Efficient Fixed-Point Trigonometry For PIC16F

**ScaleRobotics** · - 15th November 2007, 08:56

Microchip has an application note AN1061 http://ww1.microchip.com/downloads/e...tes/01061A.pdf which talks about using the ATAN function, among other things. I can't wait to use it for a project I am working on ........ I just need to know how. .....

I am a newbie when it comes to adding includes. I tried a few different ways to add the assembly code for the atan, and I could not get it to compile. I tried using the math16.asm file as an include in a new main program, I also tried cutting and pasting the assembly into a main.pbp program with asm and endasm lines on the front and back. Can someone steer me in the right direction? This cordic function would be perfect for me.

I get the following error when trying to compile with MPASM using MicroCode Studio Plus: Error[149] Directive only allowed when generating an object file.
I get this for multiple line listings of the assembly code, but this does not seem to make sense for the lines it references. Like

movlw 0x00 ; Y_H & Y_L is loaded with 0x0000

Thanks for your help.

Walter

**Darrel Taylor** · - 15th November 2007, 20:42

Hi Walter,

The MATH16.ASM file looks interesting.
It's written as Relocatable Object Code, so isn't directly compatible with PBP.

But with a bit of work you could modify it.

Statements like UDATA, CODE , GLOBAL , and END get removed, or commented.

Names with RES are variables, so they need to be defined in Basic.
Something like ...

Code:

X    VAR WORD
@X_H = _X + 1 
@X_L = _X

And some of the labels need to be renamed.
DIV and MUL already exist is PBP.

**ScaleRobotics** · - 16th November 2007, 10:11

Thanks for the pointers. I was able to get ATAN working! Wooohooo! I must have done something to the sincos function though. I get the same result, no matter what variable I enter into x. It is supposed to cos the value of x and give the result in y, and sin the value of x, and give the result in z. I'm a little brain dead right now, so I will have to check it further in the morning.

Code:

;****************************************************************************
;*	Microchip Technology Inc. 2006					*
;*	Filename: Main.asm									*
;*																*
;****************************************************************************

DEFINE __16F877A 1				; list directive to define processor
DEFINE OSC 20                          ' Define Oscillator Speed
DEFINE LOADER_USED 1

' Shutdown comparators
ADCON1 = 7                        ; Turn of all A/D
CMCON  = 7
' Set the port directions
' 0=output 1=input
TRISA=%00000011                         ' Set PORTA  0-1-3 used for AD
TRISB=%11011100                         ' Set PortB
TRISC=%10000000  
TRISD=%00000000                       ' Set PortC USART RX as an input
porta.2 = 0 
porta.3 = 0

X_H         VAR     byte
ITERATION  VAR      byte
X_L         VAR     byte
Y_H         VAR     byte
Y_L         VAR     byte
Z_H         VAR     byte
Z_L         VAR     byte
X_TMP_H     VAR     byte
X_TMP_L     VAR     byte
Y_TMP_H     VAR     byte
Y_TMP_L     VAR     byte
ITERAT_TMP  VAR     byte
Di          VAR     byte
COSCH       VAR     byte
COSCL       VAR     byte
Counter1    VAR     byte
SHIFT       VAR     byte
x           var     word
y           var     word
z           var     word
i           var     word

;---------[change these to match your hardware]------------------------------
DEFINE LCD_DREG PORTD             ; Set LCD Data port                B C   D
DEFINE LCD_DBIT 0                 ; Set starting Data bit (0 or 4)   4 0
DEFINE LCD_RSREG PORTA            ; Set LCD Register Select port     A A
DEFINE LCD_RSBIT 3                ; Set LCD Register Select bit      3 2
DEFINE LCD_EREG PORTA             ; Set LCD Enable port              A A
DEFINE LCD_EBIT 1                 ; Set LCD Enable bit               1 5
DEFINE LCD_BITS 4                 ; Set LCD bus size (4 or 8 bits)   4 4
DEFINE LCD_LINES 2                ; Set number of lines on LCD       2 2
'----------------------------------------------------------------------------
clear
lcdout $FE,1
portb.0 = 0
pause 500
lcdout $FE,1,"Test"
portb.0 = 1

Start:
x = 250
y = 0

X_L = x.byte0
X_H = x.byte1

Y_L = y.byte0             'load values of y into Y_L ,just for atan, but does not hurt to leave 
Y_H = y.byte1             'dito

call sincos
y.byte0 = Y_L             ' edit out if looking at atan
y.byte1 = Y_H              'same here

