mantissa_util: Implement ResidualErrorOnRightShift

Accurately calculate residual error that is shifted out

src/CMakeLists.txt

@@ -18,6 +18,7 @@ add_library(dynarmic
     common/crc32.h
     common/fp/fpsr.h
     common/fp/info.h
+    common/fp/mantissa_util.h
     common/fp/process_exception.cpp
     common/fp/process_exception.h
     common/fp/rounding_mode.h

src/common/fp/mantissa_util.h

@@ -0,0 +1,48 @@
+/* This file is part of the dynarmic project.
+ * Copyright (c) 2018 MerryMage
+ * This software may be used and distributed according to the terms of the GNU
+ * General Public License version 2 or any later version.
+ */
+
+#pragma once
+
+#include "common/bit_util.h"
+#include "common/common_types.h"
+
+namespace Dynarmic::FP {
+
+enum class ResidualError {
+    Zero,
+    LessThanHalf,
+    Half,
+    GreaterThanHalf,
+};
+
+template<typename MantissaT>
+ResidualError ResidualErrorOnRightShift(MantissaT mantissa, int shift_amount) {
+    if (shift_amount <= 0 || mantissa == 0) {
+        return ResidualError::Zero;
+    }
+
+    if (shift_amount > static_cast<int>(Common::BitSize<MantissaT>())) {
+        return Common::MostSignificantBit(mantissa) ? ResidualError::GreaterThanHalf : ResidualError::LessThanHalf;
+    }
+
+    const size_t half_bit_position = static_cast<size_t>(shift_amount - 1);
+    const MantissaT half = static_cast<MantissaT>(1) << half_bit_position;
+    const MantissaT error_mask = Common::Ones<MantissaT>(static_cast<size_t>(shift_amount));
+    const MantissaT error = mantissa & error_mask;
+
+    if (error == 0) {
+        return ResidualError::Zero;
+    }
+    if (error < half) {
+        return ResidualError::LessThanHalf;
+    }
+    if (error == half) {
+        return ResidualError::Half;
+    }
+    return ResidualError::GreaterThanHalf;
+}
+
+} // namespace Dynarmic::FP 

tests/CMakeLists.txt

@@ -29,6 +29,7 @@ add_executable(dynarmic_tests
     A64/inst_gen.cpp
     A64/inst_gen.h
     A64/testenv.h
+    fp/mantissa_util_tests.cpp
     fp/unpacked_tests.cpp
     main.cpp
     mp.cpp

tests/fp/mantissa_util_tests.cpp

@@ -0,0 +1,63 @@
+/* This file is part of the dynarmic project.
+ * Copyright (c) 2018 MerryMage
+ * This software may be used and distributed according to the terms of the GNU
+ * General Public License version 2 or any later version.
+ */
+
+#include <tuple>
+#include <vector>
+
+#include <catch.hpp>
+
+#include "common/fp/mantissa_util.h"
+#include "common/safe_ops.h"
+#include "rand_int.h"
+
+using namespace Dynarmic;
+using namespace Dynarmic::FP;
+
+TEST_CASE("ResidualErrorOnRightShift", "[fp]") {
+    const std::vector<std::tuple<u32, int, ResidualError>> test_cases {
+        {0x00000001, 1, ResidualError::Half},
+        {0x00000002, 1, ResidualError::Zero},
+        {0x00000001, 2, ResidualError::LessThanHalf},
+        {0x00000002, 2, ResidualError::Half},
+        {0x00000003, 2, ResidualError::GreaterThanHalf},
+        {0x00000004, 2, ResidualError::Zero},
+        {0x00000005, 2, ResidualError::LessThanHalf},
+        {0x00000006, 2, ResidualError::Half},
+        {0x00000007, 2, ResidualError::GreaterThanHalf},
+    };
+
+    for (auto [mantissa, shift, expected_result] : test_cases) {
+        const ResidualError result = ResidualErrorOnRightShift(mantissa, shift);
+        REQUIRE(result == expected_result);
+    }
+}
+
+TEST_CASE("ResidualErrorOnRightShift Randomized", "[fp]") {
+    for (size_t test = 0; test < 100000; test++) {
+        const u32 mantissa = RandInt<u32>(0, 0xFFFFFFFF);
+        const int shift = RandInt<int>(-60, 60);
+
+        const ResidualError result = ResidualErrorOnRightShift(mantissa, shift);
+
+        const u64 calculated_error = Safe::ArithmeticShiftRightDouble(Common::SignExtend<32, u64>(mantissa), u64(0), shift);
+        const ResidualError expected_result = [&]{
+            constexpr u64 half_error = 0x8000'0000'0000'0000ull;
+            if (calculated_error == 0) {
+                return ResidualError::Zero;
+            }
+            if (calculated_error < half_error) {
+                return ResidualError::LessThanHalf;
+            }
+            if (calculated_error == half_error) {
+                return ResidualError::Half;
+            }
+            return ResidualError::GreaterThanHalf;
+        }();
+
+        INFO(std::hex << "mantissa " << mantissa << " shift " << shift << " calculated_error " << calculated_error);
+        REQUIRE(result == expected_result);
+    }
+}