[CUDA] Implement Scan kernel (#2347)

* Contiguous scan

* Strided scan

* Enable tests

* Fix failing logaddexp test

* Use cexpf in Metal

mlx/backend/cuda/device/binary_ops.cuh

@@ -1,10 +1,7 @@
 // Copyright © 2025 Apple Inc.
 
-#include "mlx/backend/cuda/device/cucomplex_math.cuh"
-#include "mlx/backend/cuda/device/fp16_math.cuh"
-#include "mlx/backend/cuda/device/utils.cuh"
+#include "mlx/backend/cuda/device/unary_ops.cuh"
 
-#include <cuComplex.h>
 #include <cuda/std/array>
 
 namespace mlx::core::cu {
@@ -114,36 +111,38 @@ struct LessEqual {
 struct LogAddExp {
   template <typename T>
   __device__ T operator()(T x, T y) {
-    if (isnan(x) || isnan(y)) {
-      return cuda::std::numeric_limits<T>::quiet_NaN();
+    if constexpr (cuda::std::is_same_v<T, cuComplex>) {
+      if (isnan(cuCrealf(x)) || isnan(cuCimagf(x)) || isnan(cuCrealf(y)) ||
+          isnan(cuCimagf(y))) {
+        return {
+            cuda::std::numeric_limits<float>::quiet_NaN(),
+            cuda::std::numeric_limits<float>::quiet_NaN()};
+      }
+      auto max = cuCrealf(x) > cuCrealf(y) ? x : y;
+      auto min = cuCrealf(x) < cuCrealf(y) ? x : y;
+      auto min_real = cuCrealf(min);
+      auto max_real = cuCrealf(max);
+      if (!isfinite(min_real) && (min_real == max_real)) {
+        if (min_real < 0) {
+          return min;
+        } else {
+          return Log{}(Exp{}(min) + Exp{}(max));
+        }
+      } else {
+        return Log1p{}(Exp{}(min - max)) + max;
+      }
+    } else {
+      if (isnan(x) || isnan(y)) {
+        return cuda::std::numeric_limits<T>::quiet_NaN();
+      }
+      T maxval = max(x, y);
+      T minval = min(x, y);
+      return (minval == -cuda::std::numeric_limits<T>::infinity() ||
+              maxval == cuda::std::numeric_limits<T>::infinity())
+          ? maxval
+          : T(float(maxval) + log1p(expf(minval - maxval)));
     }
-    T maxval = max(x, y);
-    T minval = min(x, y);
-    return (minval == -cuda::std::numeric_limits<T>::infinity() ||
-            maxval == cuda::std::numeric_limits<T>::infinity())
-        ? maxval
-        : T(float(maxval) + log1p(expf(minval - maxval)));
   };
-
-  __device__ cuComplex operator()(cuComplex x, cuComplex y) {
-    if (isnan(cuCrealf(x)) || isnan(cuCimagf(x)) || isnan(cuCrealf(y)) ||
-        isnan(cuCimagf(y))) {
-      return {
-          cuda::std::numeric_limits<float>::quiet_NaN(),
-          cuda::std::numeric_limits<float>::quiet_NaN()};
-    }
-    float inf = cuda::std::numeric_limits<float>::infinity();
-    auto maxval = x > y ? x : y;
-    auto minval = x < y ? x : y;
-    if (cuCrealf(minval) == -inf || cuCrealf(maxval) == inf)
-      return maxval;
-    float m = exp(cuCrealf(minval) - cuCrealf(maxval));
-    cuComplex dexp{
-        m * cos(cuCimagf(minval) - cuCimagf(maxval)),
-        m * sin(cuCimagf(minval) - cuCimagf(maxval)),
-    };
-    return maxval + log1p(dexp);
-  }
 };
 
