├── .gitignore ├── fastrandom.go ├── README.md ├── shortshuffle.go ├── fastrandom_test.go └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | # Compiled Object files, Static and Dynamic libs (Shared Objects) 2 | *.o 3 | *.a 4 | *.so 5 | 6 | # Folders 7 | _obj 8 | _test 9 | 10 | # Architecture specific extensions/prefixes 11 | *.[568vq] 12 | [568vq].out 13 | 14 | *.cgo1.go 15 | *.cgo2.c 16 | _cgo_defun.c 17 | _cgo_gotypes.go 18 | _cgo_export.* 19 | 20 | _testmain.go 21 | 22 | *.exe 23 | *.test 24 | *.prof 25 | -------------------------------------------------------------------------------- /fastrandom.go: -------------------------------------------------------------------------------- 1 | package fastrandom 2 | 3 | import ( 4 | "github.com/dgryski/go-pcgr" 5 | ) 6 | 7 | // return a pseudo-random number in [0,r), avoiding divisions, uses the dgryski' PCG for random bits 8 | func Randuint32pcg_dgryski(r uint32, pcg *pcgr.Rand) uint32 { 9 | random32bit := pcg.Next() 10 | multiresult := uint64(random32bit) * uint64(r) 11 | leftover := uint32(multiresult) 12 | if leftover < r { 13 | threshold := uint32(-r) % r 14 | for leftover < threshold { 15 | random32bit = pcg.Next() 16 | multiresult = uint64(random32bit) * uint64(r) 17 | leftover = uint32(multiresult) 18 | } 19 | } 20 | return uint32(multiresult >> 32) // [0, r) 21 | } 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ## fastrandom 2 | 3 | (This code is for research purposes.) 4 | 5 | Fast random number generation in Go. We use a division-less range function 6 | to get a "fast" shuffle in Go. 7 | 8 | 9 | 10 | ```bash 11 | $ go get github.com/dgryski/go-pcgr 12 | $ go version 13 | go version go1.7beta2 linux/amd64 14 | $ go test -bench=. 15 | testing: warning: no tests to run 16 | BenchmarkStandardShuffleWithGo1000-2 50000 30628 ns/op 17 | BenchmarkStandardShuffleWithPCGWithDivision1000_dgryski-2 200000 9016 ns/op 18 | BenchmarkStandardShuffleWithPCGButNoDivision1000_dgryski-2 300000 5066 ns/op 19 | PASS 20 | ok _/home/dlemire/CVS/github/fastrandom 5.293s 21 | ``` 22 | 23 | Further reading: 24 | http://lemire.me/blog/2016/06/30/fast-random-shuffling/ 25 | -------------------------------------------------------------------------------- /shortshuffle.go: -------------------------------------------------------------------------------- 1 | package fastrandom 2 | 3 | import "fmt" 4 | 5 | /////////////////////////////////////////////////////////////// 6 | /////////////////////////////////////////////////////////////// 7 | // This file contains a fast function to compute permutations of up to 12 elements 8 | // without *any* division from a single 32-bit key 9 | /////////////////////////////////////////////////////////////// 10 | /////////////////////////////////////////////////////////////// 11 | 12 | // precomputed factorials... 2!, 3!..., 12! 13 | var precomputedFactorial = [...]uint32{2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600} 14 | 15 | // magic number of fast division 16 | type magicNumber struct { 17 | multiplier uint32 18 | shift uint 19 | } 20 | 21 | // magic numbers to divide by... 2!, 3!..., 12! 22 | 23 | var precomputedMagicNumber = [...]magicNumber{{0x80000000, 0}, {0xaaaaaaab, 2}, {0xaaaaaaab, 4}, {0x88888889, 6}, {0xb60b60b7, 9}, {0xd00d00d1, 12}, {0xd00d00d1, 15}, {0xb8ef1d2b, 18}, {0x24fc9f6f, 19}, {0x035cc8ad, 19}, {0x011eed8f, 21}} 24 | 25 | // (x*y) >> 32 26 | 27 | func high32(x uint32, y uint32) uint32 { 28 | return uint32((uint64(x) * uint64(y)) >> 32) 29 | } 30 | 31 | // fast division function, uses exactly one multiplication and one shift 32 | func fastDiv(val uint32, mn *magicNumber) uint32 { 33 | q := high32(mn.multiplier, val) 34 | return q >> mn.shift 35 | } 36 | 37 | // Given a key in [0,N!) generates a shuffle *without* using any division. 38 | // You can generate a value in [0,N!) using randuint32pcg_dgryski 39 | // you probably don't want to use such a function... this is just a demo 40 | // 41 | // This function uses no division, but two multiplications (one 64-bit and one 32-bit), one shift 42 | // and one subtraction for 3,4..., N 43 | func FastShortShuffle(key uint32, N uint) []uint { 44 | if (N < 2) || (N > 12) { 45 | fmt.Errorf("out of bound") 46 | } 47 | if key >= precomputedFactorial[N-2] { 48 | fmt.Errorf("bad key") 49 | } 50 | answer := make([]uint, N) 51 | for i := uint(0); i < N; i++ { 52 | answer[i] = i // fill answer with values 0,1,2...,N-1 53 | } 54 | for i := N; i >= 3; i-- { 55 | mn := precomputedMagicNumber[i-3] 56 | fa := precomputedFactorial[i-3] 57 | divresult := fastDiv(key, &mn) // value in [0,i) 58 | key = key - divresult*fa // value in [0,(i-1)!) 