# This PR introduces:
## Parsing arrays:
{1,2,3} and {1;2;3}
Note that array elements can be numbers, booleans and errors (#VALUE!)
## Evaluating arrays in the SUM function
=SUM({1,2,3}) works!
## Evaluating arithmetic operation with arrays
=SUM({1,2,3} * 8) or =SUM({1,2,3}+{2,4,5}) works
This is done with just one function (handle_arithmetic) for most operations
## Some mathematical functions implement arrays
=SUM(SIN({1,2,3})) works
This is done with macros. See fn_single_number
So that implementing new functions that supports array are easy
# Not done in this PR
## Most functions are not supporting arrays
When that happens we either through #N/IMPL! (not implemented error)
or do implicit intersection. Some functions will be rather trivial to "arraify" some will be hard
## The final result in a cell cannot be an array
The formula ={1,2,3} in a cell will result in #N/IMPL!
## Exporting arrays to Excel might not work correctly
Excel uses the cm (cell metadata) for formulas that contain dynamic arrays.
Although the present PR does not introduce dynamic arrays some formulas like =SUM(SIN({1,2,3}))
is considered a dynamic formula
## There are not a lot of tests in this delivery
The bulk of the tests will be added once we start going function by function# This PR introduces:
## Parsing arrays:
{1,2,3} and {1;2;3}
Note that array elements can be numbers, booleans and errors (#VALUE!)
## Evaluating arrays in the SUM function
=SUM({1,2,3}) works!
## Evaluating arithmetic operation with arrays
=SUM({1,2,3} * 8) or =SUM({1,2,3}+{2,4,5}) works
This is done with just one function (handle_arithmetic) for most operations
## Some mathematical functions implement arrays
=SUM(SIN({1,2,3})) works
This is done with macros. See fn_single_number
So that implementing new functions that supports array are easy
# Not done in this PR
## Most functions are not supporting arrays
When that happens we either through #N/IMPL! (not implemented error)
or do implicit intersection. Some functions will be rather trivial to "arraify" some will be hard
## The final result in a cell cannot be an array
The formula ={1,2,3} in a cell will result in #N/IMPL!
## Exporting arrays to Excel might not work correctly
Excel uses the cm (cell metadata) for formulas that contain dynamic arrays.
Although the present PR does not introduce dynamic arrays some formulas like =SUM(SIN({1,2,3}))
is considered a dynamic formula
## There are not a lot of tests in this delivery
The bulk of the tests will be added once we start going function by function
## The array parsing does not respect the locale
Locales that use ',' as a decimal separator need to use something different for arrays
## The might introduce a small performance penalty
We haven't been benchmarking, and having closures for every arithmetic operation and every function
evaluation will introduce a performance hit. Fixing that in he future is not so hard writing tailored
code for the operation
The II operator takes a range and returns a single cell that is in the same column or the same row
as the present cell.
This is needed for backwards compatibility with old Excel models and as a first step towards dynamic arrays.
In the past Excel would evaluate `=A1:A10` in cell `C3` as `A3`, but today in results in an array containing all
values in the range. To be compatible with old workbooks Excel inserts the II operator
on those cases.
So this PR performs an static analysis on all formulas inserting on import automatically the II operator
where necessary. This we call the _automatic implicit operator_. When exporting to Excel the operator is striped away.
You can also manually use the II. For instance `=SUM(@A1:A10)` in cell `C3`.
This was not possible before and such a formula would break backwards compatibility with Excel. To Excel that "non automatic"
form of the II is exported as `_xlfn.SINGLE()`.
Th static analysis has to be done for all arithmetic operations and all functions.
This is a bit of a daunting task and it is not done fully in this PR. We also need to implement arrays and dynamic arrays.
My believe is that once the core operations have been implemented we can go formula by formula writing proper tests and documentation.
After this PR formulas like `=A1:A10` for instance will return `#N/IMPL!` instead of performing the implicit intersection
The way these functions interpret their arguments is inconsistent with
Excel in a few ways:
- EmptyCell: Excel ignores arguments evaluating to these types of
values, treating them as if they didn't exist.
- Text: Text cells are ignored unless they are "TRUE" or "FALSE" (case
insensitive). EXCEPT if the string value comes from a reference, in
which case it is always ignored regardless of its value.
- Error if no args: Excel returns a #VALUE! error for these functions if
no arguments are provided, or if all arguments are ignored (see
above).
- EmptyArg: Bizarrely, Unlike EmptyCell, EmptyArg is not ignored and is
treated as if it were FALSE by Excel.
- ErrorPropagation: Excel propagates errors in the arguments and in
cells belonging to any Range arguments.
Additionally, these functions are not consistent with each other, XOR,
OR, AND vary in how they handle the cases mentioned above.
Rectify these consistency issues by re-implementing them all in terms of
a single base function which is more consistent with Excel behavior.
