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Replace Number division algorithm
* Replace division with faster algorithm. * Correct some rounding bugs in multiplication. * Add tests for rounding bugs.
This commit is contained in:
Howard Hinnant
committed by
Elliot Lee
Elliot Lee
parent
e354497f63
commit
6eaaa7bcfa
@@ -150,25 +150,94 @@ public:
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{
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testcase("test_mul");
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using Case = std::tuple<Number, Number, Number>;
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Case c[]{
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{Number{7}, Number{8}, Number{56}},
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{Number{1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{-2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{-1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{3214285714285706, -15},
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Number{3111111111111119, -15},
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Number{1000000000000000, -14}},
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{Number{1000000000000000, -32768},
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Number{1000000000000000, -32768},
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Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x * y == z);
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saveNumberRoundMode save{Number::setround(Number::to_nearest)};
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{
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Case c[]{
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{Number{7}, Number{8}, Number{56}},
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{Number{1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{-2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{-1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{3214285714285706, -15},
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Number{3111111111111119, -15},
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Number{1000000000000000, -14}},
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{Number{1000000000000000, -32768},
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Number{1000000000000000, -32768},
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Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x * y == z);
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}
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Number::setround(Number::towards_zero);
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{
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Case c[]{
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{Number{7}, Number{8}, Number{56}},
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{Number{1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{1999999999999999, -15}},
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{Number{-1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{-1999999999999999, -15}},
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{Number{-1414213562373095, -15},
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Number{-1414213562373095, -15},
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Number{1999999999999999, -15}},
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{Number{3214285714285706, -15},
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Number{3111111111111119, -15},
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Number{9999999999999999, -15}},
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{Number{1000000000000000, -32768},
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Number{1000000000000000, -32768},
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Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x * y == z);
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}
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Number::setround(Number::downward);
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{
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Case c[]{
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{Number{7}, Number{8}, Number{56}},
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{Number{1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{1999999999999999, -15}},
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{Number{-1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{-2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{-1414213562373095, -15},
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Number{1999999999999999, -15}},
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{Number{3214285714285706, -15},
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Number{3111111111111119, -15},
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Number{9999999999999999, -15}},
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{Number{1000000000000000, -32768},
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Number{1000000000000000, -32768},
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Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x * y == z);
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}
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Number::setround(Number::upward);
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{
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Case c[]{
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{Number{7}, Number{8}, Number{56}},
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{Number{1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{-1414213562373095, -15},
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Number{1414213562373095, -15},
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Number{-1999999999999999, -15}},
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{Number{-1414213562373095, -15},
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Number{-1414213562373095, -15},
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Number{2000000000000000, -15}},
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{Number{3214285714285706, -15},
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Number{3111111111111119, -15},
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Number{1000000000000000, -14}},
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{Number{1000000000000000, -32768},
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Number{1000000000000000, -32768},
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Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x * y == z);
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}
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bool caught = false;
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try
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{
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@@ -187,13 +256,78 @@ public:
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{
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testcase("test_div");
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using Case = std::tuple<Number, Number, Number>;
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Case c[]{
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{Number{1}, Number{2}, Number{5, -1}},
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{Number{1}, Number{10}, Number{1, -1}},
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{Number{1}, Number{-10}, Number{-1, -1}},
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{Number{0}, Number{100}, Number{0}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x / y == z);
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saveNumberRoundMode save{Number::setround(Number::to_nearest)};
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{
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Case c[]{
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{Number{1}, Number{2}, Number{5, -1}},
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{Number{1}, Number{10}, Number{1, -1}},
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{Number{1}, Number{-10}, Number{-1, -1}},
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{Number{0}, Number{100}, Number{0}},
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{Number{1414213562373095, -10},
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Number{1414213562373095, -10},
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Number{1}},
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{Number{9'999'999'999'999'999},
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Number{1'000'000'000'000'000},
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Number{9'999'999'999'999'999, -15}},
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{Number{2}, Number{3}, Number{6'666'666'666'666'667, -16}},
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{Number{-2}, Number{3}, Number{-6'666'666'666'666'667, -16}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x / y == z);
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}
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Number::setround(Number::towards_zero);
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{
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Case c[]{
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{Number{1}, Number{2}, Number{5, -1}},
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{Number{1}, Number{10}, Number{1, -1}},
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{Number{1}, Number{-10}, Number{-1, -1}},
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{Number{0}, Number{100}, Number{0}},
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{Number{1414213562373095, -10},
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Number{1414213562373095, -10},
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Number{1}},
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{Number{9'999'999'999'999'999},
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Number{1'000'000'000'000'000},
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Number{9'999'999'999'999'999, -15}},
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{Number{2}, Number{3}, Number{6'666'666'666'666'666, -16}},
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{Number{-2}, Number{3}, Number{-6'666'666'666'666'666, -16}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x / y == z);
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}
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Number::setround(Number::downward);
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{
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Case c[]{
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{Number{1}, Number{2}, Number{5, -1}},
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{Number{1}, Number{10}, Number{1, -1}},
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{Number{1}, Number{-10}, Number{-1, -1}},
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{Number{0}, Number{100}, Number{0}},
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{Number{1414213562373095, -10},
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Number{1414213562373095, -10},
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Number{1}},
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{Number{9'999'999'999'999'999},
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Number{1'000'000'000'000'000},
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Number{9'999'999'999'999'999, -15}},
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{Number{2}, Number{3}, Number{6'666'666'666'666'666, -16}},
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{Number{-2}, Number{3}, Number{-6'666'666'666'666'667, -16}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x / y == z);
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}
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Number::setround(Number::upward);
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{
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Case c[]{
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{Number{1}, Number{2}, Number{5, -1}},
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{Number{1}, Number{10}, Number{1, -1}},
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{Number{1}, Number{-10}, Number{-1, -1}},
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{Number{0}, Number{100}, Number{0}},
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{Number{1414213562373095, -10},
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Number{1414213562373095, -10},
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Number{1}},
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{Number{9'999'999'999'999'999},
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Number{1'000'000'000'000'000},
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Number{9'999'999'999'999'999, -15}},
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{Number{2}, Number{3}, Number{6'666'666'666'666'667, -16}},
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{Number{-2}, Number{3}, Number{-6'666'666'666'666'666, -16}}};
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for (auto const& [x, y, z] : c)
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BEAST_EXPECT(x / y == z);
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}
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bool caught = false;
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try
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{
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