Feature complete Metal FFT (#1102)

* feature complete metal fft

* fix contiguity bug

* jit fft

* simplify rader/bluestein constant computation

* remove kernel/utils.h dep

* remove bf16.h dep

* format

---------

Co-authored-by: Alex Barron <abarron22@apple.com>

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")
@@ -16,40 +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():
-    with mx.stream(mx.cpu):
-        cpu_bandwidths = run_bench(system_size=int(2**22))
+    x = np.array(range(2, 512))
+    system_size = int(2**26)
 
+    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__":