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Experimental: Scale addition operands up to preserve accuracy
This commit is contained in:
Ed Hennis
@@ -43,6 +43,15 @@ class Number_test : public beast::unit_test::Suite
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return out;
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}
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static BigInt
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toBigInt(Number const& n)
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{
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BigInt v = n.mantissa();
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for (int i = 0; i < n.exponent(); ++i)
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v *= 10;
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return v;
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}
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using dec = boost::multiprecision::cpp_dec_float_50;
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template <class T = dec>
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@@ -169,28 +178,34 @@ public:
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auto const scale = Number::getMantissaScale();
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testcase << "test_add " << to_string(scale);
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using Case = std::tuple<Number, Number, Number>;
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using Case = std::tuple<Number, Number, Number, int>;
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auto const cSmall = std::to_array<Case>(
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{{Number{1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'066, -15}},
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Number{1'000'000'000'000'066, -15},
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__LINE__},
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{Number{-1'000'000'000'000'000, -15},
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Number{-6'555'555'555'555'555, -29},
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Number{-1'000'000'000'000'066, -15}},
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Number{-1'000'000'000'000'066, -15},
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__LINE__},
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{Number{-1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{-9'999'999'999'999'344, -16}},
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Number{-9'999'999'999'999'344, -16},
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__LINE__},
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{Number{-6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'000, -15},
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Number{9'999'999'999'999'344, -16}},
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{Number{}, Number{5}, Number{5}},
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{Number{5}, Number{}, Number{5}},
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Number{9'999'999'999'999'344, -16},
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__LINE__},
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{Number{}, Number{5}, Number{5}, __LINE__},
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{Number{5}, Number{}, Number{5}, __LINE__},
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{Number{5'555'555'555'555'555, -32768},
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Number{-5'555'555'555'555'554, -32768},
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Number{0}},
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Number{0},
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__LINE__},
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{Number{-9'999'999'999'999'999, -31},
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Number{1'000'000'000'000'000, -15},
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Number{9'999'999'999'999'990, -16}}});
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Number{9'999'999'999'999'990, -16},
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__LINE__}});
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auto const cLarge = std::to_array<Case>(
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// Note that items with extremely large mantissas need to be
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// calculated, because otherwise they overflow uint64. Items from C
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@@ -198,45 +213,57 @@ public:
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{
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{Number{1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'065'556, -18}},
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Number{1'000'000'000'000'065'556, -18},
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__LINE__},
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{Number{-1'000'000'000'000'000, -15},
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Number{-6'555'555'555'555'555, -29},
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Number{-1'000'000'000'000'065'556, -18}},
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Number{-1'000'000'000'000'065'556, -18},
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__LINE__},
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{Number{-1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{-6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'000, -15},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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{Number{}, Number{5}, Number{5}},
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{Number{5}, Number{}, Number{5}},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{}, Number{5}, Number{5}, __LINE__},
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{Number{5}, Number{}, Number{5}, __LINE__},
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{Number{5'555'555'555'555'555'000, -32768},
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Number{-5'555'555'555'555'554'000, -32768},
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Number{0}},
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Number{0},
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__LINE__},
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{Number{-9'999'999'999'999'999, -31},
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Number{1'000'000'000'000'000, -15},
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Number{9'999'999'999'999'990, -16}},
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Number{9'999'999'999'999'990, -16},
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__LINE__},
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// Items from cSmall expanded for the larger mantissa
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{Number{1'000'000'000'000'000'000, -18},
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Number{6'555'555'555'555'555'555, -35},
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Number{1'000'000'000'000'000'066, -18}},
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Number{1'000'000'000'000'000'066, -18},
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__LINE__},
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{Number{-1'000'000'000'000'000'000, -18},
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Number{-6'555'555'555'555'555'555, -35},
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Number{-1'000'000'000'000'000'066, -18}},
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Number{-1'000'000'000'000'000'066, -18},
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__LINE__},
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{Number{-1'000'000'000'000'000'000, -18},
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Number{6'555'555'555'555'555'555, -35},
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Number{true, 9'999'999'999'999'999'344ULL, -19, Number::Normalized{}}},
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Number{true, 9'999'999'999'999'999'344ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{-6'555'555'555'555'555'555, -35},
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Number{1'000'000'000'000'000'000, -18},
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Number{false, 9'999'999'999'999'999'344ULL, -19, Number::Normalized{}}},
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{Number{}, Number{5}, Number{5}},
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Number{false, 9'999'999'999'999'999'344ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{}, Number{5}, Number{5}, __LINE__},
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{Number{5'555'555'555'555'555'555, -32768},
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Number{-5'555'555'555'555'555'554, -32768},
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Number{0}},
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Number{0},
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__LINE__},
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{Number{true, 9'999'999'999'999'999'999ULL, -37, Number::Normalized{}},
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Number{1'000'000'000'000'000'000, -18},
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Number{false, 9'999'999'999'999'999'990ULL, -19, Number::Normalized{}}},
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{Number{Number::kMaxRep - 1}, Number{1, 0}, Number{Number::kMaxRep}},
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Number{false, 9'999'999'999'999'999'990ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{Number::kMaxRep - 1}, Number{1, 0}, Number{Number::kMaxRep}, __LINE__},
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// Test extremes
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{
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// Each Number operand rounds up, so the actual mantissa is
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@@ -244,6 +271,7 @@ public:
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Number{false, 9'999'999'999'999'999'999ULL, 0, Number::Normalized{}},
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Number{false, 9'999'999'999'999'999'999ULL, 0, Number::Normalized{}},
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Number{2, 19},
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__LINE__,
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},
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{
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// Does not round. Mantissas are going to be > kMaxRep, so if
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@@ -254,21 +282,25 @@ public:
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Number{false, 9'999'999'999'999'999'990ULL, 0, Number::Normalized{}},
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Number{false, 9'999'999'999'999'999'990ULL, 0, Number::Normalized{}},
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Number{false, 1'999'999'999'999'999'998ULL, 1, Number::Normalized{}},
