patch (#1320)

Allows opt-in to memory efficient GPU shader at proscribed sequence
length.  Otherwise, utilizes aggregate MLX primitives for best latency.

.circleci/config.yml

@@ -144,6 +144,7 @@ jobs:
           name: Install dependencies
           command: |
             brew install python@<< parameters.python_version >>
+            brew install openmpi
             python<< parameters.python_version >> -m venv env
             source env/bin/activate
             pip install --upgrade pip

.github/workflows/pull_request.yml

@@ -17,4 +17,4 @@ jobs:
           pip install pre-commit black isort clang-format
       - name: Run lint
         run: |
-          pre-commit run --all-files
+          pre-commit run --all-files

ACKNOWLEDGMENTS.md

@@ -10,13 +10,14 @@ MLX was developed with contributions from the following individuals:
 - Nripesh Niketan: Added `softsign`, `softmax`, `hardswish`, `logsoftmax` activation functions. Added `dropout3d` ops. Added `LogicalAnd` and `LogicalOR` ops. Added `clip_grad_norm` along with `tree_reduce`.
 - Juarez Bochi: Fixed bug in cross attention.
 - Justin Deschenaux: Sine, Cosine, arange, randint, truncated normal, bernoulli, lion optimizer, Dropout2d, linear and logistic regression python example.
-- Diogo Da Cruz: Added `tri`, `tril`, `triu`, `tensordot`, `inner`, `outer`, `tile`, `StreamContext`, `stream` and safetensor support.
+- Diogo Da Cruz: Added `tri`, `tril`, `triu`, `tensordot`, `inner`, `outer`, `tile`, `StreamContext`, `stream`, safetensors support, `einsum`, and `einsum_path`.
 - Gabrijel Boduljak: Added `mlx.core.linalg`, implemented `norm` method and `InstanceNorm` layer. Implemented pooling layers and ``Upsample``.
 - Hinrik Snær Guðmundsson: Added `atleast_1d`, `atleast_2d`, `atleast_3d` ops.
 - Luca Arnaboldi: Added `Ceil` and `Floor` ops; implemented pickling, copy and deepcopy for mlx arrays.
 - Brian Keene & Atila Orhon, with Argmax Inc.: Added `fast.scaled_dot_product_attention`
 - AmirHossein Razlighi: Added chaining support for some of the ops in `nn.Module`. Comparison works for non array objects in `mlx.core.array`. Exception handling for invalid operations in `mlx.core.array`.
 - Gleb Pobudzey: Added the `where` primitive, and groups in 1D and 2D convolutions.
+- Paul Paczuski: Improved stability of BCE loss calculation
 
 <a href="https://github.com/ml-explore/mlx/graphs/contributors">
   <img class="dark-light" src="https://contrib.rocks/image?repo=ml-explore/mlx&anon=0&columns=20&max=100&r=true" />

CMakeLists.txt

@@ -24,7 +24,7 @@ option(MLX_METAL_JIT "Use JIT compilation for Metal kernels" OFF)
 option(BUILD_SHARED_LIBS "Build mlx as a shared library" OFF)
 
 if(NOT MLX_VERSION)
-  set(MLX_VERSION 0.14.0)
+  set(MLX_VERSION 0.16.3)
 endif()
 
 # --------------------- Processor tests -------------------------
@@ -83,24 +83,21 @@ elseif (MLX_BUILD_METAL)
                   OUTPUT_VARIABLE MACOS_VERSION
                   COMMAND_ERROR_IS_FATAL ANY)
 
-  message(STATUS "Building with SDK for macOS version ${MACOS_VERSION}")
-
-  if (${MACOS_VERSION} GREATER_EQUAL 14.2)
-    set(METAL_CPP_PATCH ${CMAKE_CURRENT_SOURCE_DIR}/cmake/metal.14.2.diff)
-    set(METAL_CPP_URL https://developer.apple.com/metal/cpp/files/metal-cpp_macOS14.2_iOS17.2.zip)
-    set(MLX_METAL_VERSION METAL_3_1)
-  elseif (${MACOS_VERSION} GREATER_EQUAL 14.0)
-    set(METAL_CPP_PATCH ${CMAKE_CURRENT_SOURCE_DIR}/cmake/metal.14.0.diff)
-    set(METAL_CPP_URL https://developer.apple.com/metal/cpp/files/metal-cpp_macOS14_iOS17-beta.zip)
-    set(MLX_METAL_VERSION METAL_3_0)
-  else()
+  if (${MACOS_VERSION} LESS 14.0)
     message(FATAL_ERROR "MLX requires macOS SDK >= 14.0 to be built with MLX_BUILD_METAL=ON" )
   endif()
+  message(STATUS "Building with SDK for macOS version ${MACOS_VERSION}")
+
+  set(METAL_CPP_URL https://developer.apple.com/metal/cpp/files/metal-cpp_macOS15_iOS18-beta.zip)
+  # Get the metal version
+  execute_process(
+    COMMAND zsh "-c" "echo \"__METAL_VERSION__\" | xcrun -sdk macosx metal -E -x metal -P - | tail -1 | tr -d '\n'"
+    OUTPUT_VARIABLE MLX_METAL_VERSION
+    COMMAND_ERROR_IS_FATAL ANY)
 
   FetchContent_Declare(
     metal_cpp
     URL ${METAL_CPP_URL}
-    PATCH_COMMAND /usr/bin/patch -N -i ${METAL_CPP_PATCH} || true
   )
 
   FetchContent_MakeAvailable(metal_cpp)
@@ -115,7 +112,7 @@ elseif (MLX_BUILD_METAL)
     ${FOUNDATION_LIB}
     ${QUARTZ_LIB})
 
-  add_compile_definitions(${MLX_METAL_VERSION})
+  add_compile_definitions("MLX_METAL_VERSION=${MLX_METAL_VERSION}")
 endif()
 
 if (MLX_BUILD_CPU)
@@ -169,7 +166,26 @@ endif()
 
 find_package(MPI)
 if (MPI_FOUND)
+  execute_process(
+    COMMAND zsh "-c" "mpirun --version"
+    OUTPUT_VARIABLE MPI_VERSION
+    ERROR_QUIET
+  )
+  if (${MPI_VERSION} MATCHES ".*Open MPI.*")
     target_include_directories(mlx PRIVATE ${MPI_INCLUDE_PATH})
+  elseif (MPI_VERSION STREQUAL "")
+    set(MPI_FOUND FALSE)
+    message(
+      WARNING
+      "MPI found but mpirun is not available. Building without MPI."
+    )
+  else()
+    set(MPI_FOUND FALSE)
+    message(
+      WARNING
+      "MPI which is not OpenMPI found. Building without MPI."
+    )
+  endif() 
 endif()
 
 add_subdirectory(${CMAKE_CURRENT_LIST_DIR}/mlx)

benchmarks/python/comparative/bench_torch.py

@@ -185,7 +185,7 @@ def prelu(x: torch.Tensor) -> torch.Tensor:
 def mish(x: torch.Tensor) -> torch.Tensor:
     y = x
     for _ in range(100):
-        return torch.nn.functional.mish(y)
+        y = torch.nn.functional.mish(y)
     sync_if_needed(x)
 
 
@@ -283,6 +283,14 @@ def topk(axis, x):
     sync_if_needed(x)
 
 
+@torch.no_grad()
+def step_function(x):
+    y = x
+    for i in range(100):
+        y = torch.where(y < 0, 0, 1)
+    sync_if_needed(x)
+
+
 @torch.no_grad()
 def selu(x):
     y = x
@@ -446,5 +454,11 @@ if __name__ == "__main__":
     elif args.benchmark == "topk":
         print(bench(topk, axis, x))
 
+    elif args.benchmark == "step":
+        print(bench(step_function, x))
+
+    elif args.benchmark == "selu":
+        print(bench(selu, x))
+
     else:
-        raise ValueError("Unknown benchmark")
+        raise ValueError(f"Unknown benchmark `{args.benchmark}`.")

benchmarks/python/comparative/compare.py

@@ -16,7 +16,9 @@ def run_or_raise(*args, **kwargs):
         result = run(*args, capture_output=True, **kwargs)
         return float(result.stdout)
     except ValueError:
-        raise ValueError(f"stdout: {result.stdout}\nstderr: {result.stderr}")
+        raise ValueError(
+            f"stdout: {result.stdout.decode()}\nstderr: {result.stderr.decode()}"
+        )
 
 
 def compare(args):

benchmarks/python/compile_bench.py

@@ -9,7 +9,6 @@ from time_utils import time_fn
 
 
 def bench_gelu():
-
     def gelu(x):
         return x * (1 + mx.erf(x / math.sqrt(2))) / 2
 
@@ -51,7 +50,6 @@ def bench_gelu():
 
 
 def bench_layernorm():
-
     weight = mx.random.uniform(shape=(4096,)).astype(mx.float16)
     bias = mx.random.uniform(shape=(4096,)).astype(mx.float16)
     mx.eval(weight, bias)

benchmarks/python/conv_bench.py

@@ -54,7 +54,6 @@ def make_pt_conv_2D(strides=(1, 1), padding=(0, 0), groups=1):
 
 
 def bench_shape(N, H, W, C, kH, kW, O, strides, padding, groups, np_dtype):
-
     scale = 1.0 / math.sqrt(kH * kH * C)
     a_np = np.random.uniform(0, 0.5, (N, H, W, C)).astype(np_dtype)
     b_np = np.random.uniform(-scale, scale, (O, kH, kW, int(C / groups))).astype(

benchmarks/python/einsum_bench.py

@@ -0,0 +1,84 @@
+# Copyright © 2024 Apple Inc.
+
+import time
+
+import mlx.core as mx
+import numpy as np
+
+
+def timeit(fn, its=100, args=[]):
+    for _ in range(5):
+        fn(*args)
+    tic = time.perf_counter()
+    for _ in range(its):
+        fn(*args)
+    toc = time.perf_counter()
+    return 1e3 * (toc - tic) / its
+
+
+def time_little_einsum_path():
+    subscripts = "ik,kj->ij"
+    x = mx.ones((32, 32))
+    y = mx.ones((32, 32))
+    mx_time = timeit(mx.einsum_path, args=(subscripts, x, y))
+
+    x = np.array(x)
+    y = np.array(y)
+    np_time = timeit(np.einsum_path, args=(subscripts, x, y))
+    print("Timing little einsum path...")
+    print(f"MLX ... {mx_time:.3f} ms")
+    print(f"NumPy... {np_time:.3f} ms")
+
+
+def time_big_einsum_path():
+    chars = list("abcdefgh")
+    char_to_dim = {c: v for v, c in enumerate(chars)}
+
+    num_inputs = 10
+    inputs = []
+    subscripts = []
+    for _ in range(num_inputs):
+        subscript = np.random.choice(chars, size=5, replace=False).tolist()
+        subscripts.append("".join(subscript))
+        inputs.append(np.ones(list(char_to_dim[c] for c in subscript)))
+    subscripts = ",".join(subscripts)
+
+    np_time = timeit(np.einsum_path, args=(subscripts, *inputs))
+
+    inputs = [mx.array(x) for x in inputs]
+    mx_time = timeit(mx.einsum_path, args=(subscripts, *inputs))
+    print("Timing big einsum path...")
+    print(f"MLX ... {mx_time:.3f} ms")
+    print(f"NumPy... {np_time:.3f} ms")
+
+
+def time_attention():
+    def regular_attention(x):
+        # shape [batch, sequence, num_heads, head_dim]
+        queries, keys, values = x, x, x
+        scores = queries.transpose(0, 2, 1, 3) @ keys.transpose(0, 2, 3, 1)
+        scores = mx.softmax(scores, axis=-1)
+        output = (scores @ values.transpose(0, 2, 1, 3)).swapaxes(1, 2)
+        mx.eval(output)
+
+    def einsum_attention(x):
+        # shape [batch, sequence, num_heads, head_dim]
+        queries, keys, values = x, x, x
+        scores = mx.einsum("itjk,iujk->ijtu", queries, keys)
+        scores = mx.softmax(scores, axis=-1)
+        output = mx.einsum("ijtu,iujk->itjk", scores, values)
+        mx.eval(output)
+
+    x = mx.random.uniform(shape=(8, 512, 32, 128))
+
+    regular_time = timeit(regular_attention, args=(x,))
+    ein_time = timeit(einsum_attention, args=(x,))
+    print("Timing einsum attention...")
+    print(f"Regular ... {regular_time:.3f} ms")
+    print(f"Einsum ... {ein_time:.3f} ms")
+
+
+if __name__ == "__main__":
+    time_little_einsum_path()
+    time_big_einsum_path()
+    time_attention()

benchmarks/python/fft_bench.py

@@ -3,6 +3,8 @@
 import matplotlib
 import mlx.core as mx
 import numpy as np
+import sympy
+import torch
 from time_utils import measure_runtime
 
 matplotlib.use("Agg")
@@ -16,41 +18,100 @@ def bandwidth_gb(runtime_ms, system_size):
     return system_size * bytes_per_fft / runtime_ms * ms_per_s / bytes_per_gb
 
 
-def run_bench(system_size):
-    def fft(x):
-        out = mx.fft.fft(x)
+def run_bench(system_size, fft_sizes, backend="mlx", dim=1):
+    def fft_mlx(x):
+        if dim == 1:
+            out = mx.fft.fft(x)
+        elif dim == 2:
+            out = mx.fft.fft2(x)
         mx.eval(out)
         return out
 
-    bandwidths = []
-    for k in range(4, 12):
-        n = 2**k
-        x = mx.random.uniform(shape=(system_size // n, n)).astype(mx.float32)
-        x = x.astype(mx.complex64)
-        mx.eval(x)
-        runtime_ms = measure_runtime(fft, x=x)
-        bandwidths.append(bandwidth_gb(runtime_ms, system_size))
+    def fft_mps(x):
+        if dim == 1:
+            out = torch.fft.fft(x)
+        elif dim == 2:
+            out = torch.fft.fft2(x)
+        torch.mps.synchronize()
+        return out
 
-    return bandwidths
+    bandwidths = []
+    for n in fft_sizes:
+        batch_size = system_size // n**dim
+        shape = [batch_size] + [n for _ in range(dim)]
+        if backend == "mlx":
+            x_np = np.random.uniform(size=(system_size // n, n)).astype(np.complex64)
+            x = mx.array(x_np)
+            mx.eval(x)
+            fft = fft_mlx
+        elif backend == "mps":
+            x_np = np.random.uniform(size=(system_size // n, n)).astype(np.complex64)
+            x = torch.tensor(x_np, device="mps")
+            torch.mps.synchronize()
+            fft = fft_mps
+        else:
+            raise NotImplementedError()
+        runtime_ms = measure_runtime(fft, x=x)
+        bandwidth = bandwidth_gb(runtime_ms, np.prod(shape))
+        print(n, bandwidth)
+        bandwidths.append(bandwidth)
+
+    return np.array(bandwidths)
 
 
 def time_fft():
+    x = np.array(range(2, 512))
+    system_size = int(2**26)
 
-    with mx.stream(mx.cpu):
-        cpu_bandwidths = run_bench(system_size=int(2**22))
-
+    print("MLX GPU")
     with mx.stream(mx.gpu):
-        gpu_bandwidths = run_bench(system_size=int(2**29))
+        gpu_bandwidths = run_bench(system_size=system_size, fft_sizes=x)
 
-    # plot bandwidths
-    x = [2**k for k in range(4, 12)]
-    plt.scatter(x, gpu_bandwidths, color="green", label="GPU")
-    plt.scatter(x, cpu_bandwidths, color="red", label="CPU")
-    plt.title("MLX FFT Benchmark")
-    plt.xlabel("N")
-    plt.ylabel("Bandwidth (GB/s)")
-    plt.legend()
-    plt.savefig("fft_plot.png")
+    print("MPS GPU")
+    mps_bandwidths = run_bench(system_size=system_size, fft_sizes=x, backend="mps")
+
+    print("CPU")
+    system_size = int(2**20)
+    with mx.stream(mx.cpu):
+        cpu_bandwidths = run_bench(system_size=system_size, fft_sizes=x)
+
+    x = np.array(x)
+
+    all_indices = x - x[0]
+    radix_2to13 = (
+        np.array([i for i in x if all(p <= 13 for p in sympy.primefactors(i))]) - x[0]
+    )
+    bluesteins = (
+        np.array([i for i in x if any(p > 13 for p in sympy.primefactors(i))]) - x[0]
+    )
+
+    for indices, name in [
+        (all_indices, "All"),
+        (radix_2to13, "Radix 2-13"),
+        (bluesteins, "Bluestein's"),
+    ]:
+        # plot bandwidths
+        print(name)
+        plt.scatter(x[indices], gpu_bandwidths[indices], color="green", label="GPU")
+        plt.scatter(x[indices], mps_bandwidths[indices], color="blue", label="MPS")
+        plt.scatter(x[indices], cpu_bandwidths[indices], color="red", label="CPU")
+        plt.title(f"MLX FFT Benchmark -- {name}")
+        plt.xlabel("N")
+        plt.ylabel("Bandwidth (GB/s)")
+        plt.legend()
+        plt.savefig(f"{name}.png")
+        plt.clf()
+
+    av_gpu_bandwidth = np.mean(gpu_bandwidths)
+    av_mps_bandwidth = np.mean(mps_bandwidths)
+    av_cpu_bandwidth = np.mean(cpu_bandwidths)
+    print("Average bandwidths:")
+    print("GPU:", av_gpu_bandwidth)
+    print("MPS:", av_mps_bandwidth)
+    print("CPU:", av_cpu_bandwidth)
+
+    portion_faster = len(np.where(gpu_bandwidths > mps_bandwidths)[0]) / len(x)
+    print("Percent MLX faster than MPS: ", portion_faster * 100)
 
 
 if __name__ == "__main__":

benchmarks/python/hadamard_bench.py

@@ -0,0 +1,70 @@
+import argparse
+
+import matplotlib
+import mlx.core as mx
+import numpy as np
+from time_utils import measure_runtime
+
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+
+
+def had(x):
+    y = mx.hadamard_transform(x)
+    mx.eval(y)
+
+
+def copy(x):
+    y = x + 1.0
+    mx.eval(y)
+
+
+def run(dtype):
+    system_size = 2**26
+    outputs = {}
+    for test_fn in (had, copy):
+        for m in [1, 12, 20, 28]:
+            if test_fn == copy:
+                key = "copy"
+            elif m == 1:
+                key = "had_2^k"
+            else:
+                key = "had_m*2^k"
+            outputs.setdefault(key, {})
+            for k in range(7, 14):
+                n = m * 2**k
+                if n > 2**15:
+                    continue
+                x_np = np.random.normal(size=(system_size // n, n)).astype(dtype)
+                x = mx.array(x_np)
+                runtime_ms = measure_runtime(test_fn, x=x)
+                bytes_per_gb = 1e9
+                ms_per_s = 1e3
+                bytes_per_had = np.dtype(x_np.dtype).itemsize * 2
+                bandwidth_gb = (
+                    system_size * bytes_per_had / runtime_ms * ms_per_s / bytes_per_gb
+                )
+                print(n, bandwidth_gb)
+                outputs[key][n] = bandwidth_gb
+
+    colors = {
+        "copy": "black",
+        "had_2^k": "steelblue",
+        "had_m*2^k": "skyblue",
+    }
+    for key, output in outputs.items():
+        plt.scatter(output.keys(), output.values(), color=colors[key], label=key)
+    plt.title(f"MLX Hadamard Benchmark -- {dtype.__name__}")
+    plt.xlabel("N")
+    plt.ylabel("Bandwidth (GB/s)")
+    plt.legend()
+    plt.savefig(f"bench_{dtype.__name__}.png")
+    plt.clf()
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--fp16", action="store_true")
+    args = parser.parse_args()
+    dtype = np.float16 if args.fp16 else np.float32
+    run(dtype)

benchmarks/python/sdpa_bench.py

@@ -0,0 +1,62 @@
+import argparse
+import math
+
+import mlx.core as mx
+from time_utils import time_fn
+
+MAX_SEQ = 300
+START_SEQ = 100
+SEQ_INCREMENT = 50
+
+
+def time_self_attention_primitives():
+    mx.random.seed(3)
+    B = 2
+    H = 38
+    D = 64
+    for R in range(START_SEQ, MAX_SEQ, SEQ_INCREMENT):
+        q = mx.random.uniform(shape=(B, H, R, D))
+        k = mx.random.uniform(shape=(B, H, R, D))
+        v = mx.random.uniform(shape=(B, H, R, D))
+        scale = 1.0 / math.sqrt(float(D))
+        mx.eval(q, k, v)
+
+        def sdpa_primitives(qs, ks, vs, alpha):
+            s = (alpha * qs) @ ks.transpose(0, 1, 3, 2)
+            p = mx.softmax(s.astype(mx.float32), axis=-1).astype(s.dtype)
+            o = p @ vs
+            return o
+
+        time_fn(sdpa_primitives, q, k, v, scale)
+
+
+def time_self_attention_sdpa():
+    mx.random.seed(3)
+    B = 2
+    H = 38
+    D = 64
+    for R in range(START_SEQ, MAX_SEQ, SEQ_INCREMENT):
+        q = mx.random.uniform(shape=(B, H, R, D))
+        k = mx.random.uniform(shape=(B, H, R, D))
+        v = mx.random.uniform(shape=(B, H, R, D))
+        scale = 1.0 / math.sqrt(float(D))
+        mx.eval(q, k, v)
+
+        def sdpa_fused(qs, ks, vs, alpha):
+            o = mx.fast.scaled_dot_product_attention(qs, ks, vs, scale=alpha)
+            return o
+
+        time_fn(sdpa_fused, q, k, v, scale)
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser("MLX benchmarks.")
+    parser.add_argument("--gpu", action="store_true", help="Use the Metal back-end.")
+    args = parser.parse_args()
+    if args.gpu:
+        mx.set_default_device(mx.gpu)
+    else:
+        mx.set_default_device(mx.cpu)
+
+    time_self_attention_sdpa()
+    time_self_attention_primitives()

cmake/metal.14.0.diff

@@ -1,36 +0,0 @@
-diff -ur Metal/MTLEvent.hpp MetalNew/MTLEvent.hpp
---- Metal/MTLEvent.hpp	2023-06-01 12:18:26
-+++ MetalNew/MTLEvent.hpp	2024-04-15 07:36:59
-@@ -62,6 +62,7 @@
- 
-     uint64_t                 signaledValue() const;
-     void                     setSignaledValue(uint64_t signaledValue);
-+    bool                     waitUntilSignaledValue(uint64_t signaledValue, uint64_t timeoutMS);
- };
- 
- class SharedEventHandle : public NS::SecureCoding<SharedEventHandle>
-@@ -138,6 +139,11 @@
- _MTL_INLINE void MTL::SharedEvent::setSignaledValue(uint64_t signaledValue)
- {
-     Object::sendMessage<void>(this, _MTL_PRIVATE_SEL(setSignaledValue_), signaledValue);
-+}
-+
-+// method: waitUntilSignaledValue
-+_MTL_INLINE bool MTL::SharedEvent::waitUntilSignaledValue(uint64_t signaledValue, uint64_t timeoutMS) {
-+    return Object::sendMessage<bool>(this, _MTL_PRIVATE_SEL(waitUntilSignaledValue_timeoutMS_), signaledValue, timeoutMS);
- }
- 
- // static method: alloc
-diff -ur Metal/MTLHeaderBridge.hpp MetalNew/MTLHeaderBridge.hpp
---- Metal/MTLHeaderBridge.hpp	2023-06-01 12:18:26
-+++ MetalNew/MTLHeaderBridge.hpp	2024-04-15 07:37:29
-@@ -1906,6 +1906,9 @@
-     "setShouldMaximizeConcurrentCompilation:");
- _MTL_PRIVATE_DEF_SEL(setSignaledValue_,
-     "setSignaledValue:");
-+_MTL_PRIVATE_DEF_SEL(
-+    waitUntilSignaledValue_timeoutMS_,
-+    "waitUntilSignaledValue:timeoutMS:");
- _MTL_PRIVATE_DEF_SEL(setSize_,
-     "setSize:");
- _MTL_PRIVATE_DEF_SEL(setSlice_,

cmake/metal.14.2.diff

@@ -1,36 +0,0 @@
-diff -ur Metal/MTLEvent.hpp MetalNew/MTLEvent.hpp
---- Metal/MTLEvent.hpp	2024-04-15 07:12:10
-+++ MetalNew/MTLEvent.hpp	2024-04-15 07:15:50
-@@ -62,6 +62,7 @@
- 
-     uint64_t                 signaledValue() const;
-     void                     setSignaledValue(uint64_t signaledValue);
-+    bool                     waitUntilSignaledValue(uint64_t signaledValue, uint64_t timeoutMS);
- };
- 
- class SharedEventHandle : public NS::SecureCoding<SharedEventHandle>
-@@ -138,6 +139,11 @@
- _MTL_INLINE void MTL::SharedEvent::setSignaledValue(uint64_t signaledValue)
- {
-     Object::sendMessage<void>(this, _MTL_PRIVATE_SEL(setSignaledValue_), signaledValue);
-+}
-+
-+// method: waitUntilSignaledValue
-+_MTL_INLINE bool MTL::SharedEvent::waitUntilSignaledValue(uint64_t signaledValue, uint64_t timeoutMS) {
-+    return Object::sendMessage<bool>(this, _MTL_PRIVATE_SEL(waitUntilSignaledValue_timeoutMS_), signaledValue, timeoutMS);
- }
- 
- // static method: alloc
-diff -ur Metal/MTLHeaderBridge.hpp MetalNew/MTLHeaderBridge.hpp
---- Metal/MTLHeaderBridge.hpp	2024-04-15 07:12:10
-+++ MetalNew/MTLHeaderBridge.hpp	2024-04-15 07:16:15
-@@ -1918,6 +1918,9 @@
-     "setShouldMaximizeConcurrentCompilation:");
- _MTL_PRIVATE_DEF_SEL(setSignaledValue_,
-     "setSignaledValue:");
-+_MTL_PRIVATE_DEF_SEL(
-+    waitUntilSignaledValue_timeoutMS_,
-+    "waitUntilSignaledValue:timeoutMS:");
- _MTL_PRIVATE_DEF_SEL(setSize_,
-     "setSize:");
- _MTL_PRIVATE_DEF_SEL(setSlice_,

docs/requirements.txt

@@ -1,3 +1,4 @@
 sphinx
 breathe
 sphinx-book-theme
+mlx

docs/src/conf.py

@@ -83,3 +83,15 @@ def setup(app):
 # -- Options for LaTeX output ------------------------------------------------
 
 latex_documents = [(main_doc, "MLX.tex", "MLX Documentation", author, "manual")]
+latex_elements = {
+    "preamble": r"""
+    \usepackage{enumitem}
+    \setlistdepth{5}
+    \setlist[itemize,1]{label=$\bullet$}
+    \setlist[itemize,2]{label=$\bullet$}
+    \setlist[itemize,3]{label=$\bullet$}
+    \setlist[itemize,4]{label=$\bullet$}
+    \setlist[itemize,5]{label=$\bullet$}
+    \renewlist{itemize}{itemize}{5}
+""",
+}

docs/src/dev/extensions.rst

@@ -486,9 +486,8 @@ below.
         std::ostringstream kname;
         kname << "axpby_" << "general_" << type_to_name(out);
 
-        // Make sure the metal library is available and look for it
-        // in the same folder as this executable if needed
-        d.register_library("mlx_ext", metal::get_colocated_mtllib_path);
+        // Make sure the metal library is available
+        d.register_library("mlx_ext");
 
         // Make a kernel from this metal library
         auto kernel = d.get_kernel(kname.str(), "mlx_ext");

docs/src/examples/llama-inference.rst

@@ -15,7 +15,7 @@ module to concisely define the model architecture.
 Attention layer
 ^^^^^^^^^^^^^^^^
 
-We will start with the llama attention layer which notably uses the RoPE
+We will start with the Llama attention layer which notably uses the RoPE
 positional encoding. [1]_ In addition, our attention layer will optionally use a
 key/value cache that will be concatenated with the provided keys and values to
 support efficient inference.

docs/src/examples/mlp.rst

@@ -64,7 +64,7 @@ set:
 Next, setup the problem parameters and load the data. To load the data, you need our
 `mnist data loader
 <https://github.com/ml-explore/mlx-examples/blob/main/mnist/mnist.py>`_, which
-we will import as `mnist`.
+we will import as ``mnist``.
 
 .. code-block:: python
 

docs/src/index.rst

@@ -43,6 +43,7 @@ are the CPU and GPU.
    usage/function_transforms
    usage/compile
    usage/numpy
+   usage/distributed
    usage/using_streams
 
 .. toctree::
@@ -69,6 +70,7 @@ are the CPU and GPU.
    python/metal
    python/nn
    python/optimizers
+   python/distributed
    python/tree_utils
 
 .. toctree::

docs/src/install.rst

@@ -70,36 +70,36 @@ To build and install the MLX python library from source, first, clone MLX from
 
    git clone git@github.com:ml-explore/mlx.git mlx && cd mlx
 
-Install `nanobind <https://nanobind.readthedocs.io/en/latest/>`_ with:
-
-.. code-block:: shell
-
-    pip install git+https://github.com/wjakob/nanobind.git@2f04eac452a6d9142dedb957701bdb20125561e4
-
 Then simply build and install MLX using pip:
 
 .. code-block:: shell
 
-   env CMAKE_BUILD_PARALLEL_LEVEL="" pip install .
+  CMAKE_BUILD_PARALLEL_LEVEL="" pip install .
 
-For developing use an editable install:
+For developing, install the package with development dependencies, and use an
+editable install:
 
 .. code-block:: shell
 
-  env CMAKE_BUILD_PARALLEL_LEVEL="" pip install -e .
+  CMAKE_BUILD_PARALLEL_LEVEL="" pip install -e ".[dev]"
 
-To make sure the install is working run the tests with:
+Once the development dependencies are installed, you can build faster with:
+
+.. code-block:: shell
+
+ CMAKE_BUILD_PARALLEL_LEVEL="" python setup.py build_ext -j --inplace
+
+Run the tests with:
 
 .. code-block:: shell
 
-  pip install ".[testing]"
   python -m unittest discover python/tests
 
-Optional: Install stubs to enable auto completions and type checking from your IDE:
+Optional: Install stubs to enable auto completions and type checking from your
+IDE:
 
