Chapter 12: Floats

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>

3 files changed, 199 insertions, 0 deletions

diff --git a/docs/chapter12/12-grammar.md b/docs/chapter12/12-grammar.md
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+# Grammar for Chapter 12
+
+```antlrv4
+grammar SimpleLanguage;
+
+program
+    : statement+ EOF
+    ;
+
+statement
+    : returnStatement
+    | structDeclaration
+    | declStatement
+    | blockStatment
+    | expressionStatement
+    | ifStatement
+    | whileStatement
+    | breakStatement
+    | continueStatment
+    | metaStatement
+    ;
+
+PRIMTYPE
+    : 'int'
+    | 'flt'
+    ;
+
+field
+    : PRIMTYPE IDENTIFIER ';'
+    ;
+
+fields
+    : field+
+    ;
+
+structDeclaration
+    : 'struct' IDENTIFIER '{' fields '}'
+    ;
+
+whileStatement
+    : 'while' '(' expression ')' statement
+    ;
+
+breakStatement
+    : 'break' ';'
+    ;
+
+continueStatement
+    : 'continue' ';'
+    ;
+
+ifStatement
+    : 'if' '(' expression ')' statement ('else' statement)?
+    ;
+
+metaStatement
+    : '#showGraph' ';'
+    ;
+
+expressionStatement
+    : IDENTIFIER '=' expression ';'
+    | fieldExpression '=' expression ';'
+    ;
+
+blockStatement
+    : '{' statement+ '}'
+    ;
+
+structName
+    : IDENTIFIER
+    ;
+
+declStatement
+    : PRIMTYPE IDENTIFIER '=' expression ';'
+    | structName ('?')? IDENTIFIER '=' expression ';'
+    ;
+
+returnStatement
+    : 'return' expression ';'
+    ;
+
+expression
+    : comparisonExpression
+    ;
+
+comparisonExpression
+    : additiveExpression (('==' | '!='| '>'| '<'| '>='| '<=') additiveExpression)*
+    ;
+
+additiveExpression
+    : multiplicativeExpression (('+' | '-') multiplicativeExpression)*
+    ;
+
+multiplicativeExpression
+    : unaryExpression (('*' | '/') unaryExpression)*
+    ;
+
+unaryExpression
+    : ('-') unaryExpression
+    | '!' unaryExpression
+    | primaryExpression
+    ;
+
+newExpression
+    : 'new' IDENTIFIER
+    ;
+
+fieldExpression
+    : primaryExpresson '.' IDENTIFIER
+    ;
+
+primaryExpression
+    : IDENTIFIER
+    | INTEGER_LITERAL
+    | 'true'
+    | 'false'
+    | 'null'
+    | newExpression
+    | '(' expression ')'
+    | fieldExpression
+    ;
+
+INTEGER_LITERAL
+    : [1-9][0-9]*
+    | [0]
+    ;
+
+IDENTIFIER
+    : NON_DIGIT (NON_DIGIT | DIGIT)*
+    ;
+
+NON_DIGIT: [a-zA-Z_];
+DEC_DIGIT: [0-9];
+```
diff --git a/docs/chapter12/Makefile b/docs/chapter12/Makefile
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--- /dev/null
+++ b/docs/chapter12/Makefile
@@ -0,0 +1,12 @@
+GV := $(wildcard *.gv)
+SVG := $(patsubst %.gv,%.svg,$(GV))
+
+.PHONY: all
+all: $(SVG)
+
+%.svg: %.gv
+	dot -Tsvg $< > $@
+
+.PHONY: clean
+clean:
+	@rm -f $(SVG)
diff --git a/docs/chapter12/README.md b/docs/chapter12/README.md
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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
+
+