FormulaCalc for Ewe
Version 1.1¹

Description

Welcome Display FormulaCalc is a calculator for Ewe enabled computers which accepts algebraic/trigonometric formulas and computes their values. That is, computes routines.

To learn more about Ewe please read the introduction on the Bray Mobile Applications page.

The formulas of FormulaCalc:

It can be used as a simple calculator, or one to compute complicated routines. We hope you find FormulaCalc useful.

About This Documentation

FormulaCalc is intuitive and easy to use. That seems to be contradicted by the size of this documentation. It's large because of the many features and functions. But once you become familiar with FormulaCalc we think you will agree that it is easy to use.
You really should read this entire document to fully understand FormulaCalc.

For a quick start read Installation and Quick Start.
Then after trying it out please return to this documentation to learn all of the features.

Documentation Sections


Installation

Since you are reading this documentation, you have found that the frmcalc10.zip archive contains frmcalc10Doc.zip which contains this documentation you are now reading. It also contains FormulaCalc.ewe, the executable file.

Installation Steps

  1. Install the the Ewe VM.
  2. Copy FormulaCalc.ewe to your computer(s).
These two steps are explained next.
Step 1
The first thing to do is to install the Ewe VM on your computer(s), if not already installed. Follow the instruction found on the Ewe Download and Installation Page for your computer(s). The Ewe installer will create directories on your computer and put the Ewe VM files in them.

After Ewe is installed find the Ewe directory. For example, in a Windows Desktop it will be where you told the installer to install it, and in the Pocket PC it will (probably) be in \Windows\StartMenu\Programs\Ewe. Specifically, it is the directory in which you find 'ewe.ewe'.
If you put all of your applications in this directory, when you add additional applications from Bray Mobile Applications common files can be shared.

Step 2
There is no installer for FormulaCalc.ewe. It can be put in any directory of your choice. However it is recommended that you put it in the directory with the Ewe VM you found in Step 1.

Once you find the proper directory copy FormulaCalc.ewe into that directory in what ever manner you copy files to your computer.

There is also no uninstaller for FormulaCalc. It does not use the operating system registry, so nothing is hidden. To remove FormulaCalc, simply delete: FormulaCalc.ewe, and any *.fmc formula files which you created.

Note: No matter what Regional settings are used on your computer(s), FormulaCalc always uses the '.' (period) as the decimal point, the ',' (comma) as the formula argument and data separator, and the ";" (semicolon) as the end of formula.

FormulaCalc should be ready to run. Find FormulaCalc.ewe with your File Explorer, click on it to try it out! Soon after you try out FormulaCalc and find it working, you should read the Quick Start which follows.

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Quick Start

Welcome Display When you first use FormulaCalc you will be greeted with a display as shown on the right.
The display consists of 5 areas:

The Button Trailer

If you want to use FormulaCalc as a simple calculator:

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Your First Routine

First Routine Display This is an interactive trial so install FormulaCalc now, and launch it.
In the text which follows, characters which you enter are blue, output values are green, and register names are red.

For this first trial we clear both the Output Area and Input Area by tapping the Clear button two times. (Before the Input Area is cleared a permission box pops up.)
Now with the pen and enter:   3*4-7/3   then press Compute.
The value 9.667 will appear in the output box. An "ordinary" calculator would have displayed 1.666... because it would use a left to right calculation rather than computing 3*4 then 7/3 and then subtracting as we understand algebraic formulas.

Now on the second input line enter: a=2; sr(a); a^2 then press Compute. The output box now displays 4 lines: 9.667   9.667   1.412   4.00
Press the Compute and Clear buttons several times to see what happens.

Next press the Reg button. You will see that the A register now has 2.00 and R has 4.00. That is because you stored 2 in A, and R is the result register which contains the last computed value 4.00.
Using the pen select register G, enter 20 and press Done. Now G contains 20. Press Reg again. This returns FormulaCalc to the Input/Output areas. On the third input line enter G to the end of your routine.
Your routine should now read:

  1. 3*4-7/3
  2. a=2; sr(a); a^2
  3. g
Quick Example Press Compute. You will see 20.00 added to your output lines, and if you check the resisters (Reg) R will be 20.00 since it is now the last result.

You are now an expert!

To prove that, see if you understand the example on the right.

A better formatted answer version of this is shown below.

Note: To edit input in the Input Area you can hold down the pen to pop-up a Copy/Cut/Paste action box.

