Sine Function

[Anonymous]

Hello All,

Attached is the code for a Sine function, and a main program to demo it. The function itself is very short and sweet. The demo portion is the long part, just to show you the results on an LCD.

This is totally generalized. The argument may be positive, negative or zero, and there is no limit on the size of the argument, either. The results are accurate to four decimal places.

The lookup table for quadrant I is stored in program memory, and the usual trigonometric identities are used to expand this to include all quadrants, and for positive or negative angles of any size. It really is universal.

It seems that storing a table of words in EEPROM is buggy in GC Basic. At least, I wasn't able to make that work. So, I just stored the table in program memory which works just fine.

Thomas Henry

;Implementing the Sine function in GC Basic
;Thomas Henry -- 3/19/2014

;This program demonstrates the Sine function by printing
;out its values for arguments from -720 degrees
;to 720 degrees, in one-degree increments. The actual
;function itself is very short. The main business of the
;demo program is tied up in formatting the results to
;appear neatly on an LCD.

;This Sine function is completely general purpose. It can
;handle positive, negative or zero arguments of any
;arbitrary size.

;The values returned are valid to four decimal places,
;equivalent to most printed tables, and more than accurate
;for most engineering purposes.

;The values are maintained as signed integers, scaled up by
;a factor of 10000. A lookup table stored in program
;memory is used.

;----- Configuration

#chip 16F88, 8              ;PIC16F88 running at 8 MHz
#config mclr=off            ;reset handled internally
#config osc=int             ;use internal clock

;----- Constants

#define LCD_IO      4       ;4-bit mode
#define LCD_RS      PortB.2 ;pin 8 is LCD Register Select
#define LCD_Enable  PortB.3 ;pin 9 is LCD Enable
#define LCD_DB4     PortB.4 ;DB4 on pin 10
#define LCD_DB5     PortB.5 ;DB5 on pin 11
#define LCD_DB6     PortB.6 ;DB6 on pin 12
#define LCD_DB7     PortB.7 ;DB7 on pin 13
#define LCD_NO_RW   1       ;ground the RW line on LCD

#define degree      223     ;ASCII code for degree mark

;----- Variables

dim index as byte
dim i, sign, value, arg as integer

;----- Program

dir PortB out                 ;all outputs to the LCD

for i = -720 to 720           ;values of sine from -720 to 720
  cls
  print "sin("                ;print the label
  print i                     ;and the argument
  LCDWriteChar degree         ;print degree mark
  print ")="                  ;and closing parenthesis
  locate 1,0                  ;move to the next line

  value = sin(i)              ;get the value of the sine

  if value = 0 or value = -1 or value = 1 then
    print value               ;handle whole number cases
  else
    if value < 0 then
      print "-"               ;a negative result
      value = -1 * value
    end if

    print "0."                ;format fractional number

    if value < 1000 then      ;left pad smaller results
      print "0"
    end if
    if value < 100 then
      print "0"
    end if
      if value < 10 then
      print "0"
    end if

    print value               ;then print the fraction
  end if

  wait 1 S                    ;pause to view
next i

;----- Subroutines

function sin(in arg as integer) as integer
  if arg < 0 then             ;sine is an odd function,
    sign = -1                 ;so negate negative argument
    arg = -1 * arg            ;and change sign of result
  else
    sign = 1                  ;else a positive argument
  end if

  arg = arg mod 360           ;reduce to 0 to 359 degrees

  if (arg > 270) then         ;Quadrant IV
    sign = -1 * sign
    arg = 360 - arg           ;make reference angle
  else
    if (arg > 180) then       ;Quadrant III
      sign = -1 * sign
      arg = arg - 180         ;make reference angle
    else                      ;Quadrant II
      if (arg > 90) then
        arg = 180 - arg       ;make reference angle
      end if
    end if                    ;Quadrant I by default
  end if

  index = [byte]arg+1         ;make index into table
  readTable sineTab, index, sin

  sin = sign * sin            ;create final result
end function

;----- Data

table sineTab as word
  ;Sine values for 0 through 90 degrees, scaled up by 10000.
  0
  175
  349
  523
  698
  872
  1045
  1219
  1392
  1564
  1736
  1908
  2079
  2250
  2419
  2588
  2756
  2924
  3090
  3256
  3420
  3584
  3746
  3907
  4067
  4226
  4384
  4540
  4695
  4848
  5000
  5150
  5299
  5446
  5592
  5736
  5878
  6018
  6157
  6293
  6428
  6561
  6691
  6820
  6947
  7071
  7193
  7314
  7431
  7547
  7660
  7771
  7880
  7986
  8090
  8192
  8290
  8387
  8480
  8572
  8660
  8746
  8829
  8910
  8988
  9063
  9135
  9205
  9272
  9336
  9397
  9455
  9511
  9563
  9613
  9659
  9703
  9744
  9781
  9816
  9848
  9877
  9903
  9925
  9945
  9962
  9976
  9986
  9994
  9998
  1
end table

[Anobium]

I had a look at the code regarding EEPROM and writing WORD values.

The code today supports BYTE values only. It would be practical to add WORD (I just created a test version with WORD support) but it then caused an issues with pages et, and, it may mean you would on be able to store 126 WORDs in a table.

Something for the summer to look into. I will add the list of things to investigate.

[Anobium]

Very nice. Thank you. I just ported to 16F887a and terminal all this is very good code!

Most grateful. This is code I could include in the Help File it this is acceptable to you?