'Call atan


z.byte0 = Z_L
z.byte1 = Z_H
'z=(z*100)/284                                       'corrects our output to an angle in degrees for atan
'lcdout $FE,1,#z    



portb.0 = 0
lcdout $FE,1,#y
lcdout $FE,$C0,#z 
end '***********************************

atan:
    asm
        call ATAN
    endasm
return

sincos:
    asm
        call SINCOS
    endasm
return

asm
;__________________________________________________________________________
FSR_ptr	macro	addr
	banksel	addr
	bcf		STATUS,IRP
	btfsc		STATUS,RP1
	bsf		STATUS,IRP
	movlw		LOW addr
	movwf		FSR
			endm

	#define 	Dir	_Di,0
	#define 	RV		_Di,1
	#define	_C		STATUS,0
	#define	_Z		STATUS,2

Z_stepH_tbl
	addwf	PCL,f
	dt	0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00
Z_stepL_tbl
	addwf	PCL,f
	dt	0x80,0x4C,0x28,0x14,0x0A,0x05,0x03,0x01
Z_NstepH_tbl
	addwf	PCL,f
	dt	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF
Z_NstepL_tbl
	addwf	PCL,f
	dt	0x80,0xB4,0xD8,0xEC,0xF6,0xFB,0xFD,0xFF

ATAN
	banksel	   _Z_H				; Z_H & Z_L is loaded with 0x0000
	movlw		0x00				; Y & X is the input
	movwf		_Z_H				; X(i+1)	=	Xi - Yi*_Di*2^-i
	movlw		0x00				; Y(I+1)	=	Yi + Xi*_Di*2^-i
	movwf		_Z_L				; Z(i+1)	=	Zi - _Di*ATAN(2^-i)
	banksel	   _Di					; _Di		=	1 if Yi < 0 ELSE _Di	=	0
	bsf		      RV					; Set Vectoring Mode
	goto		CORDIC_Alg		

SINCOS
	banksel	   _Y_L				; Z_H & Z_L is the input
	movlw		0x00				; Y_H & Y_L is loaded with 0x0000	
	movwf		_Y_L				; X_H & X_L is loaded with 6070 (1/An constant)
	movlw		0x00			
	movwf		_Y_H			
	movlw		LOW .6070	
	movwf		_X_L				; X(i+1)	=	Xi - Yi*_Di*2^-i
	movlw		HIGH .6070		; Y(I+1)	=	Yi + Xi*_Di*2^-i
	movwf		_X_H				; Z(i+1)	=	Zi - _Di*ATAN(2^-i)
	banksel	   _Di					; _Di		=	0 if Zi < 0 ELSE _Di	=	1
	bcf		      RV					; Set Rotational Mode

CORDIC_Alg
	banksel	_ITERATION
	clrf	_ITERATION
Rotation_loop						
BUFF_X_Y							; Buffers both X & Y into temporary registers 
	banksel 	_Y_L
	movf		_Y_L, W			; Move Y --> T_TEMP
	movwf		_Y_TMP_L
	movf		_Y_H, W
	movwf		_Y_TMP_H
	movf		_X_L, W			; Move Y --> T_TEMP
	movwf		_X_TMP_L
	movf		_X_H, W
	movwf		_X_TMP_H

	banksel	   _Di					; Vectoring or Rotational Mode?
	bcf		      Dir
	btfsc		RV
	goto		Rot
Vec
	btfss		_Z_H, 7			; Determine the state of _Di (1 OR -1)
	bsf		  Dir				; _Di=1 when Z_H is pos
	goto		Cordic
Rot
	btfsc		_Y_H, 7			; Determine the state of _Di (1 OR -1)
	bsf		  Dir				; _Di=1 when Y_H is neg

Cordic
	movfw		_ITERATION
	movwf		_SHIFT				; Load number of shifts
	bsf		      _SHIFT,7			; Shift right (Division)
	FSR_ptr	   _Y_TMP_L			; Load FSR
	call		Shifter			; Execute shift

	btfsc		Dir
	call		COM_YTEMP		; Get the 2's complement of teh TEMP register 
SUM_X								; Calculate X(i+1)
	movf		_Y_TMP_H, W		
	addwf		_X_H, F
	movf		_Y_TMP_L, W
	addwf		_X_L, F
	btfsc		_C
	incf		_X_H, F
	
	movfw		_ITERATION
	movwf		_SHIFT				; Load number of shifts
	bsf		  _SHIFT,7			; Shift right (Division)
	FSR_ptr	   _X_TMP_L			; Load FSR
	call		Shifter			; Execute shift

	btfss		Dir
	call		COM_XTEMP		; Get the 2's complement of teh TEMP register
SUM_Y								; Calulate Y(i+1)
	movf		_X_TMP_H, W		
	addwf		_Y_H, F
	movf		_X_TMP_L, W
	addwf		_Y_L, F
	btfsc		_C
	incf		_Y_H, F

	btfss		Dir
	goto		ADD_Z

	movlw		HIGH Z_NstepH_tbl	
	movwf		PCLATH
 	movfw		_ITERATION		; Fetch appropriate value from table
	call		Z_NstepH_tbl	
	addwf		_Z_H, F
	movlw		HIGH Z_NstepL_tbl
	movwf		PCLATH
 	movfw		_ITERATION
	call		Z_NstepL_tbl	
	addwf		_Z_L, F
	btfsc		_C
	incf		_Z_H, F
	goto		Rot_Loop_out