Allowable Formula Objects

The allowable operators, functions and symbols are:
arithmetic: +   -   *   /   ^   %;
functions: sr()   sq()   ln()   log()   abs()   int()   pi   deg   rad
trig: sin()   cos()   tan()   asin()   acos()   atan()
assignment: =   +=   -=   *=   /=
decision: <   <=   = =   >=   >
grouping: (   )
control: ;   if(,,)   cc:   dd:   ds:   se:   sr:
string: " "   st()   [ ]
comment: [ ]   #

The definitions for these are given below, but it is now time for you to try FormulaCalc for yourself.
When you get puzzled or you want to save a routine for future use, come back. It's all explained below.

This is the end of Quick Start.

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Using FormulaCalc

Menu Actions

Menu Items

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Storing Routines

You can store as many routines as desired in a Formula File(s). Also, there can be as many formula files as desired. By convention formula files are given the file extension of .fmc, but may be any desired file type (extension).

A Formula File has the following format:

Following is an example Formula File with two routines:

    #Compound Interest
    [Reg: I interest, P principle]
    [N years, M periods per year]
    dd:2
    (1+i/m)^(m*n)*p

    #Future Annuity
    dd:2; ((1+i/m)^(m*n)-1)/(i/m)*p

This starts the name of the routine is Compound Interest.
Next is a 2 line non-printing comment as a reminder of the register contents.
dd:2 tells FormulaCalc to show 2 decimal digits in the output.
The formula (1+i/m)^(m*n)*p follows.

The second routine in the Formula File is Future Annunity.
As many routines as desired may be in a Formula File. Each routine must start with a '#' in column 1.

See Programmed Input for control over the register values.

It is recommended that you create a Formula File, even if it is empty, in the directory with FormulaCalc.ewe.
Having such a file allows you to check out routines written in the Input Area with the pen and then export them with Menu/Export Pen when you have them working to your satisfaction.

Warning:

  1. Be sure to you choose the Formula File using Open even if there is nothing to open before you try to export the Input Area. As mentioned above exported routines are given a default name of #Exported Routine. Later you can edit the Formula File to give each a correct unique name.
  2. If you open a Formula File which has more than routine named '#Exported Routine' only the first such routine in a Formula File will be opened. Any other such routines will be ignored until you give them a unique name(s).

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Operators and Functions

This explains each of the operators and function.
The operators:

arithmetic:

  +
addition -- e.g. 4 + 8     result: [12]
  -
negation -- e.g. -4 or subtraction e.g. 5 - 2.02     [2.98]
  *
multiplication -- e.g. 12 * 6     [72],     121 * -7     [-847]
  /
division -- e.g. 36 / 4.321     [8.3314]
  ^
x to power y -- e.g. 2 ^ 3     [8]
  %
remainder of x divided by y -- e.g. 30.25 % 5     [0.05],     30.25 % 1     [0.25] the fractional part
The functions:

arithmetic:

  sr()
square root -- e.g. sr(2)     [1.1414]
  sq()
square -- e.g. sq(2)     [4]
  ln()
natural logarithm -- e.g. ln(3)     [1.0986]
  log()
base 10 logarithm -- e.g. log(1000)     [3]
  abs()
absolute value -- e.g. abs(-654)     [654]
  int()
integer part -- e.g. int(30.25)     [30]
  pi
constant pi -- e.g. pi * 2     [6.283185307]
  deg
constant 180/pi -- e.g. deg     [57.29577951]
  rad
constant pi/180 -- e.g. rad     [0.017453292]

trigonometric:

  sin()
sine -- e.g. sin(1)     [0.8415]
  cos()
cosine -- e.g. cos(1)     [0.5403]
  tan()
tangent -- e.g. tan(1)     [1.5574]
  asin()
arcsine -- e.g. asin(1)     [1.5708]
  acos()
arccosine -- e.g. acos(1)     [0.0000]
  atan()
arctangent -- e.g. atan(1.5574)     [1.0]

assignment:

  =
register store -- e.g. a = 2     [2] -- a cumulative example
  +=
add and store -- e.g. a += 13     [15]
  -=
subtract and store -- e.g. a -= 9     [6]
  *=
multiple and store -- e.g. a *= 3     [18]
  /=
divide and store -- e.g. a /= 3     [6]

decision -- used in if(,,):

  <
less than -- e.g. a < 10
  <=
less or equal -- e.g. a <= q
  ==
equal -- e.g. 20 == w
  >=
greater or equal -- e.g. t >= s
  >
greater than -- e.g. d / 3 > 10 * 7 + a
The miscellaneous statements:

string:

  " "
string -- e.g. "answer is:"     [answer is:]
  st()
convert number to string -- e.g. st(654)     [654]

comment:

