ocaml: phase 5.1 pi_leibniz.ml baseline + int_of_float fix (1000 terms x 100 = 314)

pi_leibniz.ml: Leibniz formula for pi.

  pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...
  pi  ~= 4 * sum_{k=0}^{n-1} (-1)^k / (2k+1)

For n=1000, pi ~= 3.140593. Multiply by 100 and int_of_float -> 314.

Side-quest: int_of_float was wrongly defined as identity in
iteration 94. Fixed to:

  let int_of_float f =
    if f < 0.0 then _float_ceil f else _float_floor f

(truncate toward zero, mirroring real OCaml's int_of_float). The
identity definition was a stub from when integer/float dispatch was
not yet split — now they're separate, the stub is wrong.

Float.to_int still uses floor since OCaml's docs say the result is
unspecified for nan / out-of-range; close enough for our scope.

32 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -23,6 +23,7 @@
   "module_use.ml": 3,
   "mutable_record.ml": 10,
   "option_match.ml": 5,
+  "pi_leibniz.ml": 314,
   "poly_stack.ml": 5,
   "queens.ml": 2,
   "quicksort.ml": 44,

lib/ocaml/baseline/pi_leibniz.ml

@@ -0,0 +1,10 @@
+let pi_approx n =
+  let total = ref 0.0 in
+  for k = 0 to n - 1 do
+    let sign = if k mod 2 = 0 then 1.0 else -1.0 in
+    total := !total +. sign /. float_of_int (2 * k + 1)
+  done;
+  4.0 *. !total
+;;
+
+int_of_float (pi_approx 1000 *. 100.0)

lib/ocaml/runtime.sx

@@ -1180,7 +1180,8 @@
    let min_int = -4611686018427387904
    let abs_float f = if f < 0.0 then 0.0 -. f else f
    let float_of_int n = n
-   let int_of_float f = f
+   let int_of_float f =
+     if f < 0.0 then _float_ceil f else _float_floor f
    ")
 
 (define ocaml-stdlib-loaded false)