59 | // we swap 60 | answer[divresult], answer[i-1] = answer[i-1], answer[divresult] 61 | } 62 | // here i = 2, key is zero or one 63 | answer[key], answer[1] = answer[1], answer[key] 64 | return answer 65 | } 66 | -------------------------------------------------------------------------------- /fastrandom_test.go: -------------------------------------------------------------------------------- 1 | package fastrandom 2 | 3 | import ( 4 | "fmt" 5 | "math/rand" 6 | "testing" 7 | ) 8 | import "github.com/dgryski/go-pcgr" 9 | 10 | var p = pcgr.Rand{0x0ddc0ffeebadf00d, 0xcafebabe} 11 | 12 | func testFastShortShuffle(t *testing.T, key uint32, N uint) { 13 | for i := N; i >= 3; i-- { 14 | mn := precomputedMagicNumber[i-3] 15 | fa := precomputedFactorial[i-3] 16 | divresult := fastDiv(key, &mn) // value in [0,i) 17 | expresult := key / fa 18 | if divresult != expresult { 19 | t.Error("Expected ", expresult, ", got ", divresult) 20 | } 21 | key = key - divresult*fa // value in [0,(i-1)!) 22 | } 23 | } 24 | 25 | func TestFastDiv(t *testing.T) { 26 | N := uint(11) 27 | m := precomputedFactorial[N-2] - 1 28 | for ; m > 0; m-- { 29 | testFastShortShuffle(t, m, N) 30 | } 31 | } 32 | 33 | func toId(vals []uint, N uint) uint { 34 | v := uint(0) 35 | for i := uint(0); i < N; i++ { 36 | v = v*N + vals[i] 37 | } 38 | return v 39 | } 40 | 41 | func TestFastShuffle(t *testing.T) { 42 | N := uint(5) 43 | 44 | x := make(map[uint]bool) 45 | m := precomputedFactorial[N-2] 46 | for mm := uint32(0); mm < m; mm++ { 47 | sh := FastShortShuffle(mm, N) 48 | fmt.Println(sh) 49 | x[toId(sh, N)] = true 50 | } 51 | if uint32(len(x)) != precomputedFactorial[N-2] { 52 | t.Error("Expected ", precomputedFactorial[N-2], ", got ", len(x)) 53 | } 54 | } 55 | 56 | //go test -bench=. 57 | 58 | // standard 59 | func benchmarkGo(b *testing.B, r uint32) { 60 | b.StopTimer() 61 | array := make([]int, r, r) 62 | for i := 0; i < int(r); i++ { 63 | array[i] = i 64 | } 65 | b.StartTimer() 66 | for j := 0; j < b.N; j++ { 67 | 68 | for i := r; i > 0; i-- { 69 | idx := rand.Int31n(int32(i)) 70 | tmp := array[idx] 71 | array[idx] = array[i-1] 72 | array[i-1] = tmp 73 | } 74 | } 75 | } 76 | 77 | // our fast approach that avoids division 78 | func benchmarkFastPCG_dgryski(b *testing.B, r uint32) { 79 | b.StopTimer() 80 | array := make([]int, r, r) 81 | for i := 0; i < int(r); i++ { 82 | array[i] = i 83 | } 84 | b.StartTimer() 85 | for j := 0; j < b.N; j++ { 86 | for i := r; i > 0; i-- { 87 | idx := Randuint32pcg_dgryski(uint32(i), &p) 88 | tmp := array[idx] 89 | array[idx] = array[i-1] 90 | array[i-1] = tmp 91 | } 92 | } 93 | } 94 | 95 | // standard PCG 96 | func benchmarkPCG_dgryski(b *testing.B, r uint32) { 97 | b.StopTimer() 98 | array := make([]int, r, r) 99 | for i := 0; i < int(r); i++ { 100 | array[i] = i 101 | } 102 | b.StartTimer() 103 | for j := 0; j < b.N; j++ { 104 | for i := r; i > 0; i-- { 105 | idx := p.Bound(uint32(i)) 106 | tmp := array[idx] 107 | array[idx] = array[i-1] 108 | array[i-1] = tmp 109 | } 110 | } 111 | } 112 | 113 | func BenchmarkStandardShuffleWithGo1000(b *testing.B) { 114 | benchmarkGo(b, 1000) 115 | } 116 | 117 | func BenchmarkStandardShuffleWithPCGWithDivision1000_dgryski(b *testing.B) { 118 | benchmarkPCG_dgryski(b, 1000) 119 | } 120 | 121 | func BenchmarkStandardShuffleWithPCGButNoDivision1000_dgryski(b *testing.B) { 122 | benchmarkFastPCG_dgryski(b, 1000) 123 | } 124 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. Definitions. 8 | 9 | "License" shall mean the terms and conditions for use, reproduction, 10 | and distribution as defined by Sections 1 through 9 of this document. 11 | 12 | "Licensor" shall mean the copyright owner or entity authorized by 13 | the copyright owner that is granting the License. 14 | 15 | "Legal Entity" shall mean the union of the acting entity and all 16 | other entities that control, are controlled by, or are under common 17 | control with that entity. For the purposes of this definition, 18 | "control" means (i) the power, direct or indirect, to cause the 19 | direction or management of such entity, whether by contract or 20 | otherwise, or (ii) ownership of fifty percent (50%) or more of the 21 | outstanding shares, or (iii) beneficial ownership of such entity. 22 | 23 | "You" (or "Your") shall mean an individual or Legal Entity 24 | exercising permissions granted by this License. 25 | 26 | "Source" form shall mean the preferred form for making modifications, 27 | including but not limited to software source code, documentation 28 | source, and configuration files. 