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jExacter

© Witold Kossowski, 2009

jExacter, written in Java, is an application of high precision calculus.

*** The precision is adjustable within the limit of 1 - 240 significant digits (30 by default).

*** The user can choose a System Keyboard (48 standard functions) as well as the Private one, with 48 customizable keys (right-click).

*** Every "private" button can be titled and linked to any formula entered by the operator at any moment and for permanent using.

*** Calculation is carried out starting from the formula of the length limited to 248 characters.

*** The formula, written in natural notation, is built of operators (max.73), constants and variables.

*** The syntax of the formula is verified and all error is interpreted.

*** The compilation of the formula is followed by the optimization of the calculus.

*** Incremental (for any number of variables with different incrementation values ) as well as recurrent calculus are possible.

*** The formula, as well as any argument can be modified by the user at any moment.

*** jExacter makes the direct access to any variable.

*** Any argument can be entered in fixed or scientific format.

*** In the case of periodic number, the use of the parentheses is authorized, e.g. 1,0(53) that corresponds to 1,053535353… .

*** Every entered argument is tested and all error is interpreted.

*** The largest/smallest accepted number is 1e±1.000.000.000.

*** "Infinity", "NaN" (Not a Number), "TLN" (Too Large Number, i.e. a number > 1e+1.000.000.000 and inferior to Infinity) can be entered and displayed as a result and correctly treated as an itermediate result in any context.

*** There are two predefined values, e and pi.

*** The operator has a direct access to the Help file which, among others, contains the presentation of all functions. The access to the Help file is free at any moment, and one can add his own remarks to the text.

*** The operator has at his disposal another editable system file called FORMULA FILE ("formfile"), as well as the file CONSTANTS where any constant (with or without its name and possible comments) may be registered.

*** According to the run mode chosen, the calculation may be followed by a Report containing a list of arguments and all intermediate results in chronological order.

*** A Find function was added to the Report window, as the report might be very large, especially in the case of the list of primes in some range (exemple : pra[0;10000000] gives all primes from 0 to 10 millions, e.g. 664579 primes organized in 65033 report lines).

*** Every file controlled by jExacter can be printed directly from the File menu.

*** The formula, the arguments, the result, the precision level as well as the report never disappear from the screen. When moving from one window to another, the window colors change, so the user is never lost in his action.

*** In the set of operators, one can find a division modulo as the rest of division by a real number, nth root, a logarithm with any base, a product of all successive numbers of any range, number format conversion (between any bases in the range 2...16), liste of all primes from the range[a..b], nth prime, etc.

*** The use of a special variable name "me" (memory) is authorized. The operator enters the value of "me" before the first run, and at every successive execution "me" takes the value of the last result. This enables the recursive computation.

*** Besides, jExacter has a simple and direct mode of calculation called CASH REGISTER that enables a continuous addition of numbers, products, percents and divisions (precision limited to 25 digits) with the control of the syntax of arguments and operations.

*** Supports copy / paste / cut / Save As / etc.

*** The execution time is measured and displayed.

Operators

+        addition
-        subtraction
*        multiplication
/        division
div      division (no remainder)
inv      inversion
mod      division modulo
gcd      greatest common divisor
^        power
abs      absolute value
int      integer part
inr      the nearest integer
dec      fractional part
!        factorial
pro      product  from ... thru ...

max      max. of 2 numbers
min      min. of 2 numbers
mo       increment
bas      conversion of the base-n to the base-m in the range [2..16]

r        nth root
r2       square root
ln       natural logarithm
lg2      binary logarithm
log      decimal logarithm
lg       any base logarithm

rd       degrees => radians
deg      radians => degrees
sn       sine
cn       cosine
tg       tangent
cg       cotangent
asn      anti-sine
acn      anti-cosine
atg      anti-tangent
acg      anti-cotangent

sh       hyperbolic sine
ch       hyperbolic cosine
ht       hyperbolic tangent
hc       hyperbolic cotangent
ash      hyperbolic anti-sine
ach      hyperbolic anti-cosine
aht      hyperbolic anti-tangent
ahc      hyperbolic anti-cotangent

 

pra      list of all primes from the range  [n..m]
prn      value of nth prime number
prx      prime number  nearest to x,   x : real
pr1      Is number  "i" a prime ?  (otherwise the list of all prime divisors)
pr2      list of all common prime divisors of two numbers 

Arguments

The constant and variable names (max. 3 char.) have to begin with a letter from the range [a..z], except from the operator "bas",
where the acceptable range is [g..z].

Argument formats :
natural 987 ,000178 0,321
scientific e+450 1,78 e-200000 1,14 e+500000000
periodic (23) ,02(7001) 6547(102)
mixed 15(8) e-50 ,24(62) e+89 5,45(76) e-65012572

The menus

The File menu contains, among others, the command Report that enables the immediate opening of the Report file, which is written automatically when there is an abnormal termination of the calculation or when the appropriate run mode is chosen. The Report is always placed in the application folder. The name of the Report is "calcfile" and is determinated by the application. If necessary, the command "Save as" saves a copy of the report (or any other file) under a name desired by the user.

