feat: Add Metal SVD kernel infrastructure

- Add svd.h header with kernel declarations
- Add svd.metal with placeholder Metal compute shaders
- Define SVD algorithm parameters and data structures
- Prepare foundation for Metal GPU-accelerated SVD implementation

mlx/backend/metal/kernels/svd.h

@@ -1,6 +1,9 @@
+// Copyright © 2024 Apple Inc.
+
 #pragma once
 
-namespace mlx::core {
+// Note: These structs are defined outside namespace for Metal kernel
+// compatibility Metal kernels cannot access namespaced types directly
 
 /**
  * Parameters for SVD Metal kernels
@@ -12,7 +15,7 @@ struct SVDParams {
   const int max_iterations; // Maximum Jacobi iterations
   const float tolerance; // Convergence threshold
   const int batch_size; // Number of matrices in batch
-  const int64_t matrix_stride; // Stride between matrices in batch
+  const long matrix_stride; // Stride between matrices in batch
   const bool compute_uv; // Whether to compute U and V matrices
 };
 
@@ -34,4 +37,9 @@ struct SVDConvergenceInfo {
   bool converged; // Whether algorithm has converged
 };
 
+namespace mlx::core {
+// Namespace aliases for C++ code
+using ::JacobiRotation;
+using ::SVDConvergenceInfo;
+using ::SVDParams;
 } // namespace mlx::core

mlx/backend/metal/kernels/svd.metal

@@ -16,8 +16,7 @@ template <typename T>
     const device T* A [[buffer(0)]],
     device T* AtA [[buffer(1)]],
     const constant SVDParams& params [[buffer(2)]],
-    uint3 tid [[threadgroup_position_in_grid]],
+    uint3 tid [[threadgroup_position_in_grid]]) {
-    uint3 lid [[thread_position_in_threadgroup]]) {
 
   const int M = params.M;
   const int N = params.N;
@@ -51,10 +50,8 @@ template <typename T>
 [[kernel]] void svd_jacobi_iteration(
     device T* AtA [[buffer(0)]],
     device JacobiRotation* rotations [[buffer(1)]],
-    device SVDConvergenceInfo* convergence [[buffer(2)]],
     const constant SVDParams& params [[buffer(3)]],
-    uint3 tid [[threadgroup_position_in_grid]],
+    uint3 tid [[threadgroup_position_in_grid]]) {
-    uint3 lid [[thread_position_in_threadgroup]]) {
 
   const int N = params.N;
   const int batch_idx = tid.z;
@@ -68,7 +65,7 @@ template <typename T>
   }
 
   // Convert linear pair index to (p,q) coordinates where p < q
-  int p, q;
+  int p, q = 0;
   int idx = pair_idx;
   for (p = 0; p < N - 1; p++) {
     int pairs_in_row = N - 1 - p;
@@ -218,8 +215,7 @@ template <typename T>
     device T* U [[buffer(2)]],
     device T* V [[buffer(3)]],
     const constant SVDParams& params [[buffer(4)]],
-    uint3 tid [[threadgroup_position_in_grid]],
+    uint3 tid [[threadgroup_position_in_grid]]) {
-    uint3 lid [[thread_position_in_threadgroup]]) {
 
   const int M = params.M;
   const int N = params.N;
@@ -294,18 +290,5 @@ decltype(svd_check_convergence<float>) svd_check_convergence<float>;
 template [[host_name("svd_compute_vectors_float")]] [[kernel]]
 decltype(svd_compute_vectors<float>) svd_compute_vectors<float>;
 
-// Template instantiations for double
+// Note: Metal does not support double precision
-template [[host_name("svd_preprocess_double")]] [[kernel]]
+// Double precision operations will fall back to CPU
-decltype(svd_preprocess<double>) svd_preprocess<double>;
-
-template [[host_name("svd_jacobi_iteration_double")]] [[kernel]]
-decltype(svd_jacobi_iteration<double>) svd_jacobi_iteration<double>;
-
-template [[host_name("svd_extract_singular_values_double")]] [[kernel]]
-decltype(svd_extract_singular_values<double>) svd_extract_singular_values<double>;
-
-template [[host_name("svd_check_convergence_double")]] [[kernel]]
-decltype(svd_check_convergence<double>) svd_check_convergence<double>;
-
-template [[host_name("svd_compute_vectors_double")]] [[kernel]]
-decltype(svd_compute_vectors<double>) svd_compute_vectors<double>;