#include #include "engine/random.hpp" namespace devilution { // These tests use ASSERT_EQ as the PRNG is expected to depend on state from the last call, so one failing assertion // means the rest of the results can't be trusted. TEST(RandomTest, RandomEngineParams) { // The core diablo random number generator is an LCG with Borland constants. // This RNG must be available for network/save compatibility for things such as level generation. constexpr uint32_t multiplicand = 22695477; constexpr uint32_t increment = 1; SetRndSeed(0); // Starting from a seed of 0 means the multiplicand is dropped and the state advances by increment only ASSERT_EQ(GenerateSeed(), increment) << "Increment factor is incorrect"; // LCGs use a formula of mult * seed + inc. Using a long form in the code to document the expected factors. ASSERT_EQ(GenerateSeed(), (multiplicand * 1) + increment) << "Multiplicand factor is incorrect"; // C++11 defines the default seed for a LCG engine as 1. The ten thousandth value is commonly used for sanity checking // a sequence, so as we've had one round since state 1 we need to discard another 9998 values to get to the 10000th state. // To make off by one errors more visible test the 9999th value as well as 10000th DiscardRandomValues(9997); uint32_t expectedState = 3495122800U; EXPECT_EQ(GenerateSeed(), expectedState) << "Wrong engine state after 9999 invocations"; expectedState = 3007658545U; ASSERT_EQ(GenerateSeed(), expectedState) << "Wrong engine state after 10000 invocations"; } TEST(RandomTest, AbsDistribution) { // The default distribution for RNG calls is the absolute value of the generated value interpreted as a signed int // This relies on undefined behaviour when called on std::numeric_limits::min(). See C17 7.22.6.1 // The current behaviour is this returns the same value (the most negative number of the type). SetRndSeed(1457187811); // yields -2147483648 ASSERT_EQ(AdvanceRndSeed(), std::numeric_limits::min()) << "Invalid distribution"; SetRndSeed(3604671459U); // yields 0 ASSERT_EQ(AdvanceRndSeed(), 0) << "Invalid distribution"; SetRndSeed(0); // yields +1 ASSERT_EQ(AdvanceRndSeed(), 1) << "Invalid distribution"; SetRndSeed(2914375622U); // yields -1 ASSERT_EQ(AdvanceRndSeed(), 1) << "Invalid distribution"; SetRndSeed(3604671460U); // yields +22695477 ASSERT_EQ(AdvanceRndSeed(), 22695477) << "Invalid distribution"; SetRndSeed(3604671458U); // yields -22695477 ASSERT_EQ(AdvanceRndSeed(), 22695477) << "Invalid distribution"; SetRndSeed(1902003768); // yields +429496729 ASSERT_EQ(AdvanceRndSeed(), 429496729) << "Invalid distribution"; SetRndSeed(1012371854); // yields -429496729 ASSERT_EQ(AdvanceRndSeed(), 429496729) << "Invalid distribution"; SetRndSeed(189776845); // yields +1212022642 ASSERT_EQ(AdvanceRndSeed(), 1212022642) << "Invalid distribution"; SetRndSeed(2724598777U); // yields -1212022642 ASSERT_EQ(AdvanceRndSeed(), 1212022642) << "Invalid distribution"; SetRndSeed(76596137); // yields +2147483646 ASSERT_EQ(AdvanceRndSeed(), 2147483646) << "Invalid distribution"; SetRndSeed(2837779485U); // yields -2147483646 ASSERT_EQ(AdvanceRndSeed(), 2147483646) << "Invalid distribution"; SetRndSeed(766891974); // yields +2147483647 ASSERT_EQ(AdvanceRndSeed(), 2147483647) << "Invalid distribution"; SetRndSeed(2147483648U); // yields -2147483647 ASSERT_EQ(AdvanceRndSeed(), 2147483647) << "Invalid distribution"; } // The bounded distribution function used by Diablo performs a modulo operation on the result of the AbsDistribution // tested above, with a shift operation applied before the mod when the bound is < 65535. // // The current implementation does not allow testing these operations independantly, hopefully this can be changed // with confidence from these tests. // // The result of a mod b when a is negative was implementation defined before C++11, current behaviour is to // preserve the sign of a. See C++17 [expr.mul] and C++03 TR1 [expr.mul] TEST(RandomTest, ModDistributionInvalidRange) { // Calling the modulo distribution with an upper bound <= 0 returns 0 without advancing the engine auto initialSeed = 44444444; SetRndSeed(initialSeed); EXPECT_EQ(GenerateRnd(0), 0) << "A distribution with an upper bound of 0 must return 0"; EXPECT_EQ(GetLCGEngineState(), initialSeed) << "Distribution with invalid range must not advance the engine state"; EXPECT_EQ(GenerateRnd(-1), 0) << "A distribution with a negative upper bound must return 0"; EXPECT_EQ(GetLCGEngineState(), initialSeed) << "Distribution with invalid range must not advance the engine state"; EXPECT_EQ(GenerateRnd(std::numeric_limits::min()), 0) << "A distribution with a negative upper bound must return 0"; EXPECT_EQ(GetLCGEngineState(), initialSeed) << "Distribution with invalid range must not advance the engine state"; } TEST(RandomTest, ShiftModDistributionSingleRange) { // All results mod 1 = 0; auto initialSeed = ::testing::UnitTest::GetInstance()->random_seed(); SetRndSeed(initialSeed); for (auto i = 0; i < 100; i++) ASSERT_EQ(GenerateRnd(1), 0) << "Interval [0, 1) must return 0"; ASSERT_NE(GetLCGEngineState(), initialSeed) << "Interval of 1 