How to calculate ATN (Inverse Tangent)

[Steven Pringels 3]

Hi,

I would like to know how to calculate the ArcTangent or Inverse Tangent
in code. So, not just using the great ATN function which is built in, in
PowerBasic.

Thanks in advance.

Steven

[Eddy Van Esch]

[deleted]

[Eddy Van Esch]

You can use:

                            x
    arctan(x) = arcsin (------------)
                        sqrt(1 + x^2)

If x is large (larger than 1000-1500), then better use :

    arctan(x) = (PI / 2) - arctan(1 / |x|)

and the sign of the result is the sign of original input.


If 'x' is small enough use the following series:

                 x^3     x^5     x^7     x^9
 arctan(x) = x - ---  +  ---  -  ---  +  ---  ...
                  3       5       7       9

It wil converge quickly if x is small enough.

Kind regards

[Paul Dixon]

Steve,
the fastest way is to use the ASM opcode for ATN but to do it yourself the easiest way is to follow the series shown here:

http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=2649

The more terms you use the more accurate answer you will get.

FUNCTION PBMAIN () AS LONG
#REGISTER NONE

LOCAL a,result AS EXT

a = .5

PRINT "ATN(a)=";ATN(a)

!fld a           'get the value
!fld1            'it calculate ATAN(a/b) to account for quadrants
!fpatan          'do the calculation
!fstp result     'store the result
PRINT "ASM   =";result

result = a - a^3/3 + a^5/5 - a^7/7 + a^9/9 - a^11/11 + a^13/13 - a^15/15  + a^17/17 'add more terms as needed
PRINT "Series=";result

WAITKEY$
END FUNCTION

Paul.

[Steven Pringels 3]

Thanks to all for the assistance

[Robert DeBolt]

My calculation for the last result:

#COMPILE EXE
#DIM ALL
FUNCTION PBMAIN () AS LONG
    #REGISTER NONE
 
    LOCAL i AS LONG
    LOCAL a,result,myinc,lastinc,mysign AS EXT
    a = .5##
    mysign=-1
    PRINT "ATN(a)=";ATN(a)
    !fld a           'get the value
    !fld1            'it calculate ATAN(a/b) to account for quadrants
    !fpatan          'do the calculation
    !fstp result     'store the result
    PRINT "ASM   =";result
    myinc=0.0##
    result=0.0##
    lastinc=0.0##
    FOR i = 1 TO 1000 STEP 2
        'result = a - a^3/3 + a^5/5 - a^7/7 + a^9/9 - a^11/11 + a^13/13 - a^15/15  + a^17/17 'add more terms as needed
        myinc =-mysign*a^i/i
        IF ABS(lastinc)=ABS(myinc) THEN EXIT FOR
        result=result+myinc
        lastinc=myinc
        mysign=-mysign
    NEXT i
 
    PRINT "Series=";result
    WAITKEY$
END FUNCTION

[Arthur Gomide]

Try the algorithm developed by Mr Henry Briggs (1561 - 1630) - no power, mul or div - only add and sub ... I need some time to do a search to find it here ...