ocaml: phase 6 Float module: sqrt/sin/cos/pow/floor/ceil/round/pi (+6 tests, 378 total)

Wraps host SX math primitives via _float_* builtins. Float.pi is a
Float literal in the OCaml-side module.

lib/ocaml/eval.sx

@@ -67,6 +67,14 @@
       (list "print_string"  (fn (s) (begin (print s) nil)))
       (list "print_endline" (fn (s) (begin (println s) nil)))
       (list "print_int"     (fn (i) (begin (print (str i)) nil)))
+      ;; Float math primitives.
+      (list "_float_sqrt" (fn (x) (sqrt x)))
+      (list "_float_sin"  (fn (x) (sin x)))
+      (list "_float_cos"  (fn (x) (cos x)))
+      (list "_float_pow"  (fn (a) (fn (b) (pow a b))))
+      (list "_float_floor" (fn (x) (floor x)))
+      (list "_float_ceil"  (fn (x) (ceil x)))
+      (list "_float_round" (fn (x) (round x)))
       ;; Polymorphic compare — returns negative / 0 / positive like
       ;; OCaml's Stdlib.compare. Defers to host SX `<` and `>`.
       (list "compare"

lib/ocaml/runtime.sx

@@ -316,6 +316,14 @@
 
    module Float = struct
      let to_string f = _string_of_float f
+     let sqrt f = _float_sqrt f
+     let sin f = _float_sin f
+     let cos f = _float_cos f
+     let pow a b = _float_pow a b
+     let floor f = _float_floor f
+     let ceil f = _float_ceil f
+     let round f = _float_round f
+     let pi = 3.141592653589793
    end ;;
 
    module Printf = struct

lib/ocaml/test.sh

@@ -922,6 +922,20 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 2304)
 (eval "(ocaml-type-of \"fun x y -> x +. y\")")
 
+;; ── Float module ───────────────────────────────────────────────
+(epoch 2400)
+(eval "(ocaml-run \"Float.sqrt 16.0\")")
+(epoch 2401)
+(eval "(ocaml-run \"Float.sin 0.0\")")
+(epoch 2402)
+(eval "(ocaml-run \"Float.cos 0.0\")")
+(epoch 2403)
+(eval "(ocaml-run \"Float.pow 2.0 10.0\")")
+(epoch 2404)
+(eval "(ocaml-run \"Float.floor 3.7\")")
+(epoch 2405)
+(eval "(ocaml-run \"Float.ceil 3.2\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 180 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -1458,6 +1472,14 @@ check 2302 "10.0 /. 4.0"                  '2.5'
 check 2303 "type 1.5 +. 2.5"              '"Float"'
 check 2304 "type fun x y -> x +. y"       '"Float -> Float -> Float"'
 
+# ── Float module ────────────────────────────────────────────────
+check 2400 "Float.sqrt 16"                '4'
+check 2401 "Float.sin 0"                  '0'
+check 2402 "Float.cos 0"                  '1'
+check 2403 "Float.pow 2 10"               '1024'
+check 2404 "Float.floor 3.7"              '3'
+check 2405 "Float.ceil 3.2"               '4'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -266,7 +266,8 @@ SX CEK evaluator (both JS and OCaml hosts)
       _(Pending: escaped.)_
 - [~] `Int`: `to_string`, `of_string`, `abs`, `max`, `min`.
       _(Pending: arithmetic helpers, min_int/max_int.)_
-- [~] `Float`: `to_string`. _(Pending: of_string, arithmetic helpers.)_
+- [~] `Float`: `to_string`, `sqrt`, `sin`, `cos`, `pow`, `floor`,
+      `ceil`, `round`, `pi`. _(Pending: of_string.)_
 - [~] `Printf`: stub `sprintf`/`printf`. _(Real format-string
       interpretation pending.)_
 - [ ] `String`: `length`, `get`, `sub`, `concat`, `split_on_char`, `trim`,
@@ -373,6 +374,9 @@ the "mother tongue" closure: OCaml → SX → OCaml. This means:
 
 _Newest first._
 
+- 2026-05-08 Phase 6 — Float module: sqrt/sin/cos/pow/floor/ceil/round
+  + pi constant (+6 tests, 378 total). Wraps host SX math primitives
+  via `_float_*` builtins.
 - 2026-05-08 Phase 1+5+6 — Float arithmetic (`+.` `-.` `*.` `/.`)
   (+5 tests, 372 total). Tokenizer recognises the dotted operators.
   Parser table places them at int's level (7 / 8). Eval routes them