  #
non-printing comment to end of line -- e.g. sin(30); # this is the angle     [0.500]
  [ ]
non-printing comment -- e.g. [debug line]     [ ]
programmed input -- e.g. [@t,Temperature]     [Opens a dialog box]
See Programmed Input

control:

  if(,,)
select -- e.g.   a=18;   if (a<10, a, a/3)     [6]     or a=9     [9]
  dd:
decimal digits (0-15) -- e.g. dd:4; 1234.5;     [1234.500]
  ds:
display string
    ds:s; display string start
    ds:e; display string end
e.g. ds:s; "The answer is: "; st(2^4); ds:e     [The answer is: 16]
See Output Format Control
  se:
exponent to display scientific notation (0-15) -- e.g. se:4     [ ]
  sr:
show register assignments (y or n) -- e.g. sr:y     [ ]
  cc:
compution control
    cc:d trig formulas use degree cc:d -- e.g. cc:d; sin(2)     [0.034899]
    cc:r trig use radians -- e.g. cc:r; sin(2)     [0.909297]
    cc:t scientific notation trim trailing zeros -- e.g. dd:6; se:2; cc:t; 1234;     [1.234e3]
    cc:z scientific notation show trailing zeros -- e.g. dd:6; se:2; cc:z; 1234;     [1.234000e3]

Notes: The se: value determines at what exponent value the notation is switched between fixed to scientific notation.
The cc:t or cc:z determines if trailing 0's in scientific notation are displayed.
More examples:

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Default Control Settings

The default control values are:

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Output Format Control

All numerical computation results are displayed on a single line in the Output Area, except strings. Text and numerical values can be combined by using text strings and numerical strings. Text strings are enclosed in " "'s. Numerical values are converted to strings by the st() function. The control ds:s starts a concatenation of strings, and ds:e ends a concatenation causing it to be displayed.

Strings cannot be assigned to a letter.

Instead writing the poorly formatted routine for converting Celsius to Fahrenheit and vise versa, write the routine as follow:

[F to C and C to F. Input w]
dd:1;
ds:s; st(w);" F is "; st((w-32)*5/9); " C" ds:e;
ds:s; st(w);" C is "; st(w*9/5+32); " F"; ds:e

Check it out.

Note: Numeric values not converted to a string by st() are displayed immediately, i.e. not delayed until the ds:e. Consider:

ds:s; w=10; st(w); " F is "; st((w-32)*5/9); " C"; ds:e -- Displays: 10.0000 F is -12.2222 C, but
ds:s; w=10; w; " F is "; (w-32)*5/9; " C"; ds:e -- Displays: 10.0000-12.2222 F is C

Programmed Input

The input values for the routines come from the registers. Typically values are placed in registers before the computation is started.
However a routine can request that the user input values to be stored in registers. This is done with the programmed input comment statement.

To request the user to input a register value, place the follow construct(s) at the end of a line. It has the following line. The general construct is that of a non-printing comment []:

'[@' register letter, prompt ']', for example:
[@w,Temperature].

A dialog box will open to allow the user to enter a value. The current value of the register will be displayed and highlighted.

The above routine for converting Celsius to Fahrenheit is shown next with a programmed input command.

[F to C and C to F. Input w]
[@w,Temperature]
dd:1; ds:s
st(w);" F is "; st((w-32)*5/9); " C"
ds:e; ds:s
st(w);" C is "; st(w*9/5+32); " F"
ds:e
Note: Programmed input comment statement discussion:

Operator Calculation Order

This section discusses the order in which operators are used for a calculation when not controlled by parenthesis.
The computation is done in a left to right order for the operators and functions of a given group as listed next listed next. This means that operators in a given group are computed in turn left to right and then the results of each group computation combined as specified by the order. Parenthesis modify the order forcing computation to be completed within the '( )' before combining with other values. See the example which follow the table.

Group computation order:
First: sr()   sq()   ln()   log()   int()   pi   sin()   cos()   tan()   asin()   acos()   atan()   if(,,)   deg   rad   <   <=   = =   >=   >
Second: *   /   ^   %;
Third: +   -
Last: =   +=   -=   *=   /=
Not Combined: dd:   sr:   se:   cc:   " "   [ ]   ds:   st()

Example:

          a = 10; deg                                          Left to right
          b = 2 * 3 + 5 * sin(a + 30) ^ 2 - 9 * (5 + 7)
              |   |   |     |  \   /    |    |    \  /
              |   |   |     |   40     /     |     12          Compute inside ()'s 1st
              |   |   |      \  /     /      |      |
              |   |   |      0.64    /       |      |          Then things in First
               \ /     \      /     /         \    /
                6        3.21      /            108            Then Second (leftmost)
                 \        \       /             /
                  \         10.33              /               And Second Again
                   \        /                 /
                     16.33                   /                 Then Third (leftmost)
                          \                 /
                                 -91.67                        And Third Again
          Finally the assignment

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Examples

This section explains three examples in detail. The Julian Calendar is quite complicated but it is a good example of register storage, the if(,,) statement and number encoding.

