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*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/spec/primitive.html).*
# Specification: BQN primitives
Most primitives are specified by the BQN-based implementation in [reference.bqn](reference.bqn). This document specifies the basic functionality required by those definitions. Descriptions of other primitives are for informational purposes only.
## Arithmetic
Functions here are defined for atoms only; the reference implementations extend them to arrays.
BQN uses five arithmetic functions that are standard in mathematics. The precision of these operations should be specified by the number [type](types.md).
- Add `+`
- Negate `-` and Subtract `-` invert addition, with `-๐ฉ` equivalent to `0-๐ฉ` and `๐จ-๐ฉ` equivalent to `๐จ+-๐ฉ`
- Multiply `ร` generalizes repeated addition.
- Divide `รท` inverts multiplication, with `รท๐ฉ` equivalent to `1รท๐ฉ` and `๐จรท๐ฉ` equivalent to `๐จรรท๐ฉ`
- Power `โ` generalizes repeated multiplication, and Exponential `โ` is Power with Euler's number *e* as the base.
The three higher functions `ร`, `รท`, and `โ` apply to numbers and no other atomic types. `+` and `-` apply to numbers, and possibly also to characters, according to the rules of the affine character type:
- If one argument to `+` is the character with code point `c` and the other is a number `n` (in either order), then the result is the character with code point `c+n`.
- If the left argument to `-` is the character with code point `c` and the right is a number `n`, the result is the character with code point `c-n`.
- If both arguments to `-` are characters, the result is the difference of their respective code points.
In the first two cases, if the result would not be a valid Unicode code point, then an error results. The remaining cases of `+` and `-` (adding two characters; negating a character or subtracting it from a number) are not allowed.
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