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[GitHub] [tvm] tkonolige commented on a change in pull request #7083: [RELAY,TOPI] Threefry PRNG: splittable and stateless
tkonolige commented on a change in pull request #7083:
URL: https://github.com/apache/tvm/pull/7083#discussion_r552271978
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File path: python/tvm/topi/random/kernel.py
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+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements. See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership. The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied. See the License for the
+# specific language governing permissions and limitations
+# under the License.
+"""Pseudorandom number kernels."""
+import tvm
+import tvm.topi
+from ... import tir
+from ...tir import ir_builder
+
+
+# Threefry PRNG with splitting based on
+# - J. K. Salmon, M. A. Moraes, R. O. Dror and D. E. Shaw, "Parallel random numbers: As easy as 1,
+# 2, 3," SC '11: Proceedings of 2011 International Conference for High Performance Computing,
+# Networking, Storage and Analysis, Seattle, WA, 2011, pp. 1-12, doi: 10.1145/2063384.2063405.
+# - Claessen, K. ; Palka, M. (2013) "Splittable Pseudorandom Number Generators using Cryptographic
+# Hashing". Proceedings of Haskell Symposium 2013 pp. 47-58. MLA
+# - Ferguson, Niels, et al. "The Skein hash function family." Submission to NIST (round 3) 7.7.5
+# (2010): 3.
+
+
+# Threefry is a counter based PRNG: given a unique input, it generates a unique random number. As
+# there is no state to maintain, we can apply it to a sequence of numbers (0..N) to generate a
+# sequence of random numbers in parallel. In order to make the PRNG splittable (that is we can
+# generate a sequence of random numbers in one place, and another sequence in another), we add a
+# path and key in addition to the counter. The path allows us to encode a sequence of splits (a 0 in
+# the path indicates the left result of a split, a 1 indicates the right). To avoid continuously
+# growing the path, we can compress an existing path into the key portion of the generator by
+# hashing the current key, path, and counter to create the new key (this same technique is used if
+# we run out of room for the counter).
+
+# This module use encoding e4 from the appendix of "Splittable Pseudorandom Number Generators using
+# Cryptographic Hashing" (confusingly, the definition in the paper uses e3 to define the encoding
+# function). This encoding uses a 10 element uint64 tensor where each byte means the following:
+
+# .. code-block:
+
+# gen:
+# words: 0 1 2 3 | 4 5 | 6 7 | 8 9
+# usage: key | path | counter | position of next step in path encoded in binary
+# ex: 0b00010 -> next path entry goes one from the right
+
+# Right now, counter only uses the rightmost word.
+
+# Threefry rotation constants from the Skein paper ("The Skein Hash Function Family"
+# https://www.schneier.com/wp-content/uploads/2015/01/skein.pdf)
+_ROTATIONS = {
+ 4: [[14, 16], [52, 57], [23, 40], [5, 37], [25, 33], [46, 12], [58, 22], [32, 32]],
+ 8: [
+ [46, 36, 19, 37],
+ [33, 27, 14, 42],
+ [17, 49, 36, 39],
+ [44, 9, 54, 56],
+ [39, 30, 34, 24],
+ [13, 50, 10, 17],
+ [25, 29, 39, 43],
+ [8, 35, 56, 22],
+ ],
+ 16: [
+ [24, 13, 8, 47, 8, 17, 22, 37],
+ [38, 19, 10, 55, 49, 18, 23, 52],
+ [33, 4, 51, 13, 34, 41, 59, 17],
+ [5, 20, 48, 41, 47, 28, 16, 25],
+ [41, 9, 37, 31, 12, 47, 44, 30],
+ [16, 34, 56, 51, 4, 53, 42, 41],
+ [31, 44, 47, 46, 19, 42, 44, 25],
+ [9, 48, 35, 52, 23, 31, 37, 20],
+ ],
+}
+
+# Threefry permutation constants from the Skein paper ("The Skein Hash Function Family"
+# https://www.schneier.com/wp-content/uploads/2015/01/skein.pdf)
+_PERMUTATIONS = {
+ 4: [0, 3, 2, 1],
+ 8: [2, 1, 4, 7, 6, 5, 0, 3],
+ 16: [0, 9, 2, 13, 6, 11, 4, 15, 10, 7, 12, 3, 14, 5, 8, 1],
+}
+
+
+def _threefry(
+ irb, key_buf, key_offset, counter_buf, counter_offset, out_buf, out_offset, out_shape
+):
+ """IRBuilder code for running Threefry
+
+ Parameters
+ ----------
+ irb: IRBuilder
+ IRBuilder that this code will be generated for.
