/**
@page working_with_formulas Working with Formulas

@tableofcontents


In general a formula in Excel can be used directly in the
worksheet_write_formula() function:

@code
    worksheet_write_formula(worksheet, 0, 0, "=10*B1 + C1", NULL);
@endcode

@image html working_with_formulas1.png

However, there are a few potential issues and differences that the user should
be aware of. These are explained in the following sections.


@section ww_formulas_results Formula Results

Libxlsxwriter doesn't calculate the result of a formula and instead stores the
value 0 as the formula result. It then sets a global flag in the XLSX file to
say that all formulas and functions should be recalculated when the file is
opened.

This is the method recommended in the Excel documentation and in general it
works fine with spreadsheet applications. However, applications that don't
have a facility to calculate formulas will only display the 0
results. Examples of such applications are Excel Viewer, PDF Converters, and
some mobile device applications.

If required, it is also possible to specify the calculated result of the
formula using the `result` parameter for
`worksheet_worksheet_write_formula_num()`:


@code
    worksheet_write_formula_num(worksheet, 0, 0, "=2+2", NULL, 4);
@endcode

@section ww_formulas_non_us Non US Excel functions and syntax

Excel stores formulas in the format of the US English version, regardless
of the language or locale of the end-user's version of Excel. Therefore all
formula function names written using libxlsxwriter must be in English:

@code
    // The following formula syntax is okay.
    worksheet_write_formula(worksheet, 0, 0, "=SUM(1, 2, 3)", NULL);

    // The following formula syntax is in French. Will cause error on load.
    worksheet_write_formula(worksheet, 0, 1, "=SOMME(1, 2, 3)", NULL);
@endcode

Also, formulas must be written with the US style separator/range operator
which is a comma (not semi-colon). Therefore a formula with multiple values
should be written as follows:

@code
    // The following formula syntax is okay.
    worksheet_write_formula(worksheet, 0, 0, "=SUM(1, 2, 3)", NULL);

    // The following formula use semi-colons. Will cause error on load.
    worksheet_write_formula(worksheet, 0, 1, "=SUM(1; 2; 3)", NULL);
@endcode

If you have a non-English version of Excel you can use the following
multi-lingual [Formula Translator](http://en.excel-translator.de/language/)
to help you convert the formula. It can also replace semi-colons with commas.




@section ww_formulas_dynamic_arrays Dynamic Array support

Excel introduced the concept of "Dynamic Arrays" and new functions that use
them in Office 365. The new functions are:

- `FILTER`
- `RANDARRAY`
- `SEQUENCE`
- `SORTBY`
- `SORT`
- `UNIQUE`
- `XLOOKUP`
- `XMATCH`

The following special case functions were also added with Dynamic Arrays:

- `SINGLE`: Explained below in @ref ww_formulas_intersection.
- `ANCHORARRAY`:  Explained below in @ref ww_formulas_spill.
- `LAMBDA` and `LET`: Explained below in @ref ww_formulas_lambda.

These functions are all "future functions" and need to written in
libxlsxwriter as follows:

- `_xlfn.ANCHORARRAY`
- `_xlfn.LAMBDA`
- `_xlfn.RANDARRAY`
- `_xlfn.SEQUENCE`
- `_xlfn.SINGLE`
- `_xlfn.SORTBY`
- `_xlfn.UNIQUE`
- `_xlfn.XLOOKUP`
- `_xlfn.XMATCH`
- `_xlfn._xlws.FILTER`
- `_xlfn._xlws.SORT`

Future functions are explained in the section below on @ref
ww_formulas_future.

@subsection ww_formulas_intro Dynamic Arrays - An introduction

Dynamic arrays in Excel are ranges of return values that can change in size
based on the results. For example, a function such as `FILTER()` returns an
array of values that can vary in size depending on the the filter results:

@code
    worksheet_write_dynamic_array_formula(worksheet, RANGE("F2:F2"),
                                          "=_xlfn._xlws.FILTER(A1:D17,C1:C17=K2)",
                                          NULL);
@endcode

This formula gives the results shown in the image below. The dynamic range
here is "F2:I5" but it can vary based on the filter criteria.

