Chapter 12: Floatslinear-chapter12

Co-authored-by: Dibyendu Majumdar <mobile@majumdar.org.uk>
Co-authored-by: Thalia Archibald <thalia@archibald.dev>
Co-authored-by: XmiliaH <45106915+XmiliaH@users.noreply.github.com>
Co-authored-by: Robert Obkircher <robert.obkircher@gmail.com>

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+# Chapter 12: 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 to 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 |
+
+And their own section in the Type lattice:
+
+Within the Type Lattice, we now add the following domain:
+
+* Float type - Float values.  The same shape as the Integer values, but floats
+  with a TOP, BOT and constants
+
+