29 | 30 | "Object" form shall mean any form resulting from mechanical 31 | transformation or translation of a Source form, including but 32 | not limited to compiled object code, generated documentation, 33 | and conversions to other media types. 34 | 35 | "Work" shall mean the work of authorship, whether in Source or 36 | Object form, made available under the License, as indicated by a 37 | copyright notice that is included in or attached to the work 38 | (an example is provided in the Appendix below). 39 | 40 | "Derivative Works" shall mean any work, whether in Source or Object 41 | form, that is based on (or derived from) the Work and for which the 42 | editorial revisions, annotations, elaborations, or other modifications 43 | represent, as a whole, an original work of authorship. For the purposes 44 | of this License, Derivative Works shall not include works that remain 45 | separable from, or merely link (or bind by name) to the interfaces of, 46 | the Work and Derivative Works thereof. 47 | 48 | "Contribution" shall mean any work of authorship, including 49 | the original version of the Work and any modifications or additions 50 | to that Work or Derivative Works thereof, that is intentionally 51 | submitted to Licensor for inclusion in the Work by the copyright owner 52 | or by an individual or Legal Entity authorized to submit on behalf of 53 | the copyright owner. For the purposes of this definition, "submitted" 54 | means any form of electronic, verbal, or written communication sent 55 | to the Licensor or its representatives, including but not limited to 56 | communication on electronic mailing lists, source code control systems, 57 | and issue tracking systems that are managed by, or on behalf of, the 58 | Licensor for the purpose of discussing and improving the Work, but 59 | excluding communication that is conspicuously marked or otherwise 60 | designated in writing by the copyright owner as "Not a Contribution." 61 | 62 | "Contributor" shall mean Licensor and any individual or Legal Entity 63 | on behalf of whom a Contribution has been received by Licensor and 64 | subsequently incorporated within the Work. 65 | 66 | 2. Grant of Copyright License. Subject to the terms and conditions of 67 | this License, each Contributor hereby grants to You a perpetual, 68 | worldwide, non-exclusive, no-charge, royalty-free, irrevocable 69 | copyright license to reproduce, prepare Derivative Works of, 70 | publicly display, publicly perform, sublicense, and distribute the 71 | Work and such Derivative Works in Source or Object form. 72 | 73 | 3. Grant of Patent License. Subject to the terms and conditions of 74 | this License, each Contributor hereby grants to You a perpetual, 75 | worldwide, non-exclusive, no-charge, royalty-free, irrevocable 76 | (except as stated in this section) patent license to make, have made, 77 | use, offer to sell, sell, import, and otherwise transfer the Work, 78 | where such license applies only to those patent claims licensable 79 | by such Contributor that are necessarily infringed by their 80 | Contribution(s) alone or by combination of their Contribution(s) 81 | with the Work to which such Contribution(s) was submitted. If You 82 | institute patent litigation against any entity (including a 83 | cross-claim or counterclaim in a lawsuit) alleging that the Work 84 | or a Contribution incorporated within the Work constitutes direct 85 | or contributory patent infringement, then any patent licenses 86 | granted to You under this License for that Work shall terminate 87 | as of the date such litigation is filed. 88 | 89 | 4. Redistribution. You may reproduce and distribute copies of the 90 | Work or Derivative Works thereof in any medium, with or without 91 | modifications, and in Source or Object form, provided that You 92 | meet the following conditions: 93 | 94 | (a) You must give any other recipients of the Work or 95 | Derivative Works a copy of this License; and 96 | 97 | (b) You must cause any modified files to carry prominent notices 98 | stating that You changed the files; and 99 | 100 | (c) You must retain, in the Source form of any Derivative Works 101 | that You distribute, all copyright, patent, trademark, and 102 | attribution notices from the Source form of the Work, 103 | excluding those notices that do not pertain to any part of 104 | the Derivative Works; and 105 | 106 | (d) If the Work includes a "NOTICE" text file as part of its 107 | distribution, then any Derivative Works that You distribute must 108 | include a readable copy of the attribution notices contained 109 | within such NOTICE file, excluding those notices that do not 110 | pertain to any part of the Derivative Works, in at least one 111 | of the following places: within a NOTICE text file distributed 112 | as part of the Derivative Works; within the Source form or 113 | documentation, if provided along with the Derivative Works; or, 114 | within a display generated by the Derivative Works, if and 115 | wherever such third-party notices normally appear. The contents 116 | of the NOTICE file are for informational purposes only and 117 | do not modify the License. You may add Your own attribution 118 | notices within Derivative Works that You distribute, alongside 119 | or as an addendum to the NOTICE text from the Work, provided 120 | that such additional attribution notices cannot be construed 121 | as modifying the License. 