@image html dynamic_arrays02.png


It is also possible to get dynamic array behavior with older Excel
functions. For example, the Excel function `"=LEN(A1)"` applies to a single
cell and returns a single value but it can also apply to a range of cells and
return a range of values using an array formula like `"{=LEN(A1:A3)}"`. This
type of "static" array behavior is referred to as a CSE (Ctrl+Shift+Enter)
formula and has existed in Excel since early versions. In Office 365 Excel
updated and extended this behavior to create the concept of dynamic arrays. In
Excel 365 you can now write the previous LEN function as `"=LEN(A1:A3)"` and
get a dynamic range of return values. In libxlsxwriter you can use the
`worksheet_write_array_formula()` function to get a static/CSE range and
`worksheet_write_dynamic_array_formula()` to get a dynamic range. For example:

@code
    worksheet_write_dynamic_array_formula(worksheet, RANGE("B1:B3"),
                                          "=LEN(A1:A3)",
                                          NULL);
@endcode

Which gives the following result:

@image html intersection03.png

The difference between the two types of array functions is explained in the
Microsoft documentation on [Dynamic array formulas vs. legacy CSE array
formulas](https://support.microsoft.com/en-us/office/dynamic-array-formulas-vs-legacy-cse-array-formulas-ca421f1b-fbb2-4c99-9924-df571bd4f1b4). Note
the use of the word "legacy" here. This, and the documentation itself, is a
clear indication of the future importance of dynamic arrays in Excel.

For a wider and more general introduction to dynamic arrays see the following:
[Dynamic array formulas in Excel](https://exceljet.net/dynamic-array-formulas-in-excel).

The `worksheet_write_dynamic_array_formula()` function takes a `(first_row,
first_col, last_row, last_col)` cell range to define the area that the formula
applies to. However, since the range is dynamic this generally won't be known
in advance in which case you can specify the range with the same start and end
cell. The following range is "F2:F2":

@code
    worksheet_write_dynamic_array_formula(worksheet, 1, 5, 1, 5,
                                          "=_xlfn._xlws.FILTER(A1:D17,C1:C17=K2)",
                                          NULL);
@endcode

As a syntactic shortcut you can use the `worksheet_write_dynamic_formula()`
function which only requires the start cell:

@code
    worksheet_write_dynamic_formula(worksheet, 1, 5,
                                    "=_xlfn._xlws.FILTER(A1:D17,C1:C17=K2)",
                                    NULL);
@endcode


@subsection ww_formulas_intersection Dynamic Arrays - The Implicit Intersection Operator "@"

The Implicit Intersection Operator, "@", is used by Excel 365 to indicate a
position in a formula that is implicitly returning a single value when a range
or an array could be returned.

We can see how this operator works in practice by considering the formula we
used in the last section: `=LEN(A1:A3)`. In Excel versions without support for
dynamic arrays, i.e. prior to Excel 365, this formula would operate on a
single value from the input range and return a single value, like the
following in Excel 2011:

@image html intersection01.png

There is an implicit conversion here of the range of input values, "A1:A3", to
a single value "A1". Since this was the default behavior of older versions of
Excel this conversion isn't highlighted in any way. But if you open the same
file in Excel 365 it will appear as follows:

@image html intersection02.png

The result of the formula is the same (this is important to note) and it still
operates on, and returns, a single value. However the formula now contains a
"@" operator to show that it is implicitly using a single value from the given
range.

Finally, if you entered this formula in Excel 365, or with
`worksheet_write_dynamic_array_formula()` in libxlsxwriter, it would operate
on the entire range and return an array of values:

@image html intersection03.png

If you are encountering the Implicit Intersection Operator "@" for the first
time then it is probably from a point of view of "why is Excel/libxlsxwriter
putting @s in my formulas". In practical terms if you encounter this operator,
and you don't intend it to be there, then you should probably write the
formula as a CSE or dynamic array function using
`worksheet_write_array_formula()` or `worksheet_write_dynamic_array_formula()`.


A full explanation of this operator is shown in the Microsoft documentation on
the [Implicit intersection operator: \@]
(https://support.microsoft.com/en-us/office/implicit-intersection-operator-ce3be07b-0101-4450-a24e-c1c999be2b34?ui=en-us&rs=en-us&ad=us>).

One important thing to note is that the "@" operator isn't stored with the
formula. It is just displayed by Excel 365 when reading "legacy"
formulas. However, it is possible to write it to a formula, if necessary,
using `_xlfn.SINGLE()`. The unusual cases where this may be necessary are
shown in the linked document in the previous paragraph.