The Formula menu contains two commands:
  • Formula Entry
  • Open Formula file

The Arguments menu contains three commands:

  • Argument Entry (the window for entering arguments in the order of their appearance in the formula)
  • Argument Selection (direct access to any argument)
  • Erase All Arguments

The Constants menu contains two commands:

  • Constant Entry
  • Constants file

The Exec menu contains three commands:

  • Run
  • Run & Report (attention: the intermediate results contain in general 2 digits above the precision level, so the user can partly see the tendency of the calculation)
  • Cash Register (simplified calculation)
    • Run
    • Reset to zero
    • Numbers with Separator
    • Save at Exit (if chosen, the report is kept when leaving the Cash Register mode)

Windows Formula, Arguments, Result and Report are text editors with some function buttons.

Buttons Save permit to save formulaes on the "formfile" and arguments, constants and results on "constfile".

The syntax of the formula requires sometimes the square brackets. Clicking on any operator key inserts the operator symbol as well as, if required, the brackets with the semicolon character when the operator needs two arguments.

One can also select some range of the formula and press any operator button. In such a case, the operator symbol is inserted with the selected part as the first argument. Of course, there is no obligation to use the buttons when typing the formula.

Case and blanks are ignored by the application. The user can type them to make the formula more transparent.

Some examples of formula:

r[10321;16]^n + 4,89 lg[x;2,01] ![45] - 16ab*c

Interpretation:
  • 16th root of 10321,
  • raised to the power n
  • + 4,89 multiplied by the base 2,01 logarithm of x, multiplied by the factorial of 45
  • - 16 multiplied by ab and muliplied by c

Attention:

  • 4,89 lg[x;2,.01] ![45] corresponds to 4,89 * lg[x;2,01] * ![45]
  • 16ab corresponds to 16*ab
  • abc would be interpreted as a variable "abc", so ab*c is entered

mo[a;0,5]^3

This formula is an example of incremental calculation with the argument a initially set to any value and incremented of 0,5 at every run.
The successive results are as follows:
0
+,125
+1
+3,375
+8
. . .

r2[me]

This is an example of recursive calculation with the argument "me" (memory).

After setting m=900, we will have consecutively:

+30
+5,47722557505166113456969782800802133952744695
+2,34034731932071593845914096881666601946360615
+1,52981937473700336792700567684172782592938059
. . .

 

Immediately after the validation of the formula, the message "There are arguments to enter" appears if there are the variables in the formula and if at least one of them was not entered yet.

On the contrary, when returning to the formula with variables and where one or more arguments were already entered, there appears the message "Args presented in preceding formula are initialized." during any new validation. So the user is not obliged to reenter the arguments already written.

The validation of an argument is followed by apparition of a window corresponding to the next argument.

 

The window Argument Selection is identical to the Argument Entry window with this difference that the user has to enter the variable name to access the variable directly.

The window Constant Entry is a text editor without any control of the syntax. The user can enter any constant value, preceded or followed by, for example, some remark. The Constant file can be accessed for any direct text treatment.

The field Precision is intended to set the precision of the calculation, e.g. the number of significative digits of the result. The chosen presicion is set when clicking on OK.

The field Find is intended to enter any text to be found in the file presented in the report window. Once Find clicked, the first text found is selected and the number of occurrences appears in the System Info window. At every click the next occurrence of the text is found and selected (in the loop).

The screen CASH REGISTER presents a white sheet with a header containing a date and current time. There is also a cursor in the shape of ">", which dynamically shows the place for data entry. The syntax of the arguments and operators is controlled by the application.

Example:

jExacter 1E --- CASH REGISTER
Tue Aug 08 15:38:02 CEST 2006
-------------------------------------------------------
0,00
>10000  
  10 000,.00
 
10 000,00
>%22  
  2 200,00
 
12 200,00
>200  
  200,00
 
12 400,00
>/7,88  
  1 573,60
 
13 973,60
>45,01  
  45,01
 
14 018,61
>-%15  
  -2 102,79
 
11 915,82
>*-,2  
  -2 383,16
 
9 532,66
>Undo  
 
11 915,82
>-,82  
  0,82
 
11 915,00
>  
  • The first column keeps the traces of the operation being run.
  • The second column presents the value being added to the former result.
  • The current result is shown in the third column.

In the above example, one can note consecutively:

  1. entry of the amount of 10.000,00
  2. addition of 22% of the last result
  3. addition of 200,00
  4. addition of the last result divided by 7,88
  5. addition of 45,01
  6. substraction of 15% of the last result
  7. substraction of the last result multiplied by 0,2
  8. application of the Undo
  9. substraction of 0,82
  • CTRL-L sets the result to zero, what enables starting a new calculation without erasing what was calculated before.
  • CTRL-E sets the result to zero and clears the screen.
  • CTRL -K permits to leave the screen CASH REGISTER.
Warranty This software is offered "as is" without warranty of any kind. In no event shall the author be liable for incidental or consequential damages, including but not limited to loss of use, loss of revenue or profit, loss of data or data being rendered inaccurate, or losses sustained by third parties even if the authors have been advised of the possibilities of such damages.

 

 Technical Support Sorry, no support or help is available, but please send any comments or "bug" reports via email to: jexacter@kagi.com