 struct Maximum {

mlx/backend/cuda/device/cexpf.cuh

@@ -0,0 +1,138 @@
+// Copyright © 2025 Apple Inc.
+// Copyright © 2008-2013 NVIDIA Corporation
+// Copyright © 2013 Filipe RNC Maia
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+//
+// Forked from
+// https://github.com/NVIDIA/cccl/blob/main/thrust/thrust/detail/complex/cexpf.h
+
+// TODO: We should use thrust::exp but the thrust header in old CUDA versions
+// can not be used in JIT.
+
+#pragma once
+
+#include <cuComplex.h>
+#include <cuda/std/cstdint>
+
+namespace mlx::core::cu::detail {
+
+using ieee_float_shape_type = union {
+  float value;
+  uint32_t word;
+};
+
+inline __device__ void get_float_word(uint32_t& i, float d) {
+  ieee_float_shape_type gf_u;
+  gf_u.value = (d);
+  (i) = gf_u.word;
+}
+
+inline __device__ void get_float_word(int32_t& i, float d) {
+  ieee_float_shape_type gf_u;
+  gf_u.value = (d);
+  (i) = gf_u.word;
+}
+
+inline __device__ void set_float_word(float& d, uint32_t i) {
+  ieee_float_shape_type sf_u;
+  sf_u.word = (i);
+  (d) = sf_u.value;
+}
+
+inline __device__ float frexp_expf(float x, int* expt) {
+  const uint32_t k = 235;
+  const float kln2 = 162.88958740F;
+
+  float exp_x;
+  uint32_t hx;
+
+  exp_x = expf(x - kln2);
+  get_float_word(hx, exp_x);
+  *expt = (hx >> 23) - (0x7f + 127) + k;
+  set_float_word(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23));
+  return exp_x;
+}
+
+inline __device__ cuComplex ldexp_cexpf(cuComplex z, int expt) {
+  float x, y, exp_x, scale1, scale2;
+  int ex_expt, half_expt;
+
+  x = cuCrealf(z);
+  y = cuCimagf(z);
+  exp_x = frexp_expf(x, &ex_expt);
+  expt += ex_expt;
+
+  half_expt = expt / 2;
+  set_float_word(scale1, (0x7f + half_expt) << 23);
+  half_expt = expt - half_expt;
+  set_float_word(scale2, (0x7f + half_expt) << 23);
+
+  return cuComplex{
+      cosf(y) * exp_x * scale1 * scale2, sinf(y) * exp_x * scale1 * scale2};
+}
+
+inline __device__ cuComplex cexpf(const cuComplex& z) {
+  float x, y, exp_x;
+  uint32_t hx, hy;
+
+  const uint32_t exp_ovfl = 0x42b17218, cexp_ovfl = 0x43400074;
+
+  x = cuCrealf(z);
+  y = cuCimagf(z);
+
+  get_float_word(hy, y);
+  hy &= 0x7fffffff;
+
+  /* cexp(x + I 0) = exp(x) + I 0 */
+  if (hy == 0) {
+    return cuComplex{expf(x), y};
+  }
+  get_float_word(hx, x);
+  /* cexp(0 + I y) = cos(y) + I sin(y) */
+  if ((hx & 0x7fffffff) == 0) {
+    return cuComplex{cosf(y), sinf(y)};
+  }
+  if (hy >= 0x7f800000) {
+    if ((hx & 0x7fffffff) != 0x7f800000) {
+      /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
+      return cuComplex{y - y, y - y};
+    } else if (hx & 0x80000000) {
+      /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
+      return cuComplex{0.0, 0.0};
+    } else {
+      /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
+      return cuComplex{x, y - y};
+    }
+  }
+
+  if (hx >= exp_ovfl && hx <= cexp_ovfl) {
+    /*
+     * x is between 88.7 and 192, so we must scale to avoid
+     * overflow in expf(x).
+     */
+    return ldexp_cexpf(z, 0);
+  } else {
+    /*
+     * Cases covered here:
+     *  -  x < exp_ovfl and exp(x) won't overflow (common case)
+     *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
+     *  -  x = +-Inf (generated by exp())
+     *  -  x = NaN (spurious inexact exception from y)
+     */
+    exp_x = expf(x);
+    return cuComplex{exp_x * cosf(y), exp_x * sinf(y)};
+  }
+}
+
+} // namespace mlx::core::cu::detail

