to represent the number in binary, change the base of the log function to 2:
LOG(1234567,2)=20.23557
Take the integer part, 20, and add 1, giving 21, which is the number of bits required to represent 1234567.

 

Sticking with the BCD maths, I started to implement the sweep function going on your principle of subtracting half the sweep range from the centre frequency as a start value. Taken me all week to figure out how to do subtraction with more than one byte!

Code (text):

; take 1234 from 4321

TEST
    banksel val1
    pagesel TEST
    movlw 0x43
    movwf val1+1
    movlw 0x21
    movwf val1
    movlw 0x12
    movwf val2+1
    movlw 0x34
    movwf val2

    movlw 0x99 ; convert BCD to 9's complement
    movwf temp
    movfw val1
    subwf temp,w
    movwf val1
    movfw val1+1
    subwf temp,w
    movwf val1+1
    movfw val1
    addwf val2,w
    subwf temp,w
    movwf val1 ; val1 ends up with result
    clrw
    btfss STATUS,DC
    movlw 0x06 ; low digit adjust  
    btfsc STATUS,C
    goto NEXT1
    incf val1+1,f ; borrow from next digit, is add because took from 9
    iorlw 0x60 ; high digit adjust
NEXT1    
    subwf val1,f ; apply adjust
    movfw val1+1
    addwf val2+1,w
    subwf temp,w
    movwf val1+1
    clrw
    btfss STATUS,DC
    movlw 0x06
    btfsc STATUS,C
    goto NEXT2
    incf val1+2,f
    iorlw 0x60
NEXT2
    subwf val1+1,f
 

I'm sure it could be more compact though.