altanh commented on a change in pull request #7083: URL: https://github.com/apache/tvm/pull/7083#discussion_r552146139
########## File path: python/tvm/relay/op/random/kernel.py ########## @@ -0,0 +1,134 @@ +# 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. +"""Splittable and parallelizable PRNG kernels.""" +# pylint: disable=invalid-name,unused-argument +from __future__ import absolute_import + +import sys +import numpy as np + +from ...expr import Constant +from .... import nd +from . import _make + + +def threefry_key(seed): + """Create a new Threefry random number generator key. + + Example + ------- + + .. code-block:: python + + gen = threefry_key(0) + _, random_number = threefry_generate(gen, (4,)) + + Parameters + ---------- + seed : int + Starting seed for the key + + Returns + ------- + key : relay.Expr + New key to pass to future uses of :py:func:`threefry_split` or + :py:func:`threefry_generate`. + """ + s = np.frombuffer(seed.to_bytes(32, sys.byteorder), dtype="uint64") + a = np.concatenate((s, np.array([0, 0, 0, 0, 1 << 63, 0], dtype="uint64"))) + return Constant(nd.array(a)) + + +def threefry_generate(key, shape): + """Generate an array of random bits (`uint64`) using the Threefry algorithm + + Example + ------- + + .. code-block:: python + + key = threefry_key(0) + new_key, random1 = threefry_generate(key, (4,)) + _, random2 = threefry_generate(new_key, (4,)) + # random1 and random2 are different random numbers + + Parameters + ---------- + key : relay.Expr + key that uniquely determines the random values. Multiple uses with the + same key will generate the same random values. This key should be + treated as an opaque pointer. You can create one from calling + :py:func:`threefry_key`, :py:func:`threefry_split`, or + :py:func:`threefry_generate`. **Do not use this key again after calling + this function.** + + shape : Sequence[int] + Desired outputs shape of random numbers. **Currently the total + number of elements must be a multiple of 4.** + + Returns + ------- + new_key : relay.Expr + New key to pass to future uses of :py:func:`threefry_split` or + :py:func:`threefry_generate`. + + random_array : relay.Expr + Array of random numbers. Has shape `shape`. + """ + return _make.threefry_generate(key, shape) + + +def threefry_split(key): + """Split an existing Threefry key into two new ones. + + This is useful if you have to subsequent calls which each need their own + independent random number generation. + + Example + ------- + + .. code-block:: python + + def foo(key): + new_key, num = threefry_generate(key, (1,)) Review comment: fix this example to use multiple of 4 for now, until we support non-multiples ########## File path: python/tvm/topi/random/kernel.py ########## @@ -0,0 +1,407 @@ +# 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: I see some `TODO` in this function (`_threefry`), do they affect the correctness of the algorithm? ########## File path: python/tvm/topi/random/kernel.py ########## @@ -0,0 +1,407 @@ +# 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) + + +def threefry_generate(gen, out_shape): + """Generate a series of random values + + Notes + ----- + This function uses the counter portion of the generator state to generate a series of random + numbers in parallel. Random number `i` is generated by applying Threefry to the current + generator state with the counter portion incremented by `i`. This means that each random number + is generated independently from each other random number, so we can compute them in parallel. + + If there is not enough room left in the counter to generate the desired shape of random values, + then a new generator is created by applying Threefry to the current key, path, and counter. + This new generator will have a reset counter. + + Parameters + ---------- + gen : Tensor[10, uint64] + Generator state. Can be create with :py:func:`tvm.relay.threefry_key`. This should not be + reused in another function, otherwise random numbers will be repeated. + + out_shape : Sequence[int] + Output shape of the random numbers. Product of all dimensions must be a multiple of 4. + + Returns + ------- + new_gen : Tensor[10, uint64] + The new generator state to be used in subsequent calls. + + rand : Tensor[out_shape, uint64] + Tensor of random numbers with shape `out_shape`. + """ + out_len = tir.const(1) + for s in out_shape: + out_len *= s + assert ( + out_len.value % 4 == 0 + ), f"Threefry can only generate arrays who's size is a multiple of 4 ({out_len} was provided)." + assert ( + out_len.value <= 2 ** 64 - 1 + ), f"Can only generate up to 2^64 random numbers, but {out_len} were requested." + + def gen_ir(gen_ptr, out_gen_ptr, out_array_ptr): + irb = ir_builder.create() + gen = irb.buffer_ptr(gen_ptr) + out_gen = irb.buffer_ptr(out_gen_ptr) + out_array = irb.buffer_ptr(out_array_ptr) + + # Create a temporary array to hold the generator state we will use to create the random + # numbers. We cannot use gen because we may need to update the key + path if there is not + # enough room in the counter. + tmp = irb.allocate(gen.dtype, 10, name="tmp", scope="global") + + # TODO(tkonolige): for now we only use the last word of the counter for counting. Its too + # much work to figure out how to do 128 bit addition. + + # Max value for counter should be 2**64-2 because we need to reserve a special value to + # indicate the counter is used up. + with irb.if_scope(gen[7] < tir.const(2 ** 64 - 1, dtype=gen.dtype) - out_len): + for i in range(10): + tmp[i] = gen[i] + with irb.else_scope(): + # no room left in the counter, we have to change the path or key + with irb.if_scope(gen[8] == 0 and gen[9] == 0): + # out of room in the path, have to generate new key + + # The paper says the counter that we will be hashing should be a special value of + # all ones. We need to allocate some space for it because we cannot overwrite gen. + tmp_counter = irb.allocate(gen.dtype, 2, name="tmp_counter", scope="global") + tmp_counter[0] = tir.const(0xFFFFFFFFFFFFFFFF, dtype=gen.dtype) + tmp_counter[1] = tir.const(0xFFFFFFFFFFFFFFFF, dtype=gen.dtype) + _threefry(irb, gen, 0, tmp_counter, 0, tmp, 0, 1) + tmp[4] = tir.const(0, dtype=gen.dtype) # zero path, i.e. no path + tmp[5] = tir.const(0, dtype=gen.dtype) + tmp[6] = tir.const(0, dtype=gen.dtype) # zero counter + tmp[7] = tir.const(0, dtype=gen.dtype) + tmp[8] = tir.const(1 << 63, dtype=gen.dtype) # one in the leftmost position + tmp[9] = tir.const(0, dtype=gen.dtype) + with irb.else_scope(): + tmp[0] = gen[0] + tmp[1] = gen[1] + tmp[2] = gen[2] + tmp[3] = gen[3] + tmp[4] = gen[4] | gen[8] # add a 1 to the path + tmp[5] = gen[5] | gen[9] + tmp[6] = tir.const(0, dtype=gen.dtype) # zero counter + tmp[7] = tir.const(0, dtype=gen.dtype) + _shift_right(irb, gen[8], gen[9], tmp, 8, tmp, 9) + + # Compute random values + _threefry(irb, tmp, 0, tmp, 4, out_array, 0, out_len // 4) + + # Update generator state + out_gen[0] = tmp[0] # key stays the same + out_gen[1] = tmp[1] + out_gen[2] = tmp[2] + out_gen[3] = tmp[3] + out_gen[4] = tmp[4] # path stays the same + out_gen[5] = tmp[5] + out_gen[6] = tir.const(0, dtype=gen.dtype) # unused, leave it as 0 + out_gen[7] = tmp[7] + tir.Cast(gen.dtype, out_len) # increment counter + out_gen[8] = tmp[8] # path unchanged, so no update here + out_gen[9] = tmp[9] + + return irb.get() + + out_gen = tvm.tir.decl_buffer((10,), name="out_gen", dtype="uint64") + out_array = tvm.tir.decl_buffer(out_shape, name="out_array", dtype="uint64") + return tvm.te.extern( + [out_gen.shape, out_array.shape], + [gen], + lambda ins, outs: gen_ir(ins[0], outs[0], outs[1]), + out_buffers=[out_gen, out_array], + name="threefry_generate", + tag="threefry_generate", + ) + + +def _shift_right(irb, a, b, out_a, a_off, out_b, b_off): Review comment: for clarity maybe comment if this is logical or arithmetic right shift ---------------------------------------------------------------- This is an automated message from the Apache Git Service. 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