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Testing LCG implementations based on the Borland constants as used in the Diablo video game
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| Chain looped after 4294967296 values from a total of 4294967296 candidates. | |
| AbsDistribution yielded the following values from the given prior seed and current state: | |
| -2147483648: | |
| 1457187811, 2147483648 | |
| -1: | |
| 0: | |
| 3604671459, 0 | |
| 1: | |
| 2914375622, 4294967295 | |
| 0, 1 | |
| 64: | |
| 2375410851, 4294967232 | |
| 538964771, 64 | |
| 65: | |
| 1229260608, 65 | |
| 1685115014, 4294967231 | |
| 128: | |
| 1768225379, 128 | |
| 1146150243, 4294967168 | |
| 7625: | |
| 1480523688, 7625 | |
| 1433851934, 4294959671 | |
| 32458: | |
| 531810049, 4294934838 | |
| 2382565573, 32458 | |
| 32768: | |
| 1625910243, 32768 | |
| 1288465379, 4294934528 | |
| 65534: | |
| 2561524649, 65534 | |
| 352850973, 4294901762 | |
| 65535: | |
| 3251820486, 65535 | |
| 3957522432, 4294901761 | |
| 22695477: | |
| 3604671458, 4272271819 | |
| 3604671460, 22695477 | |
| 429496729: | |
| 1012371854, 3865470567 | |
| 1902003768, 429496729 | |
| 1212022642: | |
| 189776845, 1212022642 | |
| 2724598777, 3082944654 | |
| 2147483646: | |
| 2837779485, 2147483650 | |
| 76596137, 2147483646 | |
| 2147483647: | |
| 2147483648, 2147483649 | |
| 766891974, 2147483647 |
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| //#include <fstream> | |
| #include <iomanip> | |
| #include <iostream> | |
| #include <random> | |
| #include <map> | |
| // The Diablo RNG is a Linear Congruential Generator using Borland C++ constants. | |
| // These constants result in a chain across the entire interval [0, std::numeric_limits<uint32_t>::max()] | |
| constexpr uint32_t multiplier = 0x015A4E35; //22695477 | |
| constexpr uint32_t increment = 1; // An increment of 0 would mean that the generator can never reach 0 from a non-zero | |
| // seed and a seed of 0 always results in a cycle of length 1 (0 -> 0) | |
| // The modulus term is implicitly used by choosing a datatype of uint32_t and allowing the value to wrap. | |
| constexpr auto mod = std::numeric_limits<uint32_t>::max() + 1LL; //4294967296 | |
| // The standard library defines a mod of 0 is interpreted as std::numeric_limits<T>::max() + 1 (with T being uint32_t) | |
| // This allows us to avoid having to cast to a wider datatype to represent a value larger than the target type. | |
| // The default constructor uses a default seed of 1. See C++ International Standard [rand.eng.lcong] | |
| std::linear_congruential_engine<uint32_t, multiplier, increment, 0> std_rand; | |
| // For a LCG starting with a seed of 0 results in the expression multiplier * 0 + increment, which simplifies to just increment. | |
| // Since the Borland increment is 1, 0 always generates 1 as the next in sequence which matches the std::lcg default seed. | |
| uint32_t seed = std_rand.default_seed; | |
| int32_t signedSeed = std_rand.default_seed; | |
| void AdvanceRndSeedSigned() | |
| { | |
| // This LCG implementation relies on implementation defined behaviour (converting an unsigned value to a signed | |
| // value of the same bit-field width). See C++17 [conv.integral] | |
| // In practice on two's complement systems this is treated the same as conversion from signed to unsigned, meaning | |
| // the bit pattern is unchanged. | |
| signedSeed = (multiplier * static_cast<uint32_t>(signedSeed)) + increment; // implied mod of std::numeric_limits<uint32_t>::max() | |
| //return abs(signedSeed); // this is part of the distribution function | |
| } | |
| void AdvanceRndSeedUnsigned() | |
| { | |
| seed = (multiplier * seed) + increment; | |
| //return abs(static_cast<int32_t>(seed)); // this is part of the distribution function | |
| } | |
| int main(int argc, char** argv) { | |
| //std::ofstream outFile{ "numbers.txt", std::ofstream::out }; | |
| std::map<int32_t, std::vector<std::pair<uint32_t, uint32_t>>> interestingValues; | |
| for (auto value : { | |
| std::numeric_limits<int32_t>::min(), //undefined behaviour for abs(min), implementation defined behaviour for >> | |
| -1, // should never be reached | |
| 0, | |
| 1, | |
| 64, // in case a distribution function special cases a power of 2 | |
| 65, | |
| 128, | |
| 7625, | |
| 32458, | |
| 32768, // shift mod distribution applied to int_min is expected to yield -32678. This should be treated as a distinct value | |
| 65534, // boundary cases for shift distribution function | |
| 65535, | |
| 22695477, | |
| 429496729, | |
| 1212022642, | |
| std::numeric_limits<int32_t>::max() - 1, | |
| std::numeric_limits<int32_t>::max() | |
| }) { | |
| interestingValues.emplace(value, std::move(std::vector<std::pair<uint32_t, uint32_t>>{})); | |
| }; | |
| uint64_t length = 0; | |
| auto prevSeed = std_rand.default_seed; | |
| do { | |
| AdvanceRndSeedSigned(); | |
| AdvanceRndSeedUnsigned(); | |
| const auto randSeed = std_rand(); | |
| ++length; | |
| if (randSeed != static_cast<uint32_t>(signedSeed) || randSeed != seed) { | |
| std::cout << "Chains diverged at length " << length | |
| << ", signed: " << signedSeed | |
| << ", unsigned: " << seed | |
| << ", std::random: " << randSeed << std::endl; | |
| return 1; | |
| } | |
| const auto absDistMapped = abs(static_cast<int32_t>(randSeed)); | |
| if (interestingValues.contains(absDistMapped)) { | |
| interestingValues[absDistMapped].push_back({ prevSeed, randSeed }); | |
| } | |
| prevSeed = randSeed; | |
| //uncomment if you have 40GB of space and about 6 hours to kill | |
| //outFile << seed << std::endl; | |
| } while (prevSeed != std_rand.default_seed); | |
| std::cout << "Chain looped after " << length << " values from a total of " << mod << " candidates." << std::endl; | |
| std::cout << "AbsDistribution yielded the following values from the given prior seed and current state:" << std::endl; | |
| for (auto value : interestingValues) { | |
| std::cout << value.first << ":" << std::endl; | |
| for (auto seeds : value.second) { | |
| std::cout << std::setw(14) << seeds.first << ", " << std::setw(10) << seeds.second << std::endl; | |
| } | |
| } | |
| return 0; | |
| } |
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