 .. code-block:: shell
 
-  pip install ".[dev]"
   python setup.py generate_stubs
 
 C++ API
@@ -186,8 +186,8 @@ should point to the path to the built metal library.
 Binary Size Minimization
 ~~~~~~~~~~~~~~~~~~~~~~~~
 
-To produce a smaller binary use the CMake flags `CMAKE_BUILD_TYPE=MinSizeRel`
-and `BUILD_SHARED_LIBS=ON`.
+To produce a smaller binary use the CMake flags ``CMAKE_BUILD_TYPE=MinSizeRel``
+and ``BUILD_SHARED_LIBS=ON``.
 
 The MLX CMake build has several additional options to make smaller binaries.
 For example, if you don't need the CPU backend or support for safetensors and
@@ -195,7 +195,7 @@ GGUF, you can do:
 
 .. code-block:: shell
 
-  cmake ..
+  cmake .. \
     -DCMAKE_BUILD_TYPE=MinSizeRel \
     -DBUILD_SHARED_LIBS=ON \
     -DMLX_BUILD_CPU=OFF \
@@ -203,7 +203,7 @@ GGUF, you can do:
     -DMLX_BUILD_GGUF=OFF \
     -DMLX_METAL_JIT=ON
 
-THE `MLX_METAL_JIT` flag minimizes the size of the MLX Metal library which
+THE ``MLX_METAL_JIT`` flag minimizes the size of the MLX Metal library which
 contains pre-built GPU kernels. This substantially reduces the size of the
 Metal library by run-time compiling kernels the first time they are used in MLX
 on a given machine. Note run-time compilation incurs a cold-start cost which can

docs/src/python/array.rst

@@ -24,6 +24,7 @@ Array
     array.any
     array.argmax
     array.argmin
+    array.conj
     array.cos
     array.cummax
     array.cummin
@@ -57,3 +58,4 @@ Array
     array.transpose
     array.T
     array.var
+    array.view

docs/src/python/distributed.rst

@@ -0,0 +1,19 @@
+.. _distributed:
+
+.. currentmodule:: mlx.core.distributed
+
+Distributed Communication
+==========================
+
+MLX provides a distributed communication package using MPI. The MPI library is
+loaded at runtime; if MPI is available then distributed communication is also
+made available.
+
+.. autosummary::
+   :toctree: _autosummary
+
+    Group
+    is_available
+    init
+    all_sum
+    all_gather

docs/src/python/linalg.rst

@@ -9,7 +9,9 @@ Linear Algebra
    :toctree: _autosummary 
 
     inv
+    tri_inv
     norm
     cholesky
+    cholesky_inv
     qr
     svd

docs/src/python/nn/functions.rst

@@ -17,6 +17,8 @@ simple functions.
    gelu_approx
    gelu_fast_approx
    glu
+   hard_shrink
+   hard_tanh
    hardswish
    leaky_relu
    log_sigmoid
@@ -29,6 +31,7 @@ simple functions.
    sigmoid
    silu
    softmax
+   softmin
    softplus
    softshrink
    step

docs/src/python/nn/layers.rst

@@ -21,10 +21,15 @@ Layers
    Dropout3d
    Embedding
    GELU
+   GLU
    GroupNorm
    GRU
+   HardShrink
+   HardTanh
+   Hardswish
    InstanceNorm
    LayerNorm
+   LeakyReLU
    Linear
    LSTM
    MaxPool1d
@@ -36,13 +41,19 @@ Layers
    QuantizedLinear
    RMSNorm
    ReLU
+   ReLU6
    RNN
    RoPE
    SELU
    Sequential
    SiLU
    SinusoidalPositionalEncoding
+   Softmin
    Softshrink
+   Softsign
+   Softmax
+   Softplus
    Step
+   Tanh
    Transformer
    Upsample

docs/src/python/ops.rst

@@ -57,6 +57,8 @@ Operations
    diagonal
    divide
    divmod
+   einsum
+   einsum_path
    equal
    erf
    erfinv
@@ -72,6 +74,7 @@ Operations
    gather_qmm
    greater
    greater_equal
+   hadamard_transform
    identity
    inner
    isclose
@@ -103,6 +106,7 @@ Operations
    minimum
    moveaxis
    multiply
+   nan_to_num
    negative
    not_equal
    ones
@@ -156,6 +160,7 @@ Operations
    tril
    triu
    var
+   view
    where
    zeros
    zeros_like

docs/src/python/optimizers.rst

@@ -31,6 +31,41 @@ model's parameters and the **optimizer state**.
             # Compute the new parameters but also the optimizer state.
             mx.eval(model.parameters(), optimizer.state)
 
+Saving and Loading
+------------------
+
+To serialize an optimizer, save its state. To load an optimizer, load and set
+the saved state. Here's a simple example:
+
+.. code-block:: python
+
+   import mlx.core as mx
+   from mlx.utils import tree_flatten, tree_unflatten
+   import mlx.optimizers as optim
+
+   optimizer = optim.Adam(learning_rate=1e-2)
+
+   # Perform some updates with the optimizer
+   model = {"w" : mx.zeros((5, 5))}
+   grads = {"w" : mx.ones((5, 5))}
+   optimizer.update(model, grads)
+
+   # Save the state
+   state = tree_flatten(optimizer.state)
+   mx.save_safetensors("optimizer.safetensors", dict(state))
+
+   # Later on, for example when loading from a checkpoint,
+   # recreate the optimizer and load the state
+   optimizer = optim.Adam(learning_rate=1e-2)
+
+   state = tree_unflatten(list(mx.load("optimizer.safetensors").items()))
+   optimizer.state = state
+
+Note, not every optimizer configuation parameter is saved in the state. For
+example, for Adam the learning rate is saved but the ``betas`` and ``eps``
+parameters are not. A good rule of thumb is if the parameter can be scheduled
+then it will be included in the optimizer state.
+
 .. toctree::
 
    optimizers/optimizer

docs/src/python/random.rst

@@ -44,3 +44,4 @@ we use a splittable version of Threefry, which is a counter-based PRNG.
    split
    truncated_normal
    uniform
+   laplace

docs/src/python/transforms.rst

@@ -10,6 +10,7 @@ Transforms
 
    eval
    compile
+   custom_function
    disable_compile
    enable_compile
    grad

docs/src/usage/distributed.rst

@@ -0,0 +1,166 @@
+.. _usage_distributed:
+
+Distributed Communication
+=========================
+
+.. currentmodule:: mlx.core.distributed
+
+MLX utilizes `MPI <https://en.wikipedia.org/wiki/Message_Passing_Interface>`_ to
+provide distributed communication operations that allow the computational cost
+of training or inference to be shared across many physical machines. You can
+see a list of the supported operations in the :ref:`API docs<distributed>`.
+
+.. note::
+   A lot of operations may not be supported or not as fast as they should be.
+   We are adding more and tuning the ones we have as we are figuring out the
+   best way to do distributed computing on Macs using MLX.
+
+Getting Started
+---------------
+
+MLX already comes with the ability to "talk" to MPI if it is installed on the
+machine. The minimal distributed program in MLX is as simple as:
+
+.. code:: python
+
+    import mlx.core as mx
+
+    world = mx.distributed.init()
+    x = mx.distributed.all_sum(mx.ones(10))
+    print(world.rank(), x)
+
+The program above sums the array ``mx.ones(10)`` across all
+distributed processes. If simply run with ``python``, however, only one
+process is launched and no distributed communication takes place.
+
+To launch the program in distributed mode we need to use ``mpirun`` or
+``mpiexec`` depending on the MPI installation. The simplest possible way is the
+following:
+
+.. code:: shell
+
+    $ mpirun -np 2 python test.py
+    1 array([2, 2, 2, ..., 2, 2, 2], dtype=float32)
+    0 array([2, 2, 2, ..., 2, 2, 2], dtype=float32)
+
+The above launches two processes on the same (local) machine and we can see
+both standard output streams. The processes send the array of 1s to each other
+and compute the sum which is printed. Launching with ``mpirun -np 4 ...`` would
+print 4 etc.
+
+Installing MPI
+---------------
+
+MPI can be installed with Homebrew, using the Anaconda package manager or
+compiled from source. Most of our testing is done using ``openmpi`` installed
+with the Anaconda package manager as follows:
+
+.. code:: shell
+
+    $ conda install openmpi
+
+Installing with Homebrew may require specifying the location of ``libmpi.dyld``
+so that MLX can find it and load it at runtime. This can simply be achieved by
+passing the ``DYLD_LIBRARY_PATH`` environment variable to ``mpirun``.
+
+.. code:: shell
+
+    $ mpirun -np 2 -x DYLD_LIBRARY_PATH=/opt/homebrew/lib/ python test.py
+
+Setting up Remote Hosts
+-----------------------
+
+MPI can automatically connect to remote hosts and set up the communication over
+the network if the remote hosts can be accessed via ssh. A good checklist to
+debug connectivity issues is the following:
+
+* ``ssh hostname`` works from all machines to all machines without asking for
+  password or host confirmation
+* ``mpirun`` is accessible on all machines. You can call ``mpirun`` using its
+  full path to force all machines to use a specific path.
+* Ensure that the ``hostname`` used by MPI is the one that you have configured
+  in the ``.ssh/config`` files on all machines.
+
+.. note::
+  For an example hostname ``foo.bar.com`` MPI can use only ``foo`` as
+  the hostname passed to ssh if the current hostname matches ``*.bar.com``.
+
+An easy way to pass the host names to MPI is using a host file. A host file
+looks like the following, where ``host1`` and ``host2`` should be the fully
+qualified domain names or IPs for these hosts.
+
+.. code::
+
+    host1 slots=1
+    host2 slots=1
+
+When using MLX, it is very likely that you want to use 1 slot per host, ie one
+process per host.  The hostfile also needs to contain the current
+host if you want to run on the local host. Passing the host file to
+``mpirun`` is simply done using the ``--hostfile`` command line argument.
+
+Training Example
+----------------
+
+In this section we will adapt an MLX training loop to support data parallel
+distributed training. Namely, we will average the gradients across a set of
+hosts before applying them to the model.
+
+Our training loop looks like the following code snippet if we omit the model,
+dataset and optimizer initialization.
+
+.. code:: python
+
+    model = ...
+    optimizer = ...
+    dataset = ...
+
+    def step(model, x, y):
+        loss, grads = loss_grad_fn(model, x, y)
+        optimizer.update(model, grads)
+        return loss
+
+    for x, y in dataset:
+        loss = step(model, x, y)
+        mx.eval(loss, model.parameters())
+
+All we have to do to average the gradients across machines is perform an
+:func:`all_sum` and divide by the size of the :class:`Group`. Namely we
+have to :func:`mlx.utils.tree_map` the gradients with following function.
+
+.. code:: python
+
+    def all_avg(x):
+        return mx.distributed.all_sum(x) / mx.distributed.init().size()
+
+Putting everything together our training loop step looks as follows with
+everything else remaining the same.
+
+.. code:: python
+
+    from mlx.utils import tree_map
+
+    def all_reduce_grads(grads):
+        N = mx.distributed.init()
+        if N == 1:
+            return grads
+        return tree_map(
+                lambda x: mx.distributed.all_sum(x) / N,
+                grads)
+
+    def step(model, x, y):
+        loss, grads = loss_grad_fn(model, x, y)
+        grads = all_reduce_grads(grads)  # <--- This line was added
+        optimizer.update(model, grads)
+        return loss
+
+Tuning All Reduce
+-----------------
+
+We are working on improving the performance of all reduce on MLX but for now
+the two main things one can do to extract the most out of distributed training with MLX are:
+
+1. Perform a few large reductions instead of many small ones to improve
+   bandwidth and latency
+2. Pass ``--mca btl_tcp_links 4`` to ``mpirun`` to configure it to use 4 tcp
+   connections between each host to improve bandwidth

docs/src/usage/numpy.rst

@@ -3,7 +3,11 @@
 Conversion to NumPy and Other Frameworks
 ========================================
 
-MLX array implements the `Python Buffer Protocol <https://docs.python.org/3/c-api/buffer.html>`_.
+MLX array supports conversion between other frameworks with either:  
+
+* The `Python Buffer Protocol <https://docs.python.org/3/c-api/buffer.html>`_. 
+* `DLPack <https://dmlc.github.io/dlpack/latest/>`_.  
+
 Let's convert an array to NumPy and back.
 
 .. code-block:: python

examples/cpp/distributed.cpp

@@ -16,7 +16,7 @@ int main() {
   std::cout << global_group.rank() << " / " << global_group.size() << std::endl;
 
   array x = ones({10});
-  array out = distributed::all_reduce_sum(x, global_group);
+  array out = distributed::all_sum(x, global_group);
 
   std::cout << out << std::endl;
 }

examples/extensions/axpby/axpby.cpp

@@ -249,9 +249,8 @@ void Axpby::eval_gpu(
   kname << (contiguous_kernel ? "contiguous_" : "general_");
   kname << type_to_name(out);
 
-  // Make sure the metal library is available and look for it
-  // in the same folder as this executable if needed
-  d.register_library("mlx_ext", metal::get_colocated_mtllib_path);
+  // Make sure the metal library is available
+  d.register_library("mlx_ext");
 
   // Make a kernel from this metal library
   auto kernel = d.get_kernel(kname.str(), "mlx_ext");

examples/extensions/requirements.txt

@@ -1,4 +1,4 @@
 setuptools>=42
 cmake>=3.24
-mlx>=0.9.0
-nanobind@git+https://github.com/wjakob/nanobind.git@2f04eac452a6d9142dedb957701bdb20125561e4
+mlx>=0.16.2
+nanobind==2.0

mlx/CMakeLists.txt

@@ -6,6 +6,7 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/compile.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/device.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/dtype.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/einsum.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/fast.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/fft.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/ops.cpp

mlx/array.cpp

@@ -17,6 +17,10 @@ bool in_tracing() {
   return detail::InTracing::in_tracing();
 }
 
+bool retain_graph() {
+  return detail::RetainGraph::retain_graph();
+}
+
 } // namespace
 
 array::array(const std::complex<float>& val, Dtype dtype /* = complex64 */)
@@ -102,7 +106,7 @@ void array::eval() {
 }
 
 bool array::is_tracer() const {
-  return array_desc_->is_tracer && in_tracing();
+  return array_desc_->is_tracer && in_tracing() || retain_graph();
 }
 
 void array::set_data(allocator::Buffer buffer, deleter_t d) {
@@ -171,10 +175,11 @@ array::~array() {
     return;
   }
 
-  // Ignore arrays that will be detached
-  if (status() != array::Status::unscheduled) {
+  // Ignore arrays that might be detached during eval
+  if (status() == array::Status::scheduled) {
     return;
   }
+
   // Break circular reference for non-detached arrays with siblings
   if (auto n = siblings().size(); n > 0) {
     bool do_detach = true;
@@ -206,7 +211,7 @@ void array::ArrayDesc::init() {
     strides[i] = size;
     size *= shape[i];
   }
-  for (auto& in : inputs) {
+  for (const auto& in : inputs) {
     is_tracer |= in.is_tracer();
   }
 }
@@ -231,7 +236,7 @@ array::ArrayDesc::ArrayDesc(
 
 array::ArrayDesc::~ArrayDesc() {
   // When an array description is destroyed it will delete a bunch of arrays
-  // that may also destory their corresponding descriptions and so on and so
+  // that may also destroy their corresponding descriptions and so on and so
   // forth.
   //
   // This calls recursively the destructor and can result in stack overflow, we

mlx/array.h

@@ -73,32 +73,32 @@ class array {
       this->array_desc_ = other.array_desc_;
     }
     return *this;
-  };
+  }
 
   /** The size of the array's datatype in bytes. */
   size_t itemsize() const {
     return size_of(dtype());
-  };
+  }
 
   /** The number of elements in the array. */
   size_t size() const {
     return array_desc_->size;
-  };
+  }
 
   /** The number of bytes in the array. */
   size_t nbytes() const {
     return size() * itemsize();
-  };
+  }
 
   /** The number of dimensions of the array. */
   size_t ndim() const {
     return array_desc_->shape.size();
-  };
+  }
 
   /** The shape of the array as a vector of integers. */
   const std::vector<int>& shape() const {
     return array_desc_->shape;
-  };
+  }
 
   /**
    *  Get the size of the corresponding dimension.
@@ -107,12 +107,12 @@ class array {
    *  bounds checking. */
   int shape(int dim) const {
     return shape().at(dim < 0 ? dim + ndim() : dim);
-  };
+  }
 
   /** The strides of the array. */
   const std::vector<size_t>& strides() const {
     return array_desc_->strides;
-  };
+  }
 
   /**
    *  Get the stride of the corresponding dimension.
@@ -121,12 +121,12 @@ class array {
    *  bounds checking. */
   size_t strides(int dim) const {
     return strides().at(dim < 0 ? dim + ndim() : dim);
-  };
+  }
 
   /** Get the arrays data type. */
   Dtype dtype() const {
     return array_desc_->dtype;
-  };
+  }
 
   /** Evaluate the array. */
   void eval();
@@ -160,10 +160,10 @@ class array {
 
     friend bool operator==(const ArrayIterator& a, const ArrayIterator& b) {
       return a.arr.id() == b.arr.id() && a.idx == b.idx;
-    };
+    }
     friend bool operator!=(const ArrayIterator& a, const ArrayIterator& b) {
       return !(a == b);
-    };
+    }
 
    private:
     const array& arr;
@@ -209,7 +209,7 @@ class array {
     allocator::Buffer buffer;
     deleter_t d;
     Data(allocator::Buffer buffer, deleter_t d = allocator::free)
-        : buffer(buffer), d(d) {};
+        : buffer(buffer), d(d) {}
     // Not copyable
     Data(const Data& d) = delete;
     Data& operator=(const Data& d) = delete;
@@ -230,22 +230,22 @@ class array {
   /** The array's primitive. */
   Primitive& primitive() const {
     return *(array_desc_->primitive);
-  };
+  }
 
   /** A shared pointer to the array's primitive. */
   std::shared_ptr<Primitive>& primitive_ptr() const {
     return array_desc_->primitive;
-  };
+  }
 
   /** Check if the array has an attached primitive or is a leaf node. */
   bool has_primitive() const {
     return array_desc_->primitive != nullptr;
-  };
+  }
 
   /** The array's inputs. */
   const std::vector<array>& inputs() const {
     return array_desc_->inputs;
-  };
+  }
 
   std::vector<array>& inputs() {
     return array_desc_->inputs;
@@ -259,12 +259,12 @@ class array {
   /** The array's siblings. */
   const std::vector<array>& siblings() const {
     return array_desc_->siblings;
-  };
+  }
 
   /** The array's siblings. */
   std::vector<array>& siblings() {
     return array_desc_->siblings;
-  };
+  }
 
   void set_siblings(std::vector<array> siblings, uint16_t position) {
     array_desc_->siblings = std::move(siblings);
@@ -281,7 +281,7 @@ class array {
     outputs.push_back(*this);
     outputs.insert(outputs.end(), siblings().begin() + idx, siblings().end());
     return outputs;
-  };
+  }
 
   /** Detach the array from the graph. */
   void detach();
@@ -289,19 +289,19 @@ class array {
   /** Get the Flags bit-field. */
   const Flags& flags() const {
     return array_desc_->flags;
-  };
+  }
 
   /** The size (in elements) of the underlying buffer the array points to. */
   size_t data_size() const {
     return array_desc_->data_size;
-  };
+  }
 
   allocator::Buffer& buffer() {
     return array_desc_->data->buffer;
-  };
+  }
   const allocator::Buffer& buffer() const {
     return array_desc_->data->buffer;
-  };
+  }
 
   // Return a copy of the shared pointer
   // to the array::Data struct
@@ -312,19 +312,20 @@ class array {
   template <typename T>
   T* data() {
     return static_cast<T*>(array_desc_->data_ptr);
-  };
+  }
 
   template <typename T>
   const T* data() const {
     return static_cast<T*>(array_desc_->data_ptr);
-  };
+  }
 
   enum Status { unscheduled, scheduled, available };
 
   bool is_available() const {
     return status() == Status::available;
   }
-  const Status status() const {
+
+  Status status() const {
     return array_desc_->status;
   }
 

mlx/backend/accelerate/conv.cpp

@@ -1,9 +1,9 @@
-// Copyright © 2023 Apple Inc.
+// Copyright © 2023-2024 Apple Inc.
 
 #include <cassert>
 
+#include <Accelerate/Accelerate.h>
 #include <simd/vector.h>
-#include <vecLib/vDSP.h>
 
 #include "mlx/backend/common/copy.h"
 #include "mlx/primitives.h"

mlx/backend/accelerate/matmul.cpp

@@ -2,8 +2,7 @@
 
 #include <cassert>
 
-#include <vecLib/BNNS/bnns.h>
-#include <vecLib/cblas_new.h>
+#include <Accelerate/Accelerate.h>
 
 #include "mlx/backend/accelerate/utils.h"
 #include "mlx/backend/common/copy.h"

mlx/backend/accelerate/primitives.cpp

@@ -3,8 +3,7 @@
 #include <cassert>
 #include <cmath>
 
-#include <vecLib/vDSP.h>
-#include <vecLib/vForce.h>
+#include <Accelerate/Accelerate.h>
 
 #include "mlx/allocator.h"
 #include "mlx/backend/common/binary.h"
@@ -37,7 +36,7 @@ DEFAULT(Ceil)
 DEFAULT(Concatenate)
 DEFAULT(Conjugate)
 DEFAULT(Copy)
-DEFAULT_MULTI(CustomVJP)
+DEFAULT_MULTI(CustomTransforms)
 DEFAULT_MULTI(Depends)
 DEFAULT_MULTI(DivMod)
 DEFAULT(NumberOfElements)
@@ -51,6 +50,7 @@ DEFAULT(GatherMM)
 DEFAULT(GatherQMM)
 DEFAULT(Greater)
 DEFAULT(GreaterEqual)
+DEFAULT(Hadamard)
 DEFAULT(Less)
 DEFAULT(LessEqual)
 DEFAULT(Load)
@@ -102,7 +102,7 @@ void Add::eval_cpu(const std::vector<array>& inputs, array& out) {
   auto& b = inputs[1];
 
   if (a.dtype() == float32) {
-    binary(
+    binary_op<float>(
         a,
         b,
         out,
@@ -117,7 +117,7 @@ void Add::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vadd((const float*)a, 1, (const float*)b, 1, (float*)o, 1, n);
         });
   } else if (a.dtype() == int32) {
-    binary(
+    binary_op<int>(
         a,
         b,
         out,
@@ -132,7 +132,7 @@ void Add::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vaddi((const int*)a, 1, (const int*)b, 1, (int*)o, 1, n);
         });
   } else {
-    binary(a, b, out, [](auto x, auto y) { return x + y; });
+    eval(inputs, out);
   }
 }
 
@@ -287,7 +287,7 @@ void Divide::eval_cpu(const std::vector<array>& inputs, array& out) {
   auto& b = inputs[1];
 
   if (a.dtype() == int32) {
-    binary(
+    binary_op<int>(
         a,
         b,
         out,
@@ -300,7 +300,7 @@ void Divide::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vdivi((const int*)b, 1, (const int*)a, 1, (int*)o, 1, n);
         });
   } else if (a.dtype() == float32) {
-    binary(
+    binary_op<float>(
         a,
         b,
         out,
@@ -315,7 +315,7 @@ void Divide::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vdiv((const float*)b, 1, (const float*)a, 1, (float*)o, 1, n);
         });
   } else {
-    binary(a, b, out, [](auto x, auto y) { return x / y; });
+    eval(inputs, out);
   }
 }
 
@@ -326,12 +326,8 @@ void Exp::eval_cpu(const std::vector<array>& inputs, array& out) {
     set_unary_output_data(in, out);
     auto size = in.data_size();
     vvexpf(out.data<float>(), in.data<float>(), reinterpret_cast<int*>(&size));
-  } else if (issubdtype(out.dtype(), inexact)) {
-    unary_fp(in, out, [](auto x) { return std::exp(x); });
   } else {
-    throw std::invalid_argument(
-        "[exp] Cannot exponentiate elements in array"
-        " with non floating point type.");
+    eval(inputs, out);
   }
 }
 
@@ -393,12 +389,8 @@ void Log1p::eval_cpu(const std::vector<array>& inputs, array& out) {
     auto size = in.data_size();
     vvlog1pf(
         out.data<float>(), in.data<float>(), reinterpret_cast<int*>(&size));
-  } else if (issubdtype(out.dtype(), inexact)) {
-    unary_fp(in, out, [](auto x) { return std::log1p(x); });
   } else {
-    throw std::invalid_argument(
-        "[log1p] Cannot compute log of elements in array with"
-        " non floating point type.");
+    eval(inputs, out);
   }
 }
 
@@ -408,7 +400,7 @@ void Multiply::eval_cpu(const std::vector<array>& inputs, array& out) {
   auto& b = inputs[1];
 
   if (a.dtype() == float32) {
-    binary(
+    binary_op<float>(
         a,
         b,
         out,
@@ -423,7 +415,7 @@ void Multiply::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vmul((const float*)a, 1, (const float*)b, 1, (float*)o, 1, n);
         });
   } else {
-    binary(a, b, out, [](auto x, auto y) { return x * y; });
+    eval(inputs, out);
   }
 }
 
@@ -434,7 +426,7 @@ void Negative::eval_cpu(const std::vector<array>& inputs, array& out) {
     set_unary_output_data(in, out);
     vDSP_vneg(in.data<float>(), 1, out.data<float>(), 1, in.data_size());
   } else {
-    unary(in, out, [](auto x) { return -x; });
+    eval(inputs, out);
   }
 }
 
@@ -521,7 +513,7 @@ void Square::eval_cpu(const std::vector<array>& inputs, array& out) {
     auto size = in.data_size();
     vDSP_vsq(in.data<float>(), 1, out.data<float>(), 1, size);
   } else {
-    unary(in, out, [](auto x) { return x * x; });
+    eval(inputs, out);
   }
 }
 
@@ -547,7 +539,7 @@ void Subtract::eval_cpu(const std::vector<array>& inputs, array& out) {
   auto& b = inputs[1];
 
   if (a.dtype() == float32) {
-    binary(
+    binary_op<float>(
         a,
         b,
         out,
@@ -565,7 +557,7 @@ void Subtract::eval_cpu(const std::vector<array>& inputs, array& out) {
           vDSP_vsub((const float*)b, 1, (const float*)a, 1, (float*)o, 1, n);
         });
   } else if (a.dtype() == int32) {
-    binary(
+    binary_op<int>(
         a,
         b,
         out,
@@ -577,7 +569,7 @@ void Subtract::eval_cpu(const std::vector<array>& inputs, array& out) {
         },
         UseDefaultBinaryOp());
   } else {
-    binary(a, b, out, [](auto x, auto y) { return x - y; });
+    eval(inputs, out);
   }
 }
 

mlx/backend/accelerate/reduce.cpp

@@ -2,8 +2,8 @@
 
 #include <cassert>
 
+#include <Accelerate/Accelerate.h>
 #include <simd/vector.h>
-#include <vecLib/vDSP.h>
 
 #include "mlx/backend/common/reduce.h"
 #include "mlx/primitives.h"

mlx/backend/accelerate/softmax.cpp

@@ -3,7 +3,10 @@
 #include <cassert>
 #include <limits>
 
+#if __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
 #include <arm_neon.h>
+#endif
+
 #include <simd/math.h>
 #include <simd/vector.h>
 
@@ -53,25 +56,26 @@ inline simd_float16 simd_fast_exp(simd_float16 x) {
   return (*(simd_float16*)&epart) * x;
 }
 
+#if __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
 /**
  * The ARM neon equivalent of the fast exp above.
  */
 inline float16x8_t neon_fast_exp(float16x8_t x) {
-  x = vmulq_f16(x, vdupq_n_f16(1.442695)); // multiply with log_2(e)
-  x = vmaxq_f16(x, vdupq_n_f16(-14)); // clamp under with -14
-  x = vminq_f16(x, vdupq_n_f16(14)); // clamp over with 14
+  x = vmulq_f16(x, vdupq_n_f16(float16_t(1.442695f))); // multiply with log_2(e)
+  x = vmaxq_f16(x, vdupq_n_f16(float16_t(-14.f))); // clamp under with -14
+  x = vminq_f16(x, vdupq_n_f16(float16_t(14.f))); // clamp over with 14
 
-  float16x8_t ipart = vrndmq_f16(vaddq_f16(x, vdupq_n_f16(0.5)));
+  float16x8_t ipart = vrndmq_f16(vaddq_f16(x, vdupq_n_f16(float16_t(0.5f))));
   float16x8_t fpart = vsubq_f16(x, ipart);
 
-  x = vdupq_n_f16(1.535336188319500e-4f);
-  x = vfmaq_f16(vdupq_n_f16(1.339887440266574e-3f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(1.339887440266574e-3f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(9.618437357674640e-3f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(5.550332471162809e-2f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(2.402264791363012e-1f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(6.931472028550421e-1f), x, fpart);
-  x = vfmaq_f16(vdupq_n_f16(1.000000000000000f), x, fpart);
+  x = vdupq_n_f16(float16_t(1.535336188319500e-4f));
+  x = vfmaq_f16(vdupq_n_f16(float16_t(1.339887440266574e-3f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(1.339887440266574e-3f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(9.618437357674640e-3f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(5.550332471162809e-2f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(2.402264791363012e-1f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(6.931472028550421e-1f)), x, fpart);
+  x = vfmaq_f16(vdupq_n_f16(float16_t(1.000000000000000f)), x, fpart);
 
   // generate 2**ipart in the floating point representation using integer
   // bitshifting
@@ -107,53 +111,6 @@ inline float16_t neon_reduce_add(float16x8_t x) {
   return vget_lane_f16(y, 0);
 }
 
-template <typename T, typename VT>
-struct AccelerateSimdOps {
-  VT init(T a) {
-    return a;
-  }
-
-  VT load(const T* a) {
-    return *(VT*)a;
-  }
-
-  void store(T* dst, VT x) {
-    *(VT*)dst = x;
-  }
-
-  VT max(VT a, VT b) {
-    return simd_max(a, b);
-  };
-
-  VT exp(VT x) {
-    return simd_fast_exp(x);
-  }
-
-  VT add(VT a, VT b) {
-    return a + b;
-  }
-
-  VT sub(VT a, T b) {
-    return a - b;
-  }
-
-  VT mul(VT a, VT b) {
-    return a * b;
-  }
-
-  VT mul(VT a, T b) {
-    return a * b;
-  }
-
-  T reduce_max(VT x) {
-    return simd_reduce_max(x);
-  }
-
-  T reduce_add(VT x) {
-    return simd_reduce_add(x);
-  }
-};
-
 template <typename T, typename VT>
 struct NeonFp16SimdOps {
   VT init(T a) {
@@ -170,7 +127,7 @@ struct NeonFp16SimdOps {
 
   VT max(VT a, VT b) {
     return vmaxq_f16(a, b);
-  };
+  }
 
   VT exp(VT x) {
     return neon_fast_exp(x);
@@ -201,6 +158,55 @@ struct NeonFp16SimdOps {
   }
 };
 
+#endif // __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
+
+template <typename T, typename VT>
+struct AccelerateSimdOps {
+  VT init(T a) {
+    return a;
+  }
+
+  VT load(const T* a) {
+    return *(VT*)a;
+  }
+
+  void store(T* dst, VT x) {
+    *(VT*)dst = x;
+  }
+
+  VT max(VT a, VT b) {
+    return simd_max(a, b);
+  }
+
+  VT exp(VT x) {
+    return simd_fast_exp(x);
+  }
+
+  VT add(VT a, VT b) {
+    return a + b;
+  }
+
+  VT sub(VT a, T b) {
+    return a - b;
+  }
+
+  VT mul(VT a, VT b) {
+    return a * b;
+  }
+
+  VT mul(VT a, T b) {
+    return a * b;
+  }
+
+  T reduce_max(VT x) {
+    return simd_reduce_max(x);
+  }
+
+  T reduce_add(VT x) {
+    return simd_reduce_add(x);
+  }
+};
+
 template <typename T, typename AccT, typename VT, typename Ops, int N>
 void softmax(const array& in, array& out) {
   Ops ops;
@@ -362,12 +368,16 @@ void Softmax::eval_cpu(const std::vector<array>& inputs, array& out) {
             AccelerateSimdOps<float, simd_float16>,
             16>(in, out);
       } else {
+#if __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
         softmax<
             float16_t,
             float16_t,
             float16x8_t,
             NeonFp16SimdOps<float16_t, float16x8_t>,
             8>(in, out);
+#else // __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
+        eval(inputs, out); // Redirect to common backend for consistency
+#endif // __ARM_FEATURE_FP16_VECTOR_ARITHMETIC
       }
       break;
     case bfloat16:

mlx/backend/accelerate/utils.h

@@ -1,8 +1,8 @@
-// Copyright © 2023 Apple Inc.
+// Copyright © 2023-2024 Apple Inc.
 
 #pragma once
 
-#include <vecLib/BNNS/bnns.h>
+#include <Accelerate/Accelerate.h>
 #include "mlx/dtype.h"
 
 namespace mlx::core {

mlx/backend/common/CMakeLists.txt

@@ -42,12 +42,15 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/copy.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/erf.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/fft.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/hadamard.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/masked_mm.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/primitives.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/quantized.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/reduce.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/reduce_utils.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/scan.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/select.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/slicing.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/softmax.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/sort.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/threefry.cpp

mlx/backend/common/binary.cpp

@@ -196,6 +196,20 @@ void LogAddExp::eval(const std::vector<array>& inputs, array& out) {
   }
 }
 
+void LogicalAnd::eval(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 2); // LogicalAnd requires two input arrays
+  auto& in1 = inputs[0];
+  auto& in2 = inputs[1];
+  binary(in1, in2, out, detail::LogicalAnd());
+}
+
+void LogicalOr::eval(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 2); // LogicalOr requires two input arrays
+  auto& in1 = inputs[0];
+  auto& in2 = inputs[1];
+  binary(in1, in2, out, detail::LogicalOr());
+}
+
 void Maximum::eval(const std::vector<array>& inputs, array& out) {
   assert(inputs.size() == 2);
   auto& a = inputs[0];

mlx/backend/common/common.cpp

@@ -66,7 +66,7 @@ void Copy::eval(const std::vector<array>& inputs, array& out) {
   out.copy_shared_buffer(inputs[0]);
 }
 
-void CustomVJP::eval(
+void CustomTransforms::eval(
     const std::vector<array>& inputs,
     std::vector<array>& outputs) {
   assert(inputs.size() > outputs.size());
@@ -250,49 +250,6 @@ void Split::eval(
   }
 }
 
-std::tuple<bool, int64_t, std::vector<int64_t>> Slice::prepare_slice(
-    const array& in) {
-  int64_t data_offset = 0;
-  bool copy_needed = false;
-  std::vector<int64_t> inp_strides(in.ndim(), 0);
-  for (int i = 0; i < in.ndim(); ++i) {
-    data_offset += start_indices_[i] * in.strides()[i];
-    inp_strides[i] = in.strides()[i] * strides_[i];
-
-    copy_needed |= strides_[i] < 0;
-  }
-
-  return std::make_tuple(copy_needed, data_offset, inp_strides);
-}
-
-void Slice::shared_buffer_slice(
-    const array& in,
-    const std::vector<size_t>& out_strides,
-    size_t data_offset,
-    array& out) {
-  // Compute row/col contiguity
-  auto [data_size, is_row_contiguous, is_col_contiguous] =
-      check_contiguity(out.shape(), out_strides);
-
-  auto flags = in.flags();
-  flags.row_contiguous = is_row_contiguous;
-  flags.col_contiguous = is_col_contiguous;
-
-  if (data_size == 1) {
-    // Broadcasted scalar array is contiguous.
-    flags.contiguous = true;
-  } else if (data_size == in.data_size()) {
-    // Means we sliced a broadcasted dimension so leave the "no holes" flag
-    // alone.
-  } else {
-    // We sliced something. So either we are row or col contiguous or we
-    // punched a hole.
-    flags.contiguous &= flags.row_contiguous || flags.col_contiguous;
-  }
-
-  out.copy_shared_buffer(in, out_strides, flags, data_size, data_offset);
-}
-
 std::tuple<int64_t, std::vector<int64_t>> SliceUpdate::prepare_slice(
     const array& in) {
   int64_t data_offset = 0;

mlx/backend/common/compiled.cpp

@@ -205,8 +205,8 @@ void compiled_allocate_outputs(
       // - Donatable
       // - Correct size
       // - Not a constant
-      if (in.flags().row_contiguous && in.nbytes() == outputs[o].nbytes() &&
-          in.is_donatable() &&
+      if (in.flags().row_contiguous && in.size() == outputs[o].size() &&
+          in.itemsize() == outputs[o].itemsize() && in.is_donatable() &&
           constant_ids_.find(inputs_[i].id()) == constant_ids_.end()) {
         if (move_buffers) {
           outputs[o].move_shared_buffer(

mlx/backend/common/copy.cpp

@@ -4,6 +4,7 @@
 
 #include "mlx/allocator.h"
 #include "mlx/backend/common/copy.h"
+#include "mlx/backend/common/utils.h"
 
 namespace mlx::core {
 
@@ -142,29 +143,31 @@ void copy_general(
     const std::vector<int>& data_shape,
     const std::vector<stride_t>& i_strides,
     int64_t i_offset) {
-  switch (src.ndim()) {
+  auto [new_shape, new_strides] = collapse_contiguous_dims(
+      data_shape, std::vector<std::vector<stride_t>>{i_strides});
+  switch (new_shape.size()) {
     case 1:
       copy_general_dim1<SrcT, DstT, stride_t>(
-          src, dst, data_shape, i_strides, i_offset);
+          src, dst, new_shape, new_strides[0], i_offset);
       return;
     case 2:
       copy_general_dim2<SrcT, DstT, stride_t>(
-          src, dst, data_shape, i_strides, i_offset);
+          src, dst, new_shape, new_strides[0], i_offset);
       return;
     case 3:
       copy_general_dim3<SrcT, DstT, stride_t>(
-          src, dst, data_shape, i_strides, i_offset);
