GPU: fuse the whole RK4 discharge step into one cupy kernel

The naive elementwise port launched ~60 tiny kernels per step, so the
GTX 1070 was only ~1.3x over CPU (launch-bound). Fold the entire RK4 step
(4 derivative evals + combine + overlap) into a single cupy.fuse kernel;
numpy path unchanged and still validates vs scipy. GPU correctness
re-checked against CPU on deploy.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/gausse/gpu/batch_integrator.py

@@ -109,6 +109,58 @@ def _derivatives(xp, q, i, x, v, p: BatchDischargeParams):
     return d_q, d_i, d_x, d_v
 
 
+_FUSED_STEP_CACHE = {}
+
+
+def _get_fused_step(cp):
+    """Собирает (и кэширует) cupy.fuse-ядро полного RK4-шага разряда.
+
+    Весь шаг (4 вычисления производных + сборка + overlap) сливается в ОДНО
+    GPU-ядро вместо ~60 мелких — убирает накладные на запуск ядер, из-за
+    которых наивный порт был лишь ~1.3x к CPU.
+    """
+    if "step" in _FUSED_STEP_CACHE:
+        return _FUSED_STEP_CACHE["step"]
+    LN2 = 0.6931471805599453
+
+    def _ovl(x, hs, w):
+        s1 = 0.5 * (1.0 + cp.tanh((x + hs) / w * 0.5))
+        s2 = 0.5 * (1.0 + cp.tanh((hs - x) / w * 0.5))
+        return s1 * s2, (s1 * s2 / w) * (s2 - s1)
+
+    def _der(q, i, x, v, hs, w, isat, lair, liron, C, rt, red, m):
+        ov, dov = _ovl(x, hs, w)
+        z = i / isat
+        tz = cp.tanh(z)
+        g = isat * tz
+        gp = 1.0 - tz * tz
+        az = cp.abs(z)
+        G = isat * isat * (az + cp.log1p(cp.exp(-2.0 * az)) - LN2)
+        dl_di = lair + liron * ov * gp
+        reff = rt + red * ov
+        dq = -i
+        di = (q / C - i * reff - liron * dov * g * v) / dl_di
+        dv = (liron * dov * G) / m
+        return dq, di, v, dv
+
+    @cp.fuse()
+    def step(q, i, x, v, dt, hs, w, isat, lair, liron, C, rt, red, m):
+        a = _der(q, i, x, v, hs, w, isat, lair, liron, C, rt, red, m)
+        b = _der(q + dt * 0.5 * a[0], i + dt * 0.5 * a[1], x + dt * 0.5 * a[2], v + dt * 0.5 * a[3], hs, w, isat, lair, liron, C, rt, red, m)
+        c = _der(q + dt * 0.5 * b[0], i + dt * 0.5 * b[1], x + dt * 0.5 * b[2], v + dt * 0.5 * b[3], hs, w, isat, lair, liron, C, rt, red, m)
+        d = _der(q + dt * c[0], i + dt * c[1], x + dt * c[2], v + dt * c[3], hs, w, isat, lair, liron, C, rt, red, m)
+        qn = q + dt / 6.0 * (a[0] + 2 * b[0] + 2 * c[0] + d[0])
+        in_ = i + dt / 6.0 * (a[1] + 2 * b[1] + 2 * c[1] + d[1])
+        xn = x + dt / 6.0 * (a[2] + 2 * b[2] + 2 * c[2] + d[2])
+        vn = v + dt / 6.0 * (a[3] + 2 * b[3] + 2 * c[3] + d[3])
+        ov_old, _ = _ovl(x, hs, w)
+        ov_new, _ = _ovl(xn, hs, w)
+        return qn, in_, xn, vn, ov_old, ov_new
+
+    _FUSED_STEP_CACHE["step"] = step
+    return step
+
+
 def integrate_batch_discharge(
     xp,
     q0,
@@ -139,6 +191,11 @@ def integrate_batch_discharge(
     energy_diss = xp.zeros(n, dtype=xp.float64)
 
