590 lines
26 KiB
C#
590 lines
26 KiB
C#
using System.Numerics;
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using Shouldly;
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using Xunit;
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namespace Just.PreciseMath.Tests;
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public class DoubleDoubleArithmeticTests
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{
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[Fact]
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public void CancellationRetainsBothLowSumTerms()
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{
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double small = Math.ScaleB(1.0, -54);
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double tiny = Math.ScaleB(1.0, -108);
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DoubleDouble left = DoubleDouble.FromComponents(1.0, small);
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DoubleDouble right = DoubleDouble.FromComponents(-1.0, tiny);
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Check(left + right, small, tiny);
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Check(right + left, small, tiny);
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Check(left - (-right), small, tiny);
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Check(+left, 1.0, small);
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Check(-left, -1.0, -small);
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Check(left - left, 0.0, 0.0);
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}
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[Fact]
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public void ScalarOverloadsPreserveOperandOrderAndResiduals()
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{
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DoubleDouble value = DoubleDouble.FromComponents(2.0, Math.ScaleB(1.0, -80));
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Check(3.0 - value, 1.0, -value.Low);
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Check(value - 3.0, -1.0, value.Low);
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Check(value + 3.0, 5.0, value.Low);
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Check(3.0 + value, 5.0, value.Low);
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Check(value * 2.0, 4.0, 2.0 * value.Low);
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Check(2.0 * value, 4.0, 2.0 * value.Low);
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Check(value / 2.0, 1.0, value.Low / 2.0);
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Check(6.0 / new DoubleDouble(2.0), 3.0, 0.0);
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}
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[Fact]
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public void ExpansionCancellationRetainsExactComponentsAcrossTheAdditionGuard()
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{
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// (2^e + 2^(e-54)) - (2^e - 2^(e-108)) is exactly the
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// normalized pair (2^(e-54), 2^(e-108)). The smallest residual
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// is epsilon; the largest case exercises the boundary fallback.
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foreach (int exponent in new[] { -966, -450, 0, 450, 1020, 1021 })
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{
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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double high = sign * Math.ScaleB(1.0, exponent);
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double small = sign * Math.ScaleB(1.0, exponent - 54);
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double tiny = sign * Math.ScaleB(1.0, exponent - 108);
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DoubleDouble left = DoubleDouble.FromComponents(high, small);
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DoubleDouble right = DoubleDouble.FromComponents(high, -tiny);
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CheckBoundary(left - right, small, tiny);
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CheckBoundary(right - left, -small, -tiny);
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CheckBoundary(left + (-right), small, tiny);
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CheckBoundary((-right) + left, small, tiny);
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CheckBoundary(left - left, 0.0, 0.0);
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}
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}
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}
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[Fact]
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public void ExpansionSubtractionHandlesSpecialValuesAlongsideNonzeroResiduals()
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{
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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DoubleDouble value = DoubleDouble.FromComponents(sign, sign * double.Epsilon);
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foreach (double special in new[] { 0.0, -0.0, double.NegativeInfinity, double.PositiveInfinity, double.NaN })
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{
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DoubleDouble other = new(special);
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if (special == 0.0)
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{
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CheckBoundary(value - other, value.High, value.Low);
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CheckBoundary(other - value, -value.High, -value.Low);
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}
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else
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{
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CheckBits(value - other, sign - special);
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CheckBits(other - value, special - sign);
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}
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}
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}
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}
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[Fact]
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public void ScalarLeftSubtractionAppliesTheRequestedOperandOrder()
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{
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// Review-1 §1: the former operator -(double, DoubleDouble) returned arg - lvalue,
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// so 3.0 - DD(2.0) produced -1 instead of 1.
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Check(3.0 - new DoubleDouble(2.0), 1.0, 0.0);
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Check(new DoubleDouble(2.0) - 3.0, -1.0, 0.0);
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Check(3.0 - DoubleDouble.FromComponents(2.0, Math.ScaleB(1.0, -80)), 1.0, -Math.ScaleB(1.0, -80));
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Check(DoubleDouble.FromComponents(2.0, Math.ScaleB(1.0, -80)) - 3.0, -1.0, Math.ScaleB(1.0, -80));
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}
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[Fact]
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public void DivisionByAValueCarriedOnlyInTheLowComponentIsFinite()
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{
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// Review-2 §5: with high == 0 and low != 0 the former division returned
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// Infinity because it divided by the zero high component. The public factory
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// now folds such a pair into its high component, so the quotient is finite.