@subsection ww_formulas_spill Dynamic Arrays - The Spilled Range Operator "#"

In the section above on @ref ww_formulas_intro we saw that dynamic array formulas
can return variable sized ranges of results. The Excel documentation refers to
this as a "Spilled" range/array from the idea that the results spill into the
required number of cells. This is explained in the Microsoft documentation on
[Dynamic array formulas and spilled array behavior]
(https://support.microsoft.com/en-us/office/dynamic-array-formulas-and-spilled-array-behavior-205c6b06-03ba-4151-89a1-87a7eb36e531).

Since a spilled range is variable in size a new operator is required to refer
to the range. This operator is the [Spilled range operator]
(https://support.microsoft.com/en-us/office/spilled-range-operator-3dd5899f-bca2-4b9d-a172-3eae9ac22efd)
and it is represented by "#". For example, the range `F2#` in the image
below is used to refer to a dynamic array returned by `UNIQUE()` in the cell
`F2`:

@image html spill01.png

Unfortunately, Excel doesn't store the formula like this and in libxlsxwriter
you need to use the explicit function `_xlfn.ANCHORARRAY()` to refer to a
spilled range. The example in the image above was generated using the
following:

@code
    // Same as '=COUNTA(F2#)' in Excel.
    worksheet_write_dynamic_formula(worksheet9, CELL("J2"),
                                    "=COUNTA(_xlfn.ANCHORARRAY(F2))",
                                    NULL);
@endcode


@subsection ww_formulas_lambda The Excel 365 LAMBDA() function

@note At the time of writing the `LAMBDA()` function in Excel is only
available to Excel 365 users subscribed to the Beta Channel updates.

Beta Channel versions of Excel 365 have introduced a powerful new
function/feature called `LAMBDA()`. This is similar to
[lambda expressions]
(https://docs.microsoft.com/en-us/cpp/cpp/lambda-expressions-in-cpp?view=msvc-160)
in C++ (and other languages).

Consider the following Excel example which converts the variable `temp` from Fahrenheit to Celsius:

    LAMBDA(temp, (5/9) * (temp-32))

This could be called in Excel with an argument:

    =LAMBDA(temp, (5/9) * (temp-32))(212)

Or assigned to a defined name and called as a user defined function:

    =ToCelsius(212)


    An libxlsxwriter example that replicates the described Excel functionality is
shown below:

@code
    // Write the lambda as a function.
    worksheet_write_dynamic_formula(worksheet, CELL("A2"),
                                    "=_xlfn.LAMBDA(_xlpm.temp, (5/9) * (_xlpm.temp-32))(32)",
                                    NULL);

    // Create the lambda function as a defined name and write it as a dynamic formula.
    workbook_define_name(workbook,
                         "ToCelsius",
                         "=_xlfn.LAMBDA(_xlpm.temp, (5/9) * (_xlpm.temp-32))");

    worksheet_write_dynamic_formula(worksheet, CELL("A3"), "=ToCelsius(212)", NULL);
@endcode

Note, that the formula name must have a "_xlfn." prefix and the parameters in
the `LAMBDA()` function must have a "_xlpm."  prefix for compatibility with
how the formulas are stored in Excel. These prefixes won't show up in the
formula, as shown in the image.

@image html lambda01.png

The `LET()` function is often used in conjunction with `LAMBDA()` to assign
names to calculation results.

@section ww_formulas_future Formulas added in Excel 2010 and later


Excel 2010 and later versions added functions which weren't defined in the
original file specification. These functions are referred to by Microsoft as
"Future Functions". Examples of these functions are `ACOT`, `CHISQ.DIST.RT` ,
`CONFIDENCE.NORM`, `STDEV.P`, `STDEV.S` and `WORKDAY.INTL`.

When written using `worksheet_write_formula()` these functions need to be
fully qualified with a `_xlfn.` (or other) prefix as they are shown the list
below. For example:

@code
    worksheet_write_formula(worksheet, 0, 0, "=_xlfn.STDEV.S(B1:B10)", NULL);
@endcode

They will appear without the prefix in Excel:

@image html working_with_formulas2.png

The following list is taken from
[MS XLSX extensions documentation on future functions](http://msdn.microsoft.com/en-us/library/dd907480%28v=office.12%29.aspx).