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__LINE__,
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},
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});
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auto const cLargeLegacy = std::to_array<Case>({
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{Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep / 10, 1}},
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{Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep / 10, 1}, __LINE__},
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});
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auto const cLargeCorrected = std::to_array<Case>({
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{Number{Number::kMaxRep}, Number{6, -1}, Number{(Number::kMaxRep / 10) + 1, 1}},
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{Number{Number::kMaxRep},
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Number{6, -1},
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Number{(Number::kMaxRep / 10) + 1, 1},
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__LINE__},
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});
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auto test = [this](auto const& c) {
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for (auto const& [x, y, z] : c)
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for (auto const& [x, y, z, line] : c)
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{
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auto const result = x + y;
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std::stringstream ss;
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ss << x << " + " << y << " = " << result << ". Expected: " << z;
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BEAST_EXPECTS(result == z, ss.str());
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expect(result == z, ss.str(), __FILE__, line);
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}
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};
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if (scale == MantissaRange::MantissaScale::Small)
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@@ -308,21 +340,28 @@ public:
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auto const scale = Number::getMantissaScale();
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testcase << "test_sub " << to_string(scale);
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using Case = std::tuple<Number, Number, Number>;
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using Case = std::tuple<Number, Number, Number, int>;
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auto const cSmall = std::to_array<Case>(
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{{Number{1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{9'999'999'999'999'344, -16}},
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Number{9'999'999'999'999'344, -16},
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__LINE__},
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{Number{6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'000, -15},
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Number{-9'999'999'999'999'344, -16}},
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{Number{1'000'000'000'000'000, -15}, Number{1'000'000'000'000'000, -15}, Number{0}},
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Number{-9'999'999'999'999'344, -16},
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__LINE__},
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{Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'000, -15},
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Number{0},
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__LINE__},
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{Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'001, -15},
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Number{-1'000'000'000'000'000, -30}},
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Number{-1'000'000'000'000'000, -30},
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__LINE__},
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{Number{1'000'000'000'000'001, -15},
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Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'000, -30}}});
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Number{1'000'000'000'000'000, -30},
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__LINE__}});
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auto const cLarge = std::to_array<Case>(
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// Note that items with extremely large mantissas need to be
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// calculated, because otherwise they overflow uint64. Items from C
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@@ -330,49 +369,63 @@ public:
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{
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{Number{1'000'000'000'000'000, -15},
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Number{6'555'555'555'555'555, -29},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{6'555'555'555'555'555, -29},
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Number{1'000'000'000'000'000, -15},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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{Number{1'000'000'000'000'000, -15}, Number{1'000'000'000'000'000, -15}, Number{0}},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'000, -15},
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Number{0},
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__LINE__},
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{Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'001, -15},
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Number{-1'000'000'000'000'000, -30}},
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Number{-1'000'000'000'000'000, -30},
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__LINE__},
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{Number{1'000'000'000'000'001, -15},
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Number{1'000'000'000'000'000, -15},
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Number{1'000'000'000'000'000, -30}},
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Number{1'000'000'000'000'000, -30},
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__LINE__},
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// Items from cSmall expanded for the larger mantissa
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{Number{1'000'000'000'000'000'000, -18},
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Number{6'555'555'555'555'555'555, -32},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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Number{false, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{6'555'555'555'555'555'555, -32},
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Number{1'000'000'000'000'000'000, -18},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}}},
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Number{true, 9'999'999'999'999'344'444ULL, -19, Number::Normalized{}},
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__LINE__},
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{Number{1'000'000'000'000'000'000, -18},
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Number{1'000'000'000'000'000'000, -18},
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Number{0}},
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Number{0},
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__LINE__},
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{Number{1'000'000'000'000'000'000, -18},
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Number{1'000'000'000'000'000'001, -18},
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Number{-1'000'000'000'000'000'000, -36}},
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Number{-1'000'000'000'000'000'000, -36},
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__LINE__},
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{Number{1'000'000'000'000'000'001, -18},
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Number{1'000'000'000'000'000'000, -18},
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Number{1'000'000'000'000'000'000, -36}},
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{Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep - 1}},
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Number{1'000'000'000'000'000'000, -36},
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__LINE__},
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{Number{Number::kMaxRep}, Number{6, -1}, Number{Number::kMaxRep - 1}, __LINE__},
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{Number{false, Number::kMaxRep + 1, 0, Number::Normalized{}},
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Number{1, 0},
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Number{(Number::kMaxRep / 10) + 1, 1}},
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Number{(Number::kMaxRep / 10) + 1, 1},
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__LINE__},
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{Number{false, Number::kMaxRep + 1, 0, Number::Normalized{}},
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Number{3, 0},
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Number{Number::kMaxRep}},
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{power(2, 63), Number{3, 0}, Number{Number::kMaxRep}},
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Number{Number::kMaxRep},
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__LINE__},
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{power(2, 63), Number{3, 0}, Number{Number::kMaxRep}, __LINE__},
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});
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auto test = [this](auto const& c) {
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for (auto const& [x, y, z] : c)
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for (auto const& [x, y, z, line] : c)
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{
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auto const result = x - y;
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std::stringstream ss;
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ss << x << " - " << y << " = " << result << ". Expected: " << z;
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BEAST_EXPECTS(result == z, ss.str());
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expect(result == z, ss.str(), __FILE__, line);
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}
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};
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if (scale == MantissaRange::MantissaScale::Small)
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@@ -1644,9 +1697,7 @@ public:
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BigInt const exactProduct = BigInt(kAValue) * BigInt(kBValue);
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// What Number actually stored.
