NAME

       Formula - A class for generating Excel formulas

SYNOPSIS

       See the documentation for Spreadsheet::WriteExcel

DESCRIPTION

       This module is used by Spreadsheet::WriteExcel. You do not need to use it directly.

NOTES

       The following notes are to help developers and maintainers understand the sequence of
       operation. They are also intended as a pro-memoria for the author. ;-)

       Spreadsheet::WriteExcel::Formula converts a textual representation of a formula into the
       pre-parsed binary format that Excel uses to store formulas. For example "1+2*3" is stored
       as follows: "1E 01 00 1E 02 00 1E 03 00 05 03".

       This string is comprised of operators and operands arranged in a reverse-Polish format.
       The meaning of the tokens in the above example is shown in the following table:

           Token   Name        Value
           1E      ptgInt      0001   (stored as 01 00)
           1E      ptgInt      0002   (stored as 02 00)
           1E      ptgInt      0003   (stored as 03 00)
           05      ptgMul
           03      ptgAdd

       The tokens and token names are defined in the "Excel Developer's Kit" from Microsoft
       Press. "ptg" stands for Parse ThinG (as in "That lexer can't grok it, it's a parse
       thang.")

       In general the tokens fall into two categories: operators such as "ptgMul" and operands
       such as "ptgInt". When the formula is evaluated by Excel the operand tokens push values
       onto a stack. The operator tokens then pop the required number of operands off of the
       stack, perform an operation and push the resulting value back onto the stack. This
       methodology is similar to the basic operation of a reverse-Polish (RPN) calculator.

       Spreadsheet::WriteExcel::Formula parses a formula using a "Parse::RecDescent" parser (at a
       later stage it may use a "Parse::Yapp" parser or "Parse::FastDescent").

       The parser converts the textual representation of a formula into a parse tree. Thus,
       "1+2*3" is converted into something like the following, "e" stands for expression:

                    e
                  / | \
                1   +   e
                      / | \
                    2   *   3

       The function "_reverse_tree()" recurses down through this structure swapping the order of
       operators followed by operands to produce a reverse-Polish tree. In other words the
       formula is converted from in-fix notation to post-fix. Following the above example the
       resulting tree would look like this:

                    e
                  / | \
                1   e   +
                  / | \
                2   3   *

       The result of the recursion is a single array of tokens. In our example the simplified
       form would look like the following:

           (1, 2, 3, *, +)

       The actual return value contains some additional information to help in the secondary
       parsing stage:

           (_num, 1, _num, 2, _num, 3, ptgMul, ptgAdd, _arg, 1)

       The additional tokens are:

           Token       Meaning
           _num        The next token is a number
           _str        The next token is a string
           _ref2d      The next token is a 2d cell reference
           _ref3d      The next token is a 3d cell reference
           _range2d    The next token is a 2d range
           _range3d    The next token is a 3d range
           _funcV       The next token is a function
           _arg        The next token is the number of args for a function
           _class      The next token is a function name
           _vol        The formula contains a voltile function

       The "_arg" token is generated for all lists but is only used for functions that take a
       variable number of arguments.

       The "_class" token indicates the start of the arguments to a function. This allows the
       post-processor to decide the "class" of the ref and range arguments that the function
       takes. The class can be reference, value or array. Since function calls can be nested, the
       class variable is stored on a stack in the @class array. The class of the ref or range is
       then read as the top element of the stack $class[-1]. When a "_funcV" is read it pops the
       class value.

       Certain Excel functions such as RAND() and NOW() are designated as volatile and must be
       recalculated by Excel every time that a cell is updated. Any formulas that contain one of
       these functions has a specially formatted "ptgAttr" tag prepended to it to indicate that
       it is volatile.

       A secondary parsing stage is carried out by "parse_tokens()" which converts these tokens
       into a binary string. For the "1+2*3" example this would give:

           1E 01 00 1E 02 00 1E 03 00 05 03

       This two-pass method could probably have been reduced to a single pass through the
       "Parse::RecDescent" parser. However, it was easier to develop and debug this way.

       The token values and formula values are stored in the %ptg and %functions hashes. These
       hashes and the parser object $parser are exposed as global data. This breaks the OO
       encapsulation, but means that they can be shared by several instances of
       Spreadsheet::WriteExcel called from the same program.

       Non-English function names can be added to the %functions hash using the
       "function_locale.pl" program in the "examples" directory of the distro. The supported
       languages are: German, French, Spanish, Portuguese, Dutch, Finnish, Italian and Swedish.
       These languages are not added by default because there are conflicts between functions
       names in different languages.

       The parser is initialised by "_init_parser()". The initialisation is delayed until the
       first formula is parsed. This eliminates the overhead of generating the parser in programs
       that are not processing formulas. (The parser should really be pre-compiled, this is to-do
       when the grammar stabilises).

AUTHOR

       John McNamara jmcnamara@cpan.org

COPYRIGHT

       Copyright MM-MMX, John McNamara.

       All Rights Reserved. This module is free software. It may be used, redistributed and/or
       modified under the same terms as Perl itself.