     _old_err = xp.seterr(all="ignore") if hasattr(xp, "seterr") else None  # стиффные конфиги переполняют fixed-step
+    # на cupy — слитое в одно ядро RK4-ядро (cupy.fuse), на numpy — обычный путь
+    is_cupy = xp.__name__ == "cupy"
+    if is_cupy:
+        fused = _get_fused_step(xp)
+        hs = (params.coil_length_m + params.slug_length_m) / 2
     # проверку «все ли готовы» делаем НЕ каждый шаг: на GPU это device->host
     # синхронизация, которая убивает конвейер. Раз в SYNC_EVERY шагов достаточно.
     SYNC_EVERY = 256
@@ -149,20 +206,25 @@ def integrate_batch_discharge(
 
         q_old, i_old, x_old, v_old = q, i, x, v
 
-        # RK4 от старого состояния
+        if is_cupy:
-        k1 = _derivatives(xp, q_old, i_old, x_old, v_old, params)
+            q_new, i_new, x_new, v_new, overlap_old, overlap_new = fused(
-        k2 = _derivatives(xp, q_old + dt / 2 * k1[0], i_old + dt / 2 * k1[1], x_old + dt / 2 * k1[2], v_old + dt / 2 * k1[3], params)
+                q_old, i_old, x_old, v_old, dt, hs, params.smoothing_width_m,
-        k3 = _derivatives(xp, q_old + dt / 2 * k2[0], i_old + dt / 2 * k2[1], x_old + dt / 2 * k2[2], v_old + dt / 2 * k2[3], params)
+                params.i_sat_a, params.l_air_h, params.l_iron_coeff, params.capacitance_f,
-        k4 = _derivatives(xp, q_old + dt * k3[0], i_old + dt * k3[1], x_old + dt * k3[2], v_old + dt * k3[3], params)
+                params.r_total_ohm, params.r_eddy_coeff_ohm, params.mass_kg,
-
+            )
-        q_new = q_old + dt / 6 * (k1[0] + 2 * k2[0] + 2 * k3[0] + k4[0])
+        else:
-        i_new = i_old + dt / 6 * (k1[1] + 2 * k2[1] + 2 * k3[1] + k4[1])
+            k1 = _derivatives(xp, q_old, i_old, x_old, v_old, params)
-        x_new = x_old + dt / 6 * (k1[2] + 2 * k2[2] + 2 * k3[2] + k4[2])
+            k2 = _derivatives(xp, q_old + dt / 2 * k1[0], i_old + dt / 2 * k1[1], x_old + dt / 2 * k1[2], v_old + dt / 2 * k1[3], params)
-        v_new = v_old + dt / 6 * (k1[3] + 2 * k2[3] + 2 * k3[3] + k4[3])
+            k3 = _derivatives(xp, q_old + dt / 2 * k2[0], i_old + dt / 2 * k2[1], x_old + dt / 2 * k2[2], v_old + dt / 2 * k2[3], params)
+            k4 = _derivatives(xp, q_old + dt * k3[0], i_old + dt * k3[1], x_old + dt * k3[2], v_old + dt * k3[3], params)
+            q_new = q_old + dt / 6 * (k1[0] + 2 * k2[0] + 2 * k3[0] + k4[0])
+            i_new = i_old + dt / 6 * (k1[1] + 2 * k2[1] + 2 * k3[1] + k4[1])
+            x_new = x_old + dt / 6 * (k1[2] + 2 * k2[2] + 2 * k3[2] + k4[2])
+            v_new = v_old + dt / 6 * (k1[3] + 2 * k2[3] + 2 * k3[3] + k4[3])
+            overlap_old, _ = _overlap(xp, x_old, params)
+            overlap_new, _ = _overlap(xp, x_new, params)
 
         # потери I²·R_eff (с вихревыми × overlap) и пиковый ток — только для активных
-        overlap_old, _ = _overlap(xp, x_old, params)
-        overlap_new, _ = _overlap(xp, x_new, params)
         r_eff_old = params.r_total_ohm + params.r_eddy_coeff_ohm * overlap_old
         r_eff_new = params.r_total_ohm + params.r_eddy_coeff_ohm * overlap_new
         step_diss = 0.5 * (i_old**2 * r_eff_old + i_new**2 * r_eff_new) * dt