Gpu coding
# Guide to Matrix Multiplication in Python and Metal Shading Language
This guide provides a step-by-step process to create a matrix multiplication function using both pure Python and Metal shading language. We'll then integrate the two to compare performance and fidelity.
## Step 1: Pure Python Function for Matrix Multiplication
### 1.1 Write a Python Function
import numpy as np
def matrix_multiplication_python(A, B):
return np.dot(A, B)## Step 2: Making Metal Shading Language Shader Exposed using ctypes
### 2.1 Write the Metal Shader for Matrix Multiplication
Create a file named `MatrixMultiplication.metal` with the following content:
```c
kernel void matrix_multiplication_metal(const device float *A [[ buffer(0) ]],
const device float *B [[ buffer(1) ]],
device float *C [[ buffer(2) ]],
constant uint &MATRIX_SIZE [[ buffer(3) ]],
uint2 id [[ thread_position_in_grid ]]) {
float value = 0.0;
for (int k = 0; k < MATRIX_SIZE; k++) {
value += A[id.y * MATRIX_SIZE + k] * B[k * MATRIX_SIZE + id.x];
}
C[id.y * MATRIX_SIZE + id.x] = value;
}
```
### 2.2 Write a Swift Bridge
Create a Swift file to expose the Metal shader to Python using ctypes. Save this code in `MatrixBridge.swift`:
```swift
import Metal
@available(macOS 10.13, *)
@_cdecl("swift_matrix_multiplication")
public func swift_matrix_multiplication(inputA: UnsafePointer<Float>,
inputB: UnsafePointer<Float>,
outputC: UnsafeMutablePointer<Float>,
size: Int) -> Int {
// Metal setup and calling the matrix_multiplication_metal function
}
```
### 2.3 Compile the Swift Code as a Dynamic Library
Use the following command to compile the Swift code as a dynamic library:
```bash
swiftc -emit-library MatrixBridge.swift -o MatrixBridge.dylib
```
## Step 3: Usage of the Metal Shading Language Bindings to Call It from Python
### 3.1 Load the Dynamic Library in Python
```python
import ctypes
lib = ctypes.CDLL('./MatrixBridge.dylib')
swift_matrix_multiplication = lib.swift_matrix_multiplication
```
### 3.2 Define the Input Matrices and Call Both Functions
```python
A = np.random.rand(100, 100).astype(np.float32)
B = np.random.rand(100, 100).astype(np.float32)
# Pure Python
result_python = matrix_multiplication_python(A, B)
# Metal Shader
result_metal = np.empty_like(result_python)
swift_matrix_multiplication(A.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
B.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
result_metal.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
100)
```
### 3.3 Compare Performance and Fidelity
```python
from timeit import timeit
# Performance
time_python = timeit(lambda: matrix_multiplication_python(A, B), number=1000)
time_metal = timeit(lambda: swift_matrix_multiplication(A.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
B.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
result_metal.ctypes.data_as(ctypes.POINTER(ctypes.c_float)),
100), number=1000)
print("Performance (Python):", time_python)
print("Performance (Metal):", time_metal)
# Fidelity
fidelity = np.allclose(result_python, result_metal)
print("Fidelity:", fidelity)
```
And yeah, it should be equal ( or very close )