+          src, dst, new_shape, new_strides[0], i_offset);
       return;
     case 4:
       copy_general_dim4<SrcT, DstT, stride_t>(
-          src, dst, data_shape, i_strides, i_offset);
+          src, dst, new_shape, new_strides[0], i_offset);
       return;
   }
 
   auto src_ptr = src.data<SrcT>() + i_offset;
   auto dst_ptr = dst.data<DstT>();
   for (size_t i = 0; i < dst.size(); ++i) {
-    stride_t src_elem = elem_to_loc(i, data_shape, i_strides);
+    stride_t src_elem = elem_to_loc(i, new_shape, new_strides[0]);
     dst_ptr[i] = static_cast<DstT>(src_ptr[src_elem]);
   }
 }
@@ -195,10 +198,10 @@ inline void copy_general_general_dims(
     const std::vector<int>& data_shape,
     const std::vector<stride_t>& i_strides,
     const std::vector<stride_t>& o_strides,
-    stride_t i_offset,
-    stride_t o_offset) {
+    int64_t i_offset,
+    int64_t o_offset) {
   if constexpr (D > 1) {
-    int axis = src.ndim() - D;
+    int axis = data_shape.size() - D;
     auto stride_src = i_strides[axis];
     auto stride_dst = o_strides[axis];
     auto N = data_shape[axis];
@@ -209,7 +212,7 @@ inline void copy_general_general_dims(
       o_offset += stride_dst;
     }
   } else {
-    int axis = src.ndim() - 1;
+    int axis = data_shape.size() - 1;
     auto stride_src = i_strides[axis];
     auto stride_dst = o_strides[axis];
     auto N = data_shape[axis];
@@ -230,38 +233,76 @@ void copy_general_general(
     const std::vector<int>& data_shape,
     const std::vector<stride_t>& i_strides,
     const std::vector<stride_t>& o_strides,
-    stride_t i_offset,
-    stride_t o_offset) {
-  switch (src.ndim()) {
+    int64_t i_offset,
+    int64_t o_offset) {
+  auto [new_shape, new_strides] = collapse_contiguous_dims(
+      data_shape, std::vector<std::vector<stride_t>>{i_strides, o_strides});
+  switch (new_shape.size()) {
     case 1:
       copy_general_general_dims<SrcT, DstT, stride_t, 1>(
-          src, dst, data_shape, i_strides, o_strides, i_offset, o_offset);
+          src,
+          dst,
+          new_shape,
+          new_strides[0],
+          new_strides[1],
+          i_offset,
+          o_offset);
       return;
     case 2:
       copy_general_general_dims<SrcT, DstT, stride_t, 2>(
-          src, dst, data_shape, i_strides, o_strides, i_offset, o_offset);
+          src,
+          dst,
+          new_shape,
+          new_strides[0],
+          new_strides[1],
+          i_offset,
+          o_offset);
       return;
     case 3:
       copy_general_general_dims<SrcT, DstT, stride_t, 3>(
-          src, dst, data_shape, i_strides, o_strides, i_offset, o_offset);
+          src,
+          dst,
+          new_shape,
+          new_strides[0],
+          new_strides[1],
+          i_offset,
+          o_offset);
       return;
     case 4:
       copy_general_general_dims<SrcT, DstT, stride_t, 4>(
-          src, dst, data_shape, i_strides, o_strides, i_offset, o_offset);
+          src,
+          dst,
+          new_shape,
+          new_strides[0],
+          new_strides[1],
+          i_offset,
+          o_offset);
       return;
     case 5:
       copy_general_general_dims<SrcT, DstT, stride_t, 5>(
-          src, dst, data_shape, i_strides, o_strides, i_offset, o_offset);
+          src,
+          dst,
+          new_shape,
+          new_strides[0],
+          new_strides[1],
+          i_offset,
+          o_offset);
       return;
   }
 
   int size = std::accumulate(
-      data_shape.end() - 5, data_shape.end(), 1, std::multiplies<int>());
+      new_shape.end() - 5, new_shape.end(), 1, std::multiplies<int>());
   for (int i = 0; i < src.size(); i += size) {
-    stride_t src_offset = i_offset + elem_to_loc(i, data_shape, i_strides);
-    stride_t dst_offset = o_offset + elem_to_loc(i, dst.shape(), o_strides);
+    stride_t src_offset = i_offset + elem_to_loc(i, new_shape, new_strides[0]);
+    stride_t dst_offset = o_offset + elem_to_loc(i, new_shape, new_strides[1]);
     copy_general_general_dims<SrcT, DstT, stride_t, 5>(
-        src, dst, data_shape, i_strides, o_strides, src_offset, dst_offset);
+        src,
+        dst,
+        new_shape,
+        new_strides[0],
+        new_strides[1],
+        src_offset,
+        dst_offset);
   }
 }
 
@@ -444,8 +485,17 @@ void copy_inplace(
   }
 }
 
-template <>
-void copy_inplace<int64_t>(
+template void copy_inplace<size_t>(
+    const array& src,
+    array& dst,
+    const std::vector<int>& data_shape,
+    const std::vector<size_t>& i_strides,
+    const std::vector<size_t>& o_strides,
+    int64_t i_offset,
+    int64_t o_offset,
+    CopyType ctype);
+
+template void copy_inplace<int64_t>(
     const array& src,
     array& dst,
     const std::vector<int>& data_shape,
@@ -453,24 +503,6 @@ void copy_inplace<int64_t>(
     const std::vector<int64_t>& o_strides,
     int64_t i_offset,
     int64_t o_offset,
-    CopyType ctype) {
-  switch (ctype) {
-    case CopyType::General:
-    case CopyType::GeneralGeneral:
-      return copy_inplace_dispatch(
-          src,
-          dst,
-          ctype,
-          data_shape,
-          i_strides,
-          o_strides,
-          i_offset,
-          o_offset);
-
-    case CopyType::Scalar:
-    case CopyType::Vector:
-      return copy_inplace_dispatch(src, dst, ctype);
-  }
-}
+    CopyType ctype);
 
 } // namespace mlx::core

mlx/backend/common/default_primitives.cpp

@@ -5,7 +5,6 @@
 #else
 #include <cblas.h>
 #endif
-
 #include <cstring>
 
 #include "mlx/array.h"
@@ -53,7 +52,7 @@ DEFAULT(Convolution)
 DEFAULT(Copy)
 DEFAULT(Cos)
 DEFAULT(Cosh)
-DEFAULT_MULTI(CustomVJP)
+DEFAULT_MULTI(CustomTransforms)
 DEFAULT_MULTI(Depends)
 DEFAULT(Divide)
 DEFAULT(NumberOfElements)
@@ -69,6 +68,7 @@ DEFAULT(Full)
 DEFAULT(Gather)
 DEFAULT(Greater)
 DEFAULT(GreaterEqual)
+DEFAULT(Hadamard)
 DEFAULT(Less)
 DEFAULT(LessEqual)
 DEFAULT(Load)

mlx/backend/common/hadamard.cpp

@@ -0,0 +1,107 @@
+// Copyright © 2024 Apple Inc.
+
+#include <cassert>
+
+#include "mlx/backend/common/copy.h"
+#include "mlx/backend/common/hadamard.h"
+#include "mlx/primitives.h"
+
+namespace mlx::core {
+
+// n = 2^k component
+template <typename T>
+void hadamard_n(array& out, int n, int m, float scale) {
+  for (int b = 0; b < out.size() / n; b++) {
+    size_t loc = b * n;
+    T* data_ptr = out.data<T>() + loc;
+    int h = 1;
+    int n_over_2 = n / 2;
+    while (h < n) {
+      for (int i = 0; i < n / 2; i++) {
+        int k = i & (h - 1);
+        int j = ((i - k) << 1) + k;
+        float x = *(data_ptr + j);
+        float y = *(data_ptr + j + h);
+        *(data_ptr + j) = x + y;
+        *(data_ptr + j + h) = x - y;
+        if (h == n_over_2) {
+          *(data_ptr + j) *= scale;
+          *(data_ptr + j + h) *= scale;
+        }
+      }
+      h <<= 1;
+    }
+  }
+}
+
+// m component
+template <typename T>
+void hadamard_m(array& out, int n, int m, float scale) {
+  auto h_matrices = hadamard_matrices();
+  auto& matrix = h_matrices[m];
+  auto start = 1;
+  auto end = matrix.find('\n', start);
+  std::vector<bool> hmat_vec;
+  while (end != std::string_view::npos) {
+    auto row = matrix.substr(start, end - start);
+    for (int i = 0; i < row.length(); i++) {
+      hmat_vec.push_back(row[i] == '+');
+    }
+    start = end + 1;
+    end = matrix.find('\n', start);
+  }
+
+  for (int b = 0; b < out.size() / m / n; b++) {
+    size_t loc = b * n * m;
+    T* data_ptr = out.data<T>() + loc;
+    for (int i = 0; i < n; i++) {
+      std::vector<float> out(m);
+      for (int j = 0; j < m; j++) {
+        for (int k = 0; k < m; k++) {
+          float x = *(data_ptr + i + k * n);
+          if (hmat_vec[k + j * m]) {
+            out[j] += x;
+          } else {
+            out[j] -= x;
+          }
+        }
+      }
+      for (int j = 0; j < m; j++) {
+        *(data_ptr + i + j * n) = out[j] * scale;
+      }
+    }
+  }
+}
+
+template <typename T>
+void hadamard(array& out, int n, int m, float scale) {
+  float n_scale = m > 1 ? 1.0 : scale;
+  hadamard_n<T>(out, n, m, n_scale);
+  if (m > 1) {
+    hadamard_m<T>(out, n, m, scale);
+  }
+}
+
+void Hadamard::eval(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 1);
+  auto& in = inputs[0];
+
+  // Copy input to output
+  copy(in, out, CopyType::General);
+
+  int axis = out.ndim() - 1;
+  auto [n, m] = decompose_hadamard(out.shape(axis));
+
+  switch (in.dtype()) {
+    case float32:
+      return hadamard<float>(out, n, m, scale_);
+    case float16:
+      return hadamard<float16_t>(out, n, m, scale_);
+    case bfloat16:
+      return hadamard<bfloat16_t>(out, n, m, scale_);
+    default:
+      throw std::invalid_argument("[hadamard] Unsupported type.");
+  }
+}
+
+} // namespace mlx::core

mlx/backend/common/hadamard.h

@@ -0,0 +1,105 @@
+// Copyright © 2024 Apple Inc.
+
+#pragma once
+
+#include <map>
+
+#include "mlx/utils.h"
+
+namespace mlx::core {
+
+// From http://neilsloane.com/hadamard/
+constexpr std::string_view h12 = R"(
++-++++++++++
+--+-+-+-+-+-
++++-++----++
++---+--+-++-
++++++-++----
++-+---+--+-+
+++--+++-++--
++--++---+--+
+++----+++-++
++--+-++---+-
+++++----+++-
++-+--+-++---
+)";
+
+constexpr std::string_view h20 = R"(
++----+----++--++-++-
+-+----+---+++---+-++
+--+----+---+++-+-+-+
+---+----+---+++++-+-
+----+----++--++-++-+
+-+++++-----+--+++--+
++-+++-+---+-+--+++--
+++-++--+---+-+--+++-
++++-+---+---+-+--+++
+++++-----++--+-+--++
+--++-+-++-+-----++++
+---++-+-++-+---+-+++
++---++-+-+--+--++-++
+++---++-+----+-+++-+
+-++---++-+----+++++-
+-+--+--++-+----+----
++-+-----++-+----+---
+-+-+-+---+--+----+--
+--+-+++------+----+-
++--+--++------+----+
+)";
+
+constexpr std::string_view h28 = R"(
++------++----++-+--+-+--++--
+-+-----+++-----+-+--+-+--++-
+--+-----+++---+-+-+----+--++
+---+-----+++---+-+-+-+--+--+
+----+-----+++---+-+-+++--+--
+-----+-----++++--+-+--++--+-
+------++----++-+--+-+--++--+
+--++++-+-------++--+++-+--+-
+---++++-+-----+-++--+-+-+--+
++---+++--+----++-++--+-+-+--
+++---++---+----++-++--+-+-+-
++++---+----+----++-++--+-+-+
+++++--------+-+--++-++--+-+-
+-++++--------+++--++--+--+-+
+-+-++-++--++--+--------++++-
++-+-++--+--++--+--------++++
+-+-+-++--+--++--+----+---+++
++-+-+-++--+--+---+---++---++
+++-+-+-++--+------+--+++---+
+-++-+-+-++--+------+-++++---
++-++-+---++--+------+-++++--
+-++--++-+-++-+++----++------
++-++--++-+-++-+++-----+-----
+++-++---+-+-++-+++-----+----
+-++-++-+-+-+-+--+++-----+---
+--++-++++-+-+----+++-----+--
++--++-+-++-+-+----+++-----+-
+++--++-+-++-+-+----++------+
+)";
+
+inline const std::map<int, std::string_view> hadamard_matrices() {
+  return {{12, h12}, {20, h20}, {28, h28}};
+}
+
+inline std::pair<int, int> decompose_hadamard(int n) {
+  // n = m*2^k
+  int m = 1;
+  if (!is_power_of_2(n)) {
+    auto h_matrices = hadamard_matrices();
+    for (auto [factor, _] : h_matrices) {
+      if (n % factor == 0) {
+        m = factor;
+        n /= factor;
+        break;
+      }
+    }
+    if (m == 1) {
+      throw std::invalid_argument(
+          "[hadamard] Only supports n = m*2^k where m in (1, 12, 20, 28).");
+    }
+  }
+  return {n, m};
+}
+
+} // namespace mlx::core

mlx/backend/common/inverse.cpp

@@ -10,9 +10,106 @@
 #include <lapack.h>
 #endif
 
+// Wrapper to account for differences in
+// LAPACK implementations (basically how to pass the 'uplo' string to fortran).
+int strtri_wrapper(char uplo, char diag, float* matrix, int N) {
+  int info;
+
+#ifdef LAPACK_FORTRAN_STRLEN_END
+  strtri_(
+      /* uplo = */ &uplo,
+      /* diag = */ &diag,
+      /* N = */ &N,
+      /* a = */ matrix,
+      /* lda = */ &N,
+      /* info = */ &info,
+      /* uplo_len = */ static_cast<size_t>(1),
+      /* diag_len = */ static_cast<size_t>(1));
+#else
+  strtri_(
+      /* uplo = */ &uplo,
+      /* diag = */ &diag,
+      /* N = */ &N,
+      /* a = */ matrix,
+      /* lda = */ &N,
+      /* info = */ &info);
+#endif
+
+  return info;
+}
+
 namespace mlx::core {
 
-void inverse_impl(const array& a, array& inv) {
+void general_inv(array& inv, int N, int i) {
+  int info;
+  auto ipiv = array::Data{allocator::malloc_or_wait(sizeof(int) * N)};
+  // Compute LU factorization.
+  sgetrf_(
+      /* m = */ &N,
+      /* n = */ &N,
+      /* a = */ inv.data<float>() + N * N * i,
+      /* lda = */ &N,
+      /* ipiv = */ static_cast<int*>(ipiv.buffer.raw_ptr()),
+      /* info = */ &info);
+
+  if (info != 0) {
+    std::stringstream ss;
+    ss << "inverse_impl: LU factorization failed with error code " << info;
+    throw std::runtime_error(ss.str());
+  }
+
+  static const int lwork_query = -1;
+  float workspace_size = 0;
+
+  // Compute workspace size.
+  sgetri_(
+      /* m = */ &N,
+      /* a = */ nullptr,
+      /* lda = */ &N,
+      /* ipiv = */ nullptr,
+      /* work = */ &workspace_size,
+      /* lwork = */ &lwork_query,
+      /* info = */ &info);
+
+  if (info != 0) {
+    std::stringstream ss;
+    ss << "inverse_impl: LU workspace calculation failed with error code "
+       << info;
+    throw std::runtime_error(ss.str());
+  }
+
+  const int lwork = workspace_size;
+  auto scratch = array::Data{allocator::malloc_or_wait(sizeof(float) * lwork)};
+
+  // Compute inverse.
+  sgetri_(
+      /* m = */ &N,
+      /* a = */ inv.data<float>() + N * N * i,
+      /* lda = */ &N,
+      /* ipiv = */ static_cast<int*>(ipiv.buffer.raw_ptr()),
+      /* work = */ static_cast<float*>(scratch.buffer.raw_ptr()),
+      /* lwork = */ &lwork,
+      /* info = */ &info);
+
+  if (info != 0) {
+    std::stringstream ss;
+    ss << "inverse_impl: inversion failed with error code " << info;
+    throw std::runtime_error(ss.str());
+  }
+}
+
+void tri_inv(array& inv, int N, int i, bool upper) {
+  const char uplo = upper ? 'L' : 'U';
+  const char diag = 'N';
+  int info = strtri_wrapper(uplo, diag, inv.data<float>() + N * N * i, N);
+  if (info != 0) {
+    std::stringstream ss;
+    ss << "inverse_impl: triangular inversion failed with error code " << info;
+    throw std::runtime_error(ss.str());
+  }
+}
+
+void inverse_impl(const array& a, array& inv, bool tri, bool upper) {
   // Lapack uses the column-major convention. We take advantage of the following
   // identity to avoid transposing (see
   // https://math.stackexchange.com/a/340234):
@@ -24,63 +121,11 @@ void inverse_impl(const array& a, array& inv) {
   const int N = a.shape(-1);
   const size_t num_matrices = a.size() / (N * N);
 
-  int info;
-  auto ipiv = array::Data{allocator::malloc_or_wait(sizeof(int) * N)};
-
   for (int i = 0; i < num_matrices; i++) {
-    // Compute LU factorization.
-    sgetrf_(
-        /* m = */ &N,
-        /* n = */ &N,
-        /* a = */ inv.data<float>() + N * N * i,
-        /* lda = */ &N,
-        /* ipiv = */ static_cast<int*>(ipiv.buffer.raw_ptr()),
-        /* info = */ &info);
-
-    if (info != 0) {
-      std::stringstream ss;
-      ss << "inverse_impl: LU factorization failed with error code " << info;
-      throw std::runtime_error(ss.str());
-    }
-
-    static const int lwork_query = -1;
-    float workspace_size = 0;
-
-    // Compute workspace size.
-    sgetri_(
-        /* m = */ &N,
-        /* a = */ nullptr,
-        /* lda = */ &N,
-        /* ipiv = */ nullptr,
-        /* work = */ &workspace_size,
-        /* lwork = */ &lwork_query,
-        /* info = */ &info);
-
-    if (info != 0) {
-      std::stringstream ss;
-      ss << "inverse_impl: LU workspace calculation failed with error code "
-         << info;
-      throw std::runtime_error(ss.str());
-    }
-
-    const int lwork = workspace_size;
-    auto scratch =
-        array::Data{allocator::malloc_or_wait(sizeof(float) * lwork)};
-
-    // Compute inverse.
-    sgetri_(
-        /* m = */ &N,
-        /* a = */ inv.data<float>() + N * N * i,
-        /* lda = */ &N,
-        /* ipiv = */ static_cast<int*>(ipiv.buffer.raw_ptr()),
-        /* work = */ static_cast<float*>(scratch.buffer.raw_ptr()),
-        /* lwork = */ &lwork,
-        /* info = */ &info);
-
-    if (info != 0) {
-      std::stringstream ss;
-      ss << "inverse_impl: inversion failed with error code " << info;
-      throw std::runtime_error(ss.str());
+    if (tri) {
+      tri_inv(inv, N, i, upper);
+    } else {
+      general_inv(inv, N, i);
     }
   }
 }
@@ -89,7 +134,7 @@ void Inverse::eval(const std::vector<array>& inputs, array& output) {
   if (inputs[0].dtype() != float32) {
     throw std::runtime_error("[Inverse::eval] only supports float32.");
   }
-  inverse_impl(inputs[0], output);
+  inverse_impl(inputs[0], output, tri_, upper_);
 }
 
 } // namespace mlx::core

mlx/backend/common/make_compiled_preamble.sh

@@ -28,6 +28,7 @@ const char* get_kernel_preamble() {
 return R"preamble(
 $INCLUDES
 $CONTENT
+using namespace mlx::core;
 using namespace mlx::core::detail;
 )preamble";
 }

mlx/backend/common/ops.h

@@ -108,105 +108,105 @@ struct Abs {
   template <typename T>
   T operator()(T x) {
     return std::abs(x);
-  };
+  }
   uint8_t operator()(uint8_t x) {
     return x;
-  };
+  }
   uint16_t operator()(uint16_t x) {
     return x;
-  };
+  }
   uint32_t operator()(uint32_t x) {
     return x;
-  };
+  }
   uint64_t operator()(uint64_t x) {
     return x;
-  };
+  }
   bool operator()(bool x) {
     return x;
-  };
+  }
 };
 
 struct ArcCos {
   template <typename T>
   T operator()(T x) {
     return std::acos(x);
-  };
+  }
 };
 
 struct ArcCosh {
   template <typename T>
   T operator()(T x) {
     return std::acosh(x);
-  };
+  }
 };
 
 struct ArcSin {
   template <typename T>
   T operator()(T x) {
     return std::asin(x);
-  };
+  }
 };
 
 struct ArcSinh {
   template <typename T>
   T operator()(T x) {
     return std::asinh(x);
-  };
+  }
 };
 
 struct ArcTan {
   template <typename T>
   T operator()(T x) {
     return std::atan(x);
-  };
+  }
 };
 
 struct ArcTan2 {
   template <typename T>
   T operator()(T y, T x) {
     return std::atan2(y, x);
-  };
+  }
 };
 
 struct ArcTanh {
   template <typename T>
   T operator()(T x) {
     return std::atanh(x);
-  };
+  }
 };
 
 struct Ceil {
   template <typename T>
   T operator()(T x) {
     return std::ceil(x);
-  };
+  }
   int8_t operator()(int8_t x) {
     return x;
-  };
+  }
   int16_t operator()(int16_t x) {
     return x;
-  };
+  }
   int32_t operator()(int32_t x) {
     return x;
-  };
+  }
   int64_t operator()(int64_t x) {
     return x;
-  };
+  }
   uint8_t operator()(uint8_t x) {
     return x;
-  };
+  }
   uint16_t operator()(uint16_t x) {
     return x;
-  };
+  }
   uint32_t operator()(uint32_t x) {
     return x;
-  };
+  }
   uint64_t operator()(uint64_t x) {
     return x;
-  };
+  }
   bool operator()(bool x) {
     return x;
-  };
+  }
 };
 
 struct Conjugate {
@@ -219,35 +219,35 @@ struct Cos {
   template <typename T>
   T operator()(T x) {
     return std::cos(x);
-  };
+  }
 };
 
 struct Cosh {
   template <typename T>
   T operator()(T x) {
     return std::cosh(x);
-  };
+  }
 };
 
 struct Erf {
   template <typename T>
   T operator()(T x) {
     return static_cast<T>(fast_erf(static_cast<float>(x)));
-  };
+  }
 };
 
 struct ErfInv {
   template <typename T>
   T operator()(T x) {
     return static_cast<T>(fast_erfinv(static_cast<float>(x)));
-  };
+  }
 };
 
 struct Exp {
   template <typename T>
   T operator()(T x) {
     return fast_exp(x);
-  };
+  }
 
   complex64_t operator()(complex64_t x) {
     return std::exp(x);
@@ -258,83 +258,83 @@ struct Expm1 {
   template <typename T>
   T operator()(T x) {
     return expm1(x);
-  };
+  }
 };
 
 struct Floor {
   template <typename T>
   T operator()(T x) {
     return std::floor(x);
-  };
+  }
   int8_t operator()(int8_t x) {
     return x;
-  };
+  }
   int16_t operator()(int16_t x) {
     return x;
-  };
+  }
   int32_t operator()(int32_t x) {
     return x;
-  };
+  }
   int64_t operator()(int64_t x) {
     return x;
-  };
+  }
   uint8_t operator()(uint8_t x) {
     return x;
-  };
+  }
   uint16_t operator()(uint16_t x) {
     return x;
-  };
+  }
   uint32_t operator()(uint32_t x) {
     return x;
-  };
+  }
   uint64_t operator()(uint64_t x) {
     return x;
-  };
+  }
   bool operator()(bool x) {
     return x;
-  };
+  }
 };
 
 struct Log {
   template <typename T>
   T operator()(T x) {
     return std::log(x);
-  };
+  }
 };
 
 struct Log2 {
   template <typename T>
   T operator()(T x) {
     return std::log2(x);
-  };
+  }
 };
 
 struct Log10 {
   template <typename T>
   T operator()(T x) {
     return std::log10(x);
-  };
+  }
 };
 
 struct Log1p {
   template <typename T>
   T operator()(T x) {
     return log1p(x);
-  };
+  }
 };
 
 struct LogicalNot {
   template <typename T>
   T operator()(T x) {
     return !x;
-  };
+  }
 };
 
 struct Negative {
   template <typename T>
   T operator()(T x) {
     return -x;
-  };
+  }
 };
 
 struct Round {
@@ -379,49 +379,49 @@ struct Sin {
   template <typename T>
   T operator()(T x) {
     return std::sin(x);
-  };
+  }
 };
 
 struct Sinh {
   template <typename T>
   T operator()(T x) {
     return std::sinh(x);
-  };
+  }
 };
 
 struct Square {
   template <typename T>
   T operator()(T x) {
     return x * x;
-  };
+  }
 };
 
 struct Sqrt {
   template <typename T>
   T operator()(T x) {
     return std::sqrt(x);
-  };
+  }
 };
 
 struct Rsqrt {
   template <typename T>
   T operator()(T x) {
     return static_cast<decltype(x)>(1.0) / std::sqrt(x);
-  };
+  }
 };
 
 struct Tan {
   template <typename T>
   T operator()(T x) {
     return std::tan(x);
-  };
+  }
 };
 
 struct Tanh {
   template <typename T>
   T operator()(T x) {
     return std::tanh(x);
-  };
+  }
 };
 
 struct Add {
@@ -554,7 +554,7 @@ struct LogAddExp {
         ? maxval
         : static_cast<decltype(x)>(
               maxval + std::log1p(fast_exp(minval - maxval)));
-  };
+  }
 };
 
 struct Multiply {
@@ -602,14 +602,14 @@ struct LogicalAnd {
   template <typename T>
   T operator()(T x, T y) {
     return x && y;
-  };
+  }
 };
 
 struct LogicalOr {
   template <typename T>
   T operator()(T x, T y) {
     return x || y;
-  };
+  }
 };
 
 struct Select {
@@ -623,35 +623,35 @@ struct BitwiseAnd {
   template <typename T>
   T operator()(T x, T y) {
     return x & y;
-  };
+  }
 };
 
 struct BitwiseOr {
   template <typename T>
   T operator()(T x, T y) {
     return x | y;
-  };
+  }
 };
 
 struct BitwiseXor {
   template <typename T>
   T operator()(T x, T y) {
     return x ^ y;
-  };
+  }
 };
 
 struct LeftShift {
   template <typename T>
   T operator()(T x, T y) {
     return x << y;
-  };
+  }
 };
 
 struct RightShift {
   template <typename T>
   T operator()(T x, T y) {
     return x >> y;
-  };
+  }
 };
 
 } // namespace mlx::core::detail

mlx/backend/common/primitives.cpp

@@ -8,9 +8,9 @@
 
 #include "mlx/allocator.h"
 #include "mlx/backend/common/arange.h"
-#include "mlx/backend/common/binary.h"
 #include "mlx/backend/common/copy.h"
 #include "mlx/backend/common/ops.h"
+#include "mlx/backend/common/slicing.h"
 #include "mlx/backend/common/threefry.h"
 #include "mlx/backend/common/unary.h"
 #include "mlx/backend/common/utils.h"
@@ -313,20 +313,6 @@ void LogicalNot::eval(const std::vector<array>& inputs, array& out) {
   unary(in, out, detail::LogicalNot());
 }
 
-void LogicalAnd::eval(const std::vector<array>& inputs, array& out) {
-  assert(inputs.size() == 2); // LogicalAnd requires two input arrays
-  auto& in1 = inputs[0];
-  auto& in2 = inputs[1];
-  binary(in1, in2, out, detail::LogicalAnd());
-}
-
-void LogicalOr::eval(const std::vector<array>& inputs, array& out) {
-  assert(inputs.size() == 2); // LogicalOr requires two input arrays
-  auto& in1 = inputs[0];
-  auto& in2 = inputs[1];
-  binary(in1, in2, out, detail::LogicalOr());
-}
-
 void Negative::eval(const std::vector<array>& inputs, array& out) {
   assert(inputs.size() == 1);
   auto& in = inputs[0];
@@ -419,7 +405,17 @@ void Reshape::eval(const std::vector<array>& inputs, array& out) {
   auto [copy_necessary, out_strides] = prepare_reshape(in, out);
 
   if (copy_necessary) {
-    copy(in, out, in.data_size() == 1 ? CopyType::Scalar : CopyType::General);
+    out.set_data(allocator::malloc_or_wait(out.nbytes()));
+    auto out_strides = make_contiguous_strides<size_t>(in.shape());
+    copy_inplace<size_t>(
+        in,
+        out,
+        in.shape(),
+        in.strides(),
+        out_strides,
+        0,
+        0,
+        CopyType::General);
   } else {
     shared_buffer_reshape(in, out_strides, out);
   }
@@ -492,7 +488,8 @@ void Slice::eval(const std::vector<array>& inputs, array& out) {
   auto& in = inputs[0];
 
   // Calculate out strides, initial offset and if copy needs to be made
-  auto [copy_needed, data_offset, inp_strides] = prepare_slice(in);
+  auto [copy_needed, data_offset, inp_strides] =
+      prepare_slice(in, start_indices_, strides_);
 
   // Do copy if needed
   if (copy_needed) {
@@ -590,4 +587,36 @@ void Tanh::eval(const std::vector<array>& inputs, array& out) {
   }
 }
 
+void View::eval_cpu(const std::vector<array>& inputs, array& out) {
+  assert(inputs.size() == 1);
+  auto& in = inputs[0];
+  auto ibytes = size_of(in.dtype());
+  auto obytes = size_of(out.dtype());
+  // Conditions for buffer copying (disjunction):
+  // - type size is the same
+  // - type size is smaller and the last axis is contiguous
+  // - the entire array is row contiguous
+  if (ibytes == obytes || obytes < ibytes && in.strides().back() == 1 ||
+      in.flags().row_contiguous) {
+    auto strides = in.strides();
+    for (int i = 0; i < strides.size() - 1; ++i) {
+      strides[i] *= ibytes;
+      strides[i] /= obytes;
+    }
+    out.copy_shared_buffer(
+        in, strides, in.flags(), in.data_size() * obytes / ibytes);
+  } else {
+    auto tmp = array(in.shape(), in.dtype(), nullptr, {});
+    tmp.set_data(allocator::malloc_or_wait(tmp.nbytes()));
+    copy_inplace(in, tmp, CopyType::General);
+
+    auto flags = out.flags();
+    flags.contiguous = true;
+    flags.row_contiguous = true;
+    auto max_dim = std::max_element(out.shape().begin(), out.shape().end());
+    flags.col_contiguous = out.size() <= 1 || out.size() == *max_dim;
+    out.move_shared_buffer(tmp, out.strides(), flags, out.size());
+  }
+}
+
 } // namespace mlx::core

mlx/backend/common/reduce.cpp

@@ -104,48 +104,14 @@ void reduce_dispatch_out(
     }
     case Reduce::Sum: {
       auto op = [](auto y, auto x) { (*y) = (*y) + x; };
-      switch (out.dtype()) {
-        case bool_:
-          reduction_op<InT, bool>(in, out, axes, false, op);
-          break;
-        case uint8:
-          reduction_op<InT, uint8_t>(in, out, axes, 0, op);
-          break;
-        case uint16:
-          reduction_op<InT, uint16_t>(in, out, axes, 0, op);
-          break;
-        case uint32:
-          reduction_op<InT, uint32_t>(in, out, axes, 0, op);
-          break;
-        case uint64:
-          reduction_op<InT, uint64_t>(in, out, axes, 0, op);
-          break;
-        case int8:
-          reduction_op<InT, int8_t>(in, out, axes, 0, op);
-          break;
-        case int16:
-          reduction_op<InT, int16_t>(in, out, axes, 0, op);
-          break;
-        case int32:
-          reduction_op<InT, int32_t>(in, out, axes, 0, op);
-          break;
-        case int64:
-          reduction_op<InT, int64_t>(in, out, axes, 0, op);
-          break;
-        case float16:
-          reduction_op<InT, float16_t>(in, out, axes, 0.0f, op);
-          break;
-        case float32:
-          reduction_op<InT, float>(in, out, axes, 0.0f, op);
-          break;
-        case bfloat16:
-          reduction_op<InT, bfloat16_t>(in, out, axes, 0.0f, op);
-          break;
-        case complex64:
-          reduction_op<InT, complex64_t>(in, out, axes, complex64_t{0.0f}, op);
-          break;
+      if (out.dtype() == int32) {
+        // special case since the input type can be bool
+        reduction_op<InT, int32_t>(in, out, axes, 0, op);
+      } else {
+        reduction_op<InT, InT>(in, out, axes, 0, op);
       }
-    } break;
+      break;
+    }
     case Reduce::Prod: {
       auto op = [](auto y, auto x) { (*y) *= x; };
       reduction_op<InT, InT>(in, out, axes, 1, op);
@@ -168,6 +134,29 @@ void reduce_dispatch_out(
 
 } // namespace
 
+void nd_loop(
+    std::function<void(int)> callback,
+    const std::vector<int>& shape,
+    const std::vector<size_t>& strides) {
+  std::function<void(int, int)> loop_inner;
+  loop_inner = [&](int dim, int offset) {
+    if (dim < shape.size() - 1) {
+      int size = shape[dim];
+      size_t stride = strides[dim];
+      for (int i = 0; i < size; i++) {
+        loop_inner(dim + 1, offset + i * stride);
+      }
+    } else {
+      int size = shape[dim];
+      size_t stride = strides[dim];
+      for (int i = 0; i < size; i++) {
+        callback(offset + i * stride);
+      }
+    }
+  };
+  loop_inner(0, 0);
+}
+
 void Reduce::eval(const std::vector<array>& inputs, array& out) {
   assert(inputs.size() == 1);
   auto& in = inputs[0];

mlx/backend/common/reduce.h

@@ -49,47 +49,18 @@ struct ReductionPlan {
   ReductionPlan(ReductionOpType type_) : type(type_) {}
 };
 
-namespace {
+ReductionPlan get_reduction_plan(const array& x, const std::vector<int> axes);
 
 // Helper for the ndimensional strided loop
 // Should this be in utils?
-inline void nd_loop(
+void nd_loop(
     std::function<void(int)> callback,
     const std::vector<int>& shape,
-    const std::vector<size_t>& strides) {
-  std::function<void(int, int)> loop_inner;
-  loop_inner = [&](int dim, int offset) {
-    if (dim < shape.size() - 1) {
-      int size = shape[dim];
-      size_t stride = strides[dim];
-      for (int i = 0; i < size; i++) {
-        loop_inner(dim + 1, offset + i * stride);
-      }
-    } else {
-      int size = shape[dim];
-      size_t stride = strides[dim];
-      for (int i = 0; i < size; i++) {
-        callback(offset + i * stride);
-      }
-    }
-  };
-  loop_inner(0, 0);
-}
+    const std::vector<size_t>& strides);
 
 std::pair<std::vector<int>, std::vector<size_t>> shapes_without_reduction_axes(
     const array& x,
-    const std::vector<int>& axes) {
-  std::vector<int> shape = x.shape();
-  std::vector<size_t> strides = x.strides();
-
-  for (int i = axes.size() - 1; i >= 0; i--) {
-    int a = axes[i];
-    shape.erase(shape.begin() + a);
-    strides.erase(strides.begin() + a);
-  }
-
-  return std::make_pair(shape, strides);
-}
+    const std::vector<int>& axes);
 
 template <typename T, typename U, typename Op>
 struct DefaultStridedReduce {
@@ -123,102 +94,6 @@ struct DefaultContiguousReduce {
   }
 };
 
-ReductionPlan get_reduction_plan(const array& x, const std::vector<int> axes) {
-  // The data is all there and we are reducing over everything
-  if (x.size() == x.data_size() && axes.size() == x.ndim() &&
-      x.flags().contiguous) {
-    return ContiguousAllReduce;
-  }
-
-  // Row contiguous input so the output is row contiguous
-  if (x.flags().row_contiguous) {
-    // Merge consecutive axes
-    std::vector<int> shape = {x.shape(axes[0])};
-    std::vector<size_t> strides = {x.strides()[axes[0]]};
-    for (int i = 1; i < axes.size(); i++) {
-      if (axes[i] - 1 == axes[i - 1]) {
-        shape.back() *= x.shape(axes[i]);
-        strides.back() = x.strides()[axes[i]];
-      } else {
-        shape.push_back(x.shape(axes[i]));
-        strides.push_back(x.strides()[axes[i]]);
-      }
-    }
-
-    if (strides.back() == 1) {
-      return ReductionPlan(ContiguousReduce, shape, strides);
-    } else if (strides.back() > 1) {
-      return ReductionPlan(ContiguousStridedReduce, shape, strides);
-    }
-  }
-
-  // Let's check if we can optimize our access patterns
-  //
-  // 1. We have a reduction axis with stride 1. Simply call
-  //    GeneralContiguousReduce and be done with it.
-  // 2. We have transpositions and we are not reducing over the axis with
-  //    stride 1. However, we are reducing over an axis where everything is
-  //    contiguous in memory to the right of that axis. We can call strided
-  //    reduce and be done with it.
-  // 2. We have weird transpositions and expands. Copy the strides to the
-  //    output, then call strided reduce.
-
-  // Sort reduction axes by stride in order to merge them and figure out if we
-  // have a contiguous reduction.
-  std::vector<std::pair<int, size_t>> reductions;
-  for (auto a : axes) {
-    reductions.push_back(std::make_pair(x.shape(a), x.strides()[a]));
-  }
-  std::sort(reductions.begin(), reductions.end(), [](auto a, auto b) {
-    return a.second > b.second;
-  });
-  // Extract the two smallest and try to merge them in case the contiguous
-  // reduction can be bigger than just the last axis.
-  for (int i = reductions.size() - 1; i >= 1; i--) {
-    auto a = reductions[i];
-    auto b = reductions[i - 1];
-
-    // b.stride = a.shape * a.stride then a and b are contiguous
-    if (b.second == a.first * a.second) {
-      reductions.erase(reductions.begin() + i);
-      reductions[i - 1] = std::make_pair(a.first * b.first, a.second);
-    }
-  }
-
-  std::vector<int> shape;
-  std::vector<size_t> strides;
-  for (auto r : reductions) {
-    shape.push_back(r.first);
-    strides.push_back(r.second);
-  }
-
-  // We can call the contiguous reduction op for every weird way the input is
-  // structured in the rest of the axes.
-  if (strides.back() == 1) {
-    return ReductionPlan(GeneralContiguousReduce, shape, strides);
-  }
-
-  // Delegate to the general strided reduction op if the axes after
-  // strides.back() are contiguous.
-  if (strides.back() > 1) {
-    int size = 1;
-    for (int i = x.ndim() - 1; i >= 0; i--) {
-      if (axes.back() == i) {
-        continue;
-      }
-      if (x.strides()[i] != size) {
-        break;
-      }
-      size *= x.shape(i);
-    }
-    if (size >= strides.back()) {
-      return ReductionPlan(GeneralStridedReduce, shape, strides);
-    }
-  }
-
-  return ReductionPlan(GeneralReduce, shape, strides);
-}
-
 template <typename T, typename U, typename OpS, typename OpC, typename Op>
 void reduction_op(
     const array& x,
@@ -361,6 +236,4 @@ void reduction_op(
   reduction_op<T, U>(x, out, axes, init, ops, opc, op);
 }
 
-} // namespace
-
 } // namespace mlx::core

mlx/backend/common/reduce_utils.cpp

@@ -0,0 +1,118 @@
+// Copyright © 2024 Apple Inc.
+
+#include "mlx/backend/common/reduce.h"
+
+namespace mlx::core {
+
+std::pair<std::vector<int>, std::vector<size_t>> shapes_without_reduction_axes(
+    const array& x,
+    const std::vector<int>& axes) {
+  std::vector<int> shape = x.shape();
+  std::vector<size_t> strides = x.strides();
+
+  for (int i = axes.size() - 1; i >= 0; i--) {
+    int a = axes[i];
+    shape.erase(shape.begin() + a);
+    strides.erase(strides.begin() + a);
+  }
+
+  return std::make_pair(shape, strides);
+}
+
+ReductionPlan get_reduction_plan(const array& x, const std::vector<int> axes) {
+  // The data is all there and we are reducing over everything
+  if (x.size() == x.data_size() && axes.size() == x.ndim() &&
+      x.flags().contiguous) {
+    return ContiguousAllReduce;
+  }
+
+  // Row contiguous input so the output is row contiguous
+  if (x.flags().row_contiguous) {
+    // Merge consecutive axes
+    std::vector<int> shape = {x.shape(axes[0])};
+    std::vector<size_t> strides = {x.strides()[axes[0]]};
+    for (int i = 1; i < axes.size(); i++) {
+      if (axes[i] - 1 == axes[i - 1]) {
+        shape.back() *= x.shape(axes[i]);