Example 1:
This example shows the use of arithmetic assignments to registers, and iteration.

    #Powers of 2		Routine title
    sr:y			Show register store assignments
    u += 1; v *= 2
This routine sets the output display to show register assignments. Then 1 is added to the current value of u and re-stored in u, and the current value of v is multiplied by 2 and re-stored in v.
Assume the initial value of the register u is 0, and v is 1.
Pressing Compute produces output of: 1   2 because 1 was added to u and v was multiplied by 2.
Pressing Compute again produces: 2   4 and again 3   8 etc.
Powers of 2 -- 1 raised to 2 is 2, 2 raised to 2 is 4, 3 raised to 2 is 8, etc.

Example 2:

This example shows the use of the int() function (i.e. whole number extraction).
Julian Date was defined by astronomers to have a uniform date code independent of the calendar. It makes taking the difference between 2 dates easy. (See note below.)

    #Julian Date
    sr:n; dd:2; se:10
    i=int(z/100); i=2-i+int(i/4)
    int(365.25*z)+int(30.6001*(x+1))+y+1720994.5+i
Assume that register x (month) is 10, y (day) is 15, z (year) is 1999 (October 15, 1999).
This routine sets the output display to not show register assignments; to display 2 decimal digits; don't display scientific notation for numbers <= 10 digits.
It then divides the year by 100, and fills the whole number part into register i. i is then further manipulated for leap years. The result is the integer part of a year and a month calculation, all added to the day, a constant and i.
The result displayed is: 2451466.50
It would be a good exercise to see the results of all computations by overriding sr:n. You do this by accessing Menu/Debug On
The output is then: 19   -17   2451466.50

Note: A Julian Date is defined to start at noon and show the fraction of a day. So to be accurate the day in y should be a day and a fraction. If y was 15.5 then noon on October 15, 1999 is the start of Julian Day 2451467.00
This routine is only accurate for the Oregonian calendar. A modification of this routine must be made for dates before October 15, 1582.

Example 3:

This example is really too complicated but it shows the use of the if(,,) function, and it shows how to encode 3 numbers into 1. It produces the calendar date for an Julian date, and show the fraction of a day to two decimal places.

    #Julian Calendar					Routine Title -- a comment
    dd:6; se:10; sr:n					6 decimal digits, scientific notation if exponent >= 10, no register values
    i=int((z+1-1867216.25)/36524.25);			number of centuries
    i=z+1+i-int(i/4);i=i+1524;				leap days
    j=int((i-122.1)/365.25)				a year value
    m=int(365.25*j); k=int((i-m)/30.6001)
    i=i-m-int(30.60001*k)				day of the month
    m=if(k<13.5,k-1,k-13);				month number
    if(m>2.5,j-4716,j-4715)+(m+i/100)/100		answer dependent on month value
The last line computes the year depending on the month. If the month is greater than February then the year is j-4716 otherwise it is j-4715. Add to the year a fraction of the combined month, day and fraction of a day. The form mmdddd. So the answer is yyyy.mmdddd (where dddd means: day dd -- implied decimal point -- decimal part of the day dd). In general, this scheme is a good way to display 3 different numbers as one number.
To see the result put 2451467.00 in register z. Pressing Compute produces: 1999.101500. That is, noon on October 15, 1999.

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Contact Info

FormulaCalc was created by David W. Bray, Potsdam, NY;
Copyright © 1999-2005 David W. Bray, All Rights Reserved.

The Bray Palm OS Page can be found at: http://davidbray.org/palm/

Registering

FormulaCalc is freeware no registration is required. We hope you enjoy using it. I would appreciate receiving e-mail about what computer(s) you are using FormulaCalc on, and any other feedback and suggestions you would like to share with me.

This archive may be freely redistributed, provided it is made available only in its complete, unmodified form with no additional files and for noncommercial purposes only. Any other use must have prior written authorization from David W. Bray.

Unauthorized commercial use includes, but is not limited to:

Disclaimer

This program is provided without warranty and the user accepts full responsibility for any damages, consequential or otherwise, resulting from its use.

Foot Notes

¹ Ewe is developed by Michael L Brereton. We are indebted to him for his outstanding software product and making it freely available. Thank you Michael!

Program Changes in Version 1.1

FormulaCalc for Ewe Version 1.1 Bld:511 differs from Version 1.0 Bld:438 in:
  1. Added programmed input (V1.1 Bld:511)
  2. Added horizontal scroll bar in the Input Area (V1.1 Bld:511)
Bld:511 is the current release.

To be sure that your version is up-to-date check the Bld: number in the current description of Riseset at: http://davidbray.org/mobile/