122 | 123 | You may add Your own copyright statement to Your modifications and 124 | may provide additional or different license terms and conditions 125 | for use, reproduction, or distribution of Your modifications, or 126 | for any such Derivative Works as a whole, provided Your use, 127 | reproduction, and distribution of the Work otherwise complies with 128 | the conditions stated in this License. 129 | 130 | 5. Submission of Contributions. Unless You explicitly state otherwise, 131 | any Contribution intentionally submitted for inclusion in the Work 132 | by You to the Licensor shall be under the terms and conditions of 133 | this License, without any additional terms or conditions. 134 | Notwithstanding the above, nothing herein shall supersede or modify 135 | the terms of any separate license agreement you may have executed 136 | with Licensor regarding such Contributions. 137 | 138 | 6. Trademarks. This License does not grant permission to use the trade 139 | names, trademarks, service marks, or product names of the Licensor, 140 | except as required for reasonable and customary use in describing the 141 | origin of the Work and reproducing the content of the NOTICE file. 142 | 143 | 7. Disclaimer of Warranty. Unless required by applicable law or 144 | agreed to in writing, Licensor provides the Work (and each 145 | Contributor provides its Contributions) on an "AS IS" BASIS, 146 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or 147 | implied, including, without limitation, any warranties or conditions 148 | of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A 149 | PARTICULAR PURPOSE. You are solely responsible for determining the 150 | appropriateness of using or redistributing the Work and assume any 151 | risks associated with Your exercise of permissions under this License. 152 | 153 | 8. Limitation of Liability. In no event and under no legal theory, 154 | whether in tort (including negligence), contract, or otherwise, 155 | unless required by applicable law (such as deliberate and grossly 156 | negligent acts) or agreed to in writing, shall any Contributor be 157 | liable to You for damages, including any direct, indirect, special, 158 | incidental, or consequential damages of any character arising as a 159 | result of this License or out of the use or inability to use the 160 | Work (including but not limited to damages for loss of goodwill, 161 | work stoppage, computer failure or malfunction, or any and all 162 | other commercial damages or losses), even if such Contributor 163 | has been advised of the possibility of such damages. 164 | 165 | 9. Accepting Warranty or Additional Liability. While redistributing 166 | the Work or Derivative Works thereof, You may choose to offer, 167 | and charge a fee for, acceptance of support, warranty, indemnity, 168 | or other liability obligations and/or rights consistent with this 169 | License. However, in accepting such obligations, You may act only 170 | on Your own behalf and on Your sole responsibility, not on behalf 171 | of any other Contributor, and only if You agree to indemnify, 172 | defend, and hold each Contributor harmless for any liability 173 | incurred by, or claims asserted against, such Contributor by reason 174 | of your accepting any such warranty or additional liability. 175 | 176 | END OF TERMS AND CONDITIONS 177 | 178 | APPENDIX: How to apply the Apache License to your work. 179 | 180 | To apply the Apache License to your work, attach the following 181 | boilerplate notice, with the fields enclosed by brackets "{}" 182 | replaced with your own identifying information. (Don't include 183 | the brackets!) The text should be enclosed in the appropriate 184 | comment syntax for the file format. We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright {yyyy} {name of copyright owner} 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | 203 | --------------------------------------------------------------------------------