# Excel Types Primer

This document is intended to focus on terminology and unusual behaviour of Excel itself (as opposed to XL4J) that a developer new to Excel might not find obvious.

## Document Structure

Excel documents are known as *Workbooks*. Workbooks are made up of one or more *Sheets* or *Worksheets*, which are the tabs you
can switch around at the bottom of each window. Each sheet is made up of a grid of *cells*. Each cell has a *reference* which can
be used to refer to it.

### Cell References

Cell references come in two flavours

- A1, where the column is denoted by letters and the row is denoted by a number e.g. D18.
- R1C1, where the reference refers to row and column by number e.g. R20C18. Excel uses the R1C1 format internally, and you can choose on the options to view all references in R1C1 format, although most users do not.

#### Reference behaviour when expanded

Excel has the ability to generalize a cell reference by dragging the corner of a highlighted cell. This will copy your cell reference and modify it. Typically, the reference will change relative to the source copy cell. So if we start out with

A | B | |
---|---|---|

1 | 123 | =A1 |

2 | 456 | |

3 | 789 |

and then we pull down the corner of B1 a few rows we’ll end up with

A | B | |
---|---|---|

1 | 123 | =A1 |

2 | 456 | =A2 |

3 | 789 | =A3 |

which is great. Except if we don’t want that behaviour. What if we want the reference to be anchored? In this case we use a dollar in the reference to anchor the reference to the cell:

A | B | |
---|---|---|

1 | 123 | =$A$1 |

2 | 456 | |

3 | 789 |

now becomes

A | B | |
---|---|---|

1 | 123 | =$A$1 |

2 | 456 | =$A$1 |

3 | 789 | =$A$1 |

Note that we can anchor one dimension and not the other, so $A1 will always refer to column A if it’s expanded horizontally, but its row will change relative to the original. Similarly, we can anchor the row: A$1 will always refer to row 1, but change the column relative the original. A useful keyboard shortcut is that F4 will cycle between the 4 different variants, which can save you a lot of re-typing.

Interestingly, in R1C1 format, relative references are expressed as R[*<offset>*]C[*<offset>*] where if either the R or C offset
is optional, so R[-1]C refers to the cell above the current cell. This can be more readable for complex sheets, so you might want to
use it sometimes; also, if you’re generating sheets, it can be simpler.

## Excel Cell Types

| Excel Type | Notes/Values |
|——————|————–|
| Number | All floating point, note that it’s not IEEE-compliant. In particular NaN -> #NUM!, Inf -> #NUM! and subnormals are truncated to 0. The range is 10^{307} <= abs(x) < 10^{308} |
| Boolean | TRUE or FALSE |
| String (Unicode) | 2^{15}-1 unicode characters (UTF-16?). Only displayed if value >= 32. |
| Errors | #NULL!, #DIV/0!, #VALUE!, #REF!, #NAME?, #NUM!, #N/A |
| Arrays | One and two dimensional array of mixed type objects. Literals are encoded using curly brackets row by row, with commas separating objects, with semi-colons separating rows. |

### Pseudotypes

Dates and times are represented just as numbers, specifically fractions of a day since the epoch (which is not the standard epoch). Their display is purely a formatting filter.

Percentages too are represented as numbers and their display is just a * 100 formatting filter. The % symbol is just a unary suffix operator that divides by 100.

Currency amounts are also just numbers with a label prefix or postfix - while it might technically be possible to determine the currency format applied to a cell via COM, in practice the format itself isn’t really comprehensive enough to reflect ISO currencies accurately so you will need to use a separate cell/column/row to hold currency information (e.g. there’s no visual indication to the user of a difference between a US Dollar and any other kind of Dollar).

## Input evaluation

When you input a value into a cell (by clicking and waiting or pressing F2) the value is evaluated in this chain:

- If string prefix (single quote) => String
- If prefixed with plus, minus or equals => Formula
- See if the value looks like a date, time, currency amount, percentage or number

For formulas, the process is then

- Evaluate function arguments from most nested outwards. Cell references and ranges are converted to values (unless the function in question expects a reference), which may then be converted to the expected data types if necessary. If a name is not identifiable as a function or defined name (named range or cell), then it will be replaced with #NAME? and the evaluation will fail.
- If the
*value has changed*, any dependent inputs will be recalculated. - Circular references are checked and cells may be resized.

## Type conversion at the Excel level

Conversions take place as operators are applied to values:

### The equals operator

Will convert any cell references into *values* before invoking functions and will only return one of the basic Excel types listed above

### Unary minus

Will convert a string representation of a number to a negated number representation, so double negation converts from String to Number. Booleans convert to 1 or 0, so an easy Boolean to Number conversion is achieved with double negation. Note that the unary plus operator does not have the same effect.

### Binary arithmetic operators (`+`

, `-`

, `*`

, `/`

, `^`

)

Will try to convert any values to Numbers. This includes strings in any recognised format, dates and times and percentages.

### Percentage operators (`%`

)

Highest precendence operator so binds tightly to the operand to its left. Will try and convert anything to a Number, so can be applied to dates, times and Booleans as well.

### String contatenation operator (`&`

)

Convert numbers to strings in a default number format unrelated to display format.

### Binary Boolean comparison operators (`=`

, `<`

, `>`

, `<=`

, `>=`

, `<>`

)

Acting on String the comparisons are *case insensitive*. Internally everything is converted to lower case before comparison. No other conversions are done for these operators. This means you can’t compare string and number representations and expect equality or reasonable comparisons.

### Binding to functions

Conversions also take place when binding to function parameters. Excel will try to convert to the expected type.

## Ranges and Arrays

### Ranges

Ranges are treated quite differently from arrays and can have some odd properties when evaluated in a scalar context.

. | A | B |
---|---|---|

1 | 2 | =$A$2:$A$5 |

2 | 4 | =$A$2:$A$5 |

3 | 8 | =$A$2:$A$5 |

4 | 16 | =$A$2:$A$5 |

5 | 32 | =$A$2:$A$5 |

yields the values

A | B | |
---|---|---|

1 | 2 | #VALUE! |

2 | 4 | 4 |

3 | 8 | 8 |

4 | 16 | 16 |

5 | 32 | 32 |

where each the range is converted into a scalar in a different way for each context using the *current* row/column relative to the range. Note that if the range does not overlap the current column, the result will be `#VALUE!`

### Arrays

Scalar operations on arrays are treated as matrix-style operations where each element is operated on separately. Note here that the formulas in B1:B5 are an array formula rather than multiple single formulas.

A | B | |
---|---|---|

1 | 2 | {=$A$2:$A$5} |

2 | 4 | {=$A$2:$A$5} |

3 | 8 | {=$A$2:$A$5} |

4 | 16 | {=$A$2:$A$5} |

5 | 32 | {=$A$2:$A$5} |

yields

A | B | |
---|---|---|

1 | 2 | 4 |

2 | 4 | 8 |

3 | 8 | 16 |

4 | 16 | 32 |

5 | 32 | #VALUE! |

### Explicit type conversions

There are a number of functions available to force type conversions

Function Name | Return Type | Number | String | Boolean | Error |
---|---|---|---|---|---|

N() | Number/Err | arg | 0 | 1/0 | arg |

T() | String/Err | ”” | arg | ”” | arg |

TEXT() | String/Err | String rep. of arg | convert to String and back, #VALUE! if fails | “TRUE” or “FALSE” | arg |

VALUE() | Number/Err | arg | convert to Number, #VALUE! if fails | #VALUE! | arg |