feat: add Math.sin, Math.cos, Math.atan2 trig functions

Adds trigonometric functions to the Math module across interpreter,
type system, and C backend. JS backend already supported them.
Also adds #include <math.h> to C preamble and handles Math module
calls through both Call and EffectOp paths in C backend.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/codegen/c_backend.rs

@@ -858,6 +858,7 @@ impl CBackend {
         self.writeln("#include <stdio.h>");
         self.writeln("#include <stdlib.h>");
         self.writeln("#include <string.h>");
+        self.writeln("#include <math.h>");
         self.writeln("");
         self.writeln("// === Lux Runtime Types ===");
         self.writeln("");
@@ -3029,6 +3030,10 @@ impl CBackend {
                             self.register_rc_var(&temp, "LuxString");
                             return Ok(temp);
                         }
+                        // Math module
+                        if module_name.name == "Math" {
+                            return self.emit_math_operation(&field.name, args);
+                        }
                         // Check for user-defined module function
                         let key = (module_name.name.clone(), field.name.clone());
                         if let Some(c_name) = self.module_functions.get(&key).cloned() {
@@ -3392,6 +3397,11 @@ impl CBackend {
                     }
                 }
 
+                // Math module (treated as effect by parser but handled as direct C calls)
+                if effect.name == "Math" {
+                    return self.emit_math_operation(&operation.name, args);
+                }
+
                 // Built-in Console effect
                 if effect.name == "Console" {
                     if operation.name == "print" {
@@ -3854,12 +3864,34 @@ impl CBackend {
                 }
             }
 
-            Expr::Record { fields, .. } => {
-                let field_strs: Result<Vec<_>, _> = fields.iter().map(|(name, val)| {
-                    let v = self.emit_expr(val)?;
-                    Ok(format!(".{} = {}", name.name, v))
-                }).collect();
-                Ok(format!("{{ {} }}", field_strs?.join(", ")))
+            Expr::Record {
+                spread, fields, ..
+            } => {
+                if let Some(spread_expr) = spread {
+                    // Evaluate spread source, then override fields
+                    let base = self.emit_expr(spread_expr)?;
+                    if fields.is_empty() {
+                        Ok(base)
+                    } else {
+                        // Copy spread into a temp, then override fields
+                        let temp = format!("_spread_{}", self.fresh_name());
+                        self.writeln(&format!("__auto_type {} = {};", temp, base));
+                        for (name, val) in fields {
+                            let v = self.emit_expr(val)?;
+                            self.writeln(&format!("{}.{} = {};", temp, name.name, v));
+                        }
+                        Ok(temp)
+                    }
+                } else {
+                    let field_strs: Result<Vec<_>, _> = fields
+                        .iter()
+                        .map(|(name, val)| {
+                            let v = self.emit_expr(val)?;
+                            Ok(format!(".{} = {}", name.name, v))
+                        })
+                        .collect();
+                    Ok(format!("{{ {} }}", field_strs?.join(", ")))
+                }
             }
 
             Expr::Field { object, field, .. } => {
@@ -3929,6 +3961,64 @@ impl CBackend {
         }
     }
 
+    /// Emit code for Math module operations (Math.sin, Math.cos, etc.)
+    fn emit_math_operation(&mut self, op: &str, args: &[Expr]) -> Result<String, CGenError> {
+        match op {
+            "abs" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("fabs({})", x))
+            }
+            "min" => {
+                let a = self.emit_expr(&args[0])?;
+                let b = self.emit_expr(&args[1])?;
+                Ok(format!("fmin({}, {})", a, b))
+            }
+            "max" => {
+                let a = self.emit_expr(&args[0])?;
+                let b = self.emit_expr(&args[1])?;
+                Ok(format!("fmax({}, {})", a, b))
+            }
+            "sqrt" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("sqrt({})", x))
+            }
+            "pow" => {
+                let base = self.emit_expr(&args[0])?;
+                let exp = self.emit_expr(&args[1])?;
+                Ok(format!("pow({}, {})", base, exp))
+            }
+            "floor" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("(int64_t)floor({})", x))
+            }
+            "ceil" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("(int64_t)ceil({})", x))
+            }
+            "round" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("(int64_t)round({})", x))
+            }
+            "sin" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("sin({})", x))
+            }
+            "cos" => {
+                let x = self.emit_expr(&args[0])?;
+                Ok(format!("cos({})", x))
+            }
+            "atan2" => {
+                let y = self.emit_expr(&args[0])?;
+                let x = self.emit_expr(&args[1])?;
+                Ok(format!("atan2({}, {})", y, x))
+            }
+            _ => Err(CGenError {
+                message: format!("Math.{} not supported in C backend", op),
+                span: None,
+            }),
+        }
+    }
+
     /// Emit code for List module operations (List.map, List.filter, etc.)
     fn emit_list_operation(&mut self, op: &str, args: &[Expr]) -> Result<String, CGenError> {
         match op {
@@ -5831,7 +5921,10 @@ impl CBackend {
                 }
                 self.collect_free_vars(body, &inner_bound, free);
             }
-            Expr::Record { fields, .. } => {
+            Expr::Record { spread, fields, .. } => {
+                if let Some(spread_expr) = spread {
+                    self.collect_free_vars(spread_expr, bound, free);
+                }
                 for (_, val) in fields {
                     self.collect_free_vars(val, bound, free);
                 }