关于CoreML需要外部生成randn这档子事

coremltools在转换后会固定randn结果，实现真·randn需要外部生成，再使用MLMultiArray作为输入参数传入。

太长不看

使用BNNS

import Accelerate
import CoreML

@available(iOS 16.0, *)
extension MLMultiArray {
    
    static func randnFP32(shape: consuming [NSNumber], mean: Float = 0, std: Float = 1) throws -> MLMultiArray {
        let arr = try MLMultiArray(shape: shape, dataType: .float32)
        let cnt = arr.count
        
        arr.withUnsafeMutableBufferPointer(ofType: Float.self) { ptr, strides in
            guard var des = BNNSNDArrayDescriptor(data: ptr, shape: .vector(cnt)),
                  let gen = BNNSCreateRandomGenerator(BNNSRandomGeneratorMethodAES_CTR, nil)
            else { fatalError() }
            BNNSRandomFillNormalFloat(gen, &des, mean, std)
            BNNSDestroyRandomGenerator(gen)
        }
        return arr
    }
}

胡乱折腾

已FP32为例，iOS上(个人尝试)大概3种randn实现方法。

1. BoxMuller (手动)

   torch有实现，直接抄一遍。

   func boxMuller(count: Int) -> [Float32] {
       let mean: Float32 = 0, std: Float32 = 1
       var arr = (0..<(count/16 + 1) * 16).map { _ in Float32.random(in: 0..<1) }
       for i in stride(from: 0, to: arr.count, by: 16) {
           for j in i..<(i+8) {
               let u1 = 1 - arr[j]
               let u2 = arr[j + 8]
               let radius = sqrt(-2 * log(u1))
               let theta = 2 * Float32.pi * u2
               
               arr[j] = radius * cos(theta) * std + mean
               arr[j+8] = radius * sin(theta) * std + mean
           }
       }
       return arr
   }
   

   循环生成，缺乏加速，tensor增长后性能退化最明显。

2. MPS

   BoxMuller 由 MPSGraph 提供。

   import MetalPerformanceShadersGraph
   
   @available(iOS 15.4, *)
   func mps(count: Int, seed: Int = .random(in: 0..<Int.max)) -> [Float32] {
       guard let op = MPSGraphRandomOpDescriptor(distribution: .normal, dataType: .float32) else { fatalError() }
       op.samplingMethod = .boxMuller
       let graph = MPSGraph()
       
       let y = graph.randomTensor(withShape: [count as NSNumber], descriptor: consume op, seed: seed, name: nil)
       
       guard let yData = graph.run(
           feeds: [:],
           targetTensors: [y],
           targetOperations: nil
       )[consume y] else { fatalError() }
       
       var arr = [Float32](repeating: 0, count: count)
       yData.mpsndarray().readBytes(&arr, strideBytes: nil)
       return arr
   }
   

   虽然用上GPU是件美事，然鹅在输入多为MLMultiArray的情况下，独立使用缺乏优势。除非后续网络全部接入计算图，配合编译优化才有搞头。此处只能抛砖引玉。

   众所周知，比起算力瓶颈，IO更易拖后腿。

3. BNSS

   爱，来自Accelerate。

   import Accelerate
   
   @available(iOS 16.0, *)
   func bnns(count: Int) -> [Float32] {
       let mean: Float32 = 0, std: Float32 = 1
       let arr = [Float32](unsafeUninitializedCapacity: count) { buffer, initializedCount in
           guard var des = BNNSNDArrayDescriptor(data: buffer, shape: .vector(count)),
                 let gen = BNNSCreateRandomGenerator(BNNSRandomGeneratorMethodAES_CTR, nil)
           else { fatalError() }
           
           BNNSRandomFillNormalFloat(gen, &des, mean, std)
           BNNSDestroyRandomGenerator(gen)
           initializedCount = count
       }
       return arr
   }
   

   虽然不是真BoxMuller，无法满足强迫症的严谨追求，但在生成2k随机数的 Jarque–Bera test下各方法都只剩随机波动。

   MLTensor表现上似是BNNS封装，但不知为啥性能退化；懒癌发作，放弃探究。

   在绝对的性能面前，一切纠结都是纸老虎。

性能测试

参考价值有限，各方法一次生成[100, 1000, 10_000, 100_000]个随机数

方法	耗时(ms)
BNNS	2
MPS	74
BoxMuller (手动)	148