> For the complete documentation index, see [llms.txt](https://docs.reflexer.finance/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.reflexer.finance/pyflex/numerics.md).

# Numerics

`GEB` uses different numbers representing various levels of precision.

| Type  | Precision |
| ----- | --------- |
| `Wad` | 1E-18     |
| `Ray` | 1E-27     |
| `Rad` | 1E-45     |

You can import them from pyflex:

```python
>>> from pyflex.numeric import Wad, Ray, Rad
```

Converting `Wad`, `Ray`, `Rad` to a `str` shows the numbers in a friendly format:

```python
>>> Wad.from_number(1.2)
Wad(1200000000000000000)
>>> str(Wad.from_number(1.2))
'1.200000000000000000'
```

{% hint style="warning" %}
Constructors will add a specific precision to a number  eg. `Wad(1)` is not equal to `1` but to 10^18.
{% endhint %}

```python
>>> Wad(10) == Wad.from_number(10)
False
>>> Wad(10) == Wad.from_number(10 * 1E-18)
True
```

### Operations: Addition, Subtraction, Division

`Wad`, `Ray`, and `Rad` can only perform addition, subtraction and division with another `Wad`, `Ray`, or `Rad`

```python
>>> Rad(10) + Wad(10)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/georgekellerman/reflexer/pyflex/lib/python3.8/site-packages/pyflex/numeric.py", line 320, in __add__
    raise ArithmeticError
ArithmeticError
>>> Ray(10) - Ray(5)
Ray(5)
>>> Rad(10) / Rad.from_number(2)
Rad(5)
>>> 

```

### Operations: Multiplication

`Wad`, `Ray`, and `Rad`  can be multiplied by any `Wad`, `Ray`, and `Rad`  and `int`.

The result is the type of the first number:

```python
>>> x = Wad.from_number(1.2) * Rad.from_number(1)
>>> type(x)
<class 'pyflex.numeric.Wad'>
>>> y = Rad.from_number(1) * Wad.from_number(1.2)
>>> type(y)
<class 'pyflex.numeric.Rad'>
```

### Conversion

`Wad`, `Ray`, and `Rad` all accept `Wad`, `Ray`, and `Rad` in the constructors. This is the canonical way to convert  numbers:

```python
>>> Rad(Wad(10))
Rad(10000000000000000000000000000)
```

{% hint style="warning" %}
During conversion (`Rad` to `Ray`/`Wad` or `Ray` to `Wad`) you may lose precision!
{% endhint %}

```python
>>> Wad(Rad(10))
Wad(0)
>>> Ray(Rad(20))
Ray(0)
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.reflexer.finance/pyflex/numerics.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.