element must still advance the engine state"; // Just in case -0 has a distinct representation? Shouldn't be possible but cheap to test. SetRndSeed(1457187811); ASSERT_EQ(GenerateRnd(1), 0) << "Interval [0, 1) must return 0 when AbsDistribution yields INT_MIN"; } // When called with an upper bound less than or equal to 0x7FFF this distribution function discards the low 16 bits of the output // from the default distribution by performing a shift right of 16 bits. This relies on implementation defined // behaviour for negative numbers, the expectation is shift right uses sign carry. See C++17 [expr.shift] TEST(RandomTest, ShiftModDistributionSignCarry) { // This distribution is used when the upper bound is a value in [1, 32768) // Using an upper bound of 1 means the result always maps to 0, see RandomTest_ShiftModDistributionSingleRange // The only negative value returned from AbsDistribution is -2147483648 // A sign-preserving shift right of 16 bits gives a result of -32768. // This is greater in magnitude than the limit so always results in a division. SetRndSeed(1457187811); // Test mod when a division occurs ASSERT_EQ(GenerateRnd(32767), -1) << "Distribution must map negative numbers using sign carry shifts"; } // The Diablo LCG implementation attempts to improve the quality of generated numbers that would only use the low // bits of the LCG output but due to applying this after taking the absolute value this introduces bias. This may // be an inconsistency with the implementation in devilutionx, see the comment for RandomTest_ShiftModDistributionHighBits TEST(RandomTest, ShiftModDistributionLowBits) { constexpr auto maxBound = 32767; // All the following seeds generate values less than 2^16, so after shifting they give a 0 value SetRndSeed(3604671459U); // yields 0 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 0"; SetRndSeed(0); // yields 1 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 1"; SetRndSeed(2914375622U); // yields -1 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -1"; SetRndSeed(538964771); // yields 64 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 64"; SetRndSeed(2375410851U); // yields -64 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -64"; SetRndSeed(1229260608); // yields 65 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 65"; SetRndSeed(1685115014); // yields -65 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -65"; SetRndSeed(1768225379); // yields 128 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 128"; SetRndSeed(1146150243); // yields -128 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -128"; SetRndSeed(1480523688); // yields 7625 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 7625"; SetRndSeed(1433851934); // yields -7625 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -7625"; SetRndSeed(2382565573U); // yields 32458 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 32458"; SetRndSeed(531810049); // yields -32458 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -32458"; SetRndSeed(1625910243); // yields 32768 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 32768"; SetRndSeed(1288465379); // yields -32768 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -32768"; // -1 from the max bound for the next two to ensure it's not due to a mod with no remainder SetRndSeed(2561524649U); // yields 65534 ASSERT_EQ(GenerateRnd(maxBound - 1), 0) << "Invalid distribution when generator yields 65534"; SetRndSeed(352850973U); // yields -65534 ASSERT_EQ(GenerateRnd(maxBound - 1), 0) << "Invalid distribution when generator yields -65534"; SetRndSeed(3251820486U); // yields 65535 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 65535"; SetRndSeed(3957522432U); // yields -65535 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -65535"; } // The highest value GenerateRnd can return is 32767 (0x7FFF). I suspect this is the Borland rand() implementation // Diablo appears to have reimplemented this method incorrectly as that function was implemented as the following: // uint seed = mult * seed + inc // return (seed >> 16) & 0x7FFF // i.e., no cast from unsigned to signed, no modulo when building the return value. TEST(RandomTest, ShiftModDistributionHighBits) { constexpr auto maxBound = 32767; SetRndSeed(3267226595U); // yields 65536 ASSERT_EQ(GenerateRnd(maxBound), 1) << "Invalid distribution when generator yields 65536"; SetRndSeed(3942116323U); // yields -65536 ASSERT_EQ(GenerateRnd(maxBound), 1) << "Invalid distribution when generator yields -65536"; SetRndSeed(4279561187U); // yields 131072 ASSERT_EQ(GenerateRnd(maxBound), 2) << "Invalid distribution when generator yields 131072"; SetRndSeed(2929781731U); // yields -131072 ASSERT_EQ(GenerateRnd(maxBound), 2) << "Invalid distribution when generator yields -131072"; SetRndSeed(659483619); // yields 262144 ASSERT_EQ(GenerateRnd(maxBound), 4) << "Invalid distribution when generator yields 262144"; SetRndSeed(2254892003U); // yields -262144 ASSERT_EQ(GenerateRnd(maxBound), 4) << "Invalid distribution when generator yields -262144"; SetRndSeed(3604671458U); // yields 22695477 