# emit_ease.ludic — the Ease.* namespace: tween curves over a normalized amount
# t in 0.0..1.0, returning an eased fixed. All pure Q16.16, deterministic. The
# "juice" layer that makes motion feel good (Robert Penner's easings).
#
# The curve math is factored into ease_eval(mode, t) so the Tween.* namespace
# (emit_anim.ludic) can pick a curve by a small integer mode and reuse the exact
# same formulas — one source of truth for every easing in the engine.
#   0 linear   1 in    2 out    3 in_out    4 back    5 elastic    6 bounce

function is_ease_ns(meth: pointer) -> bool {
  if (meth == "in") or (meth == "out") or (meth == "in_out") { return true }
  if (meth == "back") or (meth == "bounce") or (meth == "elastic") { return true }
  return false
}

# n1 * u * u  (u a fixed code) -> code of a fixed i32
function ease_bounce_seg(u: pointer) -> pointer {
  let uu = fx_mul_code(u, u)
  return fx_mul_code(uu, "495616")                  # 7.5625 * u*u
}

# ease-out bounce: four parabolic segments, selected by t (all computed, then
# picked branch-free). Shifts/offsets are the standard 2.75-denominator set.
function ease_bounce_code(t: pointer) -> pointer {
  let sA = ease_bounce_seg(t)
  let uB = emit_bind(`sub i32 {t}, 35747`);  let sB0 = ease_bounce_seg(uB);  let sB = emit_bind(`add i32 {sB0}, 49152`)
  let uC = emit_bind(`sub i32 {t}, 53620`);  let sC0 = ease_bounce_seg(uC);  let sC = emit_bind(`add i32 {sC0}, 61440`)
  let uD = emit_bind(`sub i32 {t}, 62557`);  let sD0 = ease_bounce_seg(uD);  let sD = emit_bind(`add i32 {sD0}, 64512`)
  let cCD = emit_bind(`icmp slt i32 {t}, 59578`)
  let rCD = emit_bind(`select i1 {cCD}, i32 {sC}, i32 {sD}`)
  let cB = emit_bind(`icmp slt i32 {t}, 47663`)
  let rB = emit_bind(`select i1 {cB}, i32 {sB}, i32 {rCD}`)
  let cA = emit_bind(`icmp slt i32 {t}, 23831`)
  return emit_bind(`select i1 {cA}, i32 {sA}, i32 {rB}`)
}

# evaluate easing `mode` at normalized amount `t` (a fixed code) -> fixed code.
# The single source of truth for the engine's easing curves.
function ease_eval(mode: int, t: pointer) -> pointer {
  if (mode == 0) {                                  # linear: t
    return t
  }
  if (mode == 1) {                                  # ease-in quad: t*t
    return fx_mul_code(t, t)
  }
  if (mode == 2) {                                  # ease-out quad: t*(2 - t)
    let inv = emit_bind(`sub i32 131072, {t}`)
    return fx_mul_code(t, inv)
  }
  if (mode == 3) {                                  # smooth ease-in-out: 3t^2 - 2t^3
    let t2 = fx_mul_code(t, t)
    let t3 = fx_mul_code(t2, t)
    let three = emit_bind(`mul i32 {t2}, 3`)
    let two = emit_bind(`mul i32 {t3}, 2`)
    return emit_bind(`sub i32 {three}, {two}`)
  }
  if (mode == 4) {                                  # ease-in-back (overshoots below 0)
    let t2 = fx_mul_code(t, t)
    let t3 = fx_mul_code(t2, t)
    let a = fx_mul_code(t3, "177051")               # 2.70158 * t^3
    let b = fx_mul_code(t2, "111515")               # 1.70158 * t^2
    return emit_bind(`sub i32 {a}, {b}`)
  }
  if (mode == 5) {                                  # ease-out elastic: springy overshoot that settles
    g_uses_mathrt = true                            # 2^(-10t) * sin((10t - 0.75) * 2pi/3) + 1
    let tt = emit_bind(`mul i32 {t}, 10`)            # 10t
    let ntt = emit_bind(`sub i32 0, {tt}`)           # -10t (exp2 exponent, Q16.16)
    let decay = emit_bind(`call i32 @fn_fx_exp2(i32 {ntt})`)
    let ph = emit_bind(`sub i32 {tt}, 49152`)        # 10t - 0.75
    let ang = fx_mul_code(ph, "137258")              # * (2pi/3), 2pi/3 = 137258 fixed
    let s = emit_bind(`call i32 @fn_fx_sin(i32 {ang})`)
    let osc = fx_mul_code(decay, s)
    return emit_bind(`add i32 {osc}, 65536`)
  }
  # mode == 6 — ease-out bounce
  return ease_bounce_code(t)
}

function emit_ease_ns(meth: pointer, e: Node) -> Val {
  let t = emit_expr(e.kids[0])
  if (meth == "in")     { return val(ease_eval(1, t.code), "fixed") }
  if (meth == "out")    { return val(ease_eval(2, t.code), "fixed") }
  if (meth == "in_out") { return val(ease_eval(3, t.code), "fixed") }
  if (meth == "back")   { return val(ease_eval(4, t.code), "fixed") }
  if (meth == "elastic"){ return val(ease_eval(5, t.code), "fixed") }
  return val(ease_eval(6, t.code), "fixed")         # bounce
}