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https://github.com/XRPLF/rippled.git
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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
@@ -185,6 +185,8 @@ Number::normalize()
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--exponent_;
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}
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Guard g;
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if (negative)
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g.set_negative();
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while (m > maxMantissa)
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{
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if (exponent_ >= maxExponent)
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@@ -364,6 +366,8 @@ Number::operator*=(Number const& y)
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auto ze = xe + ye;
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auto zn = xn * yn;
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Guard g;
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if (zn == -1)
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g.set_negative();
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while (zm > maxMantissa)
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{
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g.push(static_cast<unsigned>(zm % 10));
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@@ -402,8 +406,11 @@ Number::operator/=(Number const& y)
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{
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if (y == Number{})
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throw std::overflow_error("Number: divide by 0");
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if (*this == Number{})
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return *this;
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int np = 1;
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auto nm = mantissa();
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auto ne = exponent();
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if (nm < 0)
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{
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nm = -nm;
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@@ -411,35 +418,19 @@ Number::operator/=(Number const& y)
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}
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int dp = 1;
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auto dm = y.mantissa();
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auto de = y.exponent();
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if (dm < 0)
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{
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dm = -dm;
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dp = -1;
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}
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// Divide numerator and denominator such that the
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// denominator is in the range [1, 10).
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const int offset = -15 - y.exponent();
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Number n{nm * (np * dp), exponent() + offset};
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Number d{dm, y.exponent() + offset};
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// Quadratic least squares fit to 1/x in the range [1, 10]
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constexpr Number a0{9178756872006464, -16, unchecked{}};
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constexpr Number a1{-2149215784206187, -16, unchecked{}};
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constexpr Number a2{1405502114116773, -17, unchecked{}};
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static_assert(a0.isnormal());
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static_assert(a1.isnormal());
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static_assert(a2.isnormal());
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Number rm2{};
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Number rm1{};
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Number r = (a2 * d + a1) * d + a0;
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// Newton–Raphson iteration of 1/x - d with initial guess r
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// halt when r stops changing, checking for bouncing on the last iteration
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do
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{
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rm2 = rm1;
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rm1 = r;
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r = r + r * (one - d * r);
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} while (r != rm1 && r != rm2);
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*this = n * r;
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// Shift by 10^17 gives greatest precision while not overflowing uint128_t
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// or the cast back to int64_t
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const uint128_t f = 100'000'000'000'000'000;
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mantissa_ = static_cast<std::int64_t>(uint128_t(nm) * f / uint128_t(dm));
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exponent_ = ne - de - 17;
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mantissa_ *= np * dp;
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normalize();
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return *this;
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}
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@@ -150,6 +150,8 @@ 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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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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@@ -169,6 +171,73 @@ public:
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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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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{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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