/-- info: 2.100000 -/
#guard_msgs in
#eval (2.1 : Float32)

/-- info: 3.200000 -/
#guard_msgs in
#eval (2.1 : Float32) + 1.1

/-- info: 0.900000 -/
#guard_msgs in
#eval (2.1 : Float32) - 1.2

def test1 : IO Unit := do
  IO.println ((2 : Float32).sin);
  IO.println ((2 : Float32).cos);
  IO.println ((2 : Float32).sqrt);
  IO.println ((2 : Float32) ^ (100 : Float32));

/--
info: 0.909297
-0.416147
1.414214
1267650600228229401496703205376.000000
-/
#guard_msgs in
#eval test1

/-- info: 0.909297 -/
#guard_msgs in
#eval (2 : Float32).sin.toFloat

/-- info: 0.909297 -/
#guard_msgs in
#eval (2 : Float).sin.toFloat32

/-- info: 1606938044258990275541962092341162602522202993782792835301376.000000 -/
#guard_msgs in
#eval (2 : Float32).toFloat ^ (200 : Float32).toFloat

#guard (Float32.ofInt (-1 : Int)).toBits == 0xBF800000

-- 2^24 + 1 is the smallest Nat that can't be represented exactly in FP32 but can in FP64;
-- There are 23 bits of mantissa and an implicit leading 1. Additionally, powers of
-- 2 (within range) are exactly representable in either format.
-- This shows that we are not accidentally representing Float32 with 64 bits;
#guard
  let n := Int.pow 2 24
  (Float.ofInt n) - (Float32.ofInt n).toFloat == 0
#guard
  let n := Int.pow 2 24 + 1
  (Float.ofInt n) - (Float32.ofInt n).toFloat != 0