+        strides.back() = x.strides()[axes[i]];
+      } else {
+        shape.push_back(x.shape(axes[i]));
+        strides.push_back(x.strides()[axes[i]]);
+      }
+    }
+
+    if (strides.back() == 1) {
+      return ReductionPlan(ContiguousReduce, shape, strides);
+    } else if (strides.back() > 1) {
+      return ReductionPlan(ContiguousStridedReduce, shape, strides);
+    }
+  }
+
+  // Let's check if we can optimize our access patterns
+  //
+  // 1. We have a reduction axis with stride 1. Simply call
+  //    GeneralContiguousReduce and be done with it.
+  // 2. We have transpositions and we are not reducing over the axis with
+  //    stride 1. However, we are reducing over an axis where everything is
+  //    contiguous in memory to the right of that axis. We can call strided
+  //    reduce and be done with it.
+  // 2. We have weird transpositions and expands. Copy the strides to the
+  //    output, then call strided reduce.
+
+  // Sort reduction axes by stride in order to merge them and figure out if we
+  // have a contiguous reduction.
+  std::vector<std::pair<int, size_t>> reductions;
+  for (auto a : axes) {
+    reductions.push_back(std::make_pair(x.shape(a), x.strides()[a]));
+  }
+  std::sort(reductions.begin(), reductions.end(), [](auto a, auto b) {
+    return a.second > b.second;
+  });
+  // Extract the two smallest and try to merge them in case the contiguous
+  // reduction can be bigger than just the last axis.
+  for (int i = reductions.size() - 1; i >= 1; i--) {
+    auto a = reductions[i];
+    auto b = reductions[i - 1];
+
+    // b.stride = a.shape * a.stride then a and b are contiguous
+    if (b.second == a.first * a.second) {
+      reductions.erase(reductions.begin() + i);
+      reductions[i - 1] = std::make_pair(a.first * b.first, a.second);
+    }
+  }
+
+  std::vector<int> shape;
+  std::vector<size_t> strides;
+  for (auto r : reductions) {
+    shape.push_back(r.first);
+    strides.push_back(r.second);
+  }
+
+  // We can call the contiguous reduction op for every weird way the input is
+  // structured in the rest of the axes.
+  if (strides.back() == 1) {
+    return ReductionPlan(GeneralContiguousReduce, shape, strides);
+  }
+
+  // Delegate to the general strided reduction op if the axes after
+  // strides.back() are contiguous.
+  if (strides.back() > 1) {
+    int size = 1;
+    for (int i = x.ndim() - 1; i >= 0; i--) {
+      if (axes.back() == i) {
+        continue;
+      }
+      if (x.strides()[i] != size) {
+        break;
+      }
+      size *= x.shape(i);
+    }
+    if (size >= strides.back()) {
+      return ReductionPlan(GeneralStridedReduce, shape, strides);
+    }
+  }
+
+  return ReductionPlan(GeneralReduce, shape, strides);
+}
+
+} // namespace mlx::core

mlx/backend/common/scan.cpp

@@ -234,7 +234,7 @@ void scan_dispatch(
       auto op = [](U* o, const U* y, const T* x) { *o = (*x < *y) ? *y : *x; };
       auto init = (issubdtype(input.dtype(), floating))
           ? static_cast<U>(-std::numeric_limits<float>::infinity())
-          : std::numeric_limits<U>::max();
+          : std::numeric_limits<U>::min();
       auto opcs = DefaultContiguousScan<T, U, decltype(op)>(op, init);
       auto opss = DefaultStridedScan<T, U, decltype(op)>(op, init);
       scan_op<T, U>(opcs, opss, input, output, axis, reverse, inclusive);

mlx/backend/common/slicing.cpp

@@ -0,0 +1,52 @@
+// Copyright © 2024 Apple Inc.
+
+#include "mlx/backend/common/utils.h"
+
+namespace mlx::core {
+
+std::tuple<bool, int64_t, std::vector<int64_t>> prepare_slice(
+    const array& in,
+    std::vector<int>& start_indices,
+    std::vector<int>& strides) {
+  int64_t data_offset = 0;
+  bool copy_needed = false;
+  std::vector<int64_t> inp_strides(in.ndim(), 0);
+  for (int i = 0; i < in.ndim(); ++i) {
+    data_offset += start_indices[i] * in.strides()[i];
+    inp_strides[i] = in.strides()[i] * strides[i];
+
+    copy_needed |= strides[i] < 0;
+  }
+
+  return std::make_tuple(copy_needed, data_offset, inp_strides);
+}
+
+void shared_buffer_slice(
+    const array& in,
+    const std::vector<size_t>& out_strides,
+    size_t data_offset,
+    array& out) {
+  // Compute row/col contiguity
+  auto [data_size, is_row_contiguous, is_col_contiguous] =
+      check_contiguity(out.shape(), out_strides);
+
+  auto flags = in.flags();
+  flags.row_contiguous = is_row_contiguous;
+  flags.col_contiguous = is_col_contiguous;
+
+  if (data_size == 1) {
+    // Broadcasted scalar array is contiguous.
+    flags.contiguous = true;
+  } else if (data_size == in.data_size()) {
+    // Means we sliced a broadcasted dimension so leave the "no holes" flag
+    // alone.
+  } else {
+    // We sliced something. So either we are row or col contiguous or we
+    // punched a hole.
+    flags.contiguous &= flags.row_contiguous || flags.col_contiguous;
+  }
+
+  out.copy_shared_buffer(in, out_strides, flags, data_size, data_offset);
+}
+
+} // namespace mlx::core

mlx/backend/common/slicing.h

@@ -0,0 +1,20 @@
+// Copyright © 2024 Apple Inc.
+
+#pragma once
+
+#include "mlx/array.h"
+
+namespace mlx::core {
+
+std::tuple<bool, int64_t, std::vector<int64_t>> prepare_slice(
+    const array& in,
+    std::vector<int>& start_indices,
+    std::vector<int>& strides);
+
+void shared_buffer_slice(
+    const array& in,
+    const std::vector<size_t>& out_strides,
+    size_t data_offset,
+    array& out);
+
+} // namespace mlx::core

mlx/backend/common/sort.cpp

@@ -113,14 +113,14 @@ void sort(const array& in, array& out, int axis) {
   axis = axis < 0 ? axis + in.ndim() : axis;
   size_t n_rows = in.size() / in.shape(axis);
 
-  auto remaining_shape = in.shape();
+  auto remaining_shape = out.shape();
   remaining_shape.erase(remaining_shape.begin() + axis);
 
-  auto remaining_strides = in.strides();
+  auto remaining_strides = out.strides();
   remaining_strides.erase(remaining_strides.begin() + axis);
 
-  size_t axis_stride = in.strides()[axis];
-  int axis_size = in.shape(axis);
+  size_t axis_stride = out.strides()[axis];
+  int axis_size = out.shape(axis);
 
   // Perform sorting in place
   for (int i = 0; i < n_rows; i++) {
@@ -143,34 +143,42 @@ void argsort(const array& in, array& out, int axis) {
   axis = axis < 0 ? axis + in.ndim() : axis;
   size_t n_rows = in.size() / in.shape(axis);
 
-  auto remaining_shape = in.shape();
-  remaining_shape.erase(remaining_shape.begin() + axis);
+  auto in_remaining_shape = in.shape();
+  in_remaining_shape.erase(in_remaining_shape.begin() + axis);
 
-  auto remaining_strides = in.strides();
-  remaining_strides.erase(remaining_strides.begin() + axis);
+  auto in_remaining_strides = in.strides();
+  in_remaining_strides.erase(in_remaining_strides.begin() + axis);
 
-  size_t axis_stride = in.strides()[axis];
+  auto out_remaining_shape = out.shape();
+  out_remaining_shape.erase(out_remaining_shape.begin() + axis);
+
+  auto out_remaining_strides = out.strides();
+  out_remaining_strides.erase(out_remaining_strides.begin() + axis);
+
+  size_t in_stride = in.strides()[axis];
+  size_t out_stride = out.strides()[axis];
   int axis_size = in.shape(axis);
 
   // Perform sorting
   for (int i = 0; i < n_rows; i++) {
-    size_t loc = elem_to_loc(i, remaining_shape, remaining_strides);
-    const T* data_ptr = in.data<T>() + loc;
-    IdxT* idx_ptr = out.data<IdxT>() + loc;
+    size_t in_loc = elem_to_loc(i, in_remaining_shape, in_remaining_strides);
+    size_t out_loc = elem_to_loc(i, out_remaining_shape, out_remaining_strides);
+    const T* data_ptr = in.data<T>() + in_loc;
+    IdxT* idx_ptr = out.data<IdxT>() + out_loc;
 
-    StridedIterator st_(idx_ptr, axis_stride, 0);
-    StridedIterator ed_(idx_ptr, axis_stride, axis_size);
+    StridedIterator st_(idx_ptr, out_stride, 0);
+    StridedIterator ed_(idx_ptr, out_stride, axis_size);
 
     // Initialize with iota
     std::iota(st_, ed_, IdxT(0));
 
     // Sort according to vals
-    StridedIterator st(idx_ptr, axis_stride, 0);
-    StridedIterator ed(idx_ptr, axis_stride, axis_size);
+    StridedIterator st(idx_ptr, out_stride, 0);
+    StridedIterator ed(idx_ptr, out_stride, axis_size);
 
-    std::stable_sort(st, ed, [data_ptr, axis_stride](IdxT a, IdxT b) {
-      auto v1 = data_ptr[a * axis_stride];
-      auto v2 = data_ptr[b * axis_stride];
+    std::stable_sort(st, ed, [data_ptr, in_stride](IdxT a, IdxT b) {
+      auto v1 = data_ptr[a * in_stride];
+      auto v2 = data_ptr[b * in_stride];
       return v1 < v2 || (v1 == v2 && a < b);
     });
   }

mlx/backend/common/utils.h

@@ -29,6 +29,15 @@ inline size_t elem_to_loc(int elem, const array& a) {
   return elem_to_loc(elem, a.shape(), a.strides());
 }
 
+template <typename stride_t>
+std::vector<stride_t> make_contiguous_strides(const std::vector<int>& shape) {
+  std::vector<stride_t> strides(shape.size(), 1);
+  for (int i = shape.size() - 1; i > 0; i--) {
+    strides[i - 1] = strides[i] * shape[i];
+  }
+  return strides;
+}
+
 // Collapse dims that are contiguous to possibly route to a better kernel
 // e.g. for x = transpose(array({0, 1, 2, 3, 4, 5, 6, 7}, {2, 2, 2}), {2, 0, 1})
 // should return {{2, 4}, {{1, 2}}}.

mlx/backend/metal/CMakeLists.txt

@@ -18,7 +18,7 @@ function(make_jit_source SRC_FILE)
               ${CMAKE_C_COMPILER}
               ${PROJECT_SOURCE_DIR}
               ${SRC_FILE}
-              "-D${MLX_METAL_VERSION}"
+              "-DMLX_METAL_VERSION=${MLX_METAL_VERSION}"
     DEPENDS make_compiled_preamble.sh
             kernels/${SRC_FILE}.h
             ${ARGN}
@@ -52,6 +52,7 @@ make_jit_source(
 )
 make_jit_source(scatter)
 make_jit_source(gather)
+make_jit_source(hadamard)
 
 if (MLX_METAL_JIT) 
   target_sources(
@@ -64,6 +65,11 @@ if (MLX_METAL_JIT)
   make_jit_source(unary)
   make_jit_source(binary)
   make_jit_source(binary_two)
+  make_jit_source(
+    fft
+    kernels/fft/radix.h
+    kernels/fft/readwrite.h
+  )
   make_jit_source(ternary)
   make_jit_source(softmax)
   make_jit_source(scan)
@@ -107,6 +113,8 @@ if (MLX_METAL_JIT)
     kernels/steel/defines.h
     kernels/steel/conv/loaders/loader_general.h
   )
+  make_jit_source(quantized)
+  make_jit_source(gemv_masked)
 else()
   target_sources(
     mlx
@@ -126,6 +134,7 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/device.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/event.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/fft.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/hadamard.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/indexing.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/matmul.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/scaled_dot_product_attention.cpp
@@ -135,11 +144,13 @@ target_sources(
   ${CMAKE_CURRENT_SOURCE_DIR}/normalization.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/rope.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/scan.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/slicing.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/softmax.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/sort.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/reduce.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/ternary.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/unary.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/utils.cpp
 )
 
 if (NOT MLX_METAL_PATH)

mlx/backend/metal/allocator.cpp

@@ -242,8 +242,17 @@ void MetalAllocator::free(Buffer buffer) {
 }
 
 MetalAllocator& allocator() {
-  static MetalAllocator allocator_;
-  return allocator_;
+  // By creating the |allocator_| on heap, the destructor of MetalAllocator will
+  // not be called on exit and all the buffers will be leaked. This is necessary
+  // because releasing buffers can take more than 30sec when the program holds a
+  // lot of RAM (for example inferencing a LLM), and it would feel frozen to
+  // users when exiting.
+  // TODO(zcbenz): Consider using the `base::NoDestructor` class from Chromium
+  // when applying this pattern to more places, or when introducing sanitizers
+  // to MLX.
+  // https://source.chromium.org/chromium/chromium/src/+/main:base/no_destructor.h
+  static MetalAllocator* allocator_ = new MetalAllocator;
+  return *allocator_;
 }
 
 size_t set_cache_limit(size_t limit) {

mlx/backend/metal/binary.cpp

@@ -6,20 +6,62 @@
 #include "mlx/backend/metal/utils.h"
 #include "mlx/primitives.h"
 
+#define BINARY_GPU(func)                                              \
+  void func::eval_gpu(const std::vector<array>& inputs, array& out) { \
+    binary_op_gpu(inputs, out, get_primitive_string(this));           \
+  }
+
+#define BINARY_GPU_MULTI(func)                                         \
+  void func::eval_gpu(                                                 \
+      const std::vector<array>& inputs, std::vector<array>& outputs) { \
+    binary_op_gpu(inputs, outputs, get_primitive_string(this));        \
+  }
+
 namespace mlx::core {
 
 constexpr int MAX_BINARY_SPECIALIZED_DIMS = 5;
 
-void binary_op(
+std::string get_kernel_name(
+    BinaryOpType bopt,
+    const std::string& op,
+    const array& a,
+    bool use_2d,
+    int ndim) {
+  std::ostringstream kname;
+  switch (bopt) {
+    case BinaryOpType::ScalarScalar:
+      kname << "ss";
+      break;
+    case BinaryOpType::ScalarVector:
+      kname << (use_2d ? "sv2" : "sv");
+      break;
+    case BinaryOpType::VectorScalar:
+      kname << (use_2d ? "vs2" : "vs");
+      break;
+    case BinaryOpType::VectorVector:
+      kname << (use_2d ? "vv2" : "vv");
+      break;
+    case BinaryOpType::General:
+      kname << "g";
+      if (ndim <= MAX_BINARY_SPECIALIZED_DIMS) {
+        kname << ndim;
+      } else {
+        kname << "n";
+      }
+      break;
+  }
+  kname << op << type_to_name(a);
+  return kname.str();
+}
+
+void binary_op_gpu_inplace(
     const std::vector<array>& inputs,
     std::vector<array>& outputs,
-    const std::string op) {
-  assert(inputs.size() == 2);
+    const std::string& op,
+    const Stream& s) {
   auto& a = inputs[0];
   auto& b = inputs[1];
   auto bopt = get_binary_op_type(a, b);
-  set_binary_op_output_data(a, b, outputs[0], bopt, true);
-  set_binary_op_output_data(a, b, outputs[1], bopt, true);
 
   auto& out = outputs[0];
   if (out.size() == 0) {
@@ -32,39 +74,12 @@ void binary_op(
   auto& strides_b = strides[1];
   auto& strides_out = strides[2];
 
-  std::string kernel_name;
-  {
-    std::ostringstream kname;
-    switch (bopt) {
-      case BinaryOpType::ScalarScalar:
-        kname << "ss";
-        break;
-      case BinaryOpType::ScalarVector:
-        kname << "sv";
-        break;
-      case BinaryOpType::VectorScalar:
-        kname << "vs";
-        break;
-      case BinaryOpType::VectorVector:
-        kname << "vv";
-        break;
-      case BinaryOpType::General:
-        kname << "g";
-        if (shape.size() <= MAX_BINARY_SPECIALIZED_DIMS) {
-          kname << shape.size();
-        } else {
-          kname << "n";
-        }
-        break;
-    }
-    kname << op << type_to_name(a);
-    kernel_name = kname.str();
-  }
-
-  auto& s = out.primitive().stream();
+  bool use_2d = out.data_size() > UINT32_MAX;
+  std::string kernel_name = get_kernel_name(bopt, op, a, use_2d, shape.size());
   auto& d = metal::device(s.device);
 
-  auto kernel = get_binary_two_kernel(d, kernel_name, a, outputs[0]);
+  auto kernel =
+      get_binary_two_kernel(d, kernel_name, a.dtype(), outputs[0].dtype(), op);
 
   auto& compute_encoder = d.get_command_encoder(s.index);
   compute_encoder->setComputePipelineState(kernel);
@@ -108,9 +123,11 @@ void binary_op(
     MTL::Size grid_dims = MTL::Size(dim0, dim1, rest);
     compute_encoder.dispatchThreads(grid_dims, group_dims);
   } else {
-    // Launch a 1D grid of threads
+    // Launch a 1D or 2D grid of threads
     size_t nthreads = out.data_size();
-    MTL::Size grid_dims = MTL::Size(nthreads, 1, 1);
+    MTL::Size grid_dims = use_2d
+        ? get_2d_grid_dims(outputs[0].shape(), outputs[0].strides())
+        : MTL::Size(nthreads, 1, 1);
     NS::UInteger thread_group_size = kernel->maxTotalThreadsPerThreadgroup();
     if (thread_group_size > nthreads) {
       thread_group_size = nthreads;
@@ -120,15 +137,36 @@ void binary_op(
   }
 }
 
-void binary_op(
+void binary_op_gpu(
     const std::vector<array>& inputs,
-    array& out,
-    const std::string op) {
+    std::vector<array>& outputs,
+    const std::string& op,
+    const Stream& s) {
   assert(inputs.size() == 2);
   auto& a = inputs[0];
   auto& b = inputs[1];
   auto bopt = get_binary_op_type(a, b);
-  set_binary_op_output_data(a, b, out, bopt, true);
+  set_binary_op_output_data(a, b, outputs[0], bopt, true);
+  set_binary_op_output_data(a, b, outputs[1], bopt, true);
+  binary_op_gpu_inplace(inputs, outputs, op, s);
+}
+
+void binary_op_gpu(
+    const std::vector<array>& inputs,
+    std::vector<array>& outputs,
+    const std::string& op) {
+  auto& s = outputs[0].primitive().stream();
+  binary_op_gpu(inputs, outputs, op, s);
+}
+
+void binary_op_gpu_inplace(
+    const std::vector<array>& inputs,
+    array& out,
+    const std::string& op,
+    const Stream& s) {
+  auto& a = inputs[0];
+  auto& b = inputs[1];
+  auto bopt = get_binary_op_type(a, b);
   if (out.size() == 0) {
     return;
   }
@@ -139,39 +177,11 @@ void binary_op(
   auto& strides_b = strides[1];
   auto& strides_out = strides[2];
 
-  std::string kernel_name;
-  {
-    std::ostringstream kname;
-    switch (bopt) {
-      case BinaryOpType::ScalarScalar:
-        kname << "ss";
-        break;
-      case BinaryOpType::ScalarVector:
-        kname << "sv";
-        break;
-      case BinaryOpType::VectorScalar:
-        kname << "vs";
-        break;
-      case BinaryOpType::VectorVector:
-        kname << "vv";
-        break;
-      case BinaryOpType::General:
-        kname << "g";
-        if (shape.size() <= MAX_BINARY_SPECIALIZED_DIMS) {
-          kname << shape.size();
-        } else {
-          kname << "n";
-        }
-        break;
-    }
-    kname << op << type_to_name(a);
-    kernel_name = kname.str();
-  }
-
-  auto& s = out.primitive().stream();
+  bool use_2d = out.data_size() > UINT32_MAX;
+  std::string kernel_name = get_kernel_name(bopt, op, a, use_2d, shape.size());
   auto& d = metal::device(s.device);
 
-  auto kernel = get_binary_kernel(d, kernel_name, a, out);
+  auto kernel = get_binary_kernel(d, kernel_name, a.dtype(), out.dtype(), op);
   auto& compute_encoder = d.get_command_encoder(s.index);
   compute_encoder->setComputePipelineState(kernel);
   bool donate_a = a.data_shared_ptr() == nullptr;
@@ -208,10 +218,11 @@ void binary_op(
     MTL::Size grid_dims = MTL::Size(dim0, dim1, rest);
     compute_encoder.dispatchThreads(grid_dims, group_dims);
   } else {
-    // Launch a 1D grid of threads
-    size_t nthreads =
-        bopt == BinaryOpType::General ? out.size() : out.data_size();
-    MTL::Size grid_dims = MTL::Size(nthreads, 1, 1);
+    // Launch a 1D or 2D grid of threads
+
+    size_t nthreads = out.data_size();
+    MTL::Size grid_dims = use_2d ? get_2d_grid_dims(out.shape(), out.strides())
+                                 : MTL::Size(nthreads, 1, 1);
     NS::UInteger thread_group_size = kernel->maxTotalThreadsPerThreadgroup();
     if (thread_group_size > nthreads) {
       thread_group_size = nthreads;
@@ -221,102 +232,65 @@ void binary_op(
   }
 }
 
-void Add::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "add");
+void binary_op_gpu(
+    const std::vector<array>& inputs,
+    array& out,
+    const std::string& op,
+    const Stream& s) {
+  assert(inputs.size() == 2);
+  auto& a = inputs[0];
+  auto& b = inputs[1];
+  auto bopt = get_binary_op_type(a, b);
+  set_binary_op_output_data(a, b, out, bopt, true);
+  binary_op_gpu_inplace(inputs, out, op, s);
 }
 
-void ArcTan2::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "arctan2");
+void binary_op_gpu(
+    const std::vector<array>& inputs,
+    array& out,
+    const std::string& op) {
+  auto& s = out.primitive().stream();
+  binary_op_gpu(inputs, out, op, s);
 }
 
+BINARY_GPU(Add)
+BINARY_GPU(ArcTan2)
+BINARY_GPU(Divide)
+BINARY_GPU_MULTI(DivMod)
+BINARY_GPU(Remainder)
+BINARY_GPU(Equal)
+BINARY_GPU(Greater)
+BINARY_GPU(GreaterEqual)
+BINARY_GPU(Less)
+BINARY_GPU(LessEqual)
+BINARY_GPU(LogicalAnd)
+BINARY_GPU(LogicalOr)
+BINARY_GPU(LogAddExp)
+BINARY_GPU(Maximum)
+BINARY_GPU(Minimum)
+BINARY_GPU(Multiply)
+BINARY_GPU(NotEqual)
+BINARY_GPU(Power)
+BINARY_GPU(Subtract)
+
 void BitwiseBinary::eval_gpu(const std::vector<array>& inputs, array& out) {
   switch (op_) {
     case BitwiseBinary::And:
-      binary_op(inputs, out, "bitwise_and");
+      binary_op_gpu(inputs, out, get_primitive_string(this));
       break;
     case BitwiseBinary::Or:
-      binary_op(inputs, out, "bitwise_or");
+      binary_op_gpu(inputs, out, get_primitive_string(this));
       break;
     case BitwiseBinary::Xor:
-      binary_op(inputs, out, "bitwise_xor");
+      binary_op_gpu(inputs, out, get_primitive_string(this));
       break;
     case BitwiseBinary::LeftShift:
-      binary_op(inputs, out, "left_shift");
+      binary_op_gpu(inputs, out, get_primitive_string(this));
       break;
     case BitwiseBinary::RightShift:
-      binary_op(inputs, out, "right_shift");
+      binary_op_gpu(inputs, out, get_primitive_string(this));
       break;
   }
 }
 
-void Divide::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "div");
-}
-
-void DivMod::eval_gpu(
-    const std::vector<array>& inputs,
-    std::vector<array>& outputs) {
-  binary_op(inputs, outputs, "divmod");
-}
-
-void Remainder::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "rem");
-}
-
-void Equal::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, equal_nan_ ? "naneq" : "eq");
-}
-
-void Greater::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "ge");
-}
-
-void GreaterEqual::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "geq");
-}
-
-void Less::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "le");
-}
-
-void LessEqual::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "leq");
-}
-
-void LogicalAnd::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "land");
-}
-
-void LogicalOr::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "lor");
-}
-
-void LogAddExp::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "lae");
-}
-
-void Maximum::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "max");
-}
-
-void Minimum::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "min");
-}
-
-void Multiply::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "mul");
-}
-
-void NotEqual::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "neq");
-}
-
-void Power::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "pow");
-}
-
-void Subtract::eval_gpu(const std::vector<array>& inputs, array& out) {
-  binary_op(inputs, out, "sub");
-}
-
 } // namespace mlx::core

mlx/backend/metal/binary.h

@@ -0,0 +1,33 @@
+// Copyright © 2024 Apple Inc.
+
+#pragma once
+
+#include "mlx/array.h"
+
+namespace mlx::core {
+
+void binary_op_gpu(
+    const std::vector<array>& inputs,
+    std::vector<array>& outputs,
+    const std::string& op,
+    const Stream& s);
+
+void binary_op_gpu(
+    const std::vector<array>& inputs,
+    array& out,
+    const std::string& op,
+    const Stream& s);
+
+void binary_op_gpu_inplace(
+    const std::vector<array>& inputs,
+    std::vector<array>& outputs,
+    const std::string& op,
+    const Stream& s);
+
+void binary_op_gpu_inplace(
+    const std::vector<array>& inputs,
+    array& out,
+    const std::string& op,
+    const Stream& s);
+
+} // namespace mlx::core

mlx/backend/metal/compiled.cpp

@@ -56,12 +56,15 @@ inline void build_kernel(
     } else {
       add_indices = true;
       os << "    device const " << get_type_string(x.dtype()) << "* " << xname
-         << " [[buffer(" << cnt++ << ")]]," << std::endl
-         << "    constant const size_t* " << xname << "_strides [[buffer("
-         << cnt++ << ")]]," << std::endl;
+         << " [[buffer(" << cnt++ << ")]]," << std::endl;
     }
   }
 
+  if (add_indices) {
+    os << "    constant const size_t* in_strides [[buffer(" << cnt++
+       << ")]],\n";
+  }
+
   // Add the output arguments
   for (auto& x : outputs) {
     os << "    device " << get_type_string(x.dtype()) << "* "
@@ -110,13 +113,17 @@ inline void build_kernel(
   }
 
   // Read the inputs in tmps
-  for (auto& x : inputs) {
+  int nc_in_count = 0;
+  for (int i = 0; i < inputs.size(); ++i) {
+    auto& x = inputs[i];
     auto& xname = namer.get_name(x);
 
     if (is_constant(x)) {
-      os << "  " << get_type_string(x.dtype()) << " tmp_" << xname << " = ";
+      auto type_str = get_type_string(x.dtype());
+      os << "  auto tmp_" << xname << " = static_cast<"
+         << get_type_string(x.dtype()) << ">(";
       print_constant(os, x);
-      os << ";" << std::endl;
+      os << ");" << std::endl;
     } else if (is_scalar(x)) {
       os << "  " << get_type_string(x.dtype()) << " tmp_" << xname << " = "
          << xname << "[0];" << std::endl;
@@ -124,17 +131,20 @@ inline void build_kernel(
       os << "  " << get_type_string(x.dtype()) << " tmp_" << xname << " = "
          << xname << "[index];" << std::endl;
     } else if (!dynamic_dims) {
+      int offset = nc_in_count * ndim;
       os << "  " << get_type_string(x.dtype()) << " tmp_" << xname << " = "
          << xname << "[";
-      os << "index_0 * " << xname << "_strides[0]";
+      os << "index_0 * " << "in_strides[" << offset << "]";
       for (int i = 1; i < ndim; i++) {
-        os << " + index_" << i << " * " << xname << "_strides[" << i << "]";
+        os << " + index_" << i << " * " << "in_strides[" << offset + i << "]";
       }
       os << "];" << std::endl;
+      nc_in_count++;
     } else {
       os << "  " << get_type_string(x.dtype()) << " tmp_" << xname << " = "
-         << xname << "[elem_to_loc(index, output_shape, " << xname
-         << "_strides, ndim)];" << std::endl;
+         << xname << "[elem_to_loc(index, output_shape, in_strides + "
+         << nc_in_count * ndim << ", ndim)];" << std::endl;
+      nc_in_count++;
     }
   }
 
@@ -296,6 +306,7 @@ void Compiled::eval_gpu(
   // Put the inputs in
   int cnt = 0;
   int stride_idx = 1; // idx 0 is the output strides
+  std::vector<size_t> in_strides;
   for (int i = 0; i < inputs.size(); i++) {
     if (constant_ids_.find(inputs_[i].id()) != constant_ids_.end()) {
       continue;
@@ -303,13 +314,17 @@ void Compiled::eval_gpu(
     auto& x = inputs[i];
     compute_encoder.set_input_array(x, cnt++);
     if (!contiguous && !is_scalar(x)) {
-      compute_encoder->setBytes(
-          strides[stride_idx].data(),
-          strides[stride_idx].size() * sizeof(size_t),
-          cnt++);
+      in_strides.insert(
+          in_strides.end(),
+          strides[stride_idx].begin(),
+          strides[stride_idx].end());
       stride_idx++;
     }
   }
+  if (!in_strides.empty()) {
+    compute_encoder->setBytes(
+        in_strides.data(), in_strides.size() * sizeof(size_t), cnt++);
+  }
 
   compiled_allocate_outputs(
       inputs, outputs, inputs_, constant_ids_, contiguous, true);

mlx/backend/metal/copy.cpp

@@ -33,9 +33,6 @@ void copy_gpu(const array& in, array& out, CopyType ctype, const Stream& s) {
   } else {
     out.set_data(allocator::malloc_or_wait(out.nbytes()));
   }
-  if (out.size() == 0) {
-    return;
-  }
   if (ctype == CopyType::GeneralGeneral) {
     ctype = CopyType::General;
   }
@@ -57,22 +54,27 @@ void copy_gpu_inplace(
     int64_t out_offset,
     CopyType ctype,
     const Stream& s) {
+  if (out.size() == 0) {
+    return;
+  }
+
   // Try to collapse contiguous dims
   auto [shape, strides] = collapse_contiguous_dims(
       data_shape, std::vector{strides_in_pre, strides_out_pre});
   auto& strides_in_ = strides[0];
   auto& strides_out_ = strides[1];
 
+  bool use_2d = out.data_size() > UINT32_MAX;
   auto& d = metal::device(s.device);
   std::string kernel_name;
   {
     std::ostringstream kname;
     switch (ctype) {
       case CopyType::Scalar:
-        kname << "s";
+        kname << (use_2d ? "s2" : "s");
         break;
       case CopyType::Vector:
-        kname << "v";
+        kname << (use_2d ? "v2" : "v");
         break;
       case CopyType::General:
         kname << "g";
@@ -138,7 +140,8 @@ void copy_gpu_inplace(
     compute_encoder.dispatchThreads(grid_dims, group_dims);
   } else {
     size_t nthreads = out.data_size();
-    MTL::Size grid_dims = MTL::Size(nthreads, 1, 1);
+    MTL::Size grid_dims = use_2d ? get_2d_grid_dims(out.shape(), out.strides())
+                                 : MTL::Size(nthreads, 1, 1);
     NS::UInteger thread_group_size = kernel->maxTotalThreadsPerThreadgroup();
     if (thread_group_size > nthreads) {
       thread_group_size = nthreads;

mlx/backend/metal/device.cpp

@@ -14,7 +14,6 @@
 #include "mlx/backend/metal/device.h"
 #include "mlx/backend/metal/metal.h"
 #include "mlx/backend/metal/metal_impl.h"
-#include "mlx/backend/metal/mps/gemm.h"
 #include "mlx/backend/metal/utils.h"
 
 namespace fs = std::filesystem;
@@ -30,13 +29,29 @@ constexpr int MAX_DISPATCHES_PER_ENCODER = 2;
 constexpr const char* default_mtllib_path = METAL_PATH;
 
 constexpr auto get_metal_version() {
-#if defined METAL_3_1
+#if (MLX_METAL_VERSION >= 320)
+  return MTL::LanguageVersion3_2;
+#elif (MLX_METAL_VERSION >= 310)
   return MTL::LanguageVersion3_1;
 #else
   return MTL::LanguageVersion3_0;
 #endif
 }
 
+std::string get_colocated_mtllib_path(const std::string& lib_name) {
+  Dl_info info;
+  std::string mtllib_path;
+  std::string lib_ext = lib_name + ".metallib";
+
+  int success = dladdr((void*)get_colocated_mtllib_path, &info);
+  if (success) {
+    auto mtllib = fs::path(info.dli_fname).remove_filename() / lib_ext;
+    mtllib_path = mtllib.c_str();
+  }
+
+  return mtllib_path;
+}
+
 auto load_device() {
   auto devices = MTL::CopyAllDevices();
   auto device = static_cast<MTL::Device*>(devices->object(0))
@@ -124,6 +139,49 @@ MTL::Library* load_library(
 
 } // namespace
 
+CommandEncoder::CommandEncoder(MTL::CommandBuffer* cbuf) : cbuf(cbuf) {
+  enc = cbuf->computeCommandEncoder(MTL::DispatchTypeConcurrent);
+  enc->retain();
+}
+
+CommandEncoder::~CommandEncoder() {
+  enc->endEncoding();
+  enc->release();
+}
+
+void CommandEncoder::set_input_array(
+    const array& a,
+    int idx,
+    int64_t offset /* = 0 */) {
+  auto r_buf = static_cast<MTL::Resource*>(const_cast<void*>(a.buffer().ptr()));
+  if (auto it = outputs.find(r_buf); it != outputs.end()) {
+    // Insert a barrier
+    enc->memoryBarrier(&r_buf, 1);
+
+    // Remove the output
+    outputs.erase(it);
+  }
+  auto a_buf = static_cast<const MTL::Buffer*>(a.buffer().ptr());
+  auto base_offset = a.data<char>() -
+      static_cast<char*>(const_cast<MTL::Buffer*>(a_buf)->contents());
+  base_offset += offset;
+  enc->setBuffer(a_buf, base_offset, idx);
+}
+
+void CommandEncoder::set_output_array(
+    array& a,
+    int idx,
+    int64_t offset /* = 0 */) {
+  // Add barriers before adding the output to the output set
+  set_input_array(a, idx, offset);
+  auto buf = static_cast<MTL::Resource*>(a.buffer().ptr());
+  if (concurrent) {
+    concurrent_outputs.insert(buf);
+  } else {
+    outputs.insert(buf);
+  }
+}
+
 void CommandEncoder::dispatchThreadgroups(
     MTL::Size grid_dims,
     MTL::Size group_dims) {
@@ -253,13 +311,9 @@ void Device::register_library(
   }
 }
 
-void Device::register_library(
-    const std::string& lib_name,
-    const std::function<std::string(const std::string&)>& lib_path_func) {
+void Device::register_library(const std::string& lib_name) {
   if (auto it = library_map_.find(lib_name); it == library_map_.end()) {
-    std::string new_lib_path = lib_path_func(lib_name);
-    auto new_lib = load_library(device_, lib_name, new_lib_path.c_str());
-    library_map_.insert({lib_name, new_lib});
+    register_library(lib_name, get_colocated_mtllib_path(lib_name));
   }
 }
 
@@ -269,7 +323,7 @@ MTL::Library* Device::get_library_cache_(const std::string& lib_name) {
   if (auto it = library_map_.find(lib_name); it != library_map_.end()) {
     mtl_lib = it->second;
   } else { // Look for metallib alongside library
-    register_library(lib_name);
+    register_library(lib_name, get_colocated_mtllib_path(lib_name));
     mtl_lib = library_map_[lib_name];
   }
 

mlx/backend/metal/device.h

@@ -9,38 +9,16 @@
 #include <unordered_map>
 #include <unordered_set>
 
-#include <dlfcn.h>
-#include <filesystem>
-
 #include "mlx/array.h"
 #include "mlx/device.h"
 
-namespace fs = std::filesystem;
-
 namespace mlx::core::metal {
 
-inline std::string get_colocated_mtllib_path(const std::string& lib_name) {
-  Dl_info info;
-  std::string mtllib_path;
-  std::string lib_ext = lib_name + ".metallib";
-
-  int success = dladdr((void*)get_colocated_mtllib_path, &info);
-  if (success) {
-    auto mtllib = fs::path(info.dli_fname).remove_filename() / lib_ext;
-    mtllib_path = mtllib.c_str();
-  }
-
-  return mtllib_path;
-}
-
 using MTLFCList =
     std::vector<std::tuple<const void*, MTL::DataType, NS::UInteger>>;
 
 struct CommandEncoder {
-  CommandEncoder(MTL::CommandBuffer* cbuf) : cbuf(cbuf) {
-    enc = cbuf->computeCommandEncoder(MTL::DispatchTypeConcurrent);
-    enc->retain();
-  };
+  CommandEncoder(MTL::CommandBuffer* cbuf);
   CommandEncoder(const CommandEncoder&) = delete;
   CommandEncoder& operator=(const CommandEncoder&) = delete;
 
@@ -63,34 +41,8 @@ struct CommandEncoder {
     return enc;
   }
 
-  void set_input_array(const array& a, int idx, int64_t offset = 0) {
-    auto r_buf =
-        static_cast<MTL::Resource*>(const_cast<void*>(a.buffer().ptr()));
-    if (auto it = outputs.find(r_buf); it != outputs.end()) {
-      // Insert a barrier
-      enc->memoryBarrier(&r_buf, 1);
-
-      // Remove the output
-      outputs.erase(it);
-    }
-    auto a_buf = static_cast<const MTL::Buffer*>(a.buffer().ptr());
-    auto base_offset = a.data<char>() -
-        static_cast<char*>(const_cast<MTL::Buffer*>(a_buf)->contents());
-    base_offset += offset;
-    enc->setBuffer(a_buf, base_offset, idx);
-  }
-
-  void set_output_array(array& a, int idx, int64_t offset = 0) {
-    // Add barriers before adding the output to the output set
-    set_input_array(a, idx, offset);
-    auto buf = static_cast<MTL::Resource*>(a.buffer().ptr());
-    if (concurrent) {
-      concurrent_outputs.insert(buf);
-    } else {
-      outputs.insert(buf);
-    }
-  }
-
+  void set_input_array(const array& a, int idx, int64_t offset = 0);
+  void set_output_array(array& a, int idx, int64_t offset = 0);
   void dispatchThreadgroups(MTL::Size grid_dims, MTL::Size group_dims);
   void dispatchThreads(MTL::Size grid_dims, MTL::Size group_dims);
 
@@ -98,10 +50,7 @@ struct CommandEncoder {
     return ConcurrentContext(*this);
   }
 
-  ~CommandEncoder() {
-    enc->endEncoding();
-    enc->release();
-  }
+  ~CommandEncoder();
 
  private:
   void maybe_split();
@@ -136,10 +85,8 @@ class Device {
   void register_library(
       const std::string& lib_name,
       const std::string& lib_path);
-  void register_library(
-      const std::string& lib_name,
-      const std::function<std::string(const std::string&)>& lib_path_func =
-          get_colocated_mtllib_path);
+
+  void register_library(const std::string& lib_name);
 
