// Copyright Epic Games, Inc. All Rights Reserved. #include #include #include namespace zen { ReciprocalU64::ReciprocalU64(uint64_t Divisor) { if (Divisor <= 1) { Mul = 0; // Sentinel — Divide() returns Value directly. Shift = 0; return; } // m = ceil(2^(64+s) / d). Start with s = 0; bump s only if // the quotient doesn't fit in 64 bits (happens when d is a // power of two, since 2^64 / 2^k = 2^(64-k) exactly and the // +1 for ceil can overflow to zero). for (uint32_t S = 0; S < 64; ++S) { #if ZEN_PLATFORM_WINDOWS uint64_t Remainder = 0; uint64_t Quotient = _udiv128(uint64_t(1) << S, 0, Divisor, &Remainder); uint64_t M = Quotient + (Remainder ? 1 : 0); // ceil #else unsigned __int128 Num = (unsigned __int128)(uint64_t(1) << S) << 64; uint64_t Quotient = uint64_t(Num / Divisor); uint64_t Remainder = uint64_t(Num % Divisor); uint64_t M = Quotient + (Remainder ? 1 : 0); #endif if (M != 0) { Mul = M; Shift = S; return; } } // Unreachable for any Divisor > 1. Mul = 0; Shift = 0; } ////////////////////////////////////////////////////////////////////////// // // Testing related code follows... // #if ZEN_WITH_TESTS void intmath_forcelink() { } TEST_SUITE_BEGIN("core.intmath"); TEST_CASE("intmath") { CHECK(FloorLog2(0x00) == 0); CHECK(FloorLog2(0x01) == 0); CHECK(FloorLog2(0x0f) == 3); CHECK(FloorLog2(0x10) == 4); CHECK(FloorLog2(0x11) == 4); CHECK(FloorLog2(0x12) == 4); CHECK(FloorLog2(0x22) == 5); CHECK(FloorLog2(0x0001'0000) == 16); CHECK(FloorLog2(0x0001'000f) == 16); CHECK(FloorLog2(0x8000'0000) == 31); CHECK(FloorLog2_64(0x00ull) == 0); CHECK(FloorLog2_64(0x01ull) == 0); CHECK(FloorLog2_64(0x0full) == 3); CHECK(FloorLog2_64(0x10ull) == 4); CHECK(FloorLog2_64(0x11ull) == 4); CHECK(FloorLog2_64(0x0001'0000ull) == 16); CHECK(FloorLog2_64(0x0001'000full) == 16); CHECK(FloorLog2_64(0x8000'0000ull) == 31); CHECK(FloorLog2_64(0x0000'0001'0000'0000ull) == 32); CHECK(FloorLog2_64(0x8000'0000'0000'0000ull) == 63); CHECK(CountLeadingZeros(0x8000'0000u) == 0); CHECK(CountLeadingZeros(0x0000'0000u) == 32); CHECK(CountLeadingZeros(0x0000'0001u) == 31); CHECK(CountLeadingZeros(0x0000'8000u) == 16); CHECK(CountLeadingZeros(0x0001'0000u) == 15); CHECK(CountLeadingZeros64(0x8000'0000'0000'0000ull) == 0); CHECK(CountLeadingZeros64(0x0000'0000'0000'0000ull) == 64); CHECK(CountLeadingZeros64(0x0000'0000'0000'0001ull) == 63); CHECK(CountLeadingZeros64(0x0000'0000'8000'0000ull) == 32); CHECK(CountLeadingZeros64(0x0000'0001'0000'0000ull) == 31); CHECK(CountTrailingZeros64(0x8000'0000'0000'0000ull) == 63); CHECK(CountTrailingZeros64(0x0000'0000'0000'0000ull) == 64); CHECK(CountTrailingZeros64(0x0000'0000'0000'0001ull) == 0); CHECK(CountTrailingZeros64(0x0000'0000'8000'0000ull) == 31); CHECK(CountTrailingZeros64(0x0000'0001'0000'0000ull) == 32); CHECK(ByteSwap(uint16_t(0x6d72)) == 0x726d); CHECK(ByteSwap(uint32_t(0x2741'3965)) == 0x6539'4127); CHECK(ByteSwap(uint64_t(0x214d'6172'7469'6e21ull)) == 0x216e'6974'7261'4d21ull); } TEST_CASE("ReciprocalU64 matches integer division") { uint64_t Divisors[] = {1, 2, 3, 4, 5, 7, 10, 100, 1000, 3000, 3579}; for (uint64_t D : Divisors) { ReciprocalU64 R(D); uint64_t TestValues[] = { 0, 1, D - 1, D, D + 1, D * 2, D * 2 + 1, 1'000'000, 10'000'000, 100'000'000, 1'000'000'000ULL, 10'000'000'000ULL, 100'000'000'000ULL, 1'000'000'000'000ULL, uint64_t(~0u), }; for (uint64_t V : TestValues) { uint32_t Expected = uint32_t(V / D); uint32_t Got = R.Divide(V); CHECK_MESSAGE(Got == Expected, "V=", V, " D=", D, " expected=", Expected, " got=", Got); } } } TEST_CASE("ReciprocalU64 rounding division") { // Verify the rounding pattern used in AbsorbBatch: (Cycle + half) / d uint64_t Divisors[] = {3, 4, 5, 10, 3579}; for (uint64_t D : Divisors) { ReciprocalU64 R(D); uint64_t Half = D >> 1; uint64_t TestCycles[] = {0, 1, 100, 999'999, 1'000'000, 99'999'999, 1'000'000'000ULL, 50'000'000'000ULL}; for (uint64_t Cycle : TestCycles) { uint64_t Rounded = Cycle + Half; uint32_t Expected = uint32_t(Rounded / D); uint32_t Got = R.Divide(Rounded); CHECK_MESSAGE(Got == Expected, "Cycle=", Cycle, " D=", D, " expected=", Expected, " got=", Got); } } } TEST_SUITE_END(); #endif } // namespace zen