ADD_Z
	movlw		HIGH Z_stepL_tbl
	movwf		PCLATH
 	movfw		_ITERATION
	call		Z_stepH_tbl
	addwf		_Z_H, F
	movlw		HIGH Z_stepH_tbl
	movwf		PCLATH
 	movfw		_ITERATION
	call		Z_stepL_tbl
	addwf		_Z_L, F
	btfsc		_C
	incf		_Z_H, F

Rot_Loop_out
	incf		_ITERATION,f
	btfsc		_ITERATION,3
	return
	goto		Rotation_loop

COM_YTEMP
	comf		_Y_TMP_L, F		; Complememt Y_TMP
	comf		_Y_TMP_H, F
	movlw		01H
	addwf		_Y_TMP_L, F
	btfsc		_C
	incf		_Y_TMP_H, F
	return 
COM_XTEMP
	comf		_X_TMP_L, F		; Complememt X_TMP
	comf		_X_TMP_H, F
	movlw		01H
	addwf		_X_TMP_L, F
	btfsc		_C
	incf		_X_TMP_H, F
	return

Shifter							; Function for shifting 16bit signed REG i times 
	banksel	   _SHIFT				;  left/right MUL/DIV
	movfw		_SHIFT				; INPUTS: FSR & IRP are pointing to LOW REG
	andlw		0x0F				; SHIFT = d000 XXXX where XXXX = # of shifts 
	btfsc		_Z					; 	and d = dir of shift
	return						; check for zero interations
	movwf		_Counter1
	btfss		_SHIFT,0x7
	goto		CORDIC_MUL
	
CORDIC_DIV
	rrf		INDF, F			; Divide INDF/2 INDF --> low byte
	bcf		INDF, 7
	decf 		FSR, F
	rrf		INDF, F	 
	incf 		FSR, F
	btfsc		_C
	bsf		INDF, 7			; Carry from the upper byte to the lower byte
	decf 		FSR, F
	bcf		INDF, 7			; Check to see if TEMP should be a positive number
	btfsc		INDF, 6
	bsf		INDF, 7			; Was a negative number, force it negative again 
	incf 		FSR, F
	decfsz	_Counter1, F
	goto		CORDIC_DIV
	return
	
CORDIC_MUL
	bcf		_C
	rlf		INDF, F
	decf 		FSR, F
	rlf		INDF, F
	bcf		INDF, 7
	btfsc		_C
	bsf		INDF, 7
	incf 		FSR, F
	decfsz	_Counter1, F
	goto		CORDIC_MUL
	return
;______________________________________________________________________________
endasm

**mister_e** · - 16th November 2007, 13:25

Carefull when using Banksel and PBP, i would suggest you to replace all BANKSEL for CHK?RP

CHK?RP is to PBP what BANKSEL is to ASM.

Using BANKSEL will make weird things and lost compiler because he don't know where he was before etc etc... i understand why... i just can't explain it correctly.

Darrel could you shed some lights and explain it in english

**ScaleRobotics** · - 16th November 2007, 17:44

Thanks a lot mister_e,

I added your suggestion, which will probably help in the long run. However, I still get the same result for Cos(x) = 71 no matter what I give as x. When edited out of some of the lines that had "global" in them, as suggested in an earlier post, was I supposed to replace "global" with something else? Here are some of the lines I deleted from various places in the program:

GLOBAL X_L, X_H, Y_L, Y_H, Z_L, Z_H, SHIFT
GLOBAL ATAN
GLOBAL SINCOS
GLOBAL Shifter

I don't really understand what these lines did in the original assembly code.
I also wonder if I defined any of the variables wrong. RV, Dir, _C, and _Z are defined inside the assembly code, and the other variables are named in the pbp code. Strange that the ATAN functions great, just the SINCOS having difficulties.

**Darrel Taylor** · - 17th November 2007, 11:18

The Input to SINCOS is the Z variable. (Not X)

I've got it working here, but it seems like it's not right.
Input range is from -256 to +255.

I've plotted the results. Does it look right to you?

<img src="http://www.picbasic.co.uk/forum/attachment.php?attachmentid=2133&stc=1&d=119533895 6">
<br>

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