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DoubleDouble denominator = DoubleDouble.FromComponents(0.0, 1.0);
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Check(denominator, 1.0, 0.0);
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Check(new DoubleDouble(4.0) / denominator, 4.0, 0.0);
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Check(4.0 / denominator, 4.0, 0.0);
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Check(new DoubleDouble(4.0) / DoubleDouble.FromComponents(0.0, -2.0), -2.0, 0.0);
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}
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[Fact]
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public void ScalarCancellationPreservesTheRemainingExpansionInBothOrders()
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{
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// At a normal binade boundary, 2^e - BitDecrement(2^e) = 2^(e-53).
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// The low input becomes the representable residual of that exact difference.
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foreach (int exponent in new[] { -967, -900, -450, 0, 450, 969, 1020, 1023 })
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{
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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double high = Math.ScaleB(1.0, exponent);
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double low = sign * Math.ScaleB(1.0, exponent - 107);
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double scalar = sign * Math.BitDecrement(high);
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double difference = sign * Math.ScaleB(1.0, exponent - 53);
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DoubleDouble value = DoubleDouble.FromComponents(sign * high, low);
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Check(value - scalar, difference, low);
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Check(scalar - value, -difference, -low);
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Check(value + (-scalar), difference, low);
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Check((-scalar) + value, difference, low);
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}
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}
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}
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[Fact]
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public void MixedSpecialValuesIgnoreFiniteResidualsButPreserveResultSigns()
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{
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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DoubleDouble value = DoubleDouble.FromComponents(sign, sign * Math.ScaleB(1.0, -54));
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foreach (double scalar in new[] { double.NaN, double.NegativeInfinity, double.PositiveInfinity })
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{
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CheckBits(value + scalar, sign + scalar);
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CheckBits(scalar + value, scalar + sign);
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CheckBits(value - scalar, sign - scalar);
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CheckBits(scalar - value, scalar - sign);
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CheckBits(value * scalar, sign * scalar);
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CheckBits(scalar * value, scalar * sign);
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CheckBits(value / scalar, sign / scalar);
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CheckBits(scalar / value, scalar / sign);
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}
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foreach (double zero in new[] { 0.0, -0.0 })
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{
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CheckBits(value * zero, sign * zero);
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CheckBits(zero * value, zero * sign);
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CheckBits(value / zero, sign / zero);
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CheckBits(zero / value, zero / sign);
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Check(value + zero, value.High, value.Low);
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Check(zero + value, value.High, value.Low);
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Check(value - zero, value.High, value.Low);
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Check(zero - value, -value.High, -value.Low);
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}
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}
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}
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[Fact]
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public void ProductAndQuotientRetainExtraPrecision()
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{
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// (1 + 2^-52)(1 - 2^-52) = 1 - 2^-104 exactly.
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Check(new DoubleDouble(1.0 + Math.ScaleB(1.0, -52)) * new DoubleDouble(1.0 - Math.ScaleB(1.0, -52)),
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1.0, -Math.ScaleB(1.0, -104));
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// Binary expansion of 1/3, rounding high then residual ties-to-even.
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Check(DoubleDouble.One / 3.0, 0.3333333333333333, 1.850371707708594e-17);
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}
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[Fact]
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public void ScalarProductNormalizesACorrectionBeyondTheHighMidpoint()
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{
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// (1 + 2^-53)(1 + 2^-52) = 1 + 3*2^-53 + 2^-105, exactly.
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// The rounded high advances twice above 1; its residual is still exact.
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DoubleDouble value = DoubleDouble.FromComponents(1.0, Math.ScaleB(1.0, -53));
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double scalar = Math.BitIncrement(1.0);
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double high = 1.0 + Math.ScaleB(1.0, -51);
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double low = -Math.ScaleB(1.0, -53) + Math.ScaleB(1.0, -105);
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Check(value * scalar, high, low);
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Check(scalar * value, high, low);
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Check(value * (-scalar), -high, -low);
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Check((-scalar) * value, -high, -low);
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CheckBoundary(value * new DoubleDouble(scalar), high, low);
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CheckBoundary(new DoubleDouble(scalar) * value, high, low);
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CheckBoundary(value * new DoubleDouble(-scalar), -high, -low);
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CheckBoundary(new DoubleDouble(-scalar) * value, -high, -low);
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}
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[Fact]
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public void ExpansionProductRetainsTheLowLowTermAtFastRangeEndpoints()
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{
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// (1 + 2^-53)(1 - 2^-54) = 1 + 2^-54 - 2^-107 exactly.