+
+ key_buf: BufferVar
+ Buffer to read the key from.
+
+ key_offset: number
+ Threefry will write to :code:`key_buf[key_offset:key_offset+4]`
+
+ counter_buf: BufferVar
+ Buffer to read the counter from.
+
+ counter_offset: number
+ Threefry will write to :code:`counter_buf[counter_offset:counter_offset+4]`
+
+ out_buf: BufferVar
+ Buffer to read the counter from.
+
+ out_offset: number
+ Threefry will write to :code:`out_buf[out_offset:out_offset+4*product(out_shape)]`
+
+ out_shape: number
+ Determines the number of ouput states to generate. :code:`state[i]` will correspond to
+ counter+i.
+ """
+ nrounds = 20
+ nwords = 4
+ iwidth = 64
+ assert nrounds % 4 == 0
+ assert nwords in [4, 8, 16]
+
+ assert key_buf.dtype == "uint64" # TODO: support 32 bit inputs
+ assert key_buf.dtype == counter_buf.dtype
+
+ def mix(a, b, rotation):
+ x = a + b # TODO should be wrapping
+ y = x ^ ((b << rotation) | (b >> (iwidth - rotation)))
+ return [x, y]
+
+ # temporary buffer for holding the results of _PERMUTATIONS
+ tmp = irb.allocate(out_buf.dtype, out_shape, name="tmp", scope="global")
+ tmp_offset = 0
+
+ # Initialize entire key. It is composed of the original key with one
+ # element appended. The appended element is the xor of all key words plus a
+ # constant.
+ full_key = irb.allocate("uint64", nwords + 1, name="full_key", scope="global")
+ for i in range(nwords):
+ full_key[i] = key_buf[key_offset + i]
+ # initial key constant, full_key[nwords] is equivalent to k_{N_W} in the Skein paper.
+ full_key[nwords] = tvm.tir.const(0x1BD11BDAA9FC1A22, dtype="uint64")
+ for i in range(nwords):
+ full_key[nwords] ^= key_buf[key_offset + i] # TODO: wrapping
+
+ # TODO: overwrite counter instead?
+ with irb.for_range(0, out_shape, dtype="uint64", name="i") as i:
+ for j in range(nwords):
+ out_buf[out_offset + i * nwords + j] = counter_buf[counter_offset + j] + i
+
+ def key_schedule(s, i):
+ # Threefry uses no tweak, so the key schedule is simple
+ if i == nwords - 1:
+ return full_key[(s + i) % (nwords + 1)] + tvm.tir.const(s, dtype="uint64")
+ return full_key[(s + i) % (nwords + 1)]
+
+ with irb.for_range(0, out_shape, name="l") as l: # pylint: disable=invalid-name
+ for i in range(nrounds // 4):
+ for j in range(nwords):
+ out_buf[out_offset + l * nwords + j] += key_schedule(i, j) # TODO wrapping
+ for k in range(4):
+ for j in range(nwords // 2):
+ (
+ out_buf[out_offset + l * nwords + j * 2 + 0],
+ out_buf[out_offset + l * nwords + j * 2 + 1],
+ ) = mix(
+ out_buf[out_offset + l * nwords + j * 2 + 0],
+ out_buf[out_offset + l * nwords + j * 2 + 1],
+ _ROTATIONS[nwords][(i * 4 + k) % 8][j],
+ )
+ for j in range(nwords):
+ tmp[tmp_offset + l * nwords + j] = out_buf[
+ out_offset + l * nwords + _PERMUTATIONS[nwords][j]
+ ]
+ # number of rounds is even, so out always contains the result
+ (out_buf, tmp) = (tmp, out_buf)
+ (out_offset, tmp_offset) = (tmp_offset, out_offset)
+
Review comment:
The only one that matters is `TODO should be wrapping`. I do not know if TVM guarantees unsigned integer arithmetic to be wrapping (instead of saturating).
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