   MTL::Library* get_library(const std::string& name);
 

mlx/backend/metal/fft.cpp

@@ -1,106 +1,803 @@
-// Copyright © 2023 Apple Inc.
+// Copyright © 2024 Apple Inc.
+#include <cassert>
+#include <complex>
+#include <map>
+#include <numeric>
+#include <set>
+
+#include "mlx/3rdparty/pocketfft.h"
+#include "mlx/backend/metal/binary.h"
 #include "mlx/backend/metal/copy.h"
+#include "mlx/backend/metal/kernels.h"
+#include "mlx/backend/metal/slicing.h"
+#include "mlx/backend/metal/unary.h"
 #include "mlx/backend/metal/utils.h"
-#include "mlx/mlx.h"
-#include "mlx/primitives.h"
+#include "mlx/utils.h"
 
 namespace mlx::core {
 
-void FFT::eval_gpu(const std::vector<array>& inputs, array& out) {
-  auto& s = out.primitive().stream();
-  auto& d = metal::device(s.device);
+using MTLFC = std::tuple<const void*, MTL::DataType, NS::UInteger>;
 
-  auto& in = inputs[0];
+#define MAX_STOCKHAM_FFT_SIZE 4096
+#define MAX_RADER_FFT_SIZE 2048
+#define MAX_BLUESTEIN_FFT_SIZE 2048
+// Threadgroup memory batching improves throughput for small n
+#define MIN_THREADGROUP_MEM_SIZE 256
+// For strided reads/writes, coalesce at least this many complex64s
+#define MIN_COALESCE_WIDTH 4
 
-  if (axes_.size() == 0 || axes_.size() > 1 || inverse_ ||
-      in.dtype() != complex64 || out.dtype() != complex64) {
-    // Could also fallback to CPU implementation here.
-    throw std::runtime_error(
-        "GPU FFT is only implemented for 1D, forward, complex FFTs.");
+inline const std::vector<int> supported_radices() {
+  // Ordered by preference in decomposition.
+  return {13, 11, 8, 7, 6, 5, 4, 3, 2};
+}
+
+std::vector<int> prime_factors(int n) {
+  int z = 2;
+  std::vector<int> factors;
+  while (z * z <= n) {
+    if (n % z == 0) {
+      factors.push_back(z);
+      n /= z;
+    } else {
+      z++;
+    }
+  }
+  if (n > 1) {
+    factors.push_back(n);
+  }
+  return factors;
+}
+
+struct FourStepParams {
+  bool required = false;
+  bool first_step = true;
+  int n1 = 0;
+  int n2 = 0;
+};
+
+// Forward Declaration
+void fft_op(
+    const array& in,
+    array& out,
+    size_t axis,
+    bool inverse,
+    bool real,
+    const FourStepParams four_step_params,
+    bool inplace,
+    const Stream& s);
+
+struct FFTPlan {
+  int n = 0;
+  // Number of steps for each radix in the Stockham decomposition
+  std::vector<int> stockham;
+  // Number of steps for each radix in the Rader decomposition
+  std::vector<int> rader;
+  // Rader factor, 1 if no rader factors
+  int rader_n = 1;
+  int bluestein_n = -1;
+  // Four step FFT
+  bool four_step = false;
+  int n1 = 0;
+  int n2 = 0;
+};
+
+int next_fast_n(int n) {
+  return next_power_of_2(n);
+}
+
+std::vector<int> plan_stockham_fft(int n) {
+  auto radices = supported_radices();
+  std::vector<int> plan(radices.size(), 0);
+  int orig_n = n;
+  if (n == 1) {
+    return plan;
+  }
+  for (int i = 0; i < radices.size(); i++) {
+    int radix = radices[i];
+    // Manually tuned radices for powers of 2
+    if (is_power_of_2(orig_n) && orig_n < 512 && radix > 4) {
+      continue;
+    }
+    while (n % radix == 0) {
+      plan[i] += 1;
+      n /= radix;
+      if (n == 1) {
+        return plan;
+      }
+    }
+  }
+  throw std::runtime_error("Unplannable");
+}
+
+FFTPlan plan_fft(int n) {
+  auto radices = supported_radices();
+  std::set<int> radices_set(radices.begin(), radices.end());
+
+  FFTPlan plan;
+  plan.n = n;
+  plan.rader = std::vector<int>(radices.size(), 0);
+  auto factors = prime_factors(n);
+  int remaining_n = n;
+
+  // Four Step FFT when N is too large for shared mem.
+  if (n > MAX_STOCKHAM_FFT_SIZE && is_power_of_2(n)) {
+    // For power's of two we have a fast, no transpose four step implementation.
+    plan.four_step = true;
+    // Rough heuristic for choosing faster powers of two when we can
+    plan.n2 = n > 65536 ? 1024 : 64;
+    plan.n1 = n / plan.n2;
+    return plan;
+  } else if (n > MAX_STOCKHAM_FFT_SIZE) {
+    // Otherwise we use a multi-upload Bluestein's
+    plan.four_step = true;
+    plan.bluestein_n = next_fast_n(2 * n - 1);
+    return plan;
   }
 
-  size_t n = in.shape(axes_[0]);
+  for (int factor : factors) {
+    // Make sure the factor is a supported radix
+    if (radices_set.find(factor) == radices_set.end()) {
+      // We only support a single Rader factor currently
+      // TODO(alexbarron) investigate weirdness with large
+      // Rader sizes -- possibly a compiler issue?
+      if (plan.rader_n > 1 || n > MAX_RADER_FFT_SIZE) {
+        plan.four_step = n > MAX_BLUESTEIN_FFT_SIZE;
+        plan.bluestein_n = next_fast_n(2 * n - 1);
+        plan.stockham = plan_stockham_fft(plan.bluestein_n);
+        plan.rader = std::vector<int>(radices.size(), 0);
+        return plan;
+      }
+      // See if we can use Rader's algorithm to Stockham decompose n - 1
+      auto rader_factors = prime_factors(factor - 1);
+      int last_factor = -1;
+      for (int rf : rader_factors) {
+        // We don't nest Rader's algorithm so if `factor - 1`
+        // isn't Stockham decomposable we give up and do Bluestein's.
+        if (radices_set.find(rf) == radices_set.end()) {
+          plan.four_step = n > MAX_BLUESTEIN_FFT_SIZE;
+          plan.bluestein_n = next_fast_n(2 * n - 1);
+          plan.stockham = plan_stockham_fft(plan.bluestein_n);
+          plan.rader = std::vector<int>(radices.size(), 0);
+          return plan;
+        }
+      }
+      plan.rader = plan_stockham_fft(factor - 1);
+      plan.rader_n = factor;
+      remaining_n /= factor;
+    }
+  }
 
-  if (!is_power_of_2(n) || n > 2048 || n < 4) {
-    throw std::runtime_error(
-        "GPU FFT is only implemented for the powers of 2 from 4 -> 2048");
+  plan.stockham = plan_stockham_fft(remaining_n);
+  return plan;
+}
+
+int compute_elems_per_thread(FFTPlan plan) {
+  // Heuristics for selecting an efficient number
+  // of threads to use for a particular mixed-radix FFT.
+  auto n = plan.n;
+
+  std::vector<int> steps;
+  auto radices = supported_radices();
+  steps.insert(steps.end(), plan.stockham.begin(), plan.stockham.end());
+  steps.insert(steps.end(), plan.rader.begin(), plan.rader.end());
+  std::set<int> used_radices;
+  for (int i = 0; i < steps.size(); i++) {
+    int radix = radices[i % radices.size()];
+    if (steps[i] > 0) {
+      used_radices.insert(radix);
+    }
+  }
+
+  // Manual tuning for 7/11/13
+  if (used_radices.find(7) != used_radices.end() &&
+      (used_radices.find(11) != used_radices.end() ||
+       used_radices.find(13) != used_radices.end())) {
+    return 7;
+  } else if (
+      used_radices.find(11) != used_radices.end() &&
+      used_radices.find(13) != used_radices.end()) {
+    return 11;
+  }
+
+  // TODO(alexbarron) Some really weird stuff is going on
+  // for certain `elems_per_thread` on large composite n.
+  // Possibly a compiler issue?
+  if (n == 3159)
+    return 13;
+  if (n == 3645)
+    return 5;
+  if (n == 3969)
+    return 7;
+  if (n == 1982)
+    return 5;
+
+  if (used_radices.size() == 1) {
+    return *(used_radices.begin());
+  }
+  if (used_radices.size() == 2) {
+    if (used_radices.find(11) != used_radices.end() ||
+        used_radices.find(13) != used_radices.end()) {
+      return std::accumulate(used_radices.begin(), used_radices.end(), 0) / 2;
+    }
+    std::vector<int> radix_vec(used_radices.begin(), used_radices.end());
+    return radix_vec[1];
+  }
+  // In all other cases use the second smallest radix.
+  std::vector<int> radix_vec(used_radices.begin(), used_radices.end());
+  return radix_vec[1];
+}
+
+// Rader
+int mod_exp(int x, int y, int n) {
+  int out = 1;
+  while (y) {
+    if (y & 1) {
+      out = out * x % n;
+    }
+    y >>= 1;
+    x = x * x % n;
+  }
+  return out;
+}
+
+int primitive_root(int n) {
+  auto factors = prime_factors(n - 1);
+
+  for (int r = 2; r < n - 1; r++) {
+    bool found = true;
+    for (int factor : factors) {
+      if (mod_exp(r, (n - 1) / factor, n) == 1) {
+        found = false;
+        break;
+      }
+    }
+    if (found) {
+      return r;
+    }
+  }
+  return -1;
+}
+
+std::tuple<array, array, array> compute_raders_constants(
+    int rader_n,
+    const Stream& s) {
+  int proot = primitive_root(rader_n);
+  // Fermat's little theorem
+  int inv = mod_exp(proot, rader_n - 2, rader_n);
+  std::vector<short> g_q(rader_n - 1);
+  std::vector<short> g_minus_q(rader_n - 1);
+  for (int i = 0; i < rader_n - 1; i++) {
+    g_q[i] = mod_exp(proot, i, rader_n);
+    g_minus_q[i] = mod_exp(inv, i, rader_n);
+  }
+  array g_q_arr(g_q.begin(), {rader_n - 1});
+  array g_minus_q_arr(g_minus_q.begin(), {rader_n - 1});
+
+  std::vector<std::complex<float>> b_q(rader_n - 1);
+  for (int i = 0; i < rader_n - 1; i++) {
+    float pi_i = (float)g_minus_q[i] * -2.0 * M_PI / rader_n;
+    b_q[i] = std::exp(std::complex<float>(0, pi_i));
+  }
+
+  array b_q_fft({rader_n - 1}, complex64, nullptr, {});
+  b_q_fft.set_data(allocator::malloc_or_wait(b_q_fft.nbytes()));
+  auto b_q_fft_ptr =
+      reinterpret_cast<std::complex<float>*>(b_q_fft.data<complex64_t>());
+  std::ptrdiff_t item_size = b_q_fft.itemsize();
+  size_t fft_size = rader_n - 1;
+  // This FFT is always small (<4096, batch 1) so save some overhead
+  // and do it on the CPU
+  pocketfft::c2c(
+      /* shape= */ {fft_size},
+      /* stride_in= */ {item_size},
+      /* stride_out= */ {item_size},
+      /* axes= */ {0},
+      /* forward= */ true,
+      /* data_in= */ b_q.data(),
+      /* data_out= */ b_q_fft_ptr,
+      /* scale= */ 1.0f);
+  return std::make_tuple(b_q_fft, g_q_arr, g_minus_q_arr);
+}
+
+// Bluestein
+std::pair<array, array> compute_bluestein_constants(int n, int bluestein_n) {
+  // We need to calculate the Bluestein twiddle factors
+  // in double precision for the overall numerical stability
+  // of Bluestein's FFT algorithm to be acceptable.
+  //
+  // Metal doesn't support float64, so instead we
+  // manually implement the required operations on cpu.
+  //
+  // In numpy:
+  // w_k = np.exp(-1j * np.pi / N * (np.arange(-N + 1, N) ** 2))
+  // w_q = np.fft.fft(1/w_k)
+  // return w_k, w_q
+  int length = 2 * n - 1;
+
+  std::vector<std::complex<float>> w_k_vec(n);
+  std::vector<std::complex<float>> w_q_vec(bluestein_n, 0);
+
+  for (int i = -n + 1; i < n; i++) {
+    double theta = pow(i, 2) * M_PI / (double)n;
+    w_q_vec[i + n - 1] = std::exp(std::complex<double>(0, theta));
+    if (i >= 0) {
+      w_k_vec[i] = std::exp(std::complex<double>(0, -theta));
+    }
+  }
+
+  array w_k({n}, complex64, nullptr, {});
+  w_k.set_data(allocator::malloc_or_wait(w_k.nbytes()));
+  std::copy(w_k_vec.begin(), w_k_vec.end(), w_k.data<complex64_t>());
+
+  array w_q({bluestein_n}, complex64, nullptr, {});
+  w_q.set_data(allocator::malloc_or_wait(w_q.nbytes()));
+  auto w_q_ptr =
+      reinterpret_cast<std::complex<float>*>(w_q.data<complex64_t>());
+
+  std::ptrdiff_t item_size = w_q.itemsize();
+  size_t fft_size = bluestein_n;
+  pocketfft::c2c(
+      /* shape= */ {fft_size},
+      /* stride_in= */ {item_size},
+      /* stride_out= */ {item_size},
+      /* axes= */ {0},
+      /* forward= */ true,
+      /* data_in= */ w_q_vec.data(),
+      /* data_out= */ w_q_ptr,
+      /* scale= */ 1.0f);
+  return std::make_tuple(w_k, w_q);
+}
+
+void multi_upload_bluestein_fft(
+    const array& in,
+    array& out,
+    size_t axis,
+    bool inverse,
+    bool real,
+    FFTPlan& plan,
+    std::vector<array> copies,
+    const Stream& s) {
+  // TODO(alexbarron) Implement fused kernels for mutli upload bluestein's
+  // algorithm
+  int n = inverse ? out.shape(axis) : in.shape(axis);
+  auto [w_k, w_q] = compute_bluestein_constants(n, plan.bluestein_n);
+
+  // Broadcast w_q and w_k to the batch size
+  std::vector<size_t> b_strides(in.ndim(), 0);
+  b_strides[axis] = 1;
+  array w_k_broadcast({}, complex64, nullptr, {});
+  array w_q_broadcast({}, complex64, nullptr, {});
+  w_k_broadcast.copy_shared_buffer(w_k, b_strides, {}, w_k.data_size());
+  w_q_broadcast.copy_shared_buffer(w_q, b_strides, {}, w_q.data_size());
+
+  auto temp_shape = inverse ? out.shape() : in.shape();
+  array temp(temp_shape, complex64, nullptr, {});
+  array temp1(temp_shape, complex64, nullptr, {});
+
+  if (real && !inverse) {
+    // Convert float32->complex64
+    copy_gpu(in, temp, CopyType::General, s);
+  } else if (real && inverse) {
+    int back_offset = n % 2 == 0 ? 2 : 1;
+    auto slice_shape = in.shape();
+    slice_shape[axis] -= back_offset;
+    array slice_temp(slice_shape, complex64, nullptr, {});
+    array conj_temp(in.shape(), complex64, nullptr, {});
+    copies.push_back(slice_temp);
+    copies.push_back(conj_temp);
+
+    std::vector<int> rstarts(in.ndim(), 0);
+    std::vector<int> rstrides(in.ndim(), 1);
+    rstarts[axis] = in.shape(axis) - back_offset;
+    rstrides[axis] = -1;
+    unary_op_gpu({in}, conj_temp, "Conjugate", s);
+    slice_gpu(in, slice_temp, rstarts, rstrides, s);
+    concatenate_gpu({conj_temp, slice_temp}, temp, (int)axis, s);
+  } else if (inverse) {
+    unary_op_gpu({in}, temp, "Conjugate", s);
+  } else {
+    temp.copy_shared_buffer(in);
+  }
+
+  binary_op_gpu({temp, w_k_broadcast}, temp1, "Multiply", s);
+
+  std::vector<std::pair<int, int>> pads;
+  auto padded_shape = out.shape();
+  padded_shape[axis] = plan.bluestein_n;
+  array pad_temp(padded_shape, complex64, nullptr, {});
+  pad_gpu(temp1, array(complex64_t{0.0f, 0.0f}), pad_temp, {(int)axis}, {0}, s);
+
+  array pad_temp1(padded_shape, complex64, nullptr, {});
+  fft_op(
+      pad_temp,
+      pad_temp1,
+      axis,
+      /*inverse=*/false,
+      /*real=*/false,
+      FourStepParams(),
+      /*inplace=*/false,
+      s);
+
+  binary_op_gpu_inplace({pad_temp1, w_q_broadcast}, pad_temp, "Multiply", s);
+
+  fft_op(
+      pad_temp,
+      pad_temp1,
+      axis,
+      /* inverse= */ true,
+      /* real= */ false,
+      FourStepParams(),
+      /*inplace=*/true,
+      s);
+
+  int offset = plan.bluestein_n - (2 * n - 1);
+  std::vector<int> starts(in.ndim(), 0);
+  std::vector<int> strides(in.ndim(), 1);
+  starts[axis] = plan.bluestein_n - offset - n;
+  slice_gpu(pad_temp1, temp, starts, strides, s);
+
+  binary_op_gpu_inplace({temp, w_k_broadcast}, temp1, "Multiply", s);
+
+  if (real && !inverse) {
+    std::vector<int> rstarts(in.ndim(), 0);
+    std::vector<int> rstrides(in.ndim(), 1);
+    slice_gpu(temp1, out, rstarts, strides, s);
+  } else if (real && inverse) {
+    std::vector<size_t> b_strides(in.ndim(), 0);
+    auto inv_n = array({1.0f / n}, {1}, float32);
+    array temp_float(out.shape(), out.dtype(), nullptr, {});
+    copies.push_back(temp_float);
+    copies.push_back(inv_n);
+
+    copy_gpu(temp1, temp_float, CopyType::General, s);
+    binary_op_gpu({temp_float, inv_n}, out, "Multiply", s);
+  } else if (inverse) {
+    auto inv_n = array({1.0f / n}, {1}, complex64);
+    unary_op_gpu({temp1}, temp, "Conjugate", s);
+    binary_op_gpu({temp, inv_n}, out, "Multiply", s);
+    copies.push_back(inv_n);
+  } else {
+    out.copy_shared_buffer(temp1);
+  }
+
+  copies.push_back(w_k);
+  copies.push_back(w_q);
+  copies.push_back(w_k_broadcast);
+  copies.push_back(w_q_broadcast);
+  copies.push_back(temp);
+  copies.push_back(temp1);
+  copies.push_back(pad_temp);
+  copies.push_back(pad_temp1);
+}
+
+void four_step_fft(
+    const array& in,
+    array& out,
+    size_t axis,
+    bool inverse,
+    bool real,
+    FFTPlan& plan,
+    std::vector<array> copies,
+    const Stream& s) {
+  auto& d = metal::device(s.device);
+
+  if (plan.bluestein_n == -1) {
+    // Fast no transpose implementation for powers of 2.
+    FourStepParams four_step_params = {
+        /* required= */ true, /* first_step= */ true, plan.n1, plan.n2};
+    auto temp_shape = (real && inverse) ? out.shape() : in.shape();
+    array temp(temp_shape, complex64, nullptr, {});
+    fft_op(
+        in, temp, axis, inverse, real, four_step_params, /*inplace=*/false, s);
+    four_step_params.first_step = false;
+    fft_op(
+        temp, out, axis, inverse, real, four_step_params, /*inplace=*/false, s);
+    copies.push_back(temp);
+  } else {
+    multi_upload_bluestein_fft(in, out, axis, inverse, real, plan, copies, s);
+  }
+}
+
+void fft_op(
+    const array& in,
+    array& out,
+    size_t axis,
+    bool inverse,
+    bool real,
+    const FourStepParams four_step_params,
+    bool inplace,
+    const Stream& s) {
+  auto& d = metal::device(s.device);
+
+  size_t n = out.dtype() == float32 ? out.shape(axis) : in.shape(axis);
+  if (n == 1) {
+    out.copy_shared_buffer(in);
+    return;
+  }
+
+  if (four_step_params.required) {
+    // Four Step FFT decomposes into two FFTs: n1 on columns, n2 on rows
+    n = four_step_params.first_step ? four_step_params.n1 : four_step_params.n2;
   }
 
   // Make sure that the array is contiguous and has stride 1 in the FFT dim
   std::vector<array> copies;
-  auto check_input = [this, &copies, &s](const array& x) {
+  auto check_input = [&axis, &copies, &s](const array& x) {
     // TODO: Pass the strides to the kernel so
     // we can avoid the copy when x is not contiguous.
-    bool no_copy = x.strides()[axes_[0]] == 1 && x.flags().row_contiguous ||
-        x.flags().col_contiguous;
+    bool no_copy = x.strides()[axis] == 1 &&
+        (x.flags().row_contiguous || x.flags().col_contiguous);
     if (no_copy) {
       return x;
     } else {
       array x_copy(x.shape(), x.dtype(), nullptr, {});
       std::vector<size_t> strides;
-      size_t cur_stride = x.shape(axes_[0]);
-      for (int axis = 0; axis < x.ndim(); axis++) {
-        if (axis == axes_[0]) {
+      size_t cur_stride = x.shape(axis);
+      for (int a = 0; a < x.ndim(); a++) {
+        if (a == axis) {
           strides.push_back(1);
         } else {
           strides.push_back(cur_stride);
-          cur_stride *= x.shape(axis);
+          cur_stride *= x.shape(a);
         }
       }
 
       auto flags = x.flags();
-      size_t f_stride = 1;
-      size_t b_stride = 1;
-      flags.col_contiguous = true;
-      flags.row_contiguous = true;
-      for (int i = 0, ri = x.ndim() - 1; i < x.ndim(); ++i, --ri) {
-        flags.col_contiguous &= (strides[i] == f_stride || x.shape(i) == 1);
-        f_stride *= x.shape(i);
-        flags.row_contiguous &= (strides[ri] == b_stride || x.shape(ri) == 1);
-        b_stride *= x.shape(ri);
-      }
-      // This is probably over-conservative
-      flags.contiguous = false;
+      auto [data_size, is_row_contiguous, is_col_contiguous] =
+          check_contiguity(x.shape(), strides);
+
+      flags.col_contiguous = is_row_contiguous;
+      flags.row_contiguous = is_col_contiguous;
+      flags.contiguous = data_size == x_copy.size();
 
       x_copy.set_data(
-          allocator::malloc_or_wait(x.nbytes()), x.data_size(), strides, flags);
+          allocator::malloc_or_wait(x.nbytes()), data_size, strides, flags);
       copy_gpu_inplace(x, x_copy, CopyType::GeneralGeneral, s);
       copies.push_back(x_copy);
       return x_copy;
     }
   };
-  const array& in_contiguous = check_input(inputs[0]);
+  const array& in_contiguous = check_input(in);
+
+  // real to complex: n -> (n/2)+1
+  // complex to real: (n/2)+1 -> n
+  auto out_strides = in_contiguous.strides();
+  size_t out_data_size = in_contiguous.data_size();
+  if (in.shape(axis) != out.shape(axis)) {
+    for (int i = 0; i < out_strides.size(); i++) {
+      if (out_strides[i] != 1) {
+        out_strides[i] = out_strides[i] / in.shape(axis) * out.shape(axis);
+      }
+    }
+    out_data_size = out_data_size / in.shape(axis) * out.shape(axis);
+  }
+
+  auto plan = plan_fft(n);
+  if (plan.four_step) {
+    four_step_fft(in, out, axis, inverse, real, plan, copies, s);
+    d.get_command_buffer(s.index)->addCompletedHandler(
+        [copies](MTL::CommandBuffer*) mutable { copies.clear(); });
+    return;
+  }
 
   // TODO: allow donation here
-  out.set_data(
-      allocator::malloc_or_wait(out.nbytes()),
-      in_contiguous.data_size(),
-      in_contiguous.strides(),
-      in_contiguous.flags());
+  if (!inplace) {
+    out.set_data(
+        allocator::malloc_or_wait(out.nbytes()),
+        out_data_size,
+        out_strides,
+        in_contiguous.flags());
+  }
 
-  // We use n / 4 threads by default since radix-4
-  // is the largest single threaded radix butterfly
-  // we currently implement.
-  size_t m = n / 4;
-  size_t batch = in.size() / in.shape(axes_[0]);
+  auto radices = supported_radices();
+  int fft_size = plan.bluestein_n > 0 ? plan.bluestein_n : n;
+
+  // Setup function constants
+  bool power_of_2 = is_power_of_2(fft_size);
+
+  auto make_int = [](int* a, int i) {
+    return std::make_tuple(a, MTL::DataType::DataTypeInt, i);
+  };
+  auto make_bool = [](bool* a, int i) {
+    return std::make_tuple(a, MTL::DataType::DataTypeBool, i);
+  };
+
+  std::vector<MTLFC> func_consts = {
+      make_bool(&inverse, 0), make_bool(&power_of_2, 1)};
+
+  // Start of radix/rader step constants
+  int index = 4;
+  for (int i = 0; i < plan.stockham.size(); i++) {
+    func_consts.push_back(make_int(&plan.stockham[i], index));
+    index += 1;
+  }
+  for (int i = 0; i < plan.rader.size(); i++) {
+    func_consts.push_back(make_int(&plan.rader[i], index));
+    index += 1;
+  }
+  int elems_per_thread = compute_elems_per_thread(plan);
+  func_consts.push_back(make_int(&elems_per_thread, 2));
+
+  int rader_m = n / plan.rader_n;
+  func_consts.push_back(make_int(&rader_m, 3));
+
+  // The overall number of FFTs we're going to compute for this input
+  int size = out.dtype() == float32 ? out.size() : in.size();
+  if (real && inverse && four_step_params.required) {
+    size = out.size();
+  }
+  int total_batch_size = size / n;
+  int threads_per_fft = (fft_size + elems_per_thread - 1) / elems_per_thread;
+
+  // We batch among threadgroups for improved efficiency when n is small
+  int threadgroup_batch_size = std::max(MIN_THREADGROUP_MEM_SIZE / fft_size, 1);
+  if (four_step_params.required) {
+    // Require a threadgroup batch size of at least 4 for four step FFT
+    // so we can coalesce the memory accesses.
+    threadgroup_batch_size =
+        std::max(threadgroup_batch_size, MIN_COALESCE_WIDTH);
+  }
+  int threadgroup_mem_size = next_power_of_2(threadgroup_batch_size * fft_size);
+  // FFTs up to 2^20 are currently supported
+  assert(threadgroup_mem_size <= MAX_STOCKHAM_FFT_SIZE);
+
+  // ceil divide
+  int batch_size =
+      (total_batch_size + threadgroup_batch_size - 1) / threadgroup_batch_size;
+
+  if (real && !four_step_params.required) {
+    // We can perform 2 RFFTs at once so the batch size is halved.
+    batch_size = (batch_size + 2 - 1) / 2;
+  }
+  int out_buffer_size = out.size();
 
   auto& compute_encoder = d.get_command_encoder(s.index);
+  auto in_type_str = in.dtype() == float32 ? "float" : "float2";
+  auto out_type_str = out.dtype() == float32 ? "float" : "float2";
+  // Only required by four step
+  int step = -1;
   {
     std::ostringstream kname;
-    kname << "fft_" << n;
-    auto kernel = d.get_kernel(kname.str());
+    std::string inv_string = inverse ? "true" : "false";
+    std::string real_string = real ? "true" : "false";
+    std::string func_name;
+    if (plan.bluestein_n > 0) {
+      kname << "bluestein_fft_mem_" << threadgroup_mem_size << "_"
+            << in_type_str << "_" << out_type_str;
+      func_name = "bluestein_fft";
+    } else if (plan.rader_n > 1) {
+      kname << "rader_fft_mem_" << threadgroup_mem_size << "_" << in_type_str
+            << "_" << out_type_str;
+      func_name = "rader_fft";
+    } else if (four_step_params.required) {
+      step = four_step_params.first_step ? 0 : 1;
+      kname << "four_step_mem_" << threadgroup_mem_size << "_" << in_type_str
+            << "_" << out_type_str << "_" << step << "_" << real_string;
+      func_name = "four_step_fft";
+    } else {
+      kname << "fft_mem_" << threadgroup_mem_size << "_" << in_type_str << "_"
+            << out_type_str;
+      func_name = "fft";
+    }
+    std::string base_name = kname.str();
+    // We use a specialized kernel for each FFT size
+    kname << "_n" << fft_size << "_inv_" << inverse;
+    std::string hash_name = kname.str();
+    auto template_def = func_name == "four_step_fft" ? get_template_definition(
+                                                           base_name,
+                                                           func_name,
+                                                           threadgroup_mem_size,
+                                                           in_type_str,
+                                                           out_type_str,
+                                                           step,
+                                                           real)
+                                                     : get_template_definition(
+                                                           base_name,
+                                                           func_name,
+                                                           threadgroup_mem_size,
+                                                           in_type_str,
+                                                           out_type_str);
+    auto kernel =
+        get_fft_kernel(d, base_name, hash_name, func_consts, template_def);
 
-    bool donated = in.data_shared_ptr() == nullptr;
     compute_encoder->setComputePipelineState(kernel);
     compute_encoder.set_input_array(in_contiguous, 0);
     compute_encoder.set_output_array(out, 1);
 
-    auto group_dims = MTL::Size(1, m, 1);
-    auto grid_dims = MTL::Size(batch, m, 1);
-    compute_encoder.dispatchThreads(grid_dims, group_dims);
+    if (plan.bluestein_n > 0) {
+      // Precomputed twiddle factors for Bluestein's
+      auto [w_k, w_q] = compute_bluestein_constants(n, plan.bluestein_n);
+      copies.push_back(w_q);
+      copies.push_back(w_k);
+
+      compute_encoder.set_input_array(w_q, 2); // w_q
+      compute_encoder.set_input_array(w_k, 3); // w_k
+      compute_encoder->setBytes(&n, sizeof(int), 4);
+      compute_encoder->setBytes(&plan.bluestein_n, sizeof(int), 5);
+      compute_encoder->setBytes(&total_batch_size, sizeof(int), 6);
+    } else if (plan.rader_n > 1) {
+      auto [b_q, g_q, g_minus_q] = compute_raders_constants(plan.rader_n, s);
+      copies.push_back(b_q);
+      copies.push_back(g_q);
+      copies.push_back(g_minus_q);
+
+      compute_encoder.set_input_array(b_q, 2);
+      compute_encoder.set_input_array(g_q, 3);
+      compute_encoder.set_input_array(g_minus_q, 4);
+      compute_encoder->setBytes(&n, sizeof(int), 5);
+      compute_encoder->setBytes(&total_batch_size, sizeof(int), 6);
+      compute_encoder->setBytes(&plan.rader_n, sizeof(int), 7);
+    } else if (four_step_params.required) {
+      compute_encoder->setBytes(&four_step_params.n1, sizeof(int), 2);
+      compute_encoder->setBytes(&four_step_params.n2, sizeof(int), 3);
+      compute_encoder->setBytes(&total_batch_size, sizeof(int), 4);
+    } else {
+      compute_encoder->setBytes(&n, sizeof(int), 2);
+      compute_encoder->setBytes(&total_batch_size, sizeof(int), 3);
+    }
+
+    auto group_dims = MTL::Size(1, threadgroup_batch_size, threads_per_fft);
+    auto grid_dims =
+        MTL::Size(batch_size, threadgroup_batch_size, threads_per_fft);
+    compute_encoder->dispatchThreads(grid_dims, group_dims);
   }
   d.get_command_buffer(s.index)->addCompletedHandler(
       [copies](MTL::CommandBuffer*) mutable { copies.clear(); });
 }
 
+void fft_op(
+    const array& in,
+    array& out,
+    size_t axis,
+    bool inverse,
+    bool real,
+    bool inplace,
+    const Stream& s) {
+  fft_op(in, out, axis, inverse, real, FourStepParams(), inplace, s);
+}
+
+void nd_fft_op(
+    const array& in,
+    array& out,
+    const std::vector<size_t>& axes,
+    bool inverse,
+    bool real,
+    const Stream& s) {
+  // Perform ND FFT on GPU as a series of 1D FFTs
+  auto temp_shape = inverse ? in.shape() : out.shape();
+  array temp1(temp_shape, complex64, nullptr, {});
+  array temp2(temp_shape, complex64, nullptr, {});
+  std::vector<array> temp_arrs = {temp1, temp2};
+  for (int i = axes.size() - 1; i >= 0; i--) {
+    int reverse_index = axes.size() - i - 1;
+    // For 5D and above, we don't want to reallocate our two temporary arrays
+    bool inplace = reverse_index >= 3 && i != 0;
+    // Opposite order for fft vs ifft
+    int index = inverse ? reverse_index : i;
+    size_t axis = axes[index];
+    // Mirror np.fft.(i)rfftn and perform a real transform
+    // only on the final axis.
+    bool step_real = (real && index == axes.size() - 1);
+    int step_shape = inverse ? out.shape(axis) : in.shape(axis);
+    const array& in_arr = i == axes.size() - 1 ? in : temp_arrs[1 - i % 2];
+    array& out_arr = i == 0 ? out : temp_arrs[i % 2];
+    fft_op(in_arr, out_arr, axis, inverse, step_real, inplace, s);
+  }
+
+  auto& d = metal::device(s.device);
+  d.get_command_buffer(s.index)->addCompletedHandler(
+      [temp_arrs](MTL::CommandBuffer*) mutable { temp_arrs.clear(); });
+}
+
+void FFT::eval_gpu(const std::vector<array>& inputs, array& out) {
+  auto& s = stream();
+  auto& in = inputs[0];
+
+  if (axes_.size() > 1) {
+    nd_fft_op(in, out, axes_, inverse_, real_, s);
+  } else {
+    fft_op(in, out, axes_[0], inverse_, real_, /*inplace=*/false, s);
+  }
+}
+
 } // namespace mlx::core

mlx/backend/metal/hadamard.cpp

@@ -0,0 +1,203 @@
+// Copyright © 2024 Apple Inc.
+
+#include <map>
+
+#include "mlx/backend/common/compiled.h"
+#include "mlx/backend/common/hadamard.h"
+#include "mlx/backend/common/utils.h"
+#include "mlx/backend/metal/copy.h"
+#include "mlx/backend/metal/device.h"
+#include "mlx/backend/metal/jit/includes.h"
+#include "mlx/backend/metal/kernels.h"
+#include "mlx/backend/metal/utils.h"
+#include "mlx/primitives.h"
+
+namespace mlx::core {
+
+constexpr int MAX_HADAMARD_THREADS_PER_GROUP = 256;
+constexpr int MAX_HADAMARD_BYTES = 32768; // 32KB
+
+std::string gen_hadamard_codelet(int m) {
+  // Generate a O(m^2) hadamard codelet for a given M
+  // using the hadamard matrices above
+  //
+  // e.g. m = 2
+  // METAL_FUNC void hadamard_m(thread float *x) {
+  //   float tmp[2];
+  //   tmp[0] = + x[0] + x[1];
+  //   tmp[1] = + x[0] - x[1];
+  //   for (int i = 0; i < 2; i++) { x[i] = tmp[i]; }
+  // }
+  //
+  auto h_matrices = hadamard_matrices();
+  auto& matrix = h_matrices[m];
+
+  std::ostringstream source;
+  source << "METAL_FUNC void hadamard_radix_m(thread float *x) {" << std::endl;
+  if (m == 1) {
+    source << "}" << std::endl;
+    return source.str();
+  }
+  source << "  float tmp[" << m << "];" << std::endl;
+  auto start = 1;
+  auto end = matrix.find('\n', start);
+
+  int index = 0;
+  while (end != std::string_view::npos) {
+    source << "  tmp[" << index << "] = ";
+    auto row = matrix.substr(start, end - start);
+    for (int i = 0; i < row.length(); i++) {
+      source << " " << row[i] << " x[" << i << "]";
+    }
+    source << ";" << std::endl;
+    start = end + 1;
+    end = matrix.find('\n', start);
+    index++;
+  }
+  source << "  for (int i = 0; i < " << m << "; i++) { x[i] = tmp[i]; }"
+         << std::endl;
+  source << "}" << std::endl;
+  return source.str();
+}
+
+void launch_hadamard(
+    const array& in,
+    array& out,
+    int batch_size,
+    int threads_per,
+    const std::string kernel_name,
+    float scale,
+    const Stream& s) {
+  auto& d = metal::device(s.device);
+
+  const auto& lib_name = kernel_name.substr(1);
+  auto lib = d.get_library(lib_name);
+  auto kernel = d.get_kernel(kernel_name, lib);
+  assert(threads_per <= kernel->maxTotalThreadsPerThreadgroup());
+
+  auto& compute_encoder = d.get_command_encoder(s.index);
+  compute_encoder->setComputePipelineState(kernel);
+  compute_encoder.set_input_array(in, 0);
+  compute_encoder.set_output_array(out, 1);
+  compute_encoder->setBytes(&scale, sizeof(float), 2);
+
+  MTL::Size group_dims = MTL::Size(1, threads_per, 1);
+  MTL::Size grid_dims = MTL::Size(batch_size, threads_per, 1);
+  compute_encoder->dispatchThreads(grid_dims, group_dims);
+}
+
+void Hadamard::eval_gpu(const std::vector<array>& inputs, array& out) {
+  auto& s = stream();
+
+  auto& in = inputs[0];
+
+  std::vector<array> copies;
+  // Only support the last axis for now
+  int axis = in.ndim() - 1;
+  auto check_input = [&copies, &s](const array& x) {
+    // TODO(alexbarron) pass strides to kernel to relax this constraint
+    bool no_copy = x.flags().row_contiguous;
+    if (no_copy) {
+      return x;
+    } else {
+      copies.push_back(array(x.shape(), x.dtype(), nullptr, {}));
+      copy_gpu(x, copies.back(), CopyType::General, s);
+      return copies.back();
+    }
+  };
+  const array& in_contiguous = check_input(in);
+
+  if (in_contiguous.is_donatable()) {
+    out.move_shared_buffer(in_contiguous);
+  } else {
+    out.set_data(allocator::malloc_or_wait(out.nbytes()));
+  }
+
+  auto [n, m] = decompose_hadamard(in.shape(axis));
+
+  if (n * (int)size_of(in.dtype()) > MAX_HADAMARD_BYTES) {
+    throw std::invalid_argument(
+        "[hadamard] For n = m*2^k, 2^k > 8192 for FP32 or 2^k > 16384 for FP16/BF16 NYI");
+  }
+
+  int max_radix = std::min(n, 16);
+  // Use read_width 2 for m = 28 to avoid register spilling
+  int read_width = (n == 2 || m == 28) ? 2 : 4;
+
+  std::ostringstream kname;
+  kname << "hadamard_" << n * m << "_" << type_to_name(out);
+  auto kernel_name = kname.str();
+  auto& d = metal::device(s.device);
+  const auto& lib_name = kernel_name;
+  auto lib = d.get_library(lib_name);
+  if (lib == nullptr) {
+    std::ostringstream kernel_source;
+    auto codelet = gen_hadamard_codelet(m);
+    kernel_source << metal::utils() << codelet << metal::hadamard();
+    kernel_source << get_template_definition(
+        "n" + kernel_name,
+        "hadamard_n",
+        get_type_string(in.dtype()),
+        n,
+        max_radix,
+        read_width);
+    kernel_source << get_template_definition(
+        "m" + kernel_name,
+        "hadamard_m",
+        get_type_string(in.dtype()),
+        n,
+        m,
+        read_width);
+    lib = d.get_library(lib_name, kernel_source.str());
+  }
+
+  int batch_size = in.size() / n;
+  int threads_per = n / max_radix;
+
+  if (m > 1) {
+    // When m is greater than 1, we decompose the
+    // computation into two uploads to the GPU:
+    //
+    // e.g. len(x) = 12*4 = 48, m = 12, n = 4
+    //
+    // y = h48 @ x
+    //
+    // Upload 1:
+    // tmp = a.reshape(12, 4) @ h4
+    //
+    // Upload 2:
+    // y = h12 @ tmp
+    array temp(in.shape(), in.dtype(), nullptr, {});
+    temp.set_data(allocator::malloc_or_wait(temp.nbytes()));
+    copies.push_back(temp);
+
+    launch_hadamard(
+        in_contiguous,
+        temp,
+        batch_size,
+        threads_per,
+        "n" + kernel_name,
+        1.0,
+        s);
+
+    // Metal sometimes reports 256 max threads per group for hadamard_m kernel
+    threads_per = std::min(n / read_width, MAX_HADAMARD_THREADS_PER_GROUP);
+    batch_size = in.size() / m / read_width / threads_per;
+    launch_hadamard(
+        temp, out, batch_size, threads_per, "m" + kernel_name, scale_, s);
+  } else {
+    launch_hadamard(
+        in_contiguous,
+        out,
+        batch_size,