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// Its residual is BitDecrement(2^-54); omitting low*low loses that bit.
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// Power-of-two scaling keeps both expected components representable,
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// including exponent sums at each inclusive fast-path endpoint.
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foreach (int leftExponent in new[] { -450, 0, 450 })
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{
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foreach (int rightExponent in new[] { -450, 0, 450 })
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{
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foreach (double leftSign in new[] { -1.0, 1.0 })
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{
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foreach (double rightSign in new[] { -1.0, 1.0 })
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{
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DoubleDouble left = DoubleDouble.FromComponents(leftSign * Math.ScaleB(1.0, leftExponent),
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leftSign * Math.ScaleB(1.0, leftExponent - 53));
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DoubleDouble right = DoubleDouble.FromComponents(rightSign * Math.ScaleB(1.0, rightExponent),
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-rightSign * Math.ScaleB(1.0, rightExponent - 54));
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int exponent = leftExponent + rightExponent;
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double sign = leftSign * rightSign;
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double high = sign * Math.ScaleB(1.0, exponent);
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double low = sign * Math.ScaleB(Math.BitDecrement(Math.ScaleB(1.0, -54)), exponent);
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CheckBoundary(left * right, high, low);
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CheckBoundary(right * left, high, low);
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}
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}
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}
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}
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}
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[Fact]
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public void ScalarDivisionRetainsNumeratorAndDenominatorResiduals()
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{
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double low = Math.ScaleB(1.0, -80);
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DoubleDouble value = DoubleDouble.FromComponents(1.0, low);
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Check(value / 1.0, 1.0, low);
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Check(value / (-1.0), -1.0, -low);
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// Compare the reciprocal to its exact rational, not another DD operator.
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BigInteger numerator = BigInteger.One << 2148;
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AssertRelative(1.0 / value, numerator, Units(value));
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AssertRelative(-1.0 / value, -numerator, Units(value));
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}
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[Fact]
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public void DivisionRetainsSubnormalCorrectionsWithOrdinaryHighComponents()
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{
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// Dividing (1 + epsilon) by +/-1 is exact. The outer division is
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// ordinary, but its second residual product can use the boundary path.
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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DoubleDouble numerator = DoubleDouble.FromComponents(sign, sign * double.Epsilon);
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foreach (double denominator in new[] { -1.0, 1.0 })
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{
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double high = sign / denominator;
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double low = high * double.Epsilon;
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CheckBoundary(numerator / new DoubleDouble(denominator), high, low);
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CheckBoundary(numerator / denominator, high, low);
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}
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}
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}
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[Fact]
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public void SubnormalProductsWithLargeNormalsRetainExactResultsInBothOrders()
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{
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// 2^-1074 * 2^1023 = 2^-51 exactly, despite the subnormal input.
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foreach (double leftSign in new[] { -1.0, 1.0 })
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{
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foreach (double rightSign in new[] { -1.0, 1.0 })
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{
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double tiny = leftSign * double.Epsilon;
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double large = rightSign * Math.ScaleB(1.0, 1023);
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double expected = (leftSign * rightSign) * Math.ScaleB(1.0, -51);
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DoubleDouble left = new(tiny);
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DoubleDouble right = new(large);
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CheckBoundary(left * right, expected, 0.0);
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CheckBoundary(right * left, expected, 0.0);
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CheckBoundary(left * large, expected, 0.0);
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CheckBoundary(large * left, expected, 0.0);
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CheckBoundary(tiny * right, expected, 0.0);
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CheckBoundary(right * tiny, expected, 0.0);
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}
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}
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}
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[Fact]
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public void ExtremeFiniteOperationsDoNotOverflowIntermediates()
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{
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DoubleDouble maximum = new(double.MaxValue);
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DoubleDouble third = maximum / 3.0;
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DoubleDouble thirdPair = maximum / new DoubleDouble(3.0);
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DoubleDouble thirdScalar = double.MaxValue / new DoubleDouble(3.0);
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AssertRelative(third, Units(maximum), 3);
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thirdPair.ShouldBe(third);
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thirdScalar.ShouldBe(third);
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Check(new DoubleDouble(double.Epsilon) / new DoubleDouble(double.Epsilon), 1.0, 0.0);
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Check(new DoubleDouble(double.Epsilon) * new DoubleDouble(Math.ScaleB(1.0, 1023)), Math.ScaleB(1.0, -51), 0.0);
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Check(new DoubleDouble(Math.ScaleB(1.0, -1022)) / 2.0, Math.ScaleB(1.0, -1023), 0.0);
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Check(maximum * 2.0, double.PositiveInfinity, 0.0);
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Check(maximum + maximum, double.PositiveInfinity, 0.0);
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// High-only addition overflows, but the complete sum is exactly MaxValue.
