Add random source that matches PyTorch

This added random source that matches PyTorch on CPU. In particular, it
matches: `torch.randn([], dtype=torch.float)` result.

PyTorch's RNG is a bit convoluted and not claimed to be version-stable
(will open a separate issue in PyTorch repo on this). However, the
current implementation on CPU is fairly straightforward^*.

1. If it is less than 16 elements, it uses Gaussian distribution sampled
   from MT19937 for double + Box-Muller transformation.

2. If it is more than 16 (16 included), it first do uniform sampling
   with whatever the resulting data type would be (in this case, torch.float),
   and then apply Box-Muller transformation over 16-element segment at a
   type, treating the first floating-point and the 8th as a pair, so on
   so forth.

3. If it is not a multiple of 16, trace back from the end for 16
   elements and redo step 2.

swift/StableDiffusion/pipeline/TorchRandomSource.swift

@@ -0,0 +1,152 @@
+// For licensing see accompanying LICENSE.md file.
+// Copyright (C) 2022 Apple Inc. All Rights Reserved.
+
+import Foundation
+import CoreML
+
+/// A random source consistent with PyTorch
+///
+///  This implementation matches:
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/core/DistributionsHelper.h
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/cpu/DistributionTemplates.h
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/cpu/DistributionKernels.cpp
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/core/TransformationHelper.h
+///
+@available(iOS 16.2, macOS 13.1, *)
+struct TorchRandomSource: RandomNumberGenerator {
+
+  struct State {
+    var key = [UInt32](repeating: 0, count: 624)
+    var pos: Int = 0
+    var nextGauss: Double? = nil
+  }
+
+  var state: State
+
+  /// Initialize with a random seed
+  ///
+  /// - Parameters
+  ///     - seed: Seed for underlying Mersenne Twister 19937 generator
+  /// - Returns random source
+  init(seed: UInt32) {
+    state = .init()
+    var s = seed & 0xffff_ffff
+    for i in 0..<state.key.count {
+      state.key[i] = s
+      s = UInt32((UInt64(1_812_433_253) * UInt64(s ^ (s >> 30)) + UInt64(i) + 1) & 0xffff_ffff)
+    }
+    state.pos = state.key.count
+    state.nextGauss = nil
+  }
+
+  /// Generate next UInt32 using fast 32bit Mersenne Twister
+  mutating func nextUInt32() -> UInt32 {
+    let n = 624
+    let m = 397
+    let matrixA: UInt64 = 0x9908_b0df
+    let upperMask: UInt32 = 0x8000_0000
+    let lowerMask: UInt32 = 0x7fff_ffff
+
+    var y: UInt32
+    if state.pos == state.key.count {
+      for i in 0..<(n - m) {
+        y = (state.key[i] & upperMask) | (state.key[i + 1] & lowerMask)
+        state.key[i] = state.key[i + m] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      }
+      for i in (n - m)..<(n - 1) {
+        y = (state.key[i] & upperMask) | (state.key[i + 1] & lowerMask)
+        state.key[i] = state.key[i + (m - n)] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      }
+      y = (state.key[n - 1] & upperMask) | (state.key[0] & lowerMask)
+      state.key[n - 1] = state.key[m - 1] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      state.pos = 0
+    }
+    y = state.key[state.pos]
+    state.pos += 1
+
+    y ^= (y >> 11)
+    y ^= (y << 7) & 0x9d2c_5680
+    y ^= (y << 15) & 0xefc6_0000
+    y ^= (y >> 18)
+
+    return y
+  }
+
+  mutating func next() -> UInt64 {
+    let high = nextUInt32()
+    let low = nextUInt32()
+    return (UInt64(high) << 32) | UInt64(low)
+  }
+
+  /// Generate next random double value
+  mutating func nextDouble() -> Double {
+    let a = next()
+    return Double(a & 9_007_199_254_740_991) * (1.0 / 9007199254740992.0)
+  }
+
+  /// Generate next random float value
+  mutating func nextFloat() -> Float {
+    let a = nextUInt32()
+    return Float(a & 16_777_215) * (1.0 / 16777216.0)
+  }
+
+  /// Generate next random value from a standard normal
+  mutating func nextGauss() -> Double {
+    if let nextGauss = state.nextGauss {
+      state.nextGauss = nil
+      return nextGauss
+    }
+    // Box-Muller transform
+    let u1: Double = nextDouble()
+    let u2: Double = 1 - nextDouble()
+    let radius = sqrt(-2.0 * log(u2))
+    let theta = 2.0 * .pi * u1
+    state.nextGauss = radius * sin(theta)
+    return radius * cos(theta)
+  }
+
+  /// Generates an array of random values from a normal distribution with given mean and standard deviation.
+  /// This simulates torch.randn([1, 4, 64, 64], dtype=torch.float), note that for dtype=torch.double, it
+  /// will be slightly different.
+  mutating func normalArray(count: Int, mean: Double = 0.0, stdev: Double = 1.0) -> [Double] {
+    // If it is smaller than 16 elements, Torch generates from Box-Muller transform directly.
+    // Note that even if this is used to generate Float, it will use Double underneath.
+    guard count >= 16 else {
+      return (0..<count).map { _ in nextGauss() * stdev + mean }
+    }
+    // Otherwise, Torch first fill a uniform distribution array, then do Box-Muller
+    // transformation over this array.
+    var data = (0..<count).map { _ in Double(nextFloat()) }
+    for i in stride(from: 0, to: count - 15, by: 16) {
+      for j in 0..<8 {
+        let u1 = 1 - data[i + j]
+        let u2 = data[i + j + 8]
+        let radius = sqrt(-2.0 * log(u1))
+        let theta = 2.0 * .pi * u2
+        data[i + j] = radius * cos(theta) * stdev + mean
+        data[i + j + 8] = radius * sin(theta) * stdev + mean
+      }
+    }
+    if count % 16 != 0 {
+      for i in (count - 16)..<count {
+        data[i] = nextDouble()
+      }
+      let i = count - 16
+      for j in 0..<8 {
+        let u1 = 1 - data[i + j]
+        let u2 = data[i + j + 8]
+        let radius = sqrt(-2.0 * log(u1))
+        let theta = 2.0 * .pi * u2
+        data[i + j] = radius * cos(theta) * stdev + mean
+        data[i + j + 8] = radius * sin(theta) * stdev + mean
+      }
+    }
+    return data
+  }
+
+  /// Generate a shaped array with scalars from a normal distribution with given mean and standard deviation.
+  mutating func normalShapedArray(_ shape: [Int], mean: Double = 0.0, stdev: Double = 1.0) -> MLShapedArray<Double> {
+    let count = shape.reduce(1, *)
+    return .init(scalars: normalArray(count: count, mean: mean, stdev: stdev), shape: shape)
+  }
+}