+        threads_per,
+        "n" + kernel_name,
+        scale_,
+        s);
+  }
+
+  d.get_command_buffer(s.index)->addCompletedHandler(
+      [copies](MTL::CommandBuffer*) mutable { copies.clear(); });
+}
+
+} // namespace mlx::core

mlx/backend/metal/indexing.cpp

@@ -293,7 +293,18 @@ void Scatter::eval_gpu(const std::vector<array>& inputs, array& out) {
         out.shape().data(), out.shape().size() * sizeof(int), 3);
     compute_encoder->setBytes(
         out.strides().data(), out.strides().size() * sizeof(size_t), 4);
-    compute_encoder->setBytes(&upd_size, sizeof(size_t), 5);
+
+    size_t out_ndim = out.ndim();
+    compute_encoder->setBytes(&out_ndim, sizeof(out_ndim), 5);
+    if (upd_ndim <= 1) {
+      // Placeholder so Metal doesn't compalain
+      int shape_ = 0;
+      compute_encoder->setBytes(&shape_, sizeof(int), 6);
+    } else {
+      compute_encoder->setBytes(upd.shape().data(), upd_ndim * sizeof(int), 6);
+    }
+    compute_encoder->setBytes(&upd_ndim, sizeof(size_t), 7);
+    compute_encoder->setBytes(&upd_size, sizeof(size_t), 8);
 
     // Set index buffers
     for (int i = 0; i < nidx; ++i) {

mlx/backend/metal/jit/binary.h

@@ -1,87 +0,0 @@
-// Copyright © 2024 Apple Inc.
-
-constexpr std::string_view binary_kernels = R"(
-template [[host_name("ss{0}")]] [[kernel]]
-void binary_ss<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("vs{0}")]] [[kernel]]
-void binary_vs<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("sv{0}")]] [[kernel]]
-void binary_sv<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("vv{0}")]] [[kernel]]
-void binary_vv<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("g4{0}")]] [[kernel]] void
-binary_g_nd<{1}, {2}, {3}, 4>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const int shape[4],
-    constant const size_t a_strides[4],
-    constant const size_t b_strides[4],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-template [[host_name("g5{0}")]] [[kernel]] void
-binary_g_nd<{1}, {2}, {3}, 5>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const int shape[5],
-    constant const size_t a_strides[5],
-    constant const size_t b_strides[5],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-
-template [[host_name("g1{0}")]] [[kernel]] void
-binary_g_nd1<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const size_t& a_stride,
-    constant const size_t& b_stride,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("g2{0}")]] [[kernel]] void
-binary_g_nd2<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const size_t a_strides[2],
-    constant const size_t b_strides[2],
-    uint2 index [[thread_position_in_grid]],
-    uint2 grid_dim [[threads_per_grid]]);
-template [[host_name("g3{0}")]] [[kernel]] void
-binary_g_nd3<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const size_t a_strides[3],
-    constant const size_t b_strides[3],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-
-template [[host_name("gn{0}")]] [[kernel]]
-void binary_g<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    constant const int* shape,
-    constant const size_t* a_strides,
-    constant const size_t* b_strides,
-    constant const int& ndim,
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-)";

mlx/backend/metal/jit/binary_two.h

@@ -1,98 +0,0 @@
-// Copyright © 2024 Apple Inc.
-
-constexpr std::string_view binary_two_kernels = R"(
-template [[host_name("ss{0}")]] [[kernel]]
-void binary_ss<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("vs{0}")]] [[kernel]]
-void binary_vs<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("sv{0}")]] [[kernel]]
-void binary_sv<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("vv{0}")]] [[kernel]]
-void binary_vv<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    uint index [[thread_position_in_grid]]);
-
-template [[host_name("g4{0}")]] [[kernel]] void
-binary_g_nd<{1}, {2}, {3}, 4>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const int shape[4],
-    constant const size_t a_strides[4],
-    constant const size_t b_strides[4],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-template [[host_name("g5{0}")]] [[kernel]] void
-binary_g_nd<{1}, {2}, {3}, 5>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const int shape[5],
-    constant const size_t a_strides[5],
-    constant const size_t b_strides[5],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-
-template [[host_name("g1{0}")]] [[kernel]] void
-binary_g_nd1<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const size_t& a_stride,
-    constant const size_t& b_stride,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("g2{0}")]] [[kernel]] void
-binary_g_nd2<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const size_t a_strides[2],
-    constant const size_t b_strides[2],
-    uint2 index [[thread_position_in_grid]],
-    uint2 grid_dim [[threads_per_grid]]);
-template [[host_name("g3{0}")]] [[kernel]] void
-binary_g_nd3<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const size_t a_strides[3],
-    constant const size_t b_strides[3],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-
-template [[host_name("gn{0}")]] [[kernel]]
-void binary_g<{1}, {2}, {3}>(
-    device const {1}* a,
-    device const {1}* b,
-    device {2}* c,
-    device {2}* d,
-    constant const int* shape,
-    constant const size_t* a_strides,
-    constant const size_t* b_strides,
-    constant const int& ndim,
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-)";

mlx/backend/metal/jit/gemv_masked.h

@@ -0,0 +1,25 @@
+// Copyright © 2024 Apple Inc.
+
+constexpr std::string_view gemv_masked_kernel = R"(
+template [[host_name("{name}")]] [[kernel]] void
+gemv_{trans}masked<{itype}, {outm_t}, {opm_t}, {bm}, {bn}, {sm}, {sn}, {tm}, {tn}, {nc}>(
+    const device {itype}* mat [[buffer(0)]],
+    const device {itype}* in_vec [[buffer(1)]],
+    device {itype}* out_vec [[buffer(3)]],
+    const constant int& in_vec_size [[buffer(4)]],
+    const constant int& out_vec_size [[buffer(5)]],
+    const constant int& marix_ld [[buffer(6)]],
+    const constant int& batch_ndim [[buffer(9)]],
+    const constant int* batch_shape [[buffer(10)]],
+    const constant size_t* vector_batch_stride [[buffer(11)]],
+    const constant size_t* matrix_batch_stride [[buffer(12)]],
+    const device {outm_t}* out_mask [[buffer(20)]],
+    const device {opm_t}* mat_mask [[buffer(21)]],
+    const device {opm_t}* vec_mask [[buffer(22)]],
+    const constant int* mask_strides [[buffer(23)]],
+    const constant size_t* mask_batch_strides [[buffer(24)]],
+    uint3 tid [[threadgroup_position_in_grid]],
+    uint3 lid [[thread_position_in_threadgroup]],
+    uint simd_gid [[simdgroup_index_in_threadgroup]],
+    uint simd_lid [[thread_index_in_simdgroup]]);
+)";

mlx/backend/metal/jit/includes.h

@@ -17,6 +17,9 @@ const char* unary();
 const char* binary();
 const char* binary_two();
 const char* copy();
+const char* fft();
+const char* hadamard();
+const char* quantized();
 const char* ternary();
 const char* scan();
 const char* softmax();
@@ -30,5 +33,6 @@ const char* steel_gemm_splitk();
 const char* conv();
 const char* steel_conv();
 const char* steel_conv_general();
+const char* gemv_masked();
 
 } // namespace mlx::core::metal

mlx/backend/metal/jit/indexing.h

@@ -38,12 +38,24 @@ constexpr std::string_view scatter_kernels = R"(
     device mlx_atomic<{1}>* out [[buffer(2)]],
     const constant int* out_shape [[buffer(3)]],
     const constant size_t* out_strides [[buffer(4)]],
-    const constant size_t& upd_size [[buffer(5)]],
+    const constant size_t& out_ndim [[buffer(5)]],
+    const constant int* upd_shape [[buffer(6)]],
+    const constant size_t& upd_ndim [[buffer(7)]],
+    const constant size_t& upd_size [[buffer(8)]],
     {5}
     uint2 gid [[thread_position_in_grid]]) {{
   const array<const device {2}*, {4}> idx_buffers = {{ {6} }};
   return scatter_1d_index_impl<{1}, {2}, {3}, {4}>(
-      updates, out, out_shape, out_strides, upd_size, idx_buffers, gid);
+      updates,
+      out,
+      out_shape,
+      out_strides,
+      out_ndim,
+      upd_shape,
+      upd_ndim,
+      upd_size,
+      idx_buffers,
+      gid);
 }}
 
 [[kernel]] void scatter{0}_{4}(

mlx/backend/metal/jit/sort.h

@@ -1,81 +0,0 @@
-// Copyright © 2024 Apple Inc.
-
-constexpr std::string_view block_sort_kernels = R"(
-template [[host_name("carg_{0}")]] [[kernel]] void
-block_sort<{1}, {2}, true, {3}, {4}>(
-    const device {1}* inp [[buffer(0)]],
-    device {2}* out [[buffer(1)]],
-    const constant int& size_sorted_axis [[buffer(2)]],
-    const constant int& stride_sorted_axis [[buffer(3)]],
-    const constant int& stride_segment_axis [[buffer(4)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-template [[host_name("ncarg_{0}")]] [[kernel]] void
-block_sort_nc<{1}, {2}, true, {3}, {4}>(
-    const device {1}* inp [[buffer(0)]],
-    device {2}* out [[buffer(1)]],
-    const constant int& size_sorted_axis [[buffer(2)]],
-    const constant int& stride_sorted_axis [[buffer(3)]],
-    const constant int& nc_dim [[buffer(4)]],
-    const device int* nc_shape [[buffer(5)]],
-    const device size_t* nc_strides [[buffer(6)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-template [[host_name("c_{0}")]] [[kernel]] void
-block_sort<{1}, {2}, false, {3}, {4}>(
-    const device {1}* inp [[buffer(0)]],
-    device {2}* out [[buffer(1)]],
-    const constant int& size_sorted_axis [[buffer(2)]],
-    const constant int& stride_sorted_axis [[buffer(3)]],
-    const constant int& stride_segment_axis [[buffer(4)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-template [[host_name("nc_{0}")]] [[kernel]] void
-block_sort_nc<{1}, {2}, false, {3}, {4}>(
-    const device {1}* inp [[buffer(0)]],
-    device {2}* out [[buffer(1)]],
-    const constant int& size_sorted_axis [[buffer(2)]],
-    const constant int& stride_sorted_axis [[buffer(3)]],
-    const constant int& nc_dim [[buffer(4)]],
-    const device int* nc_shape [[buffer(5)]],
-    const device size_t* nc_strides [[buffer(6)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-)";
-
-constexpr std::string_view multiblock_sort_kernels = R"(
-template [[host_name("sort_{0}")]] [[kernel]] void
-mb_block_sort<{1}, {2}, true, {3}, {4}>(
-    const device {1}* inp [[buffer(0)]],
-    device {1}* out_vals [[buffer(1)]],
-    device {2}* out_idxs [[buffer(2)]],
-    const constant int& size_sorted_axis [[buffer(3)]],
-    const constant int& stride_sorted_axis [[buffer(4)]],
-    const constant int& nc_dim [[buffer(5)]],
-    const device int* nc_shape [[buffer(6)]],
-    const device size_t* nc_strides [[buffer(7)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-template [[host_name("partition_{0}")]] [[kernel]] void
-mb_block_partition<{1}, {2}, true, {3}, {4}>(
-    device {2}* block_partitions [[buffer(0)]],
-    const device {1}* dev_vals [[buffer(1)]],
-    const device {2}* dev_idxs [[buffer(2)]],
-    const constant int& size_sorted_axis [[buffer(3)]],
-    const constant int& merge_tiles [[buffer(4)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]],
-    uint3 tgp_dims [[threads_per_threadgroup]]);
-template [[host_name("merge_{0}")]] [[kernel]] void
-mb_block_merge<{1}, {2}, true, {3}, {4}>(
-    const device {2}* block_partitions [[buffer(0)]],
-    const device {1}* dev_vals_in [[buffer(1)]],
-    const device {2}* dev_idxs_in [[buffer(2)]],
-    device {1}* dev_vals_out [[buffer(3)]],
-    device {2}* dev_idxs_out [[buffer(4)]],
-    const constant int& size_sorted_axis [[buffer(5)]],
-    const constant int& merge_tiles [[buffer(6)]],
-    const constant int& num_tiles [[buffer(7)]],
-    uint3 tid [[threadgroup_position_in_grid]],
-    uint3 lid [[thread_position_in_threadgroup]]);
-)";

mlx/backend/metal/jit/ternary.h

@@ -1,80 +0,0 @@
-// Copyright © 2024 Apple Inc.
-
-constexpr std::string_view ternary_kernels = R"(
-template [[host_name("v_{0}")]] [[kernel]] void ternary_v<{1}, {2}>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    uint index [[thread_position_in_grid]]);
-
-template [[host_name("g_{0}")]] [[kernel]] void ternary_g<{1}, {2}>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const int* shape,
-    constant const size_t* a_strides,
-    constant const size_t* b_strides,
-    constant const size_t* c_strides,
-    constant const int& ndim,
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-
-template [[host_name("g1_{0}")]] [[kernel]] void
-ternary_g_nd1<{1}, {2}>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const size_t& a_strides,
-    constant const size_t& b_strides,
-    constant const size_t& c_strides,
-    uint index [[thread_position_in_grid]]);
-template [[host_name("g2_{0}")]] [[kernel]] void
-ternary_g_nd2<{1}, {2}>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const size_t a_strides[2],
-    constant const size_t b_strides[2],
-    constant const size_t c_strides[2],
-    uint2 index [[thread_position_in_grid]],
-    uint2 grid_dim [[threads_per_grid]]);
-template [[host_name("g3_{0}")]] [[kernel]] void
-ternary_g_nd3<{1}, {2}>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const size_t a_strides[3],
-    constant const size_t b_strides[3],
-    constant const size_t c_strides[3],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-template [[host_name("g4_{0}")]] [[kernel]] void
-ternary_g_nd<{1}, {2}, 4>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const int shape[4],
-    constant const size_t a_strides[4],
-    constant const size_t b_strides[4],
-    constant const size_t c_strides[4],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-template [[host_name("g5_{0}")]] [[kernel]] void
-ternary_g_nd<{1}, {2}, 5>(
-    device const bool* a,
-    device const {1}* b,
-    device const {1}* c,
-    device {1}* d,
-    constant const int shape[5],
-    constant const size_t a_strides[5],
-    constant const size_t b_strides[5],
-    constant const size_t c_strides[5],
-    uint3 index [[thread_position_in_grid]],
-    uint3 grid_dim [[threads_per_grid]]);
-)";

mlx/backend/metal/jit/unary.h

@@ -1,16 +0,0 @@
-// Copyright © 2024 Apple Inc.
-
-constexpr std::string_view unary_kernels = R"(
-template [[host_name("v{0}")]] [[kernel]] void unary_v<{1}, {2}>(
-    device const {1}* in,
-    device {1}* out,
-    uint index [[thread_position_in_grid]]);
-
-template [[host_name("g{0}")]] [[kernel]] void unary_g<{1}, {2}>(
-    device const {1}* in,
-    device {1}* out,
-    device const int* in_shape,
-    device const size_t* in_strides,
-    device const int& ndim,
-    uint index [[thread_position_in_grid]]);
-)";

mlx/backend/metal/jit_kernels.cpp

@@ -1,20 +1,16 @@
 // Copyright © 2024 Apple Inc.
-#include <fmt/format.h>
+#include <map>
 
 #include "mlx/backend/common/compiled.h"
 #include "mlx/backend/metal/jit/arange.h"
-#include "mlx/backend/metal/jit/binary.h"
-#include "mlx/backend/metal/jit/binary_two.h"
 #include "mlx/backend/metal/jit/copy.h"
+#include "mlx/backend/metal/jit/gemv_masked.h"
 #include "mlx/backend/metal/jit/includes.h"
 #include "mlx/backend/metal/jit/reduce.h"
 #include "mlx/backend/metal/jit/scan.h"
 #include "mlx/backend/metal/jit/softmax.h"
-#include "mlx/backend/metal/jit/sort.h"
 #include "mlx/backend/metal/jit/steel_conv.h"
 #include "mlx/backend/metal/jit/steel_gemm.h"
-#include "mlx/backend/metal/jit/ternary.h"
-#include "mlx/backend/metal/jit/unary.h"
 #include "mlx/backend/metal/kernels.h"
 #include "mlx/backend/metal/utils.h"
 
@@ -47,38 +43,81 @@ MTL::ComputePipelineState* get_arange_kernel(
 MTL::ComputePipelineState* get_unary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& out) {
+    Dtype out_type,
+    const std::string op) {
   std::string lib_name = kernel_name.substr(1);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
+    auto u_def = get_template_definition(
+        "v" + lib_name, "unary_v", get_type_string(out_type), op);
+    auto u2_def = get_template_definition(
+        "v2" + lib_name, "unary_v2", get_type_string(out_type), op);
+    auto g_def = get_template_definition(
+        "g" + lib_name, "unary_g", get_type_string(out_type), op);
     kernel_source << metal::utils() << metal::unary_ops() << metal::unary()
-                  << fmt::format(
-                         unary_kernels,
-                         lib_name,
-                         get_type_string(out.dtype()),
-                         op_name(out));
+                  << u_def << u2_def << g_def;
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
 }
 
+void add_binary_kernels(
+    const std::string lib_name,
+    Dtype in_type,
+    Dtype out_type,
+    const std::string op,
+    std::ostringstream& kernel_source) {
+  const std::map<std::string, std::string> kernel_types = {
+      {"ss", "binary_ss"},
+      {"vs", "binary_vs"},
+      {"sv", "binary_sv"},
+      {"vv", "binary_vv"},
+      {"vs2", "binary_vs2"},
+      {"sv2", "binary_sv2"},
+      {"vv2", "binary_vv2"},
+      {"g1", "binary_g_nd1"},
+      {"g2", "binary_g_nd2"},
+      {"g3", "binary_g_nd3"},
+      {"g4", "binary_g_nd"},
+      {"g5", "binary_g_nd"},
+      {"gn", "binary_g"},
+  };
+  for (auto [name, func] : kernel_types) {
+    std::string template_def;
+    if (name == "g4" || name == "g5") {
+      int dim = std::stoi(name.substr(1));
+      template_def = get_template_definition(
+          name + lib_name,
+          func,
+          get_type_string(in_type),
+          get_type_string(out_type),
+          op,
+          dim);
+    } else {
+      template_def = get_template_definition(
+          name + lib_name,
+          func,
+          get_type_string(in_type),
+          get_type_string(out_type),
+          op);
+    }
+    kernel_source << template_def;
+  }
+}
+
 MTL::ComputePipelineState* get_binary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& in,
-    const array& out) {
+    Dtype in_type,
+    Dtype out_type,
+    const std::string op) {
   std::string lib_name = kernel_name.substr(2);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
-    kernel_source << metal::utils() << metal::binary_ops() << metal::binary()
-                  << fmt::format(
-                         binary_kernels,
-                         lib_name,
-                         get_type_string(in.dtype()),
-                         get_type_string(out.dtype()),
-                         op_name(out));
+    kernel_source << metal::utils() << metal::binary_ops() << metal::binary();
+    add_binary_kernels(lib_name, in_type, out_type, op, kernel_source);
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -87,20 +126,16 @@ MTL::ComputePipelineState* get_binary_kernel(
 MTL::ComputePipelineState* get_binary_two_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& in,
-    const array& out) {
+    Dtype in_type,
+    Dtype out_type,
+    const std::string op) {
   std::string lib_name = kernel_name.substr(2);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
     kernel_source << metal::utils() << metal::binary_ops()
-                  << metal::binary_two()
-                  << fmt::format(
-                         binary_two_kernels,
-                         lib_name,
-                         get_type_string(in.dtype()),
-                         get_type_string(out.dtype()),
-                         op_name(out));
+                  << metal::binary_two();
+    add_binary_kernels(lib_name, in_type, out_type, op, kernel_source);
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -109,17 +144,35 @@ MTL::ComputePipelineState* get_binary_two_kernel(
 MTL::ComputePipelineState* get_ternary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& out) {
+    Dtype type,
+    const std::string op) {
   std::string lib_name = kernel_name.substr(kernel_name.find("_") + 1);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
-    kernel_source << metal::utils() << metal::ternary_ops() << metal::ternary()
-                  << fmt::format(
-                         ternary_kernels,
-                         lib_name,
-                         get_type_string(out.dtype()),
-                         op_name(out));
+    const std::map<std::string, std::string> kernel_types = {
+        {"v", "ternary_v"},
+        {"v2", "ternary_v2"},
+        {"g", "ternary_g"},
+        {"g1", "ternary_g_nd1"},
+        {"g2", "ternary_g_nd2"},
+        {"g3", "ternary_g_nd3"},
+        {"g4", "ternary_g_nd"},
+        {"g5", "ternary_g_nd"},
+    };
+    kernel_source << metal::utils() << metal::ternary_ops() << metal::ternary();
+    for (auto [name, func] : kernel_types) {
+      std::string template_def;
+      if (name == "g4" || name == "g5") {
+        int dim = std::stoi(name.substr(1));
+        template_def = get_template_definition(
+            name + "_" + lib_name, func, get_type_string(type), op, dim);
+      } else {
+        template_def = get_template_definition(
+            name + "_" + lib_name, func, get_type_string(type), op);
+      }
+      kernel_source << template_def;
+    }
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -170,11 +223,14 @@ MTL::ComputePipelineState* get_scan_kernel(
     const std::string& kernel_name,
     bool reverse,
     bool inclusive,
+    const std::string& reduce_type,
     const array& in,
     const array& out) {
   std::string lib_name = kernel_name.substr(kernel_name.find("_") + 1);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
+    std::string op_name = "Cum" + reduce_type;
+    op_name[3] = toupper(op_name[3]);
     std::ostringstream kernel_source;
     kernel_source << metal::utils() << metal::scan()
                   << fmt::format(
@@ -182,7 +238,7 @@ MTL::ComputePipelineState* get_scan_kernel(
                          lib_name,
                          get_type_string(in.dtype()),
                          get_type_string(out.dtype()),
-                         op_name(out),
+                         op_name,
                          inclusive,
                          reverse);
     lib = d.get_library(lib_name, kernel_source.str());
@@ -201,14 +257,29 @@ MTL::ComputePipelineState* get_sort_kernel(
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
-    kernel_source << metal::utils() << metal::sort()
-                  << fmt::format(
-                         block_sort_kernels,
-                         lib_name,
-                         get_type_string(in.dtype()),
-                         get_type_string(out.dtype()),
-                         bn,
-                         tn);
+    auto in_type = get_type_string(in.dtype());
+    auto out_type = get_type_string(out.dtype());
+    kernel_source << metal::utils() << metal::sort();
+    for (bool is_argsort : {true, false}) {
+      std::string bool_string = is_argsort ? "true" : "false";
+      std::string func_string = is_argsort ? "carg_" : "c_";
+      kernel_source << get_template_definition(
+          func_string + lib_name,
+          "block_sort",
+          in_type,
+          out_type,
+          bool_string,
+          bn,
+          tn);
+      kernel_source << get_template_definition(
+          "n" + func_string + lib_name,
+          "block_sort_nc",
+          in_type,
+          out_type,
+          bool_string,
+          bn,
+          tn);
+    }
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -225,14 +296,21 @@ MTL::ComputePipelineState* get_mb_sort_kernel(
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
     std::ostringstream kernel_source;
-    kernel_source << metal::utils() << metal::sort()
-                  << fmt::format(
-                         multiblock_sort_kernels,
-                         lib_name,
-                         get_type_string(in.dtype()),
-                         get_type_string(idx.dtype()),
-                         bn,
-                         tn);
+    kernel_source << metal::utils() << metal::sort();
+    std::vector<std::pair<std::string, std::string>> kernel_types = {
+        {"sort_", "mb_block_sort"},
+        {"partition_", "mb_block_partition"},
+        {"merge_", "mb_block_merge"}};
+    for (auto [name, func] : kernel_types) {
+      kernel_source << get_template_definition(
+          name + lib_name,
+          func,
+          get_type_string(in.dtype()),
+          get_type_string(idx.dtype()),
+          "true",
+          bn,
+          tn);
+    }
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -259,11 +337,14 @@ MTL::ComputePipelineState* get_reduce_init_kernel(
 MTL::ComputePipelineState* get_reduce_kernel(
     metal::Device& d,
     const std::string& kernel_name,
+    const std::string& op_name,
     const array& in,
     const array& out) {
   std::string lib_name = kernel_name.substr(kernel_name.find("_") + 1);
   auto lib = d.get_library(lib_name);
   if (lib == nullptr) {
+    std::string op_type = op_name;
+    op_type[0] = std::toupper(op_name[0]);
     bool non_atomic = out.dtype() == int64 || out.dtype() == uint64;
     std::ostringstream kernel_source;
     kernel_source << metal::utils() << metal::reduce_utils() << metal::reduce()
@@ -273,7 +354,7 @@ MTL::ComputePipelineState* get_reduce_kernel(
                          lib_name,
                          get_type_string(in.dtype()),
                          get_type_string(out.dtype()),
-                         op_name(out));
+                         op_type);
     lib = d.get_library(lib_name, kernel_source.str());
   }
   return d.get_kernel(kernel_name, lib);
@@ -422,6 +503,49 @@ MTL::ComputePipelineState* get_steel_gemm_masked_kernel(
   return d.get_kernel(kernel_name, lib);
 }
 
+MTL::ComputePipelineState* get_gemv_masked_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const array& out,
+    const std::optional<array>& mask_out,
+    const std::optional<array>& mask_op,
+    bool transpose_mat,
+    int bm,
+    int bn,
+    int sm,
+    int sn,
+    int tm,
+    int tn,
+    bool contiguous) {
+  const auto& lib_name = kernel_name;
+  auto lib = d.get_library(lib_name);
+  if (lib == nullptr) {
+    std::ostringstream kernel_source;
+    auto out_mask_type = mask_out.has_value()
+        ? get_type_string((*mask_out).dtype())
+        : "nomask_t";
+    auto op_mask_type =
+        mask_op.has_value() ? get_type_string((*mask_op).dtype()) : "nomask_t";
+    kernel_source << metal::utils() << metal::gemv_masked()
+                  << fmt::format(
+                         gemv_masked_kernel,
+                         "name"_a = lib_name,
+                         "itype"_a = get_type_string(out.dtype()),
+                         "outm_t"_a = out_mask_type,
+                         "opm_t"_a = op_mask_type,
+                         "bm"_a = bm,
+                         "bn"_a = bn,
+                         "sm"_a = sm,
+                         "sn"_a = sn,
+                         "tm"_a = tm,
+                         "tn"_a = tn,
+                         "trans"_a = transpose_mat ? "t_" : "",
+                         "nc"_a = contiguous ? "0" : "1");
+    lib = d.get_library(lib_name, kernel_source.str());
+  }
+  return d.get_kernel(kernel_name, lib);
+}
+
 MTL::ComputePipelineState* get_steel_conv_kernel(
     metal::Device& d,
     const std::string& kernel_name,
@@ -483,4 +607,36 @@ MTL::ComputePipelineState* get_steel_conv_general_kernel(
   return d.get_kernel(kernel_name, lib);
 }
 
+MTL::ComputePipelineState* get_fft_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const std::string& hash_name,
+    const metal::MTLFCList& func_consts,
+    const std::string& template_def) {
+  const auto& lib_name = kernel_name;
+  auto lib = d.get_library(lib_name);
+  if (lib == nullptr) {
+    std::ostringstream kernel_source;
+    std::string kernel_string;
+    kernel_source << metal::fft() << template_def;
+    lib = d.get_library(lib_name, kernel_source.str());
+  }
+  return d.get_kernel(kernel_name, lib, hash_name, func_consts);
+}
+
+MTL::ComputePipelineState* get_quantized_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const std::string& template_def) {
+  const auto& lib_name = kernel_name;
+  auto lib = d.get_library(lib_name);
+  if (lib == nullptr) {
+    std::ostringstream kernel_source;
+    kernel_source << metal::utils() << metal::gemm() << metal::quantized()
+                  << template_def;
+    lib = d.get_library(lib_name, kernel_source.str());
+  }
+  return d.get_kernel(kernel_name, lib);
+}
+
 } // namespace mlx::core

mlx/backend/metal/kernels.h

@@ -1,5 +1,7 @@
 // Copyright © 2024 Apple Inc.
 
+#include <fmt/format.h>
+
 #include "mlx/array.h"
 #include "mlx/backend/metal/device.h"
 
@@ -13,24 +15,28 @@ MTL::ComputePipelineState* get_arange_kernel(
 MTL::ComputePipelineState* get_unary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& out);
+    Dtype out_type,
+    const std::string op);
 
 MTL::ComputePipelineState* get_binary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& in,
-    const array& out);
+    Dtype in_type,
+    Dtype out_type,
+    const std::string op);
 
 MTL::ComputePipelineState* get_binary_two_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& in,
-    const array& out);
+    Dtype in_type,
+    Dtype out_type,
+    const std::string op);
 
 MTL::ComputePipelineState* get_ternary_kernel(
     metal::Device& d,
     const std::string& kernel_name,
-    const array& out);
+    Dtype type,
+    const std::string op);
 
 MTL::ComputePipelineState* get_copy_kernel(
     metal::Device& d,
@@ -49,6 +55,7 @@ MTL::ComputePipelineState* get_scan_kernel(
     const std::string& kernel_name,
     bool reverse,
     bool inclusive,
+    const std::string& reduce_type,
     const array& in,
     const array& out);
 
@@ -76,6 +83,7 @@ MTL::ComputePipelineState* get_reduce_init_kernel(
 MTL::ComputePipelineState* get_reduce_kernel(
     metal::Device& d,
     const std::string& kernel_name,
+    const std::string& op_name,
     const array& in,
     const array& out);
 
@@ -143,6 +151,21 @@ MTL::ComputePipelineState* get_steel_conv_kernel(
     int n_channel_specialization,
     bool small_filter);
 
+MTL::ComputePipelineState* get_gemv_masked_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const array& out,
+    const std::optional<array>& mask_out,
+    const std::optional<array>& mask_op,
+    bool transpose_mat,
+    int bm,
+    int bn,
+    int sm,
+    int sn,
+    int tm,
+    int tn,
+    bool contiguous);
+
 MTL::ComputePipelineState* get_steel_conv_general_kernel(
     metal::Device& d,
     const std::string& kernel_name,
@@ -153,4 +176,38 @@ MTL::ComputePipelineState* get_steel_conv_general_kernel(
     int wm,
     int wn);
 
+MTL::ComputePipelineState* get_fft_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const std::string& hash_name,
+    const metal::MTLFCList& func_consts,
+    const std::string& template_def);
+
+MTL::ComputePipelineState* get_quantized_kernel(
+    metal::Device& d,
+    const std::string& kernel_name,
+    const std::string& template_def);
+
+// Create a GPU kernel template definition for JIT compilation
+template <typename... Args>
+std::string
+get_template_definition(std::string name, std::string func, Args... args) {
+  std::ostringstream s;
+  s << func << "<";
+  bool first = true;
+  auto add_arg = [&s, &first](const auto& arg) {
+    if (!first) {
+      s << ", ";
+    }
+    first = false;
+    s << arg;
+  };
+  (add_arg(args), ...);
+  s << ">";
+  std::string base_string = R"(
+template [[host_name("{0}")]] [[kernel]] decltype({1}) {1};
+  )";
+  return fmt::format(base_string, name, s.str());
+}
+
 } // namespace mlx::core

mlx/backend/metal/kernels/CMakeLists.txt

@@ -1,66 +1,15 @@
 set(
-  HEADERS
+  BASE_HEADERS
   bf16.h
   bf16_math.h
   complex.h
   defines.h
+  expm1f.h
   utils.h
-  steel/conv/params.h
 )
 
-set(
-  KERNELS
-  "arg_reduce"
-  "conv"
-  "fft"
-  "gemv"
-  "quantized"
-  "random"
-  "rms_norm"
-  "layer_norm"
-  "rope"
-  "scaled_dot_product_attention"
-)
-
-if (NOT MLX_METAL_JIT)
-set(
-  KERNELS
-  ${KERNELS}
-  "arange"
-  "binary"
-  "binary_two"
-  "unary"
-  "ternary"
-  "copy"
-  "softmax"
-  "sort"
-  "scan"
-  "reduce"
-)
-set(
-  HEADERS 
-  ${HEADERS}
-  atomic.h
-  arange.h
-  unary_ops.h
-  unary.h
-  binary_ops.h
-  binary.h
-  ternary.h
-  copy.h
-  softmax.h
-  sort.h
-  scan.h
-  reduction/ops.h
-  reduction/reduce_init.h
-  reduction/reduce_all.h
-  reduction/reduce_col.h
-  reduction/reduce_row.h
-)
-endif()
-
 function(build_kernel_base TARGET SRCFILE DEPS)
-  set(METAL_FLAGS -Wall -Wextra -fno-fast-math -D${MLX_METAL_VERSION})
+  set(METAL_FLAGS -Wall -Wextra -fno-fast-math)
   if(MLX_METAL_DEBUG)
     set(METAL_FLAGS ${METAL_FLAGS}
         -gline-tables-only
@@ -72,7 +21,7 @@ function(build_kernel_base TARGET SRCFILE DEPS)
                   -c ${SRCFILE}
                   -I${PROJECT_SOURCE_DIR}
                   -o ${TARGET}.air
-    DEPENDS ${SRCFILE} ${DEPS}
+    DEPENDS ${SRCFILE} ${DEPS} ${BASE_HEADERS}
     OUTPUT ${TARGET}.air
     COMMENT "Building ${TARGET}.air"
     VERBATIM
@@ -81,49 +30,100 @@ endfunction(build_kernel_base)
 
 function(build_kernel KERNEL)
   set(SRCFILE ${CMAKE_CURRENT_SOURCE_DIR}/${KERNEL}.metal)
-  build_kernel_base(${KERNEL} ${SRCFILE} "${HEADERS}")
+  cmake_path(GET KERNEL STEM TARGET)
+  build_kernel_base(${TARGET} ${SRCFILE} "${ARGN}")
+  set(KERNEL_AIR ${TARGET}.air ${KERNEL_AIR} PARENT_SCOPE)
 endfunction(build_kernel)
 
-foreach(KERNEL ${KERNELS})
-  build_kernel(${KERNEL})
-  set(KERNEL_AIR ${KERNEL}.air ${KERNEL_AIR})
-endforeach()
+build_kernel(arg_reduce)
+build_kernel(conv steel/conv/params.h)
+build_kernel(gemv steel/utils.h)
+build_kernel(layer_norm)
+build_kernel(random)
+build_kernel(rms_norm)
+build_kernel(rope)
+build_kernel(
+  scaled_dot_product_attention
+  scaled_dot_product_attention_params.h
+  steel/defines.h
+  steel/gemm/transforms.h
+  steel/utils.h
+)
+
+set(
+  STEEL_HEADERS 
+  steel/defines.h
+  steel/utils.h
+  steel/conv/conv.h
+  steel/conv/loader.h
+  steel/conv/loaders/loader_channel_l.h
+  steel/conv/loaders/loader_channel_n.h
+  steel/conv/loaders/loader_general.h
+  steel/conv/kernels/steel_conv.h
+  steel/conv/kernels/steel_conv_general.h
+  steel/gemm/gemm.h
+  steel/gemm/mma.h
+  steel/gemm/loader.h
+  steel/gemm/transforms.h
+  steel/gemm/kernels/steel_gemm_fused.h
+  steel/gemm/kernels/steel_gemm_masked.h
+  steel/gemm/kernels/steel_gemm_splitk.h
+)
 
 if (NOT MLX_METAL_JIT)
-  set(
-    STEEL_KERNELS
-    ${CMAKE_CURRENT_SOURCE_DIR}/steel/conv/kernels/steel_conv.metal
-    ${CMAKE_CURRENT_SOURCE_DIR}/steel/conv/kernels/steel_conv_general.metal
-    ${CMAKE_CURRENT_SOURCE_DIR}/steel/gemm/kernels/steel_gemm_fused.metal
-    ${CMAKE_CURRENT_SOURCE_DIR}/steel/gemm/kernels/steel_gemm_masked.metal
-    ${CMAKE_CURRENT_SOURCE_DIR}/steel/gemm/kernels/steel_gemm_splitk.metal
-  )
-  set(
-    STEEL_HEADERS 
-    steel/defines.h
-    steel/utils.h
-    steel/conv/conv.h
-    steel/conv/loader.h
-    steel/conv/loaders/loader_channel_l.h
-    steel/conv/loaders/loader_channel_n.h
-    steel/conv/loaders/loader_general.h
-    steel/conv/kernels/steel_conv.h
-    steel/conv/kernels/steel_conv_general.h
-    steel/gemm/gemm.h
-    steel/gemm/mma.h
-    steel/gemm/loader.h
-    steel/gemm/transforms.h
-    steel/gemm/kernels/steel_gemm_fused.h
-    steel/gemm/kernels/steel_gemm_masked.h
-    steel/gemm/kernels/steel_gemm_splitk.h
-  )
-  foreach(KERNEL ${STEEL_KERNELS})
-    cmake_path(GET KERNEL STEM TARGET)