  | Future Functions                 |
  | -------------------------------- |
  | `_xlfn.ACOT`                     |
  | `_xlfn.ACOTH`                    |
  | `_xlfn.AGGREGATE`                |
  | `_xlfn.ARABIC`                   |
  | `_xlfn.BASE`                     |
  | `_xlfn.BETA.DIST`                |
  | `_xlfn.BETA.INV`                 |
  | `_xlfn.BINOM.DIST`               |
  | `_xlfn.BINOM.DIST.RANGE`         |
  | `_xlfn.BINOM.INV`                |
  | `_xlfn.BITAND`                   |
  | `_xlfn.BITLSHIFT`                |
  | `_xlfn.BITOR`                    |
  | `_xlfn.BITRSHIFT`                |
  | `_xlfn.BITXOR`                   |
  | `_xlfn.CEILING.MATH`             |
  | `_xlfn.CEILING.PRECISE`          |
  | `_xlfn.CHISQ.DIST`               |
  | `_xlfn.CHISQ.DIST.RT`            |
  | `_xlfn.CHISQ.INV`                |
  | `_xlfn.CHISQ.INV.RT`             |
  | `_xlfn.CHISQ.TEST`               |
  | `_xlfn.COMBINA`                  |
  | `_xlfn.CONCAT`                   |
  | `_xlfn.CONFIDENCE.NORM`          |
  | `_xlfn.CONFIDENCE.T`             |
  | `_xlfn.COT`                      |
  | `_xlfn.COTH`                     |
  | `_xlfn.COVARIANCE.P`             |
  | `_xlfn.COVARIANCE.S`             |
  | `_xlfn.CSC`                      |
  | `_xlfn.CSCH`                     |
  | `_xlfn.DAYS`                     |
  | `_xlfn.DECIMAL`                  |
  | `ECMA.CEILING`                   |
  | `_xlfn.ERF.PRECISE`              |
  | `_xlfn.ERFC.PRECISE`             |
  | `_xlfn.EXPON.DIST`               |
  | `_xlfn.F.DIST`                   |
  | `_xlfn.F.DIST.RT`                |
  | `_xlfn.F.INV`                    |
  | `_xlfn.F.INV.RT`                 |
  | `_xlfn.F.TEST`                   |
  | `_xlfn.FILTERXML`                |
  | `_xlfn.FLOOR.MATH`               |
  | `_xlfn.FLOOR.PRECISE`            |
  | `_xlfn.FORECAST.ETS`             |
  | `_xlfn.FORECAST.ETS.CONFINT`     |
  | `_xlfn.FORECAST.ETS.SEASONALITY` |
  | `_xlfn.FORECAST.ETS.STAT`        |
  | `_xlfn.FORECAST.LINEAR`          |
  | `_xlfn.FORMULATEXT`              |
  | `_xlfn.GAMMA`                    |
  | `_xlfn.GAMMA.DIST`               |
  | `_xlfn.GAMMA.INV`                |
  | `_xlfn.GAMMALN.PRECISE`          |
  | `_xlfn.GAUSS`                    |
  | `_xlfn.HYPGEOM.DIST`             |
  | `_xlfn.IFNA`                     |
  | `_xlfn.IFS`                      |
  | `_xlfn.IMCOSH`                   |
  | `_xlfn.IMCOT`                    |
  | `_xlfn.IMCSC`                    |
  | `_xlfn.IMCSCH`                   |
  | `_xlfn.IMSEC`                    |
  | `_xlfn.IMSECH`                   |
  | `_xlfn.IMSINH`                   |
  | `_xlfn.IMTAN`                    |
  | `_xlfn.ISFORMULA`                |
  | `ISO.CEILING`                    |
  | `_xlfn.ISOWEEKNUM`               |
  | `_xlfn.LOGNORM.DIST`             |
  | `_xlfn.LOGNORM.INV`              |
  | `_xlfn.MAXIFS`                   |
  | `_xlfn.MINIFS`                   |
  | `_xlfn.MODE.MULT`                |
  | `_xlfn.MODE.SNGL`                |
  | `_xlfn.MUNIT`                    |
  | `_xlfn.NEGBINOM.DIST`            |
  | `NETWORKDAYS.INTL`               |
  | `_xlfn.NORM.DIST`                |
  | `_xlfn.NORM.INV`                 |
  | `_xlfn.NORM.S.DIST`              |
  | `_xlfn.NORM.S.INV`               |
  | `_xlfn.NUMBERVALUE`              |
  | `_xlfn.PDURATION`                |
  | `_xlfn.PERCENTILE.EXC`           |
  | `_xlfn.PERCENTILE.INC`           |
  | `_xlfn.PERCENTRANK.EXC`          |
  | `_xlfn.PERCENTRANK.INC`          |
  | `_xlfn.PERMUTATIONA`             |
  | `_xlfn.PHI`                      |
  | `_xlfn.POISSON.DIST`             |
  | `_xlfn.QUARTILE.EXC`             |
  | `_xlfn.QUARTILE.INC`             |
  | `_xlfn.QUERYSTRING`              |
  | `_xlfn.RANK.AVG`                 |
  | `_xlfn.RANK.EQ`                  |
  | `_xlfn.RRI`                      |
  | `_xlfn.SEC`                      |
  | `_xlfn.SECH`                     |
  | `_xlfn.SHEET`                    |
  | `_xlfn.SHEETS`                   |
  | `_xlfn.SKEW.P`                   |
  | `_xlfn.STDEV.P`                  |
  | `_xlfn.STDEV.S`                  |
  | `_xlfn.SWITCH`                   |
  | `_xlfn.T.DIST`                   |
  | `_xlfn.T.DIST.2T`                |
  | `_xlfn.T.DIST.RT`                |
  | `_xlfn.T.INV`                    |
  | `_xlfn.T.INV.2T`                 |
  | `_xlfn.T.TEST`                   |
  | `_xlfn.TEXTJOIN`                 |
  | `_xlfn.UNICHAR`                  |
  | `_xlfn.UNICODE`                  |
  | `_xlfn.VAR.P`                    |
  | `_xlfn.VAR.S`                    |
  | `_xlfn.WEBSERVICE`               |
  | `_xlfn.WEIBULL.DIST`             |
  | `WORKDAY.INTL`                   |
  | `_xlfn.XOR`                      |
  | `_xlfn.Z.TEST`                   |


