floats iter 4.4: codegen neg/int_to_float/float_to_int_truncate/is_nan + float_to_str-deferred

crates/ail/tests/snapshots/hello.ll

@@ -8,6 +8,7 @@ declare i32 @printf(ptr, ...)
 declare i32 @puts(ptr)
 declare ptr @GC_malloc(i64)
 declare i32 @strcmp(ptr, ptr)
+declare i64 @llvm.fptosi.sat.i64.f64(double)
 
 @ail_hello_main_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_hello_main_adapter, ptr null }
 define i8 @ail_hello_main() {

crates/ail/tests/snapshots/list.ll

@@ -8,6 +8,7 @@ declare i32 @printf(ptr, ...)
 declare i32 @puts(ptr)
 declare ptr @GC_malloc(i64)
 declare i32 @strcmp(ptr, ptr)
+declare i64 @llvm.fptosi.sat.i64.f64(double)
 
 @ail_list_sum_list_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_list_sum_list_adapter, ptr null }
 @ail_list_main_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_list_main_adapter, ptr null }

crates/ail/tests/snapshots/max3.ll

@@ -8,6 +8,7 @@ declare i32 @printf(ptr, ...)
 declare i32 @puts(ptr)
 declare ptr @GC_malloc(i64)
 declare i32 @strcmp(ptr, ptr)
+declare i64 @llvm.fptosi.sat.i64.f64(double)
 
 @ail_max3_max_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_max3_max_adapter, ptr null }
 @ail_max3_max3_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_max3_max3_adapter, ptr null }

crates/ail/tests/snapshots/sum.ll

@@ -8,6 +8,7 @@ declare i32 @printf(ptr, ...)
 declare i32 @puts(ptr)
 declare ptr @GC_malloc(i64)
 declare i32 @strcmp(ptr, ptr)
+declare i64 @llvm.fptosi.sat.i64.f64(double)
 
 @ail_sum_sum_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_sum_sum_adapter, ptr null }
 @ail_sum_main_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_sum_main_adapter, ptr null }

crates/ail/tests/snapshots/ws_main.ll

@@ -8,6 +8,7 @@ declare i32 @printf(ptr, ...)
 declare i32 @puts(ptr)
 declare ptr @GC_malloc(i64)
 declare i32 @strcmp(ptr, ptr)
+declare i64 @llvm.fptosi.sat.i64.f64(double)
 
 @ail_ws_lib_add_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_ws_lib_add_adapter, ptr null }
 @ail_ws_main_main_clos = private unnamed_addr constant { ptr, ptr } { ptr @ail_ws_main_main_adapter, ptr null }

crates/ailang-codegen/src/lib.rs

@@ -472,7 +472,13 @@ fn lower_workspace_inner(ws: &Workspace, alloc: AllocStrategy) -> Result<String>
     // Iter 16e: `==` on `Str` lowers to `@strcmp` followed by
     // `icmp eq i32 0`. NUL-terminated strings make this a one-liner;
     // libc supplies `strcmp` so no extra link flag is needed.
-    out.push_str("declare i32 @strcmp(ptr, ptr)\n\n");
+    out.push_str("declare i32 @strcmp(ptr, ptr)\n");
+    // Floats iter 4.4: saturating fp-to-int intrinsic for
+    // float_to_int_truncate. NaN → 0, +Inf → i64::MAX, -Inf →
+    // i64::MIN, finite-out-of-range saturates, finite-in-range
+    // truncates toward zero. LLVM 12+, always available with
+    // clang 22.
+    out.push_str("declare i64 @llvm.fptosi.sat.i64.f64(double)\n\n");
     out.push_str(&header);
     out.push_str(&body);
 
@@ -1789,6 +1795,73 @@ impl<'a> Emitter<'a> {
             return Ok((dst, "i1".into()));
         }
 