-    build_kernel_base(${TARGET} ${KERNEL} "${STEEL_HEADERS}")
-    set(KERNEL_AIR ${TARGET}.air ${KERNEL_AIR})
-  endforeach()
+build_kernel(arange arange.h)
+build_kernel(binary binary.h binary_ops.h)
+build_kernel(binary_two binary_two.h)
+build_kernel(copy copy.h)
+build_kernel(
+  fft
+  fft.h
+  fft/radix.h
+  fft/readwrite.h
+)
+build_kernel(
+  reduce
+  atomic.h
+  reduction/ops.h
+  reduction/reduce_init.h
+  reduction/reduce_all.h
+  reduction/reduce_col.h
+  reduction/reduce_row.h
+)
+build_kernel(
+  quantized
+  quantized.h
+  ${STEEL_HEADERS}
+)
+build_kernel(scan scan.h)
+build_kernel(softmax softmax.h)
+build_kernel(sort sort.h)
+build_kernel(ternary ternary.h ternary_ops.h)
+build_kernel(unary unary.h unary_ops.h)
+build_kernel(
+  steel/conv/kernels/steel_conv
+  ${STEEL_HEADERS}
+)
+build_kernel(
+  steel/conv/kernels/steel_conv_general
+  ${STEEL_HEADERS}
+)
+build_kernel(
+  steel/gemm/kernels/steel_gemm_fused
+  ${STEEL_HEADERS}
+)
+build_kernel(
+  steel/gemm/kernels/steel_gemm_masked
+  ${STEEL_HEADERS}
+)
+build_kernel(
+  steel/gemm/kernels/steel_gemm_splitk
+  ${STEEL_HEADERS}
+)
+build_kernel(gemv_masked steel/utils.h)
 endif()
 
+
 add_custom_command(
   OUTPUT ${MLX_METAL_PATH}/mlx.metallib
   COMMAND xcrun -sdk macosx metallib ${KERNEL_AIR} -o ${MLX_METAL_PATH}/mlx.metallib

mlx/backend/metal/kernels/bf16.h

@@ -6,7 +6,7 @@
 
 using namespace metal;
 
-#if defined METAL_3_1 || (__METAL_VERSION__ >= 310)
+#if (MLX_METAL_VERSION >= 310) || (__METAL_VERSION__ >= 310)
 
 typedef bfloat bfloat16_t;
 

mlx/backend/metal/kernels/bf16_math.h

@@ -369,7 +369,7 @@ instantiate_metal_math_funcs(
     return static_cast<otype>(__metal_simd_xor(static_cast<ctype>(data)));     \
   }
 
-#if defined METAL_3_1 || (__METAL_VERSION__ >= 310)
+#if (MLX_METAL_VERSION >= 310) || (__METAL_VERSION__ >= 310)
 
 #define bfloat16_to_uint16(x) as_type<uint16_t>(x)
 #define uint16_to_bfloat16(x) as_type<bfloat16_t>(x)

mlx/backend/metal/kernels/binary.h

@@ -36,6 +36,39 @@ template <typename T, typename U, typename Op>
   c[index] = Op()(a[index], b[index]);
 }
 
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_sv2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  c[offset] = Op()(a[0], b[offset]);
+}
+
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_vs2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  c[offset] = Op()(a[offset], b[0]);
+}
+
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_vv2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  c[offset] = Op()(a[offset], b[offset]);
+}
+
 template <typename T, typename U, typename Op>
 [[kernel]] void binary_g_nd1(
     device const T* a,

mlx/backend/metal/kernels/binary.metal

@@ -4,148 +4,94 @@
 #include <metal_math>
 
 // clang-format off
+#include "mlx/backend/metal/kernels/defines.h"
 #include "mlx/backend/metal/kernels/utils.h"
 #include "mlx/backend/metal/kernels/binary_ops.h"
 #include "mlx/backend/metal/kernels/binary.h"
 
-#define instantiate_binary(name, itype, otype, op, bopt)                      \
-  template                                                                    \
-      [[host_name(name)]] [[kernel]] void binary_##bopt<itype, otype, op>(    \
-          device const itype* a,                                              \
-          device const itype* b,                                              \
-          device otype* c,                                                    \
-          uint index [[thread_position_in_grid]]);
+#define instantiate_binary_all(op, tname, itype, otype)                 \
+  instantiate_kernel("ss" #op #tname, binary_ss, itype, otype, op)      \
+  instantiate_kernel("sv" #op #tname, binary_sv, itype, otype, op)      \
+  instantiate_kernel("vs" #op #tname, binary_vs, itype, otype, op)      \
+  instantiate_kernel("vv" #op #tname, binary_vv, itype, otype, op)      \
+  instantiate_kernel("sv2" #op #tname, binary_sv2, itype, otype, op)    \
+  instantiate_kernel("vs2" #op #tname, binary_vs2, itype, otype, op)    \
+  instantiate_kernel("vv2" #op #tname, binary_vv2, itype, otype, op)    \
+  instantiate_kernel("gn" #op #tname, binary_g, itype, otype, op)       \
+  instantiate_kernel("g1" #op #tname, binary_g_nd1, itype, otype, op)   \
+  instantiate_kernel("g2" #op #tname, binary_g_nd2, itype, otype, op)   \
+  instantiate_kernel("g3" #op #tname, binary_g_nd3, itype, otype, op)   \
+  instantiate_kernel("g4" #op #tname, binary_g_nd, itype, otype, op, 4) \
+  instantiate_kernel("g5" #op #tname, binary_g_nd,  itype, otype, op, 5)
 
-#define instantiate_binary_g_dim(name, itype, otype, op, dims) \
-  template [[host_name("g" #dims name)]] [[kernel]] void       \
-  binary_g_nd<itype, otype, op, dims>(                         \
-      device const itype* a,                                   \
-      device const itype* b,                                   \
-      device otype* c,                                         \
-      constant const int shape[dims],                          \
-      constant const size_t a_strides[dims],                   \
-      constant const size_t b_strides[dims],                   \
-      uint3 index [[thread_position_in_grid]],                 \
-      uint3 grid_dim [[threads_per_grid]]);
+#define instantiate_binary_integer(op)                   \
+  instantiate_binary_all(op, uint8, uint8_t, uint8_t)    \
+  instantiate_binary_all(op, uint16, uint16_t, uint16_t) \
+  instantiate_binary_all(op, uint32, uint32_t, uint32_t) \
+  instantiate_binary_all(op, uint64, uint64_t, uint64_t) \
+  instantiate_binary_all(op, int8, int8_t, int8_t)       \
+  instantiate_binary_all(op, int16, int16_t, int16_t)    \
+  instantiate_binary_all(op, int32, int32_t, int32_t)    \
+  instantiate_binary_all(op, int64, int64_t, int64_t)
 
-#define instantiate_binary_g_nd(name, itype, otype, op) \
-  template [[host_name("g1" name)]] [[kernel]] void     \
-  binary_g_nd1<itype, otype, op>(                       \
-      device const itype* a,                            \
-      device const itype* b,                            \
-      device otype* c,                                  \
-      constant const size_t& a_stride,                  \
-      constant const size_t& b_stride,                  \
-      uint index [[thread_position_in_grid]]);          \
-  template [[host_name("g2" name)]] [[kernel]] void     \
-  binary_g_nd2<itype, otype, op>(                       \
-      device const itype* a,                            \
-      device const itype* b,                            \
-      device otype* c,                                  \
-      constant const size_t a_strides[2],               \
-      constant const size_t b_strides[2],               \
-      uint2 index [[thread_position_in_grid]],          \
-      uint2 grid_dim [[threads_per_grid]]);             \
-  template [[host_name("g3" name)]] [[kernel]] void     \
-  binary_g_nd3<itype, otype, op>(                       \
-      device const itype* a,                            \
-      device const itype* b,                            \
-      device otype* c,                                  \
-      constant const size_t a_strides[3],               \
-      constant const size_t b_strides[3],               \
-      uint3 index [[thread_position_in_grid]],          \
-      uint3 grid_dim [[threads_per_grid]]);             \
-  instantiate_binary_g_dim(name, itype, otype, op, 4)   \
-  instantiate_binary_g_dim(name, itype, otype, op, 5)
+#define instantiate_binary_float(op)                \
+  instantiate_binary_all(op, float16, half, half)   \
+  instantiate_binary_all(op, float32, float, float) \
+  instantiate_binary_all(op, bfloat16, bfloat16_t, bfloat16_t)
 
-#define instantiate_binary_g(name, itype, otype, op)                            \
-  template [[host_name("gn" name)]] [[kernel]] void binary_g<itype, otype, op>( \
-      device const itype* a,                                                    \
-      device const itype* b,                                                    \
-      device otype* c,                                                          \
-      constant const int* shape,                                                \
-      constant const size_t* a_strides,                                         \
-      constant const size_t* b_strides,                                         \
-      constant const int& ndim,                                                 \
-      uint3 index [[thread_position_in_grid]],                                  \
-      uint3 grid_dim [[threads_per_grid]]);
+#define instantiate_binary_types(op)                              \
+  instantiate_binary_all(op, bool_, bool, bool)                   \
+  instantiate_binary_integer(op)                                  \
+  instantiate_binary_all(op, complex64, complex64_t, complex64_t) \
+  instantiate_binary_float(op)
 
-#define instantiate_binary_all(name, tname, itype, otype, op) \
-  instantiate_binary("ss" #name #tname, itype, otype, op, ss) \
-  instantiate_binary("sv" #name #tname, itype, otype, op, sv) \
-  instantiate_binary("vs" #name #tname, itype, otype, op, vs) \
-  instantiate_binary("vv" #name #tname, itype, otype, op, vv) \
-  instantiate_binary_g(#name #tname, itype, otype, op)        \
-  instantiate_binary_g_nd(#name #tname, itype, otype, op)
+#define instantiate_binary_types_bool(op)                \
+  instantiate_binary_all(op, bool_, bool, bool)          \
+  instantiate_binary_all(op, uint8, uint8_t, bool)       \
+  instantiate_binary_all(op, uint16, uint16_t, bool)     \
+  instantiate_binary_all(op, uint32, uint32_t, bool)     \
+  instantiate_binary_all(op, uint64, uint64_t, bool)     \
+  instantiate_binary_all(op, int8, int8_t, bool)         \
+  instantiate_binary_all(op, int16, int16_t, bool)       \
+  instantiate_binary_all(op, int32, int32_t, bool)       \
+  instantiate_binary_all(op, int64, int64_t, bool)       \
+  instantiate_binary_all(op, float16, half, bool)        \
+  instantiate_binary_all(op, float32, float, bool)       \
+  instantiate_binary_all(op, bfloat16, bfloat16_t, bool) \
+  instantiate_binary_all(op, complex64, complex64_t, bool)
 
-#define instantiate_binary_integer(name, op)                   \
-  instantiate_binary_all(name, uint8, uint8_t, uint8_t, op)    \
-  instantiate_binary_all(name, uint16, uint16_t, uint16_t, op) \
-  instantiate_binary_all(name, uint32, uint32_t, uint32_t, op) \
-  instantiate_binary_all(name, uint64, uint64_t, uint64_t, op) \
-  instantiate_binary_all(name, int8, int8_t, int8_t, op)       \
-  instantiate_binary_all(name, int16, int16_t, int16_t, op)    \
-  instantiate_binary_all(name, int32, int32_t, int32_t, op)    \
-  instantiate_binary_all(name, int64, int64_t, int64_t, op)
-
-#define instantiate_binary_float(name, op)                \
-  instantiate_binary_all(name, float16, half, half, op)   \
-  instantiate_binary_all(name, float32, float, float, op) \
-  instantiate_binary_all(name, bfloat16, bfloat16_t, bfloat16_t, op)
-
-#define instantiate_binary_types(name, op)                              \
-  instantiate_binary_all(name, bool_, bool, bool, op)                   \
-  instantiate_binary_integer(name, op)                                  \
-  instantiate_binary_all(name, complex64, complex64_t, complex64_t, op) \
-  instantiate_binary_float(name, op)
-
-#define instantiate_binary_types_bool(name, op)                \
-  instantiate_binary_all(name, bool_, bool, bool, op)          \
-  instantiate_binary_all(name, uint8, uint8_t, bool, op)       \
-  instantiate_binary_all(name, uint16, uint16_t, bool, op)     \
-  instantiate_binary_all(name, uint32, uint32_t, bool, op)     \
-  instantiate_binary_all(name, uint64, uint64_t, bool, op)     \
-  instantiate_binary_all(name, int8, int8_t, bool, op)         \
-  instantiate_binary_all(name, int16, int16_t, bool, op)       \
-  instantiate_binary_all(name, int32, int32_t, bool, op)       \
-  instantiate_binary_all(name, int64, int64_t, bool, op)       \
-  instantiate_binary_all(name, float16, half, bool, op)        \
-  instantiate_binary_all(name, float32, float, bool, op)       \
-  instantiate_binary_all(name, bfloat16, bfloat16_t, bool, op) \
-  instantiate_binary_all(name, complex64, complex64_t, bool, op)
-
-instantiate_binary_types(add, Add)
-instantiate_binary_types(div, Divide)
-instantiate_binary_types_bool(eq, Equal)
-instantiate_binary_types_bool(ge, Greater)
-instantiate_binary_types_bool(geq, GreaterEqual)
-instantiate_binary_types_bool(le, Less)
-instantiate_binary_types_bool(leq, LessEqual)
-instantiate_binary_types_bool(neq, NotEqual)
-instantiate_binary_float(lae, LogAddExp)
-instantiate_binary_types(max, Maximum)
-instantiate_binary_types(min, Minimum)
-instantiate_binary_types(mul, Multiply)
-instantiate_binary_types(sub, Subtract)
-instantiate_binary_types(pow, Power)
-instantiate_binary_types(rem, Remainder)
-instantiate_binary_float(arctan2, ArcTan2)
+instantiate_binary_types(Add)
+instantiate_binary_types(Divide)
+instantiate_binary_types_bool(Equal)
+instantiate_binary_types_bool(Greater)
+instantiate_binary_types_bool(GreaterEqual)
+instantiate_binary_types_bool(Less)
+instantiate_binary_types_bool(LessEqual)
+instantiate_binary_types_bool(NotEqual)
+instantiate_binary_float(LogAddExp)
+instantiate_binary_types(Maximum)
+instantiate_binary_types(Minimum)
+instantiate_binary_types(Multiply)
+instantiate_binary_types(Subtract)
+instantiate_binary_types(Power)
+instantiate_binary_types(Remainder)
+instantiate_binary_float(ArcTan2)
 
 // NaNEqual only needed for floating point types with boolean output
-instantiate_binary_all(naneq, float16, half, bool, NaNEqual)
-instantiate_binary_all(naneq, float32, float, bool, NaNEqual)
-instantiate_binary_all(naneq, bfloat16, bfloat16_t, bool, NaNEqual)
-instantiate_binary_all(naneq, complex64, complex64_t, bool, NaNEqual)
+instantiate_binary_all(NaNEqual, float16, half, bool)
+instantiate_binary_all(NaNEqual, float32, float, bool)
+instantiate_binary_all(NaNEqual, bfloat16, bfloat16_t, bool)
+instantiate_binary_all(NaNEqual, complex64, complex64_t, bool)
 
-instantiate_binary_all(lor, bool_, bool, bool, LogicalOr)
-instantiate_binary_all(land, bool_, bool, bool, LogicalAnd)
+instantiate_binary_all(LogicalOr, bool_, bool, bool)
+instantiate_binary_all(LogicalAnd, bool_, bool, bool)
 
 // Bitwise ops only need integer types and bool (except for l/r shift)
-instantiate_binary_integer(bitwise_and, BitwiseAnd)
-instantiate_binary_all(bitwise_and, bool_, bool, bool, BitwiseAnd)
-instantiate_binary_integer(bitwise_or, BitwiseOr)
-instantiate_binary_all(bitwise_or, bool_, bool, bool, BitwiseOr)
-instantiate_binary_integer(bitwise_xor, BitwiseXor)
-instantiate_binary_all(bitwise_xor, bool_, bool, bool, BitwiseXor)
-instantiate_binary_integer(left_shift, LeftShift)
-instantiate_binary_integer(right_shift, RightShift) // clang-format on
+instantiate_binary_integer(BitwiseAnd)
+instantiate_binary_all(BitwiseAnd, bool_, bool, bool)
+instantiate_binary_integer(BitwiseOr)
+instantiate_binary_all(BitwiseOr, bool_, bool, bool)
+instantiate_binary_integer(BitwiseXor)
+instantiate_binary_all(BitwiseXor, bool_, bool, bool)
+instantiate_binary_integer(LeftShift)
+instantiate_binary_integer(RightShift) // clang-format on

mlx/backend/metal/kernels/binary_two.h

@@ -48,6 +48,48 @@ template <typename T, typename U, typename Op>
   d[index] = out[1];
 }
 
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_sv2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    device U* d,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  auto out = Op()(a[0], b[offset]);
+  c[offset] = out[0];
+  d[offset] = out[1];
+}
+
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_vs2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    device U* d,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  auto out = Op()(a[offset], b[0]);
+  c[offset] = out[0];
+  d[offset] = out[1];
+}
+
+template <typename T, typename U, typename Op>
+[[kernel]] void binary_vv2(
+    device const T* a,
+    device const T* b,
+    device U* c,
+    device U* d,
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  auto out = Op()(a[offset], b[offset]);
+  c[offset] = out[0];
+  d[offset] = out[1];
+}
+
 template <typename T, typename U, typename Op>
 [[kernel]] void binary_g_nd1(
     device const T* a,

mlx/backend/metal/kernels/binary_two.metal

@@ -7,99 +7,37 @@
 #include "mlx/backend/metal/kernels/binary_ops.h"
 #include "mlx/backend/metal/kernels/binary_two.h"
 
-#define instantiate_binary(name, itype, otype, op, bopt)       \
-  template [[host_name(name)]] [[kernel]] void                 \
-      binary_##bopt<itype, otype, op>(                         \
-          device const itype* a,                               \
-          device const itype* b,                               \
-          device otype* c,                                     \
-          device otype* d,                                     \
-          uint index [[thread_position_in_grid]]);
+#define instantiate_binary_all(op, tname, itype, otype)                 \
+  instantiate_kernel("ss" #op #tname, binary_ss, itype, otype, op)      \
+  instantiate_kernel("sv" #op #tname, binary_sv, itype, otype, op)      \
+  instantiate_kernel("vs" #op #tname, binary_vs, itype, otype, op)      \
+  instantiate_kernel("vv" #op #tname, binary_vv, itype, otype, op)      \
+  instantiate_kernel("sv2" #op #tname, binary_sv2, itype, otype, op)    \
+  instantiate_kernel("vs2" #op #tname, binary_vs2, itype, otype, op)    \
+  instantiate_kernel("vv2" #op #tname, binary_vv2, itype, otype, op)    \
+  instantiate_kernel("gn" #op #tname, binary_g, itype, otype, op)       \
+  instantiate_kernel("g1" #op #tname, binary_g_nd1, itype, otype, op)   \
+  instantiate_kernel("g2" #op #tname, binary_g_nd2, itype, otype, op)   \
+  instantiate_kernel("g3" #op #tname, binary_g_nd3, itype, otype, op)   \
+  instantiate_kernel("g4" #op #tname, binary_g_nd, itype, otype, op, 4) \
+  instantiate_kernel("g5" #op #tname, binary_g_nd,  itype, otype, op, 5)
 
-#define instantiate_binary_g_dim(name, itype, otype, op, dims)       \
-  template [[host_name("g" #dims name)]] [[kernel]] void             \
-  binary_g_nd<itype, otype, op, dims>(                               \
-      device const itype* a,                                         \
-      device const itype* b,                                         \
-      device otype* c,                                               \
-      device otype* d,                                               \
-      constant const int shape[dims],                                \
-      constant const size_t a_strides[dims],                         \
-      constant const size_t b_strides[dims],                         \
-      uint3 index [[thread_position_in_grid]],                       \
-      uint3 grid_dim [[threads_per_grid]]);
+#define instantiate_binary_float(op)                \
+  instantiate_binary_all(op, float16, half, half)   \
+  instantiate_binary_all(op, float32, float, float) \
+  instantiate_binary_all(op, bfloat16, bfloat16_t, bfloat16_t)
 
-#define instantiate_binary_g_nd(name, itype, otype, op)       \
-  template [[host_name("g1" name)]] [[kernel]] void           \
-  binary_g_nd1<itype, otype, op>(                             \
-      device const itype* a,                                  \
-      device const itype* b,                                  \
-      device otype* c,                                        \
-      device otype* d,                                        \
-      constant const size_t& a_stride,                        \
-      constant const size_t& b_stride,                        \
-      uint index [[thread_position_in_grid]]);                \
-  template [[host_name("g2" name)]] [[kernel]] void           \
-  binary_g_nd2<itype, otype, op>(                             \
-      device const itype* a,                                  \
-      device const itype* b,                                  \
-      device otype* c,                                        \
-      device otype* d,                                        \
-      constant const size_t a_strides[2],                     \
-      constant const size_t b_strides[2],                     \
-      uint2 index [[thread_position_in_grid]],                \
-      uint2 grid_dim [[threads_per_grid]]);                   \
-  template [[host_name("g3" name)]] [[kernel]] void           \
-  binary_g_nd3<itype, otype, op>(                             \
-      device const itype* a,                                  \
-      device const itype* b,                                  \
-      device otype* c,                                        \
-      device otype* d,                                        \
-      constant const size_t a_strides[3],                     \
-      constant const size_t b_strides[3],                     \
-      uint3 index [[thread_position_in_grid]],                \
-      uint3 grid_dim [[threads_per_grid]]);                   \
-  instantiate_binary_g_dim(name, itype, otype, op, 4)         \
-  instantiate_binary_g_dim(name, itype, otype, op, 5)
+#define instantiate_binary_types(op)                              \
+  instantiate_binary_all(op, bool_, bool, bool)                   \
+  instantiate_binary_all(op, uint8, uint8_t, uint8_t)             \
+  instantiate_binary_all(op, uint16, uint16_t, uint16_t)          \
+  instantiate_binary_all(op, uint32, uint32_t, uint32_t)          \
+  instantiate_binary_all(op, uint64, uint64_t, uint64_t)          \
+  instantiate_binary_all(op, int8, int8_t, int8_t)                \
+  instantiate_binary_all(op, int16, int16_t, int16_t)             \
+  instantiate_binary_all(op, int32, int32_t, int32_t)             \
+  instantiate_binary_all(op, int64, int64_t, int64_t)             \
+  instantiate_binary_all(op, complex64, complex64_t, complex64_t) \
+  instantiate_binary_float(op)
 
-#define instantiate_binary_g(name, itype, otype, op)       \
-  template [[host_name("gn" name)]] [[kernel]] void        \
-  binary_g<itype, otype, op>(                              \
-      device const itype* a,                               \
-      device const itype* b,                               \
-      device otype* c,                                     \
-      device otype* d,                                     \
-      constant const int* shape,                           \
-      constant const size_t* a_strides,                    \
-      constant const size_t* b_strides,                    \
-      constant const int& ndim,                            \
-      uint3 index [[thread_position_in_grid]],             \
-      uint3 grid_dim [[threads_per_grid]]);
-
-#define instantiate_binary_all(name, tname, itype, otype, op) \
-  instantiate_binary("ss" #name #tname, itype, otype, op, ss) \
-  instantiate_binary("sv" #name #tname, itype, otype, op, sv) \
-  instantiate_binary("vs" #name #tname, itype, otype, op, vs) \
-  instantiate_binary("vv" #name #tname, itype, otype, op, vv) \
-  instantiate_binary_g(#name #tname, itype, otype, op)    \
-  instantiate_binary_g_nd(#name #tname, itype, otype, op)
-
-#define instantiate_binary_float(name, op)                \
-  instantiate_binary_all(name, float16, half, half, op)   \
-  instantiate_binary_all(name, float32, float, float, op) \
-  instantiate_binary_all(name, bfloat16, bfloat16_t, bfloat16_t, op)
-
-#define instantiate_binary_types(name, op)                              \
-  instantiate_binary_all(name, bool_, bool, bool, op)                   \
-  instantiate_binary_all(name, uint8, uint8_t, uint8_t, op)             \
-  instantiate_binary_all(name, uint16, uint16_t, uint16_t, op)          \
-  instantiate_binary_all(name, uint32, uint32_t, uint32_t, op)          \
-  instantiate_binary_all(name, uint64, uint64_t, uint64_t, op)          \
-  instantiate_binary_all(name, int8, int8_t, int8_t, op)                \
-  instantiate_binary_all(name, int16, int16_t, int16_t, op)             \
-  instantiate_binary_all(name, int32, int32_t, int32_t, op)             \
-  instantiate_binary_all(name, int64, int64_t, int64_t, op)             \
-  instantiate_binary_all(name, complex64, complex64_t, complex64_t, op) \
-  instantiate_binary_float(name, op)
-
-instantiate_binary_types(divmod, DivMod) // clang-format on
+instantiate_binary_types(DivMod) // clang-format on

mlx/backend/metal/kernels/conv.metal

@@ -344,12 +344,12 @@ winograd_conv_2d_weight_transform(
   const short sn = (qid & 2) * 2 + (simd_lane_id % 2) * 2;
 
   // Initialize G matrix
-  simdgroup_matrix<T, 8, 8> G;
+  simdgroup_matrix<float, 8, 8> G;
   G.thread_elements()[0] = WGT::wt_transform[sm][sn];
   G.thread_elements()[1] = WGT::wt_transform[sm][sn + 1];
 
   // Initialize Gt matrix
-  simdgroup_matrix<T, 8, 8> Gt;
+  simdgroup_matrix<float, 8, 8> Gt;
   Gt.thread_elements()[0] = WGT::wt_transform[sn][sm];
   Gt.thread_elements()[1] = WGT::wt_transform[sn + 1][sm];
 
@@ -381,15 +381,15 @@ winograd_conv_2d_weight_transform(
     threadgroup_barrier(mem_flags::mem_threadgroup);
     // Do transform and store the result
     for (int c = 0; c < BC; ++c) {
-      simdgroup_matrix<T, 8, 8> g;
+      simdgroup_matrix<float, 8, 8> g;
       g.thread_elements()[0] =
           sm < R && sn < R ? Ws[simd_group_id][sm][sn][c] : T(0);
       g.thread_elements()[1] =
           sm < R && sn + 1 < R ? Ws[simd_group_id][sm][sn + 1][c] : T(0);
 
-      simdgroup_matrix<T, 8, 8> g_out = (G * g) * Gt;
-      wt_out_0[c * O] = g_out.thread_elements()[0];
-      wt_out_1[c * O] = g_out.thread_elements()[1];
+      simdgroup_matrix<float, 8, 8> g_out = (G * g) * Gt;
+      wt_out_0[c * O] = static_cast<T>(g_out.thread_elements()[0]);
+      wt_out_1[c * O] = static_cast<T>(g_out.thread_elements()[1]);
     }
 
     wt_in += BC;
@@ -433,12 +433,12 @@ winograd_conv_2d_input_transform(
   const short sn = (qid & 2) * 2 + (simd_lane_id % 2) * 2;
 
   // Initialize B matrix
-  simdgroup_matrix<T, 8, 8> B;
+  simdgroup_matrix<float, 8, 8> B;
   B.thread_elements()[0] = WGT::in_transform[sm][sn];
   B.thread_elements()[1] = WGT::in_transform[sm][sn + 1];
 
   // Initialize Bt matrix
-  simdgroup_matrix<T, 8, 8> Bt;
+  simdgroup_matrix<float, 8, 8> Bt;
   Bt.thread_elements()[0] = WGT::in_transform[sn][sm];
   Bt.thread_elements()[1] = WGT::in_transform[sn + 1][sm];
 
@@ -493,13 +493,13 @@ winograd_conv_2d_input_transform(
     threadgroup_barrier(mem_flags::mem_threadgroup);
     // Do transform and store the result
     for (int c = simd_group_id; c < BC; c += N_SIMD_GROUPS) {
-      simdgroup_matrix<T, 8, 8> I;
+      simdgroup_matrix<float, 8, 8> I;
       I.thread_elements()[0] = Is[sm][sn][c];
       I.thread_elements()[1] = Is[sm][sn + 1][c];
 
-      simdgroup_matrix<T, 8, 8> I_out = (Bt * I) * B;
-      inp_out_0[c] = I_out.thread_elements()[0];
-      inp_out_1[c] = I_out.thread_elements()[1];
+      simdgroup_matrix<float, 8, 8> I_out = (Bt * I) * B;
+      inp_out_0[c] = static_cast<T>(I_out.thread_elements()[0]);
+      inp_out_1[c] = static_cast<T>(I_out.thread_elements()[1]);
     }
 
     inp_in += BC;
@@ -543,12 +543,12 @@ winograd_conv_2d_output_transform(
   const short sn = (qid & 2) * 2 + (simd_lane_id % 2) * 2;
 
   // Initialize A matrix
-  simdgroup_matrix<T, 8, 8> B;
+  simdgroup_matrix<float, 8, 8> B;
   B.thread_elements()[0] = WGT::out_transform[sm][sn];
   B.thread_elements()[1] = WGT::out_transform[sm][sn + 1];
 
   // Initialize At matrix
-  simdgroup_matrix<T, 8, 8> Bt;
+  simdgroup_matrix<float, 8, 8> Bt;
   Bt.thread_elements()[0] = WGT::out_transform[sn][sm];
   Bt.thread_elements()[1] = WGT::out_transform[sn + 1][sm];
 
@@ -597,16 +597,16 @@ winograd_conv_2d_output_transform(
     threadgroup_barrier(mem_flags::mem_threadgroup);
     // Do transform and store the result
     for (int c = simd_group_id; c < BO; c += N_SIMD_GROUPS) {
-      simdgroup_matrix<T, 8, 8> O_mat;
+      simdgroup_matrix<float, 8, 8> O_mat;
       O_mat.thread_elements()[0] = out_in_0[c];
       O_mat.thread_elements()[1] = out_in_1[c];
 
-      simdgroup_matrix<T, 8, 8> O_out = (Bt * (O_mat * B));
+      simdgroup_matrix<float, 8, 8> O_out = (Bt * (O_mat * B));
       if ((sm < M) && (sn < M)) {
-        Os[sm][sn][c] = O_out.thread_elements()[0];
+        Os[sm][sn][c] = static_cast<T>(O_out.thread_elements()[0]);
       }
       if ((sm < M) && ((sn + 1) < M)) {
-        Os[sm][sn + 1][c] = O_out.thread_elements()[1];
+        Os[sm][sn + 1][c] = static_cast<T>(O_out.thread_elements()[1]);
       }
     }
 
@@ -650,4 +650,5 @@ winograd_conv_2d_output_transform(
 
 // clang-format off
 instantiate_winograd_conv_2d(float32, float);
+instantiate_winograd_conv_2d(bfloat16, bfloat16_t);
 instantiate_winograd_conv_2d(float16, half); // clang-format on

mlx/backend/metal/kernels/copy.h

@@ -16,6 +16,26 @@ template <typename T, typename U>
   dst[index] = static_cast<U>(src[index]);
 }
 
+template <typename T, typename U>
+[[kernel]] void copy_s2(
+    device const T* src [[buffer(0)]],
+    device U* dst [[buffer(1)]],
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  dst[offset] = static_cast<U>(src[0]);
+}
+
+template <typename T, typename U>
+[[kernel]] void copy_v2(
+    device const T* src [[buffer(0)]],
+    device U* dst [[buffer(1)]],
+    uint2 index [[thread_position_in_grid]],
+    uint2 grid_dim [[threads_per_grid]]) {
+  size_t offset = index.x + grid_dim.x * size_t(index.y);
+  dst[offset] = static_cast<U>(src[offset]);
+}
+
 template <typename T, typename U>
 [[kernel]] void copy_g_nd1(
     device const T* src [[buffer(0)]],

mlx/backend/metal/kernels/copy.metal

@@ -5,95 +5,23 @@
 #include "mlx/backend/metal/kernels/bf16.h"
 #include "mlx/backend/metal/kernels/copy.h"
 
-#define instantiate_copy(name, itype, otype, ctype)                        \
-  template [[host_name(name)]] [[kernel]] void copy_##ctype<itype, otype>( \
-      device const itype* src [[buffer(0)]],                               \
-      device otype* dst [[buffer(1)]],                                     \
-      uint index [[thread_position_in_grid]]);
-
-#define instantiate_copy_g_dim(name, itype, otype, dims)      \
-  template [[host_name("g" #dims "_" name)]] [[kernel]] void  \
-  copy_g_nd<itype, otype, dims>(                              \
-      device const itype* src [[buffer(0)]],                  \
-      device otype* dst [[buffer(1)]],                        \
-      constant const int* src_shape [[buffer(2)]],            \
-      constant const int64_t* src_strides [[buffer(3)]],      \
-      uint3 index [[thread_position_in_grid]],                \
-      uint3 grid_dim [[threads_per_grid]]);                   \
-  template [[host_name("gg" #dims "_" name)]] [[kernel]] void \
-  copy_gg_nd<itype, otype, dims>(                             \
-      device const itype* src [[buffer(0)]],                  \
-      device otype* dst [[buffer(1)]],                        \
-      constant const int* src_shape [[buffer(2)]],            \
-      constant const int64_t* src_strides [[buffer(3)]],      \
-      constant const int64_t* dst_strides [[buffer(4)]],      \
-      uint3 index [[thread_position_in_grid]]);
-
-#define instantiate_copy_g_nd(name, itype, otype)                              \
-  template [[host_name("g1_" name)]] [[kernel]] void copy_g_nd1<itype, otype>( \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t& src_stride [[buffer(3)]],                        \
-      uint index [[thread_position_in_grid]]);                                 \
-  template [[host_name("g2_" name)]] [[kernel]] void copy_g_nd2<itype, otype>( \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t* src_strides [[buffer(3)]],                       \
-      uint2 index [[thread_position_in_grid]],                                 \
-      uint2 grid_dim [[threads_per_grid]]);                                    \
-  template [[host_name("g3_" name)]] [[kernel]] void copy_g_nd3<itype, otype>( \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t* src_strides [[buffer(3)]],                       \
-      uint3 index [[thread_position_in_grid]],                                 \
-      uint3 grid_dim [[threads_per_grid]]);                                    \
-  template [[host_name("gg1_" name )]] [[kernel]] void                         \
-  copy_gg_nd1<itype, otype>(                                                   \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t& src_stride [[buffer(3)]],                        \
-      constant const int64_t& dst_stride [[buffer(4)]],                        \
-      uint index [[thread_position_in_grid]]);                                 \
-  template [[host_name("gg2_" name)]] [[kernel]] void                          \
-  copy_gg_nd2<itype, otype>(                                                   \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t* src_strides [[buffer(3)]],                       \
-      constant const int64_t* dst_strides [[buffer(4)]],                       \
-      uint2 index [[thread_position_in_grid]]);                                \
-  template [[host_name("gg3_" name)]] [[kernel]] void                          \
-  copy_gg_nd3<itype, otype>(                                                   \
-      device const itype* src [[buffer(0)]],                                   \
-      device otype* dst [[buffer(1)]],                                         \
-      constant const int64_t* src_strides [[buffer(3)]],                       \
-      constant const int64_t* dst_strides [[buffer(4)]],                       \
-      uint3 index [[thread_position_in_grid]]);                                \
-  instantiate_copy_g_dim(name, itype, otype, 4)                                \
-  instantiate_copy_g_dim(name, itype, otype, 5)
-
-#define instantiate_copy_g(name, itype, otype)                              \
-  template [[host_name("g_" name)]] [[kernel]] void copy_g<itype, otype>(   \
-      device const itype* src [[buffer(0)]],                                \
-      device otype* dst [[buffer(1)]],                                      \
-      constant const int* src_shape [[buffer(2)]],                          \
-      constant const int64_t* src_strides [[buffer(3)]],                    \
-      constant const int& ndim [[buffer(5)]],                               \
-      uint3 index [[thread_position_in_grid]],                              \
-      uint3 grid_dim [[threads_per_grid]]);                                 \
-  template [[host_name("gg_" name)]] [[kernel]] void copy_gg<itype, otype>( \
-      device const itype* src [[buffer(0)]],                                \
-      device otype* dst [[buffer(1)]],                                      \
-      constant const int* src_shape [[buffer(2)]],                          \
-      constant const int64_t* src_strides [[buffer(3)]],                    \
-      constant const int64_t* dst_strides [[buffer(4)]],                    \
-      constant const int& ndim [[buffer(5)]],                               \
-      uint3 index [[thread_position_in_grid]]);
-
 #define instantiate_copy_all(tname, itype, otype)    \
-  instantiate_copy("s_copy" #tname, itype, otype, s) \
-  instantiate_copy("v_copy" #tname, itype, otype, v) \
-  instantiate_copy_g("copy" #tname, itype, otype)    \
