| | """
|
| | RNG - imitating torch cuda randn on CPU
|
| |
|
| | Usage:
|
| | ```
|
| | g = Generator(seed=0)
|
| | print(g.randn(shape=(3, 4)))
|
| | ```
|
| |
|
| | Expected output:
|
| | ```
|
| | [
|
| | [-0.92466259, -0.42534415, -2.6438457, 0.14518388],
|
| | [-0.12086647, -0.57972564, -0.62285122, -0.32838709],
|
| | [-1.07454231, -0.36314407, -1.67105067, 2.26550497]
|
| | ]
|
| | ```
|
| | """
|
| |
|
| | import numpy as np
|
| |
|
| | philox_m = [0xD2511F53, 0xCD9E8D57]
|
| | philox_w = [0x9E3779B9, 0xBB67AE85]
|
| |
|
| | two_pow32_inv = np.array([2.3283064e-10], dtype=np.float32)
|
| | two_pow32_inv_2pi = np.array([2.3283064e-10 * 6.2831855], dtype=np.float32)
|
| |
|
| |
|
| | def uint32(x):
|
| | """Converts (N,) np.uint64 array into (2, N) np.unit32 array"""
|
| | return x.view(np.uint32).reshape(-1, 2).transpose(1, 0)
|
| |
|
| |
|
| | def philox4_round(counter, key):
|
| | """A single round of the Philox 4x32 random number generator"""
|
| |
|
| | v1 = uint32(counter[0].astype(np.uint64) * philox_m[0])
|
| | v2 = uint32(counter[2].astype(np.uint64) * philox_m[1])
|
| |
|
| | counter[0] = v2[1] ^ counter[1] ^ key[0]
|
| | counter[1] = v2[0]
|
| | counter[2] = v1[1] ^ counter[3] ^ key[1]
|
| | counter[3] = v1[0]
|
| |
|
| |
|
| | def philox4_32(counter, key, rounds=10):
|
| | """
|
| | Generates 32-bit random numbers using the Philox 4x32 random number generator.
|
| |
|
| | Parameters:
|
| | counter (numpy.ndarray): A 4xN array of 32-bit integers representing the counter values (offset into generation).
|
| | key (numpy.ndarray): A 2xN array of 32-bit integers representing the key values (seed).
|
| | rounds (int): The number of rounds to perform.
|
| |
|
| | Returns:
|
| | numpy.ndarray: A 4xN array of 32-bit integers containing the generated random numbers.
|
| | """
|
| |
|
| | for _ in range(rounds - 1):
|
| | philox4_round(counter, key)
|
| |
|
| | key[0] = key[0] + philox_w[0]
|
| | key[1] = key[1] + philox_w[1]
|
| |
|
| | philox4_round(counter, key)
|
| | return counter
|
| |
|
| |
|
| | def box_muller(x, y):
|
| | """Returns just the first out of two numbers generated by Box–Muller transform algorithm"""
|
| | u = x * two_pow32_inv + two_pow32_inv / 2
|
| | v = y * two_pow32_inv_2pi + two_pow32_inv_2pi / 2
|
| |
|
| | s = np.sqrt(-2.0 * np.log(u))
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| |
|
| | r1 = s * np.sin(v)
|
| | return r1.astype(np.float32)
|
| |
|
| |
|
| | class Generator:
|
| | """RNG that produces same outputs as torch.randn(..., device='cuda') on CPU"""
|
| |
|
| | def __init__(self, seed):
|
| | self.seed = seed
|
| | self.offset = 0
|
| |
|
| | def randn(self, shape):
|
| | """Generate a sequence of n standard normal random variables using the Philox 4x32 random number generator and the Box-Muller transform"""
|
| |
|
| | n = 1
|
| | for x in shape:
|
| | n *= x
|
| |
|
| | counter = np.zeros((4, n), dtype=np.uint32)
|
| | counter[0] = self.offset
|
| | counter[2] = np.arange(n, dtype=np.uint32)
|
| | self.offset += 1
|
| |
|
| | key = np.empty(n, dtype=np.uint64)
|
| | key.fill(self.seed)
|
| | key = uint32(key)
|
| |
|
| | g = philox4_32(counter, key)
|
| |
|
| | return box_muller(g[0], g[1]).reshape(shape)
|
| |
|