mlx/backend/cuda/device/unary_ops.cuh

@@ -2,6 +2,8 @@
 
 #pragma once
 
+#include "mlx/backend/cuda/device/cexpf.cuh"
+#include "mlx/backend/cuda/device/cucomplex_math.cuh"
 #include "mlx/backend/cuda/device/fp16_math.cuh"
 #include "mlx/backend/cuda/device/utils.cuh"
 
@@ -150,8 +152,7 @@ struct Exp {
   template <typename T>
   __device__ T operator()(T x) {
     if constexpr (cuda::std::is_same_v<T, cuComplex>) {
-      auto m = exp(cuCrealf(x));
-      return {m * cos(cuCimagf(x)), m * sinh(cuCimagf(x))};
+      return detail::cexpf(x);
     } else {
       return exp(x);
     }
@@ -228,8 +229,25 @@ struct Log10 {
 
 struct Log1p {
   template <typename T>
-  __device__ T operator()(T x) {
-    return log1p(x);
+  __device__ T operator()(T z) {
+    if constexpr (cuda::std::is_same_v<T, cuComplex>) {
+      float x = cuCrealf(z);
+      float y = cuCimagf(z);
+      float zabs = cuCrealf(Abs{}(z));
+      float theta = atan2f(y, x + 1);
+      if (zabs < 0.5f) {
+        float r = x * (2 + x) + y * y;
+        if (r == 0) { // handle underflow
+          return {x, theta};
+        }
+        return {0.5f * log1pf(r), theta};
+      } else {
+        float z0 = hypotf(x + 1, y);
+        return {logf(z0), theta};
+      }
+    } else {
+      return log1p(z);
+    }
   }
 };
 
@@ -387,19 +405,19 @@ struct Tanh {
   }
 };
 
-__device__ cuComplex ArcCos::operator()(cuComplex x) {
+inline __device__ cuComplex ArcCos::operator()(cuComplex x) {
   auto i = cuComplex{0.0, 1.0};
   auto y = Log{}(x + i * Sqrt{}(1.0 - x * x));
   return {cuCimagf(y), -cuCrealf(y)};
 };
 
-__device__ cuComplex ArcSin::operator()(cuComplex x) {
+inline __device__ cuComplex ArcSin::operator()(cuComplex x) {
   auto i = cuComplex{0.0f, 1.0f};
   auto y = Log{}(i * x + Sqrt{}(1.0f - x * x));
   return {cuCimagf(y), -cuCrealf(y)};
 };
 
-__device__ cuComplex ArcTan::operator()(cuComplex x) {
+inline __device__ cuComplex ArcTan::operator()(cuComplex x) {
   auto i = cuComplex{0.0f, 1.0f};
   auto ix = i * x;
   return (1.0f / cuComplex{0.0f, 2.0f}) * Log{}((1.0f + ix) / (1.0f - ix));

mlx/backend/cuda/device/utils.cuh

@@ -359,21 +359,4 @@ struct LoopedElemToLoc<1, false, OffsetT> {
   }
 };
 
-inline __device__ cuComplex log1p(cuComplex in) {
-  float x = cuCrealf(in);
-  float y = cuCimagf(in);
-  float zabs = sqrt(x * x + y * y);
-  float theta = atan2f(y, x + 1);
-  if (zabs < 0.5f) {
-    float r = x * (2 + x) + y * y;
-    if (r == 0) { // handle underflow
-      return {x, theta};
-    }
-    return {0.5f * log1pf(r), theta};
-  } else {
-    auto z0 = sqrt((x + 1) * (x + 1) + y * y);
-    return {log(z0), theta};
-  }
-}
-
 } // namespace mlx::core::cu