ASSERT_EQ(GenerateRnd(maxBound), 346) << "Invalid distribution when generator yields 22695477"; SetRndSeed(3604671460U); // yields -22695477 ASSERT_EQ(GenerateRnd(maxBound), 346) << "Invalid distribution when generator yields -22695477"; SetRndSeed(1012371854); // yields 429496729 ASSERT_EQ(GenerateRnd(maxBound), 6553) << "Invalid distribution when generator yields 429496729"; SetRndSeed(1902003768); // yields -429496729 ASSERT_EQ(GenerateRnd(maxBound), 6553) << "Invalid distribution when generator yields -429496729"; SetRndSeed(189776845); // yields 1212022642 ASSERT_EQ(GenerateRnd(maxBound), 18493) << "Invalid distribution when generator yields 1212022642"; SetRndSeed(2724598777); // yields -1212022642 ASSERT_EQ(GenerateRnd(maxBound), 18493) << "Invalid distribution when generator yields -1212022642"; SetRndSeed(76596137); // yields 2147483646 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 2147483646"; SetRndSeed(2837779485); // yields -2147483646 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -2147483646"; SetRndSeed(766891974); // yields 2147483647 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields 2147483647"; SetRndSeed(2147483648); // yields -2147483647 ASSERT_EQ(GenerateRnd(maxBound), 0) << "Invalid distribution when generator yields -2147483647"; } TEST(RandomTest, ModDistributionSignPreserving) { // This distribution is used when the upper bound is a value in [32768, 2147483647] // Sign preserving modulo when no division is performed cannot be tested in isolation with the current implementation. SetRndSeed(1457187811); ASSERT_EQ(GenerateRnd(32768), 0) << "Distribution must map negative numbers using sign preserving modulo"; SetRndSeed(1457187811); ASSERT_EQ(GenerateRnd(32769), -2) << "Distribution must map negative numbers using sign preserving modulo"; SetRndSeed(1457187811); ASSERT_EQ(GenerateRnd(65535), -32768) << "Distribution must map negative numbers using sign preserving modulo"; SetRndSeed(1457187811); ASSERT_EQ(GenerateRnd(std::numeric_limits::max()), -1) << "Distribution must map negative numbers using sign preserving modulo"; } TEST(RandomTest, NegativeReturnValues) { // The bug in vanilla RNG stemming from mod instead of bitmasking means that negative values are possible for // non-power of 2 arguments to GenerateRnd SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(3), -2) << "Unexpected return value for a limit of 3"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(5), -3) << "Unexpected return value for a limit of 5"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(6), -2) << "Unexpected return value for a limit of 6"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(7), -1) << "Unexpected return value for a limit of 7"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(11), -10) << "Unexpected return value for a limit of 11"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(17), -9) << "Unexpected return value for a limit of 17"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(19), -12) << "Unexpected return value for a limit of 19"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(22), -10) << "Unexpected return value for a limit of 22"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(23), -16) << "Unexpected return value for a limit of 23"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(25), -18) << "Unexpected return value for a limit of 25"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(27), -17) << "Unexpected return value for a limit of 27"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(29), -27) << "Unexpected return value for a limit of 29"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(31), -1) << "Unexpected return value for a limit of 31"; for (int i : { 9, 10, 12, 13, 14, 15, 18, 20, 21, 24, 26, 28, 30 }) { SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(i), -8) << "Unexpected return value for a limit of " << i; } // The following values are/were used throughout the code SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(37), -23) << "Unexpected return value for a limit of 37"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(38), -12) << "Unexpected return value for a limit of 38"; SetRndSeed(1457187811); // commonly used for dungeon megatile coordinates EXPECT_EQ(GenerateRnd(40), -8) << "Unexpected return value for a limit of 40"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(41), -9) << "Unexpected return value for a limit of 41"; SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(52), -8) << "Unexpected return value for a limit of 52"; SetRndSeed(1457187811); // commonly used for dungeon tile coordinates EXPECT_EQ(GenerateRnd(80), -48) << "Unexpected return value for a limit of 80"; SetRndSeed(1457187811); // commonly used for percentage rolls (typically in a context that 0 and -68 lead to the same outcome) EXPECT_EQ(GenerateRnd(100), -68) << "Unexpected return value for a limit of 100"; for (int i = 1; i < 32768; i *= 2) { SetRndSeed(1457187811); EXPECT_EQ(GenerateRnd(i), 0) << "Expect powers of 2 such as " << i << " to cleanly divide the int_min RNG value "; } } } // namespace devilution