FUNCTIO         function-analysis on the ATARI Portfolio

FUNCTIO.EXE is a program that uses the graphic capabilities of the ATARI
Portfolio. The program plots X-Y diagrams from any equation the user supplies,
where Y is a function of X.


Getting started:

1.     Copy the program to the Portfolio, using either the serial or parallel
       interface. Make sure there is enough space : functio.exe at the moment
       occupies 14480 bytes.

2.     Start by typing FUNCTIO <enter>.

3.     After the title screen (<enter>) you are asked to supply an equation
       for Y=....
       Type : sin(x)/x          (see below for other examples)
       The usual editing- keys can be used to change or correct the current
       equation.
       (Only 30 characters fit on the input line , but the maximum length
       of the equation is 60 characters. Editing the second half occurs
       automatically if your input line exceeds thirty positions or if you put
       a '>' at the end of the first line.)
       If you just type <enter> you're ready.

3.     You are asked for the starting value for X ; 
       Type  -10

       (All numbers you type in are six-byte real numbers, with a range from
       2.9 E-39 to 1.7 E+38. Other possible starting values for X could be:
              -2.9E-39
              3^8
              -PI
       Try them out later).


4.     .... and for the max value of X....
       Type 10

5.     The Portfolio then starts calculating the max and min values in the Y
       direction. The formula is being evaluated 240 times so this does take some
       time.
       The values appear to be -0.2172042652 and 0.9997082473 ...(all
       calculations also have an accuracy of 6-byte real variables). When you hit
       <enter> the graphic screen appears.

The program calculates where and how many numbers have to be printed alongside
the axes. You can repeat steps 3 to 5 as many times as you want, for instance to
make ever larger 'blow-ups' of the diagrams, just by entering different min/max
values. 
You can try this out for the same formula Y=SIN(X)/X with the next sequence of
values :
MINimum and MAXimum values for X:
     MIN       MAX
     -30        30
      0         30
      5         10
      6         6.5
      6.28      6.29

You see that FUNCTIO can be an accurate help for finding points of intersection.

The complexity of the equation you type in is only limited by the length of the
input line of 30 characters.

The equation further may contain:
      X
      brackets         as many as you like, but always as many (( as there are )).
      real numbers ( for instance 3 , but also 12.3 E10 is possible)
      PI
      the normal operators  + addition
                            - substraction
                            * multiplication
                            / division
                            ^ power
                            SIN en COS(use S and C for short)

for the square root you can use X^0.5 and the TANgent of X for instance can be
accomplished by SIN(X)/COS(X).

Other suggestions :

try:

X^(SIN(X)) for  X= -10 to 10

-2^X       for  X=   0 to  8

sin(x)+sin(3x)+sin(5x)+sin(7x)+sin(9x)+sin(11x) for X= -PI to PI

If there is enough white space left then the graphic display also contains the
equation you entered and the name of the program.




FUNCTIO.EXE was written to make use of the graphic possibilities of the ATARI
Portfolio pocket computer. It also runs on MS-DOS computer with a CGA graphic
card, though the screen is limited to 240x64 pixels.
The program was written using Borland's Turbo Pascal 5.5 ,using some special
techniques to compile an EXE file small enough for the Portfolio.

FUNCTIO.EXE and this documentation are FREEWARE , which I consider to be FREE 
for anyone to copy, but NOT FREE for anyone to alter.
Other versions of FUNCTIO include bigger screen versions for HERCULES and
EGA/VGA graphic cards.

If you're interested these, or in programming for the ATARI Portfolio you could
contact me through the Dutch BBS of Atari Benelux (+31 3473 77584 and 77376),
through Atari Benelux in COMPUSERVE [72347,2124] or by mail:

S.J. Spoelstra
Korenmolen 24
2906 RA Capelle a/d IJssel
Holland.