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# Chapter 12: Floats
[Previous: Chapter 11](../chapter11/README.md) |
[Next: Chapter 13](../chapter13/README.md)
# Table of Contents
1. [Float](#floats)
In this chapter, we add a floating point type and values.
You can also read [this chapter](https://github.com/SeaOfNodes/Simple/tree/linear-chapter12) in a linear Git revision history on the [linear](https://github.com/SeaOfNodes/Simple/tree/linear) branch and [compare](https://github.com/SeaOfNodes/Simple/compare/linear-chapter11...linear-chapter12) it to the previous chapter.
## Floats
Floating point values start with the `flt` type and compute IEEE754 64-bit arithmetic.
Integer expressions auto-widen to floats when involved in a float expression.
```java
flt f = 0.5;
int x = 2;
f = f+x; // Auto-widen x to 2.0, result is 2.5
f = f+true; // Since bools are just synonyms for integers 0,1 they auto-widen also
```
There is no corresponding way right now to round a `flt` back to an `int`:
```java
int x = 3.14; // error
```
Here is Newton's method for computing a square root:
```java
flt guess = arg; // Initial guess is just argument
while( true ) {
// Next guess from Newton's method
flt next = (arg/guess + guess)/2;
// Break if hit fixed point
if( next == guess ) break;
guess = next;
}
return guess;
```
When run with argument 2.0, produces 1.414213562373095.
Floating point operations have their own Nodes:
| Node | Op |
|------------------------|----------------------|
| AddF, SubF, MulF, DivF | Basic binary FP ops |
| MinusF | Unary negate |
| EQF, LTF, LEF | FP compare operators |
Within the Type lattice, we add the following domain:
*  - Float values. The same shape as the Integer values, but floats
with a top (`TOP`, ⊤), bottom (`BOT`, ⊥), and constants.
The other domains retain Chapter 10b's named structs, nullable pointers, and
precise memory aliases.
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