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BigInt storedValue = BigInt(product.mantissa());
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for (int i = 0; i < product.exponent(); ++i)
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storedValue *= 10;
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BigInt storedValue = toBigInt(product);
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BigInt const signedDifference = storedValue - exactProduct;
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@@ -1900,18 +1951,83 @@ public:
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<< " Downward = " << downward << "\n\n";
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log.flush();
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// Upward round UP
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BEAST_EXPECT(upward == above);
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switch (scale)
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{
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case MantissaRange::MantissaScale::Small:
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// With the small mantissa, everything rounds up
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// ToNearest rounds UP when the DOWN neighbor is strictly closer
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BEAST_EXPECT(toNearest != above);
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BEAST_EXPECT(toNearest == below);
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// Upward round UP
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BEAST_EXPECT(upward > above);
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// Downward undershoots: it returns a value below `below`
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BEAST_EXPECT(downward == below);
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// ToNearest rounds UP when the DOWN neighbor is strictly closer
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BEAST_EXPECT(toNearest > above);
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BEAST_EXPECT(toNearest == below);
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// Both should have given the same answer, but they differ
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BEAST_EXPECT(toNearest == downward);
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// Downward undershoots: it returns a value below `below`
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BEAST_EXPECT(downward < below);
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// Both should have given the same answer, but they differ
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BEAST_EXPECT(toNearest > downward);
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break;
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case MantissaRange::MantissaScale::LargeLegacy:
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// Upward round UP
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BEAST_EXPECT(upward == above);
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// ToNearest rounds UP when the DOWN neighbor is strictly closer
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BEAST_EXPECT(toNearest == above);
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BEAST_EXPECT(toNearest > below);
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// Downward undershoots: it returns a value below `below`
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BEAST_EXPECT(downward < below);
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// Both should have given the same answer, but they differ
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BEAST_EXPECT(toNearest > downward);
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break;
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default:
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// Upward round UP
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BEAST_EXPECT(upward == above);
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// ToNearest rounds UP when the DOWN neighbor is strictly closer
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BEAST_EXPECT(toNearest != above);
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BEAST_EXPECT(toNearest == below);
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// Downward undershoots: it returns a value below `below`
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BEAST_EXPECT(downward == below);
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// Both should have given the same answer, but they differ
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BEAST_EXPECT(toNearest == downward);
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}
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||||
}
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{
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testcase << "operator+ TowardsZero rounds away from zero " << to_string(scale);
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||||
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Number const a{1LL, 20};
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Number const b{-1'000'000'000'000'000'001LL};
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BEAST_EXPECT(toBigInt(a) == BigInt{"100000000000000000000"});
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if (scale != MantissaRange::MantissaScale::Small)
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BEAST_EXPECT(toBigInt(b) == BigInt{"-1000000000000000001"});
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else
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||||
BEAST_EXPECT(toBigInt(b) == BigInt{"-1000000000000000000"});
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||||
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||||
Number sum;
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||||
{
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||||
NumberRoundModeGuard const roundGuard{Number::RoundingMode::TowardsZero};
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||||
sum = a + b;
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||||
}
|
||||
|
||||
BigInt const exact = toBigInt(a) + toBigInt(b);
|
||||
BigInt const stored = toBigInt(sum);
|
||||
|
||||
log << "\n exact a + b = " << exact.str() << "\n TowardsZero = " << stored.str()
|
||||
<< "\n";
|
||||
log.flush();
|
||||
|
||||
if (scale != MantissaRange::MantissaScale::LargeLegacy)
|
||||
BEAST_EXPECT(stored == exact);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user