// Tencent is pleased to support the open source community by making RapidJSON available. // // Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip. All rights reserved. // // Licensed under the MIT License (the "License"); you may not use this file except // in compliance with the License. You may obtain a copy of the License at // // http://opensource.org/licenses/MIT // // Unless required by applicable law or agreed to in writing, software distributed // under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR // CONDITIONS OF ANY KIND, either express or implied. See the License for the // specific language governing permissions and limitations under the License. #include "unittest.h" #include "rapidjson/internal/strtod.h" #define BIGINTEGER_LITERAL(s) BigInteger(s, sizeof(s) - 1) using namespace rapidjson::internal; TEST(Strtod, CheckApproximationCase) { static const int kSignificandSize = 52; static const int kExponentBias = 0x3FF; static const uint64_t kExponentMask = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000); static const uint64_t kSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF); static const uint64_t kHiddenBit = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000); // http://www.exploringbinary.com/using-integers-to-check-a-floating-point-approximation/ // Let b = 0x1.465a72e467d88p-149 // = 5741268244528520 x 2^-201 union { double d; uint64_t u; }u; u.u = 0x465a72e467d88 | ((static_cast<uint64_t>(-149 + kExponentBias)) << kSignificandSize); const double b = u.d; const uint64_t bInt = (u.u & kSignificandMask) | kHiddenBit; const int bExp = ((u.u & kExponentMask) >> kSignificandSize) - kExponentBias - kSignificandSize; EXPECT_DOUBLE_EQ(1.7864e-45, b); EXPECT_EQ(RAPIDJSON_UINT64_C2(0x001465a7, 0x2e467d88), bInt); EXPECT_EQ(-201, bExp); // Let d = 17864 x 10-49 const char dInt[] = "17864"; const int dExp = -49; // Let h = 2^(bExp-1) const int hExp = bExp - 1; EXPECT_EQ(-202, hExp); int dS_Exp2 = 0; int dS_Exp5 = 0; int bS_Exp2 = 0; int bS_Exp5 = 0; int hS_Exp2 = 0; int hS_Exp5 = 0; // Adjust for decimal exponent if (dExp >= 0) { dS_Exp2 += dExp; dS_Exp5 += dExp; } else { bS_Exp2 -= dExp; bS_Exp5 -= dExp; hS_Exp2 -= dExp; hS_Exp5 -= dExp; } // Adjust for binary exponent if (bExp >= 0) bS_Exp2 += bExp; else { dS_Exp2 -= bExp; hS_Exp2 -= bExp; } // Adjust for half ulp exponent if (hExp >= 0) hS_Exp2 += hExp; else { dS_Exp2 -= hExp; bS_Exp2 -= hExp; } // Remove common power of two factor from all three scaled values int common_Exp2 = std::min(dS_Exp2, std::min(bS_Exp2, hS_Exp2)); dS_Exp2 -= common_Exp2; bS_Exp2 -= common_Exp2; hS_Exp2 -= common_Exp2; EXPECT_EQ(153, dS_Exp2); EXPECT_EQ(0, dS_Exp5); EXPECT_EQ(1, bS_Exp2); EXPECT_EQ(49, bS_Exp5); EXPECT_EQ(0, hS_Exp2); EXPECT_EQ(49, hS_Exp5); BigInteger dS = BIGINTEGER_LITERAL(dInt); dS.MultiplyPow5(dS_Exp5) <<= dS_Exp2; BigInteger bS(bInt); bS.MultiplyPow5(bS_Exp5) <<= bS_Exp2; BigInteger hS(1); hS.MultiplyPow5(hS_Exp5) <<= hS_Exp2; EXPECT_TRUE(BIGINTEGER_LITERAL("203970822259994138521801764465966248930731085529088") == dS); EXPECT_TRUE(BIGINTEGER_LITERAL("203970822259994122305215569213032722473144531250000") == bS); EXPECT_TRUE(BIGINTEGER_LITERAL("17763568394002504646778106689453125") == hS); EXPECT_EQ(1, dS.Compare(bS)); BigInteger delta(0); EXPECT_FALSE(dS.Difference(bS, &delta)); EXPECT_TRUE(BIGINTEGER_LITERAL("16216586195252933526457586554279088") == delta); EXPECT_TRUE(bS.Difference(dS, &delta)); EXPECT_TRUE(BIGINTEGER_LITERAL("16216586195252933526457586554279088") == delta); EXPECT_EQ(-1, delta.Compare(hS)); }