Formula - A class for generating Excel formulas

See the documentation for Spreadsheet::WriteExcel

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

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 CW1+2*3 is stored as follows: CW1E 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. CWptg 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 CWptgMul and operands such as CWptgInt. 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 CWParse::RecDescent parser (at a later stage it may use a CWParse::Yapp parser or CWParse::FastDescent).

The parser converts the textual representation of a formula into a parse tree. Thus, CW1+2*3 is converted into something like the following, CWe stands for expression:

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

The function CW_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
    _func       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 CW_arg token is generated for all lists but is only used for functions that take a variable number of arguments.

The CW_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 CW@class array. The class of the ref or range is then read as the top element of the stack CW$class[-1]. When a CW_func 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 CWptgAttr tag prepended to it to indicate that it is volatile.

A secondary parsing stage is carried out by CWparse_tokens() which converts these tokens into a binary string. For the CW1+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 CWParse::RecDescent parser. However, it was easier to develop and debug this way.

The token values and formula values are stored in the CW%ptg and CW%functions hashes. These hashes and the parser object CW$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 CW%functions hash using the CWfunction_locale.pl program in the CWexamples 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 CW_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).

John McNamara jmcnamara@cpan.org

© MM-MMVI, 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.