├── .gitignore ├── LICENSE ├── README.md ├── fastrange.h └── tests ├── c ├── Makefile └── tests.c └── cpp ├── Makefile └── tests.cpp /.gitignore: -------------------------------------------------------------------------------- 1 | # Compiled Object files 2 | *.slo 3 | *.lo 4 | *.o 5 | *.obj 6 | 7 | # Precompiled Headers 8 | *.gch 9 | *.pch 10 | 11 | # Compiled Dynamic libraries 12 | *.so 13 | *.dylib 14 | *.dll 15 | 16 | # Fortran module files 17 | *.mod 18 | *.smod 19 | 20 | # Compiled Static libraries 21 | *.lai 22 | *.la 23 | *.a 24 | *.lib 25 | 26 | # Executables 27 | *.exe 28 | *.out 29 | *.app 30 | -------------------------------------------------------------------------------- /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. 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This is common in hashing and probabilistic 8 | algorithms. 9 | 10 | In computing, the modulo operation finds the remainder after division of one number by another (called the modulus of the operation). Given two positive numbers, a and n, a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. 11 | 12 | The standard approach to this problem is the modulo reduction (``x % p``). 13 | Though a modulo reduction works fine and has several nice properties, 14 | it can be slow even on recent processors because it relies on an 15 | integer division. 16 | 17 | Thankfully, there is a faster way: we can replace the modulo by a multiplication 18 | followed by a shift. 19 | 20 | [It has accelerated some operations in Google's Tensorflow by 10% to 20%](https://github.com/tensorflow/tensorflow/commit/a47a300185026fe7829990def9113bf3a5109fed). 21 | 22 | Further reading : http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/ 23 | 24 | 25 | See also: 26 | 27 | * Daniel Lemire, [Fast Random Integer Generation in an Interval](https://arxiv.org/abs/1805.10941), ACM Transactions on Modeling and Computer Simulation, January 2019 Article No. 3 https://doi.org/10.1145/3230636 28 | 29 | 30 | This library provides a single portable header file that you should 31 | be able to just drop in your C/C++ projects. The API is simple: 32 | 33 | 34 | ```C 35 | #include "fastrange" 36 | 37 | // given a value word, produces an integer in [0,p) without division 38 | uint32_t fastrange32(uint32_t word, uint32_t p); 39 | uint64_t fastrange64(uint64_t word, uint64_t p); 40 | size_t fastrangesize(size_t word, size_t p); 41 | int fastrangeint(int word, int p); 42 | ``` 43 | ## Pre-conditions 44 | 45 | For this code to give the desired result, the provided words should span the whole range (e.g., all 32-bit integers). The C ``rand`` function does not meet this requirement. If you must use the ``rand`` function, wrap it like so: 46 | 47 | ``` 48 | uint32_t get32rand() { 49 | return (rand() ^ (rand() << 15) ^ (rand() << 30)); 50 | } 51 | 52 | uint64_t get64rand() { 53 | return (((uint64_t)get32rand()) << 32) | get32rand(); 54 | } 55 | ``` 56 | 57 | 58 | However, the underlying idea is general: we only require that the word values span an interval of the form ``[0,1<> L `` to get a fair map from ``[0,1<> 16``. 59 | 60 | 61 | ## Unbiased range functions 62 | 63 | To generate an unbiased random number in a range, you can use an extension of this approach: 64 | 65 | ```C 66 | uint32_t random_bounded(uint32_t range) { 67 | uint64_t random32bit = random32(); //32-bit random number 68 | multiresult = random32bit * range; 69 | leftover = (uint32_t) multiresult; 70 | if(leftover < range ) { 71 | threshold = -range % range ; 72 | while (leftover < threshold) { 73 | random32bit = random32(); 74 | multiresult = random32bit * range; 75 | leftover = (uint32_t) multiresult; 76 | } 77 | } 78 | return multiresult >> 32; 79 | } 80 | ``` 81 | 82 | See http://lemire.me/blog/2016/06/30/fast-random-shuffling/ 83 | -------------------------------------------------------------------------------- /fastrange.h: -------------------------------------------------------------------------------- 1 | /** 2 | * Fair maps to intervals without division. 3 | * Reference : http://lemire.me/blog/2016/06/27/a-fast-alternative-to-the-modulo-reduction/ 4 | * 5 | * (c) Daniel Lemire 6 | * Apache License 2.0 7 | */ 8 | #ifndef INCLUDE_FASTRANGE_H 9 | #define INCLUDE_FASTRANGE_H 10 | #include // mostly for Microsoft compilers 11 | #include // part of Visual Studio 2010 and better 12 | #include // for size_t in C 13 | #include // for size_t in C 14 | 15 | /** 16 | * Given a value "word", produces an integer in [0,p) without division. 17 | * The function is as fair as possible in the sense that if you iterate 18 | * through all possible values of "word", then you will generate all 19 | * possible outputs as uniformly as possible. 