The dynamic array functions shown in the @ref ww_formulas_dynamic_arrays
section above are also future functions:


  | Dynamic Array Functions          |
  | -------------------------------- |
  | `_xlfn.ANCHORARRAY`              |
  | `_xlfn.LAMBDA`                   |
  | `_xlfn.RANDARRAY`                |
  | `_xlfn.SEQUENCE`                 |
  | `_xlfn.SINGLE`                   |
  | `_xlfn.SORTBY`                   |
  | `_xlfn.UNIQUE`                   |
  | `_xlfn.XLOOKUP`                  |
  | `_xlfn.XMATCH`                   |
  | `_xlfn._xlws.FILTER`             |
  | `_xlfn._xlws.SORT`               |


@section ww_formulas_errors Dealing with formula errors

If there is an error in the syntax of a formula it is usually displayed in
Excel as @c \#NAME?. Alternatively you may get a warning from Excel when the
file is loaded. If you encounter an error like this you can debug it as
follows:

1.  Ensure the formula is valid in Excel by copying and pasting it into a
    cell. Note, this should be done in Excel and @b not other applications
    such as OpenOffice or LibreOffice since they may have slightly different
    syntax.

2.  Ensure the formula is using comma separators instead of semi-colons, see
    @ref ww_formulas_non_us above.

3.  Ensure the formula is in English, see @ref ww_formulas_non_us above.

4.  Ensure that the formula doesn't contain an Excel 2010+ future function as
    listed above (@ref ww_formulas_future). If it does then ensure that the
    correct prefix is used.

5. If the function loads in Excel but appears with one or more ``@`` symbols
   added then it is probably an array function and should be written using
   `worksheet_write_array_formula()` or
   `worksheet_write_dynamic_array_formula()` (see the sections above on @ref
   ww_formulas_dynamic_arrays and @ref ww_formulas_intersection).


Finally if you have completed all the previous steps and still get a
@c \#NAME? error you can examine a valid Excel file to see what the correct
syntax should be. To do this you should create a valid formula in Excel and
save the file. You can then examine the XML in the unzipped file.

The following shows how to do that using Linux `unzip` and `libxml's
[xmllint](http://xmlsoft.org/xmllint.html) to format the XML for clarity:

    $ unzip myfile.xlsx -d myfile
    $ xmllint --format myfile/xl/worksheets/sheet1.xml | grep '</f>'

            <f>SUM(1, 2, 3)</f>


Next: @ref working_with_dates

*/