+        // Floats iter 4.4: polymorphic neg + 3 monomorphic fn builtins.
+        if name == "neg" {
+            if args.len() != 1 {
+                return Err(CodegenError::Internal("neg arity".into()));
+            }
+            let arg_ty = self.synth_arg_type(&args[0])?;
+            let (a, _) = self.lower_term(&args[0])?;
+            let dst = self.fresh_ssa();
+            match &arg_ty {
+                Type::Con { name, .. } if name == "Int" => {
+                    self.body.push_str(&format!("  {dst} = sub i64 0, {a}\n"));
+                    return Ok((dst, "i64".into()));
+                }
+                Type::Con { name, .. } if name == "Float" => {
+                    // LLVM 8+ `fneg` correctly handles -0.0.
+                    self.body.push_str(&format!("  {dst} = fneg double {a}\n"));
+                    return Ok((dst, "double".into()));
+                }
+                other => return Err(CodegenError::Internal(format!(
+                    "`neg` not supported for type `{}`",
+                    ailang_core::pretty::type_to_string(other)
+                ))),
+            }
+        }
+        if name == "int_to_float" {
+            if args.len() != 1 {
+                return Err(CodegenError::Internal("int_to_float arity".into()));
+            }
+            let (a, _) = self.lower_term(&args[0])?;
+            let dst = self.fresh_ssa();
+            self.body.push_str(&format!("  {dst} = sitofp i64 {a} to double\n"));
+            return Ok((dst, "double".into()));
+        }
+        if name == "float_to_int_truncate" {
+            if args.len() != 1 {
+                return Err(CodegenError::Internal("float_to_int_truncate arity".into()));
+            }
+            let (a, _) = self.lower_term(&args[0])?;
+            let dst = self.fresh_ssa();
+            self.body.push_str(&format!(
+                "  {dst} = call i64 @llvm.fptosi.sat.i64.f64(double {a})\n"
+            ));
+            return Ok((dst, "i64".into()));
+        }
+        if name == "is_nan" {
+            if args.len() != 1 {
+                return Err(CodegenError::Internal("is_nan arity".into()));
+            }
+            let (a, _) = self.lower_term(&args[0])?;
+            let dst = self.fresh_ssa();
+            // `fcmp uno x, x` returns `i1 1` iff `x` is NaN — only
+            // NaN compares unordered against itself.
+            self.body.push_str(&format!("  {dst} = fcmp uno double {a}, {a}\n"));
+            return Ok((dst, "i1".into()));
+        }
+        if name == "float_to_str" {
+            // Deferred to iter 5+: needs runtime-allocated Str
+            // (currently the codegen Str path uses only static
+            // `@.str_*` globals; no malloc-backed dynamic-Str
+            // infrastructure). The typecheck path in iter 3
+            // installs `float_to_str : (Float) -> Str`; until the
+            // runtime gets a Str allocator, calling it crashes
+            // codegen. This is intentional: don't ship an
+            // unimplemented call to the LLM-author surface.
+            unimplemented!("Floats milestone iter 5+: float_to_str needs dynamic Str allocation");
+        }
+
         // Cross-module call: exactly one dot in the name → resolve via import map.
         // Logic identical to the typechecker (see `synth` for `Term::Var`).
         if name.matches('.').count() == 1 {
@@ -2101,6 +2174,15 @@ impl<'a> Emitter<'a> {
         if is_arithmetic_or_comparison_op(name) || name == "==" || name == "not" {
             return true;
         }
+        // Floats iter 4.4: new fn-builtins (`neg`, `int_to_float`,
+        // `float_to_int_truncate`, `is_nan`, `float_to_str`) lower
+        // inline in `lower_app`, parallel to the operator path.
+        if matches!(
+            name,
+            "neg" | "int_to_float" | "float_to_int_truncate" | "is_nan" | "float_to_str"
+        ) {
+            return true;
+        }
         if name.matches('.').count() == 1 {
             return true;
         }
@@ -3076,4 +3158,56 @@ mod tests {
         assert!(ir.contains("icmp ne i64"), "Int `!=` regressed: {ir}");
         assert!(ir.contains("icmp eq i64"), "Int `==` regressed: {ir}");
     }
+
+    /// Floats iter 4.4 RED: four new fn-builtins lower to the spec'd
+    /// LLVM ops. `neg` polymorphic dispatches to `sub i64 0, %x` for
+    /// Int and `fneg double %x` for Float (NOT `fsub 0.0, %x`, which
+    /// is wrong for `-0.0`). `int_to_float` → `sitofp`. `is_nan` →
+    /// `fcmp uno double %x, %x`. `float_to_int_truncate` →
+    /// `@llvm.fptosi.sat.i64.f64` intrinsic call.
+    #[test]
+    fn lowers_float_fn_builtins() {
+        use ailang_core::ast::*;
+        fn fn_def(name: &str, body: Term, ret_ty: Type) -> Def {
+            Def::Fn(FnDef {
+                name: name.into(),
+                ty: Type::Fn {
+                    params: vec![], ret: Box::new(ret_ty), effects: vec![],
+                    param_modes: vec![], ret_mode: ParamMode::Implicit,
+                },
+                params: vec![], body, suppress: vec![], doc: None,
+            })
+        }
+        fn app1(callee: &str, arg: Term) -> Term {
+            Term::App {
+                callee: Box::new(Term::Var { name: callee.into() }),
+                args: vec![arg], tail: false,
+            }
+        }
+        let neg_int = app1("neg", Term::Lit { lit: Literal::Int { value: 5 } });
+        let neg_float = app1("neg", Term::Lit { lit: Literal::Float { bits: 0x3ff8_0000_0000_0000u64 } });
+        let i2f = app1("int_to_float", Term::Lit { lit: Literal::Int { value: 5 } });
+        let f2i = app1("float_to_int_truncate", Term::Lit { lit: Literal::Float { bits: 0x3ff8_0000_0000_0000u64 } });
+        let isnan = app1("is_nan", Term::Lit { lit: Literal::Float { bits: 0x3ff8_0000_0000_0000u64 } });
+        let main_def = fn_def("main", Term::Lit { lit: Literal::Unit }, Type::unit());
+        let m = Module {
+            schema: ailang_core::SCHEMA.to_string(),
+            name: "t".into(),
+            imports: vec![],
+            defs: vec![
+                fn_def("ni", neg_int, Type::int()),
+                fn_def("nf", neg_float, Type::float()),
+                fn_def("c1", i2f, Type::float()),
+                fn_def("c2", f2i, Type::int()),
+                fn_def("isn", isnan, Type::bool_()),
+                main_def,
+            ],
+        };
+        let ir = emit_ir(&m).unwrap();
+        assert!(ir.contains("sub i64 0,"), "neg Int missing: {ir}");
+        assert!(ir.contains("fneg double"), "neg Float missing (must use fneg, not fsub-from-zero): {ir}");
+        assert!(ir.contains("sitofp i64"), "int_to_float missing: {ir}");
+        assert!(ir.contains("@llvm.fptosi.sat.i64.f64"), "float_to_int_truncate intrinsic missing: {ir}");
+        assert!(ir.contains("fcmp uno double"), "is_nan missing (must be fcmp uno x, x): {ir}");
+    }
 }