20 | */ 21 | static inline uint32_t fastrange32(uint32_t word, uint32_t p) { 22 | return (uint32_t)(((uint64_t)word * (uint64_t)p) >> 32); 23 | } 24 | 25 | #if defined(_MSC_VER) && defined (_WIN64) 26 | #include // should be part of all recent Visual Studio 27 | #pragma intrinsic(_umul128) 28 | #endif // defined(_MSC_VER) && defined (_WIN64) 29 | 30 | 31 | /** 32 | * Given a value "word", produces an integer in [0,p) without division. 33 | * The function is as fair as possible in the sense that if you iterate 34 | * through all possible values of "word", then you will generate all 35 | * possible outputs as uniformly as possible. 36 | */ 37 | static inline uint64_t fastrange64(uint64_t word, uint64_t p) { 38 | #ifdef __SIZEOF_INT128__ // then we know we have a 128-bit int 39 | return (uint64_t)(((__uint128_t)word * (__uint128_t)p) >> 64); 40 | #elif defined(_MSC_VER) && defined(_WIN64) 41 | // supported in Visual Studio 2005 and better 42 | uint64_t highProduct; 43 | _umul128(word, p, &highProduct); // ignore output 44 | return highProduct; 45 | unsigned __int64 _umul128( 46 | unsigned __int64 Multiplier, 47 | unsigned __int64 Multiplicand, 48 | unsigned __int64 *HighProduct 49 | ); 50 | #else 51 | return word % p; // fallback 52 | #endif // __SIZEOF_INT128__ 53 | } 54 | 55 | 56 | #ifndef UINT32_MAX 57 | #define UINT32_MAX (0xffffffff) 58 | #endif // UINT32_MAX 59 | 60 | /** 61 | * Given a value "word", produces an integer in [0,p) without division. 62 | * The function is as fair as possible in the sense that if you iterate 63 | * through all possible values of "word", then you will generate all 64 | * possible outputs as uniformly as possible. 65 | */ 66 | static inline size_t fastrangesize(size_t word, size_t p) { 67 | #if (SIZE_MAX == UINT32_MAX) 68 | return (size_t)fastrange32(word, p); 69 | #else // assume 64-bit 70 | return (size_t)fastrange64(word, p); 71 | #endif // SIZE_MAX == UINT32_MAX 72 | } 73 | 74 | /** 75 | * Given a value "word", produces an integer in [0,p) without division. 76 | * The function is as fair as possible in the sense that if you iterate 77 | * through all possible values of "word", then you will generate all 78 | * possible outputs as uniformly as possible. 79 | */ 80 | static inline int fastrangeint(int word, int p) { 81 | #if (SIZE_MAX == UINT32_MAX) 82 | return (int)fastrange32(word, p); 83 | #else // assume 64-bit 84 | return (int)fastrange64(word, p); 85 | #endif // (SIZE_MAX == UINT32_MAX) 86 | } 87 | 88 | #endif// INCLUDE_FASTRANGE_H 89 | -------------------------------------------------------------------------------- /tests/c/Makefile: -------------------------------------------------------------------------------- 1 | .SUFFIXES: 2 | # 3 | .SUFFIXES: .cpp .o .c .h 4 | 5 | 6 | all: tests.c 7 | $(CC) -o tests tests.c -Wall -Wextra 8 | 9 | clean: 10 | rm -f *.o tests 11 | -------------------------------------------------------------------------------- /tests/c/tests.c: -------------------------------------------------------------------------------- 1 | #include 2 | #include "../../fastrange.h" 3 | 4 | // this just checks that we can compile successfully 5 | 6 | int main() { 7 | for(uint32_t x = 0; x < 1000000; ++x) assert(fastrange32(x,5) < 5); 8 | for(uint64_t x = 0; x < 1000000; ++x) assert(fastrange64(x,5) < 5); 9 | } 10 | -------------------------------------------------------------------------------- /tests/cpp/Makefile: -------------------------------------------------------------------------------- 1 | .SUFFIXES: 2 | # 3 | .SUFFIXES: .cpp .o .c .h 4 | 5 | 6 | all: tests.cpp 7 | $(CXX) -o tests tests.cpp -Wall -Wextra 8 | 9 | clean: 10 | rm -f *.o tests 11 | -------------------------------------------------------------------------------- /tests/cpp/tests.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | #include "../../fastrange.h" 5 | 6 | 7 | ///////////////////// 8 | // rand returns a random integer between 0 and RAND_MAX 9 | // where RAND_MAX is at least 32767 10 | // Note: this means that (uint64_t)rand() << 32 | rand() is NOT a proper 11 | // way to generate random 64-bit integers in general. 12 | ///////////////////// 13 | 14 | static uint32_t get32rand() { 15 | return (rand() ^ (rand() << 15) ^ (rand() << 30)); 16 | } 17 | 18 | static uint64_t get64rand() { 19 | return (((uint64_t)get32rand()) << 32) | get32rand(); 20 | } 21 | 22 | void fill(int number) { 23 | std::set set; 24 | while(set.size() < (size_t) number) { 25 | set.insert(fastrangesize(get64rand(), number)); 26 | } 27 | } 28 | 29 | int main() { 30 | for(uint32_t x = 0; x < 1000000; ++x) assert(fastrange32(x,5)<5); 31 | for(uint64_t x = 0; x < 1000000; ++x) assert(fastrange64(x,5)<5); 32 | for(int x = 1; x < 1000; ++x) fill(x); 33 | } 34 | --------------------------------------------------------------------------------