General instructions
exporting and importing / formulas syntax

Formulas typed into the main activity's text field are evaluated and added to the top of the history list displayed below (if no error occurred during the evaluation). The result is displayed and stored into an automatically named variable, for use in later formulas.

When the history list reaches its maximum size, it is reduced by a given number of lines; references in the remaining formulas to the removed variables are replaced by their explicit numerical values and remaining variables are automatically renumbered. Before this reduction takes place, the program offers to save the whole history in external storage (like the export menu option). The settings menu option gives access to the maximum size and reduction step of the history list.

The clear menu option destroys the whole history list without asking for confirmation.

By selecting (touching) a formula in the history list, one can import the formula in the text editor, remove the formula (the program then performs a list reduction with variables substitutions as explained above) or change its value. In this latter case a new formula is evaluated and, in the absence of error, is substituted to the selected one. The value of the corresponding variable is changed and all later formulas are re-computed (since this might be a lengthy operation, it is performed in the background and a "progress" dialog box is displayed). A fourth option inserts a new formula below the selected one. In this case, the program renames all subsequent variables (neither substitutions nor recomputing are required).

Two special kinds of formulas (equations and curves) may (and should) use the variable associated to them in their final expression (and only there). It is a syntax error (forward reference) for other types of formulas to refer to their own result. The expression located after the > token is considered as a function of the variable associated to the formula. The result of the evaluation of an equation is a zero of this function or a local minimum of its absolute value (see remarks below). In the case of curves, the value assigned to the variable is always NAN (Not A Number). Equations define a search interval and curves a drawing interval; in both cases the function may be plotted inside the defined interval and a fifth option to do so (draw curve) is displayed when touching the formula in the history list.

Exporting and importing
general instructions / formulas syntax
When the program terminates gracefully, the history list is automatically saved in a private storage location. It is restored from this location when the application restarts. Furthermore, it is possible (before a list reduction or by choosing the export menu option) to save an intermediary snapshot of the history list into a text file.

The program's output files may be stored in any external storage location (if several ones are available, a dialog box is displayed to let choose a destination). They are written in folders named FormulaCalculator (created when necessary) and are named Formulas@date_time.txt, where date and time are the date and time of the export operation.
These files start by a list of formulas (one per line, oldest first), followed by a list of results values:
#0=12/7
#1=ln #0
…
*** Results ***
#0=1.7142857142857143
#1=0.5389965007326870
…

The files menu option starts an activity displaying all files of proper name (see above) located in the FormulaCalculator folders. By selecting a file one can:

1. destroy it
   (if the operation succeeds and the FormulaCalculator folder where the file was located is empty, then the folder is also destroyed)
   
   
2. display its contents
   (the program tries and launches a viewer or editor for MIME plain/text data type; it may happen that none is found on the device: Formula Calculator does not provide one)
   
   
3. (re)load its formulas
   the Files Manager activity closes and the program

• clears the history list,
  
• loads formulas from the selected file, which should have the format described above, stopping at the end of the formulas section or at the first error
  (the results section is not used nor read though the "*** Results ***" line is expected; white spaces are not significant)
  
• re-computes the values of all formulas, starting at number 0
  (potentially lengthy operation, performed in the background with a "progress" dialog box displayed)
• in case of error, the faulty formula is deleted as well as all later ones (the re-computing operation stops)

Formulas syntax
general instructions / exporting and importing
important remarks syntax description conventions:

Symbol	Meaning
( )	single element
[ ]	optionally
{ }	one or several times
|	or
:=	is defined by
bold text	keyword or operator

Syntax

formula	:=	expression | equation | curve
expression	:=	product [{( + | - ) product}]
product	:=	power [{( * | / | % ) power}]
power	:=	term [{ ^ term }]
term	:=	constant | variable | ( function term ) | ( ( expression ) )
constant	:=	IEEE positive floating point constant | $pi | $e
variable	:=	#integer
function	:=

	-	sign change
	abs	absolute value
	acos	arc cosine
	asin	arc sine
	atan	arc tangent
	cos	cosine
	cosh	hyperbolic cosine
	ln	natural logarithm
	log	base 10 logarithm
	sin	sine
	sinh	hyperbolic sine
	sqrt	square root
	tan	tangent
	tanh	hyperbolic tangent
	deg	radians to degrees conversion
	rad	degrees to radians conversion
	int	integer conversion towards 0
	rnd	rounding to nearest integer

equation	:=	? expression , expression [, expression] ; expression [; expression [; expression [; expression]]] > expression
curve	:=	! expression , expression > expression

Remarks
Contrary to C language,

• associativity is from right to left:
  #0/2*#1 means #0/(2*#1)
and not (#0/2)*#1
1-3+2 means 1-(3+2) and is equal to -4 rather than to 0
  
• minus sign has a high priority:
  -#0^#3 means (-#0)^#3
and not -(#0^#3)
• function calls do not require parentheses:
  atan sqrt #3 is a well formed formula meaning atan(sqrt(#3))
• function and constant names are not case sensitive

Equations:

• The first expression gives the lower bound and the second expression the upper bound of the search interval.
• The third (optional) expression gives the initial guess for the solution. The default value is the middle point of the search interval. The initial guess must lie strictly inside the search interval.
  
• The fourth expression gives the maximum number of iterations. If the value of this expression is less than 1000, the default value (1000) is used.
  
• The optional fifth and sixth expressions give the absolute precision for the solution and the minimum significant variation of the function (default values: 10-4, 10-6). If one of these expressions is negative, the default value is used.
  
• The seventh (optional) expression is the bracketing factor (in case the value of the function is of the same sign at the bounds of the search interval, this interval is split in sub-intervals in order to find a sign change; the bracketing factor gives the number of sub-intervals to test). If the value of this expression is less than 4, the default value (4) is used.
• The eighth expression is the function to equate to zero. It must refer to the variable associated to the formula (the unknown).

Note on the algorithm:

it first searches for of a sign change and, in case of failure, tries and finds a local minimum of the absolute value of the function; since the search is bounded, this algorithm always converges.

Curves:

• The first expression gives the lower bound and the second expression the upper bound of the drawing interval.
• The third expression is the function to plot.
  

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