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