-  instantiate_copy_g_nd("copy" #tname, itype, otype)
+  instantiate_kernel("s_copy" #tname, copy_s, itype, otype) \
+  instantiate_kernel("v_copy" #tname, copy_v, itype, otype) \
+  instantiate_kernel("s2_copy" #tname, copy_s2, itype, otype) \
+  instantiate_kernel("v2_copy" #tname, copy_v2, itype, otype) \
+  instantiate_kernel("g1_copy" #tname, copy_g_nd1, itype, otype) \
+  instantiate_kernel("g2_copy" #tname, copy_g_nd2, itype, otype) \
+  instantiate_kernel("g3_copy" #tname, copy_g_nd3, itype, otype) \
+  instantiate_kernel("gg1_copy" #tname, copy_gg_nd1, itype, otype) \
+  instantiate_kernel("gg2_copy" #tname, copy_gg_nd2, itype, otype) \
+  instantiate_kernel("gg3_copy" #tname, copy_gg_nd3, itype, otype) \
+  instantiate_kernel("g4_copy" #tname, copy_g_nd, itype, otype, 4) \
+  instantiate_kernel("g5_copy" #tname, copy_g_nd, itype, otype, 5) \
+  instantiate_kernel("gg4_copy" #tname, copy_gg_nd, itype, otype, 4) \
+  instantiate_kernel("gg5_copy" #tname, copy_gg_nd, itype, otype, 5) \
+  instantiate_kernel("g_copy" #tname, copy_g, itype, otype) \
+  instantiate_kernel("gg_copy" #tname, copy_gg, itype, otype)
 
 #define instantiate_copy_itype(itname, itype)                \
   instantiate_copy_all(itname ##bool_, itype, bool)          \

mlx/backend/metal/kernels/defines.h

@@ -13,3 +13,11 @@ static MTL_CONST constexpr int REDUCE_N_READS = 16;
 static MTL_CONST constexpr int SOFTMAX_N_READS = 4;
 static MTL_CONST constexpr int RMS_N_READS = 4;
 static MTL_CONST constexpr int RMS_LOOPED_LIMIT = 4096;
+
+// Instantiate a templated kernel.
+// Extra args are used as template parameters:
+// e.g. instantiate_kernel(binary_int, binary, a, b) ->
+// [[host_name(binary_int)]] [kernel] binary<a, b>
+#define instantiate_kernel(name, func, ...) \
+  template [[host_name(                     \
+      name)]] [[kernel]] decltype(func<__VA_ARGS__>) func<__VA_ARGS__>;

mlx/backend/metal/kernels/expm1f.h

@@ -83,6 +83,7 @@ float expm1f(float a) {
   r = expm1f_scaled_unchecked(a, 1.0f);
   /* handle severe overflow and underflow */
   if (abs(a - 1.0f) > 88.0f) {
+    r = pow(2, a);
     r = fma(r, r, -1.0f);
   }
   return r;

mlx/backend/metal/kernels/fft.h

@@ -0,0 +1,486 @@
+// Copyright © 2024 Apple Inc.
+
+// Metal FFT using Stockham's algorithm
+//
+// References:
+// - VkFFT (https://github.com/DTolm/VkFFT)
+// - Eric Bainville's excellent page (http://www.bealto.com/gpu-fft.html)
+
+#include <metal_common>
+
+#include "mlx/backend/metal/kernels/fft/radix.h"
+#include "mlx/backend/metal/kernels/fft/readwrite.h"
+#include "mlx/backend/metal/kernels/steel/defines.h"
+
+using namespace metal;
+
+#define MAX_RADIX 13
+// Reached when elems_per_thread_ = 6, max_radix = 13
+// and some threads have to do 3 radix 6s requiring 18 float2s.
+#define MAX_OUTPUT_SIZE 18
+
+// Specialize for a particular value of N at runtime
+STEEL_CONST bool inv_ [[function_constant(0)]];
+STEEL_CONST bool is_power_of_2_ [[function_constant(1)]];
+STEEL_CONST int elems_per_thread_ [[function_constant(2)]];
+// rader_m = n / rader_n
+STEEL_CONST int rader_m_ [[function_constant(3)]];
+// Stockham steps
+STEEL_CONST int radix_13_steps_ [[function_constant(4)]];
+STEEL_CONST int radix_11_steps_ [[function_constant(5)]];
+STEEL_CONST int radix_8_steps_ [[function_constant(6)]];
+STEEL_CONST int radix_7_steps_ [[function_constant(7)]];
+STEEL_CONST int radix_6_steps_ [[function_constant(8)]];
+STEEL_CONST int radix_5_steps_ [[function_constant(9)]];
+STEEL_CONST int radix_4_steps_ [[function_constant(10)]];
+STEEL_CONST int radix_3_steps_ [[function_constant(11)]];
+STEEL_CONST int radix_2_steps_ [[function_constant(12)]];
+// Rader steps
+STEEL_CONST int rader_13_steps_ [[function_constant(13)]];
+STEEL_CONST int rader_11_steps_ [[function_constant(14)]];
+STEEL_CONST int rader_8_steps_ [[function_constant(15)]];
+STEEL_CONST int rader_7_steps_ [[function_constant(16)]];
+STEEL_CONST int rader_6_steps_ [[function_constant(17)]];
+STEEL_CONST int rader_5_steps_ [[function_constant(18)]];
+STEEL_CONST int rader_4_steps_ [[function_constant(19)]];
+STEEL_CONST int rader_3_steps_ [[function_constant(20)]];
+STEEL_CONST int rader_2_steps_ [[function_constant(21)]];
+
+// See "radix.h" for radix codelets
+typedef void (*RadixFunc)(thread float2*, thread float2*);
+
+// Perform a single radix n butterfly with appropriate twiddles
+template <int radix, RadixFunc radix_func>
+METAL_FUNC void radix_butterfly(
+    int i,
+    int p,
+    thread float2* x,
+    thread short* indices,
+    thread float2* y) {
+  // i: the index in the overall DFT that we're processing.
+  // p: the size of the DFTs we're merging at this step.
+  // m: how many threads are working on this DFT.
+  int k, j;
+
+  // Use faster bitwise operations when working with powers of two
+  constexpr bool radix_p_2 = (radix & (radix - 1)) == 0;
+  if (radix_p_2 && is_power_of_2_) {
+    constexpr short power = __builtin_ctz(radix);
+    k = i & (p - 1);
+    j = ((i - k) << power) + k;
+  } else {
+    k = i % p;
+    j = (i / p) * radix * p + k;
+  }
+
+  // Apply twiddles
+  if (p > 1) {
+    float2 twiddle_1 = get_twiddle(k, radix * p);
+    float2 twiddle = twiddle_1;
+    x[1] = complex_mul(x[1], twiddle);
+
+    STEEL_PRAGMA_UNROLL
+    for (int t = 2; t < radix; t++) {
+      twiddle = complex_mul(twiddle, twiddle_1);
+      x[t] = complex_mul(x[t], twiddle);
+    }
+  }
+
+  radix_func(x, y);
+
+  STEEL_PRAGMA_UNROLL
+  for (int t = 0; t < radix; t++) {
+    indices[t] = j + t * p;
+  }
+}
+
+// Perform all the radix steps required for a
+// particular radix size n.
+template <int radix, RadixFunc radix_func>
+METAL_FUNC void radix_n_steps(
+    int i,
+    thread int* p,
+    int m,
+    int n,
+    int num_steps,
+    thread float2* inputs,
+    thread short* indices,
+    thread float2* values,
+    threadgroup float2* buf) {
+  int m_r = n / radix;
+  // When combining different sized radices, we have to do
+  // multiple butterflies in a single thread.
+  // E.g. n = 28 = 4 * 7
+  // 4 threads, 7 elems_per_thread
+  // All threads do 1 radix7 butterfly.
+  // 3 threads do 2 radix4 butterflies.
+  // 1 thread does 1 radix4 butterfly.
+  int max_radices_per_thread = (elems_per_thread_ + radix - 1) / radix;
+
+  int index = 0;
+  int r_index = 0;
+  for (int s = 0; s < num_steps; s++) {
+    for (int t = 0; t < max_radices_per_thread; t++) {
+      index = i + t * m;
+      if (index < m_r) {
+        for (int r = 0; r < radix; r++) {
+          inputs[r] = buf[index + r * m_r];
+        }
+        radix_butterfly<radix, radix_func>(
+            index, *p, inputs, indices + t * radix, values + t * radix);
+      }
+    }
+
+    // Wait until all threads have read their inputs into thread local mem
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+
+    for (int t = 0; t < max_radices_per_thread; t++) {
+      index = i + t * m;
+      if (index < m_r) {
+        for (int r = 0; r < radix; r++) {
+          r_index = t * radix + r;
+          buf[indices[r_index]] = values[r_index];
+        }
+      }
+    }
+
+    // Wait until all threads have written back to threadgroup mem
+    threadgroup_barrier(mem_flags::mem_threadgroup);
+    *p *= radix;
+  }
+}
+
+#define RADIX_STEP(radix, radix_func, num_steps) \
+  radix_n_steps<radix, radix_func>(              \
+      fft_idx, p, m, n, num_steps, inputs, indices, values, buf);
+
+template <bool rader = false>
+METAL_FUNC void
+perform_fft(int fft_idx, thread int* p, int m, int n, threadgroup float2* buf) {
+  float2 inputs[MAX_RADIX];
+  short indices[MAX_OUTPUT_SIZE];
+  float2 values[MAX_OUTPUT_SIZE];
+
+  RADIX_STEP(2, radix2, rader ? rader_2_steps_ : radix_2_steps_);
+  RADIX_STEP(3, radix3, rader ? rader_3_steps_ : radix_3_steps_);
+  RADIX_STEP(4, radix4, rader ? rader_4_steps_ : radix_4_steps_);
+  RADIX_STEP(5, radix5, rader ? rader_5_steps_ : radix_5_steps_);
+  RADIX_STEP(6, radix6, rader ? rader_6_steps_ : radix_6_steps_);
+  RADIX_STEP(7, radix7, rader ? rader_7_steps_ : radix_7_steps_);
+  RADIX_STEP(8, radix8, rader ? rader_8_steps_ : radix_8_steps_);
+  RADIX_STEP(11, radix11, rader ? rader_11_steps_ : radix_11_steps_);
+  RADIX_STEP(13, radix13, rader ? rader_13_steps_ : radix_13_steps_);
+}
+
+// Each FFT is computed entirely in shared GPU memory.
+//
+// N is decomposed into radix-n DFTs:
+// e.g. 128 = 2 * 4 * 4 * 4
+template <int tg_mem_size, typename in_T, typename out_T>
+[[kernel]] void fft(
+    const device in_T* in [[buffer(0)]],
+    device out_T* out [[buffer(1)]],
+    constant const int& n,
+    constant const int& batch_size,
+    uint3 elem [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  threadgroup float2 shared_in[tg_mem_size];
+
+  thread ReadWriter<in_T, out_T> read_writer = ReadWriter<in_T, out_T>(
+      in,
+      &shared_in[0],
+      out,
+      n,
+      batch_size,
+      elems_per_thread_,
+      elem,
+      grid,
+      inv_);
+
+  if (read_writer.out_of_bounds()) {
+    return;
+  };
+  read_writer.load();
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  int p = 1;
+  int fft_idx = elem.z; // Thread index in DFT
+  int m = grid.z; // Threads per DFT
+  int tg_idx = elem.y * n; // Index of this DFT in threadgroup
+  threadgroup float2* buf = &shared_in[tg_idx];
+
+  perform_fft(fft_idx, &p, m, n, buf);
+
+  read_writer.write();
+}
+
+template <int tg_mem_size, typename in_T, typename out_T>
+[[kernel]] void rader_fft(
+    const device in_T* in [[buffer(0)]],
+    device out_T* out [[buffer(1)]],
+    const device float2* raders_b_q [[buffer(2)]],
+    const device short* raders_g_q [[buffer(3)]],
+    const device short* raders_g_minus_q [[buffer(4)]],
+    constant const int& n,
+    constant const int& batch_size,
+    constant const int& rader_n,
+    uint3 elem [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  // Use Rader's algorithm to compute fast FFTs
+  // when a prime factor `p` of `n` is greater than 13 but
+  // has `p - 1` Stockham decomposable into to prime factors <= 13.
+  //
+  // E.g. n = 102
+  //        = 2 * 3 * 17
+  // .      = 2 * 3 * RADER(16)
+  // .      = 2 * 3 * RADER(4 * 4)
+  //
+  // In numpy:
+  //   x_perm = x[g_q]
+  //   y = np.fft.fft(x_perm) * b_q
+  //   z = np.fft.ifft(y) + x[0]
+  //   out = z[g_minus_q]
+  //   out[0]  = x[1:].sum()
+  //
+  // Where the g_q and g_minus_q are permutations formed
+  // by the group under multiplicative modulo N using the
+  // primitive root of N and b_q is a constant.
+  // See https://en.wikipedia.org/wiki/Rader%27s_FFT_algorithm
+  //
+  // Rader's uses fewer operations than Bluestein's and so
+  // is more accurate. It's also faster in most cases.
+  threadgroup float2 shared_in[tg_mem_size];
+
+  thread ReadWriter<in_T, out_T> read_writer = ReadWriter<in_T, out_T>(
+      in,
+      &shared_in[0],
+      out,
+      n,
+      batch_size,
+      elems_per_thread_,
+      elem,
+      grid,
+      inv_);
+
+  if (read_writer.out_of_bounds()) {
+    return;
+  };
+  read_writer.load();
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  // The number of the threads we're using for each DFT
+  int m = grid.z;
+
+  int fft_idx = elem.z;
+  int tg_idx = elem.y * n;
+  threadgroup float2* buf = &shared_in[tg_idx];
+
+  // rader_m = n / rader_n;
+  int rader_m = rader_m_;
+
+  // We have to load two x_0s for each thread since sometimes
+  // elems_per_thread_ crosses a boundary.
+  // E.g. with n = 34, rader_n = 17, elems_per_thread_ = 4
+  // 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8
+  // 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+  short x_0_index =
+      metal::min(fft_idx * elems_per_thread_ / (rader_n - 1), rader_m - 1);
+  float2 x_0[2] = {buf[x_0_index], buf[x_0_index + 1]};
+
+  // Do the Rader permutation in shared memory
+  float2 temp[MAX_RADIX];
+  int max_index = n - rader_m - 1;
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, max_index);
+    short g_q = raders_g_q[index / rader_m];
+    temp[e] = buf[rader_m + (g_q - 1) * rader_m + index % rader_m];
+  }
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, max_index);
+    buf[index + rader_m] = temp[e];
+  }
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  // Rader FFT on x[rader_m:]
+  int p = 1;
+  perform_fft</*rader=*/true>(fft_idx, &p, m, n - rader_m, buf + rader_m);
+
+  // x_1 + ... + x_n is computed for us in the first FFT step so
+  // we save it in the first rader_m indices of the array for later.
+  int x_sum_index = metal::min(fft_idx, rader_m - 1);
+  buf[x_sum_index] = buf[rader_m + x_sum_index * (rader_n - 1)];
+
+  float2 inv = {1.0f, -1.0f};
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, max_index);
+    short interleaved_index =
+        index / rader_m + (index % rader_m) * (rader_n - 1);
+    temp[e] = complex_mul(
+        buf[rader_m + interleaved_index],
+        raders_b_q[interleaved_index % (rader_n - 1)]);
+  }
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, max_index);
+    buf[rader_m + index] = temp[e] * inv;
+  }
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  // Rader IFFT on x[rader_m:]
+  p = 1;
+  perform_fft</*rader=*/true>(fft_idx, &p, m, n - rader_m, buf + rader_m);
+
+  float2 rader_inv_factor = {1.0f / (rader_n - 1), -1.0f / (rader_n - 1)};
+
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, n - rader_m - 1);
+    short diff_index = index / (rader_n - 1) - x_0_index;
+    temp[e] = buf[rader_m + index] * rader_inv_factor + x_0[diff_index];
+  }
+
+  // Use the sum of elements that was computed in the first FFT
+  float2 x_sum = buf[x_0_index] + x_0[0];
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  for (int e = 0; e < elems_per_thread_; e++) {
+    short index = metal::min(fft_idx * elems_per_thread_ + e, max_index);
+    short g_q_index = index % (rader_n - 1);
+    short g_q = raders_g_minus_q[g_q_index];
+    short out_index = index - g_q_index + g_q + (index / (rader_n - 1));
+    buf[out_index] = temp[e];
+  }
+
+  buf[x_0_index * rader_n] = x_sum;
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  p = rader_n;
+  perform_fft(fft_idx, &p, m, n, buf);
+
+  read_writer.write();
+}
+
+template <int tg_mem_size, typename in_T, typename out_T>
+[[kernel]] void bluestein_fft(
+    const device in_T* in [[buffer(0)]],
+    device out_T* out [[buffer(1)]],
+    const device float2* w_q [[buffer(2)]],
+    const device float2* w_k [[buffer(3)]],
+    constant const int& length,
+    constant const int& n,
+    constant const int& batch_size,
+    uint3 elem [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  // Computes arbitrary length FFTs with Bluestein's algorithm
+  //
+  // In numpy:
+  //   bluestein_n = next_power_of_2(2*n - 1)
+  //   out = w_k * np.fft.ifft(np.fft.fft(w_k * in, bluestein_n) * w_q)
+  //
+  // Where w_k and w_q are precomputed on CPU in high precision as:
+  //   w_k = np.exp(-1j * np.pi / n * (np.arange(-n + 1, n) ** 2))
+  //   w_q = np.fft.fft(1/w_k[-n:])
+  threadgroup float2 shared_in[tg_mem_size];
+
+  thread ReadWriter<in_T, out_T> read_writer = ReadWriter<in_T, out_T>(
+      in,
+      &shared_in[0],
+      out,
+      n,
+      batch_size,
+      elems_per_thread_,
+      elem,
+      grid,
+      inv_);
+
+  if (read_writer.out_of_bounds()) {
+    return;
+  };
+  read_writer.load_padded(length, w_k);
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  int p = 1;
+  int fft_idx = elem.z; // Thread index in DFT
+  int m = grid.z; // Threads per DFT
+  int tg_idx = elem.y * n; // Index of this DFT in threadgroup
+  threadgroup float2* buf = &shared_in[tg_idx];
+
+  // fft
+  perform_fft(fft_idx, &p, m, n, buf);
+
+  float2 inv = float2(1.0f, -1.0f);
+  for (int t = 0; t < elems_per_thread_; t++) {
+    int index = fft_idx + t * m;
+    buf[index] = complex_mul(buf[index], w_q[index]) * inv;
+  }
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  // ifft
+  p = 1;
+  perform_fft(fft_idx, &p, m, n, buf);
+
+  read_writer.write_padded(length, w_k);
+}
+
+template <
+    int tg_mem_size,
+    typename in_T,
+    typename out_T,
+    int step,
+    bool real = false>
+[[kernel]] void four_step_fft(
+    const device in_T* in [[buffer(0)]],
+    device out_T* out [[buffer(1)]],
+    constant const int& n1,
+    constant const int& n2,
+    constant const int& batch_size,
+    uint3 elem [[thread_position_in_grid]],
+    uint3 grid [[threads_per_grid]]) {
+  // Fast four step FFT implementation for powers of 2.
+  int overall_n = n1 * n2;
+  int n = step == 0 ? n1 : n2;
+  int stride = step == 0 ? n2 : n1;
+
+  // The number of the threads we're using for each DFT
+  int m = grid.z;
+  int fft_idx = elem.z;
+
+  threadgroup float2 shared_in[tg_mem_size];
+  threadgroup float2* buf = &shared_in[elem.y * n];
+
+  using read_writer_t = ReadWriter<in_T, out_T, step, real>;
+  read_writer_t read_writer = read_writer_t(
+      in,
+      &shared_in[0],
+      out,
+      n,
+      batch_size,
+      elems_per_thread_,
+      elem,
+      grid,
+      inv_);
+
+  if (read_writer.out_of_bounds()) {
+    return;
+  };
+  read_writer.load_strided(stride, overall_n);
+
+  threadgroup_barrier(mem_flags::mem_threadgroup);
+
+  int p = 1;
+  perform_fft(fft_idx, &p, m, n, buf);
+
+  read_writer.write_strided(stride, overall_n);
+}

mlx/backend/metal/kernels/fft.metal

@@ -1,199 +1,67 @@
 // Copyright © 2024 Apple Inc.
 
-// Metal FFT using Stockham's algorithm
-//
-// References:
-// - VkFFT (https://github.com/DTolm/VkFFT)
-// - Eric Bainville's excellent page (http://www.bealto.com/gpu-fft.html)
-
-#include <metal_common>
-#include <metal_math>
-
 #include "mlx/backend/metal/kernels/defines.h"
-#include "mlx/backend/metal/kernels/utils.h"
+#include "mlx/backend/metal/kernels/fft.h"
 
-using namespace metal;
+#define instantiate_fft(tg_mem_size, in_T, out_T)   \
+  instantiate_kernel(                               \
+      "fft_mem_" #tg_mem_size "_" #in_T "_" #out_T, \
+      fft,                                          \
+      tg_mem_size,                                  \
+      in_T,                                         \
+      out_T)
 
-float2 complex_mul(float2 a, float2 b) {
-  float2 c;
-  c.x = a.x * b.x - a.y * b.y;
-  c.y = a.x * b.y + a.y * b.x;
-  return c;
-}
+#define instantiate_rader(tg_mem_size, in_T, out_T)       \
+  instantiate_kernel(                                     \
+      "rader_fft_mem_" #tg_mem_size "_" #in_T "_" #out_T, \
+      rader_fft,                                          \
+      tg_mem_size,                                        \
+      in_T,                                               \
+      out_T)
 
-float2 get_twiddle(int k, int p) {
-  float theta = -1.0f * k * M_PI_F / (2 * p);
+#define instantiate_bluestein(tg_mem_size, in_T, out_T)       \
+  instantiate_kernel(                                         \
+      "bluestein_fft_mem_" #tg_mem_size "_" #in_T "_" #out_T, \
+      bluestein_fft,                                          \
+      tg_mem_size,                                            \
+      in_T,                                                   \
+      out_T)
 
-  float2 twiddle;
-  twiddle.x = metal::fast::cos(theta);
-  twiddle.y = metal::fast::sin(theta);
-  return twiddle;
-}
+#define instantiate_four_step(tg_mem_size, in_T, out_T, step, real)           \
+  instantiate_kernel(                                                         \
+      "four_step_mem_" #tg_mem_size "_" #in_T "_" #out_T "_" #step "_" #real, \
+      four_step_fft,                                                          \
+      tg_mem_size,                                                            \
+      in_T,                                                                   \
+      out_T,                                                                  \
+      step,                                                                   \
+      real)
 
-// single threaded radix2 implemetation
-void radix2(
-    int i,
-    int p,
-    int m,
-    threadgroup float2* read_buf,
-    threadgroup float2* write_buf) {
-  float2 x_0 = read_buf[i];
-  float2 x_1 = read_buf[i + m];
-
-  // The index within this sub-DFT
-  int k = i & (p - 1);
-
-  float2 twiddle = get_twiddle(k, p);
-
-  float2 z = complex_mul(x_1, twiddle);
-
-  float2 y_0 = x_0 + z;
-  float2 y_1 = x_0 - z;
-
-  int j = (i << 1) - k;
-
-  write_buf[j] = y_0;
-  write_buf[j + p] = y_1;
-}
-
-// single threaded radix4 implemetation
-void radix4(
-    int i,
-    int p,
-    int m,
-    threadgroup float2* read_buf,
-    threadgroup float2* write_buf) {
-  float2 x_0 = read_buf[i];
-  float2 x_1 = read_buf[i + m];
-  float2 x_2 = read_buf[i + 2 * m];
-  float2 x_3 = read_buf[i + 3 * m];
-
-  // The index within this sub-DFT
-  int k = i & (p - 1);
-
-  float2 twiddle = get_twiddle(k, p);
-  // e^a * e^b = e^(a + b)
-  float2 twiddle_2 = complex_mul(twiddle, twiddle);
-  float2 twiddle_3 = complex_mul(twiddle, twiddle_2);
-
-  x_1 = complex_mul(x_1, twiddle);
-  x_2 = complex_mul(x_2, twiddle_2);
-  x_3 = complex_mul(x_3, twiddle_3);
-
-  float2 minus_i;
-  minus_i.x = 0;
-  minus_i.y = -1;
-
-  // Hard coded twiddle factors for DFT4
-  float2 z_0 = x_0 + x_2;
-  float2 z_1 = x_0 - x_2;
-  float2 z_2 = x_1 + x_3;
-  float2 z_3 = complex_mul(x_1 - x_3, minus_i);
-
-  float2 y_0 = z_0 + z_2;
-  float2 y_1 = z_1 + z_3;
-  float2 y_2 = z_0 - z_2;
-  float2 y_3 = z_1 - z_3;
-
-  int j = ((i - k) << 2) + k;
-
-  write_buf[j] = y_0;
-  write_buf[j + p] = y_1;
-  write_buf[j + 2 * p] = y_2;
-  write_buf[j + 3 * p] = y_3;
-}
-
-// Each FFT is computed entirely in shared GPU memory.
-//
-// N is decomposed into radix-2 and radix-4 DFTs:
-// e.g. 128 = 2 * 4 * 4 * 4
-//
-// At each step we use n / 4 threads, each performing
-// a single-threaded radix-4 or radix-2 DFT.
-//
-// We provide the number of radix-2 and radix-4
-// steps at compile time for a ~20% performance boost.
-template <size_t n, size_t radix_2_steps, size_t radix_4_steps>
-[[kernel]] void fft(
-    const device float2* in [[buffer(0)]],
-    device float2* out [[buffer(1)]],
-    uint3 thread_position_in_grid [[thread_position_in_grid]],
-    uint3 threads_per_grid [[threads_per_grid]]) {
-  // Index of the DFT in batch
-  int batch_idx = thread_position_in_grid.x * n;
-  // The index in the DFT we're working on
-  int i = thread_position_in_grid.y;
-  // The number of the threads we're using for each DFT
-  int m = threads_per_grid.y;
-
-  // Allocate 2 shared memory buffers for Stockham.
-  // We alternate reading from one and writing to the other at each radix step.
-  threadgroup float2 shared_in[n];
-  threadgroup float2 shared_out[n];
-
-  // Pointers to facilitate Stockham buffer swapping
-  threadgroup float2* read_buf = shared_in;
-  threadgroup float2* write_buf = shared_out;
-  threadgroup float2* tmp;
-
-  // Copy input into shared memory
-  shared_in[i] = in[batch_idx + i];
-  shared_in[i + m] = in[batch_idx + i + m];
-  shared_in[i + 2 * m] = in[batch_idx + i + 2 * m];
-  shared_in[i + 3 * m] = in[batch_idx + i + 3 * m];
-
-  threadgroup_barrier(mem_flags::mem_threadgroup);
-
-  int p = 1;
-
-  for (size_t r = 0; r < radix_2_steps; r++) {
-    radix2(i, p, m * 2, read_buf, write_buf);
-    radix2(i + m, p, m * 2, read_buf, write_buf);
-    p *= 2;
-
-    threadgroup_barrier(mem_flags::mem_threadgroup);
-
-    // Stockham switch of buffers
-    tmp = write_buf;
-    write_buf = read_buf;
-    read_buf = tmp;
-  }
-
-  for (size_t r = 0; r < radix_4_steps; r++) {
-    radix4(i, p, m, read_buf, write_buf);
-    p *= 4;
-
-    threadgroup_barrier(mem_flags::mem_threadgroup);
-
-    // Stockham switch of buffers
-    tmp = write_buf;
-    write_buf = read_buf;
-    read_buf = tmp;
-  }
-
-  // Copy shared memory to output
-  out[batch_idx + i] = read_buf[i];
-  out[batch_idx + i + m] = read_buf[i + m];
-  out[batch_idx + i + 2 * m] = read_buf[i + 2 * m];
-  out[batch_idx + i + 3 * m] = read_buf[i + 3 * m];
-}
-
-#define instantiate_fft(name, n, radix_2_steps, radix_4_steps)   \
-  template [[host_name("fft_" #name)]] [[kernel]] void           \
-  fft<n, radix_2_steps, radix_4_steps>(                          \
-      const device float2* in [[buffer(0)]],                     \
-      device float2* out [[buffer(1)]],                          \
-      uint3 thread_position_in_grid [[thread_position_in_grid]], \
-      uint3 threads_per_grid [[threads_per_grid]]);
-
-// Explicitly define kernels for each power of 2.
 // clang-format off
-instantiate_fft(4, /* n= */ 4, /* radix_2_steps= */ 0, /* radix_4_steps= */ 1)
-instantiate_fft(8, 8, 1, 1) instantiate_fft(16, 16, 0, 2)
-instantiate_fft(32, 32, 1, 2) instantiate_fft(64, 64, 0, 3)
-instantiate_fft(128, 128, 1, 3) instantiate_fft(256, 256, 0, 4)
-instantiate_fft(512, 512, 1, 4)
-instantiate_fft(1024, 1024, 0, 5)
-// 2048 is the max that will fit into 32KB of threadgroup memory.
-// TODO: implement 4 step FFT for larger n.
-instantiate_fft(2048, 2048, 1, 5) // clang-format on
+#define instantiate_ffts(tg_mem_size)                        \
+  instantiate_fft(tg_mem_size, float2, float2) \
+  instantiate_fft(tg_mem_size, float, float2) \
+  instantiate_fft(tg_mem_size, float2, float) \
+  instantiate_rader(tg_mem_size, float2, float2) \
+  instantiate_rader(tg_mem_size, float, float2) \
+  instantiate_rader(tg_mem_size, float2, float) \
+  instantiate_bluestein(tg_mem_size, float2, float2) \
+  instantiate_bluestein(tg_mem_size, float, float2) \
+  instantiate_bluestein(tg_mem_size, float2, float) \
+  instantiate_four_step(tg_mem_size, float2, float2, 0, /*real=*/false) \
+  instantiate_four_step(tg_mem_size, float2, float2, 1, /*real=*/false) \
+  instantiate_four_step(tg_mem_size, float, float2, 0, /*real=*/true) \
+  instantiate_four_step(tg_mem_size, float2, float2, 1, /*real=*/true) \
+  instantiate_four_step(tg_mem_size, float2, float2, 0, /*real=*/true) \
+  instantiate_four_step(tg_mem_size, float2, float, 1, /*real=*/true)
+
+// It's substantially faster to statically define the
+// threadgroup memory size rather than using
+// `setThreadgroupMemoryLength` on the compute encoder.
+// For non-power of 2 sizes we round up the shared memory.
+instantiate_ffts(256)
+instantiate_ffts(512)
+instantiate_ffts(1024)
+instantiate_ffts(2048)
+// 4096 is the max that will fit into 32KB of threadgroup memory.
+instantiate_ffts(4096) // clang-format on

mlx/backend/metal/kernels/fft/radix.h

@@ -0,0 +1,328 @@
+// Copyright © 2024 Apple Inc.
+
+/* Radix kernels
+
+We provide optimized, single threaded Radix codelets
+for n=2,3,4,5,6,7,8,10,11,12,13.
+
+For n=2,3,4,5,6 we hand write the codelets.
+For n=8,10,12 we combine smaller codelets.
+For n=7,11,13 we use Rader's algorithm which decomposes
+them into (n-1)=6,10,12 codelets. */
+
+#pragma once
+
+#include <metal_common>
+#include <metal_math>
+#include <metal_stdlib>
+
+METAL_FUNC float2 complex_mul(float2 a, float2 b) {
+  return float2(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
+}
+
+// Complex mul followed by conjugate
+METAL_FUNC float2 complex_mul_conj(float2 a, float2 b) {
+  return float2(a.x * b.x - a.y * b.y, -a.x * b.y - a.y * b.x);
+}
+
+// Compute an FFT twiddle factor
+METAL_FUNC float2 get_twiddle(int k, int p) {
+  float theta = -2.0f * k * M_PI_F / p;
+
+  float2 twiddle = {metal::fast::cos(theta), metal::fast::sin(theta)};
+  return twiddle;
+}
+
+METAL_FUNC void radix2(thread float2* x, thread float2* y) {
+  y[0] = x[0] + x[1];
+  y[1] = x[0] - x[1];
+}
+
+METAL_FUNC void radix3(thread float2* x, thread float2* y) {
+  float pi_2_3 = -0.8660254037844387;
+
+  float2 a_1 = x[1] + x[2];
+  float2 a_2 = x[1] - x[2];
+
+  y[0] = x[0] + a_1;
+  float2 b_1 = x[0] - 0.5 * a_1;
+  float2 b_2 = pi_2_3 * a_2;
+
+  float2 b_2_j = {-b_2.y, b_2.x};
+  y[1] = b_1 + b_2_j;
+  y[2] = b_1 - b_2_j;
+}
+
+METAL_FUNC void radix4(thread float2* x, thread float2* y) {
+  float2 z_0 = x[0] + x[2];
+  float2 z_1 = x[0] - x[2];
+  float2 z_2 = x[1] + x[3];
+  float2 z_3 = x[1] - x[3];
+  float2 z_3_i = {z_3.y, -z_3.x};
+
+  y[0] = z_0 + z_2;
+  y[1] = z_1 + z_3_i;
+  y[2] = z_0 - z_2;
+  y[3] = z_1 - z_3_i;
+}
+
+METAL_FUNC void radix5(thread float2* x, thread float2* y) {
+  float2 root_5_4 = 0.5590169943749475;
+  float2 sin_2pi_5 = 0.9510565162951535;
+  float2 sin_1pi_5 = 0.5877852522924731;
+
+  float2 a_1 = x[1] + x[4];
+  float2 a_2 = x[2] + x[3];
+  float2 a_3 = x[1] - x[4];
+  float2 a_4 = x[2] - x[3];
+
+  float2 a_5 = a_1 + a_2;
+  float2 a_6 = root_5_4 * (a_1 - a_2);
+  float2 a_7 = x[0] - a_5 / 4;
+  float2 a_8 = a_7 + a_6;
+  float2 a_9 = a_7 - a_6;
+  float2 a_10 = sin_2pi_5 * a_3 + sin_1pi_5 * a_4;
+  float2 a_11 = sin_1pi_5 * a_3 - sin_2pi_5 * a_4;
+  float2 a_10_j = {a_10.y, -a_10.x};
+  float2 a_11_j = {a_11.y, -a_11.x};
+
+  y[0] = x[0] + a_5;
+  y[1] = a_8 + a_10_j;
+  y[2] = a_9 + a_11_j;
+  y[3] = a_9 - a_11_j;
+  y[4] = a_8 - a_10_j;
+}
+
+METAL_FUNC void radix6(thread float2* x, thread float2* y) {
+  float sin_pi_3 = 0.8660254037844387;
+  float2 a_1 = x[2] + x[4];
+  float2 a_2 = x[0] - a_1 / 2;
+  float2 a_3 = sin_pi_3 * (x[2] - x[4]);
+  float2 a_4 = x[5] + x[1];
+  float2 a_5 = x[3] - a_4 / 2;
+  float2 a_6 = sin_pi_3 * (x[5] - x[1]);
+  float2 a_7 = x[0] + a_1;
+
+  float2 a_3_i = {a_3.y, -a_3.x};
+  float2 a_6_i = {a_6.y, -a_6.x};
+  float2 a_8 = a_2 + a_3_i;
+  float2 a_9 = a_2 - a_3_i;
+  float2 a_10 = x[3] + a_4;
+  float2 a_11 = a_5 + a_6_i;
+  float2 a_12 = a_5 - a_6_i;
+
+  y[0] = a_7 + a_10;
+  y[1] = a_8 - a_11;
+  y[2] = a_9 + a_12;
+  y[3] = a_7 - a_10;
+  y[4] = a_8 + a_11;
+  y[5] = a_9 - a_12;
+}
+
+METAL_FUNC void radix7(thread float2* x, thread float2* y) {
+  // Rader's algorithm
+  float2 inv = {1 / 6.0, -1 / 6.0};
+
+  // fft
+  float2 in1[6] = {x[1], x[3], x[2], x[6], x[4], x[5]};
+  radix6(in1, y + 1);
+
+  y[0] = y[1] + x[0];
+
+  // b_q
+  y[1] = complex_mul_conj(y[1], float2(-1, 0));
+  y[2] = complex_mul_conj(y[2], float2(2.44013336, -1.02261879));
+  y[3] = complex_mul_conj(y[3], float2(2.37046941, -1.17510629));
+  y[4] = complex_mul_conj(y[4], float2(0, -2.64575131));
+  y[5] = complex_mul_conj(y[5], float2(2.37046941, 1.17510629));
+  y[6] = complex_mul_conj(y[6], float2(-2.44013336, -1.02261879));
+
+  // ifft
+  radix6(y + 1, x + 1);
+
+  y[1] = x[1] * inv + x[0];
+  y[5] = x[2] * inv + x[0];
+  y[4] = x[3] * inv + x[0];
+  y[6] = x[4] * inv + x[0];
+  y[2] = x[5] * inv + x[0];
+  y[3] = x[6] * inv + x[0];
+}
+
+METAL_FUNC void radix8(thread float2* x, thread float2* y) {
+  float cos_pi_4 = 0.7071067811865476;
+  float2 w_0 = {cos_pi_4, -cos_pi_4};
+  float2 w_1 = {-cos_pi_4, -cos_pi_4};
+  float2 temp[8] = {x[0], x[2], x[4], x[6], x[1], x[3], x[5], x[7]};
+  radix4(temp, x);
+  radix4(temp + 4, x + 4);
+
+  y[0] = x[0] + x[4];
+  y[4] = x[0] - x[4];
+  float2 x_5 = complex_mul(x[5], w_0);
+  y[1] = x[1] + x_5;
+  y[5] = x[1] - x_5;
+  float2 x_6 = {x[6].y, -x[6].x};
+  y[2] = x[2] + x_6;
+  y[6] = x[2] - x_6;
+  float2 x_7 = complex_mul(x[7], w_1);
+  y[3] = x[3] + x_7;
+  y[7] = x[3] - x_7;
+}
+
+template <bool raders_perm>
+METAL_FUNC void radix10(thread float2* x, thread float2* y) {
+  float2 w[4];
+  w[0] = {0.8090169943749475, -0.5877852522924731};
+  w[1] = {0.30901699437494745, -0.9510565162951535};
+  w[2] = {-w[1].x, w[1].y};
+  w[3] = {-w[0].x, w[0].y};
+
+  if (raders_perm) {
+    float2 temp[10] = {
+        x[0], x[3], x[4], x[8], x[2], x[1], x[7], x[9], x[6], x[5]};
+    radix5(temp, x);
+    radix5(temp + 5, x + 5);
+  } else {
+    float2 temp[10] = {
+        x[0], x[2], x[4], x[6], x[8], x[1], x[3], x[5], x[7], x[9]};
+    radix5(temp, x);
+    radix5(temp + 5, x + 5);
+  }
+
+  y[0] = x[0] + x[5];
+  y[5] = x[0] - x[5];
+  for (int t = 1; t < 5; t++) {
+    float2 a = complex_mul(x[t + 5], w[t - 1]);
+    y[t] = x[t] + a;
+    y[t + 5] = x[t] - a;
+  }
+}
+
+METAL_FUNC void radix11(thread float2* x, thread float2* y) {
+  // Raders Algorithm
+  float2 inv = {1 / 10.0, -1 / 10.0};
+
+  // fft
+  radix10<true>(x + 1, y + 1);
+
+  y[0] = y[1] + x[0];
+
+  // b_q
+  y[1] = complex_mul_conj(y[1], float2(-1, 0));
+  y[2] = complex_mul_conj(y[2], float2(0.955301878, -3.17606649));
+  y[3] = complex_mul_conj(y[3], float2(2.63610556, 2.01269656));
+  y[4] = complex_mul_conj(y[4], float2(2.54127802, 2.13117479));
+  y[5] = complex_mul_conj(y[5], float2(2.07016210, 2.59122150));
+  y[6] = complex_mul_conj(y[6], float2(0, -3.31662479));
+  y[7] = complex_mul_conj(y[7], float2(2.07016210, -2.59122150));
+  y[8] = complex_mul_conj(y[8], float2(-2.54127802, 2.13117479));
+  y[9] = complex_mul_conj(y[9], float2(2.63610556, -2.01269656));
+  y[10] = complex_mul_conj(y[10], float2(-0.955301878, -3.17606649));
+
+  // ifft
+  radix10<false>(y + 1, x + 1);
+
+  y[1] = x[1] * inv + x[0];
+  y[6] = x[2] * inv + x[0];
+  y[3] = x[3] * inv + x[0];
+  y[7] = x[4] * inv + x[0];
+  y[9] = x[5] * inv + x[0];
+  y[10] = x[6] * inv + x[0];
+  y[5] = x[7] * inv + x[0];
+  y[8] = x[8] * inv + x[0];
+  y[4] = x[9] * inv + x[0];
+  y[2] = x[10] * inv + x[0];
+}
+
+template <bool raders_perm>
+METAL_FUNC void radix12(thread float2* x, thread float2* y) {
+  float2 w[6];
+  float sin_pi_3 = 0.8660254037844387;
+  w[0] = {sin_pi_3, -0.5};
+  w[1] = {0.5, -sin_pi_3};
+  w[2] = {0, -1};
+  w[3] = {-0.5, -sin_pi_3};
+  w[4] = {-sin_pi_3, -0.5};
+
+  if (raders_perm) {
+    float2 temp[12] = {
+        x[0],
+        x[3],
+        x[2],
+        x[11],
+        x[8],
+        x[9],
+        x[1],
+        x[7],
+        x[5],
+        x[10],
+        x[4],
+        x[6]};
+    radix6(temp, x);
+    radix6(temp + 6, x + 6);
+  } else {
+    float2 temp[12] = {
+        x[0],
+        x[2],
+        x[4],
+        x[6],
+        x[8],
+        x[10],
+        x[1],
+        x[3],
+        x[5],
+        x[7],
+        x[9],
+        x[11]};
+    radix6(temp, x);
+    radix6(temp + 6, x + 6);
+  }
+
+  y[0] = x[0] + x[6];
+  y[6] = x[0] - x[6];
+  for (int t = 1; t < 6; t++) {
+    float2 a = complex_mul(x[t + 6], w[t - 1]);
+    y[t] = x[t] + a;
+    y[t + 6] = x[t] - a;
+  }
+}
+
+METAL_FUNC void radix13(thread float2* x, thread float2* y) {
+  // Raders Algorithm
+  float2 inv = {1 / 12.0, -1 / 12.0};
+
+  // fft
+  radix12<true>(x + 1, y + 1);
+
+  y[0] = y[1] + x[0];
+
+  // b_q
+  y[1] = complex_mul_conj(y[1], float2(-1, 0));
+  y[2] = complex_mul_conj(y[2], float2(3.07497206, -1.88269669));
+  y[3] = complex_mul_conj(y[3], float2(3.09912468, 1.84266823));
+  y[4] = complex_mul_conj(y[4], float2(3.45084438, -1.04483161));
+  y[5] = complex_mul_conj(y[5], float2(0.91083583, 3.48860690));
+  y[6] = complex_mul_conj(y[6], float2(-3.60286363, 0.139189267));
+  y[7] = complex_mul_conj(y[7], float2(3.60555128, 0));
+  y[8] = complex_mul_conj(y[8], float2(3.60286363, 0.139189267));
+  y[9] = complex_mul_conj(y[9], float2(0.91083583, -3.48860690));
+  y[10] = complex_mul_conj(y[10], float2(-3.45084438, -1.04483161));
+  y[11] = complex_mul_conj(y[11], float2(3.09912468, -1.84266823));
+  y[12] = complex_mul_conj(y[12], float2(-3.07497206, -1.88269669));
+
+  // ifft
+  radix12<false>(y + 1, x + 1);
+
+  y[1] = x[1] * inv + x[0];
+  y[7] = x[2] * inv + x[0];
+  y[10] = x[3] * inv + x[0];
+  y[5] = x[4] * inv + x[0];
+  y[9] = x[5] * inv + x[0];
+  y[11] = x[6] * inv + x[0];
+  y[12] = x[7] * inv + x[0];
+  y[6] = x[8] * inv + x[0];
+  y[3] = x[9] * inv + x[0];
+  y[8] = x[10] * inv + x[0];
+  y[4] = x[11] * inv + x[0];
+  y[2] = x[12] * inv + x[0];
+}