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DoubleDouble below = DoubleDouble.FromComponents(double.MaxValue, -Math.ScaleB(1.0, 969));
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Check(below + Math.ScaleB(1.0, 969), double.MaxValue, 0.0);
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}
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[Fact]
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public void SubnormalHighProductsRetainANormalPartnersResidual()
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{
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// (2^-1074, 0) * (2^1023, 2^969) = (2^-51, 2^-105), exactly.
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// The high product is ordinary despite the subnormal input high.
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foreach (double leftSign in new[] { -1.0, 1.0 })
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{
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foreach (double rightSign in new[] { -1.0, 1.0 })
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{
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double scalar = leftSign * double.Epsilon;
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DoubleDouble tiny = new(scalar);
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DoubleDouble large = DoubleDouble.FromComponents(rightSign * Math.ScaleB(1.0, 1023),
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rightSign * Math.ScaleB(1.0, 969));
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double high = (leftSign * rightSign) * Math.ScaleB(1.0, -51);
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double low = (leftSign * rightSign) * Math.ScaleB(1.0, -105);
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CheckBoundary(tiny * large, high, low);
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CheckBoundary(large * tiny, high, low);
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CheckBoundary(scalar * large, high, low);
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CheckBoundary(large * scalar, high, low);
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}
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}
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}
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[Theory]
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[InlineData(1.0)]
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[InlineData(-1.0)]
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public void ExactOverflowMidpointStillOverflows(double sign)
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{
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DoubleDouble maximum = new(sign * double.MaxValue);
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double halfUlp = sign * Math.ScaleB(1.0, 970);
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Check(maximum + halfUlp, sign * double.PositiveInfinity, 0.0);
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Check(maximum - (-halfUlp), sign * double.PositiveInfinity, 0.0);
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Check(DoubleDouble.FromComponents(sign * double.MaxValue, halfUlp), sign * double.PositiveInfinity, 0.0);
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}
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[Theory]
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[InlineData(-1)]
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[InlineData(0)]
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[InlineData(1)]
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public void ProductAndQuotientCrossTheExactOverflowMidpoint(int side)
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{
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// M = 2^1024 - 2^970. M/2 is the normalized pair (2^1023, -2^969).
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// Its adjacent normalized pairs use different highs across this tie:
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// below uses (MaxValue/2, BitDecrement(2^969)), above increments -2^969.
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// Doubling gives M +/- 2^917; below has residual BitDecrement(2^970).
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// The tie rounds to the even significand at 2^1024, hence infinity.
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double high = side < 0 ? Math.ScaleB(double.MaxValue, -1) : Math.ScaleB(1.0, 1023);
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double low = side switch
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{
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-1 => Math.BitDecrement(Math.ScaleB(1.0, 969)),
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1 => Math.BitIncrement(-Math.ScaleB(1.0, 969)),
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_ => -Math.ScaleB(1.0, 969)
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};
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BigInteger midpointUnits = Units(double.MaxValue) + Units(Math.ScaleB(1.0, 970));
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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DoubleDouble value = DoubleDouble.FromComponents(sign * high, sign * low);
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(BigInteger.Abs(Units(value)) * 2).ShouldBe(midpointUnits + (side * Units(Math.ScaleB(1.0, 917))));
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double expectedHigh = sign * (side < 0 ? double.MaxValue : double.PositiveInfinity);
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double expectedLow = side < 0 ? sign * Math.BitDecrement(Math.ScaleB(1.0, 970)) : 0.0;
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CheckBoundary(value * new DoubleDouble(2.0), expectedHigh, expectedLow);
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CheckBoundary(new DoubleDouble(2.0) * value, expectedHigh, expectedLow);
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CheckBoundary(value * 2.0, expectedHigh, expectedLow);
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CheckBoundary(2.0 * value, expectedHigh, expectedLow);
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CheckBoundary(value / new DoubleDouble(0.5), expectedHigh, expectedLow);
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CheckBoundary(value / 0.5, expectedHigh, expectedLow);
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}
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}
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[Theory]
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[InlineData(false)]
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[InlineData(true)]
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public void ScalarLeftDivisionStraddlesTheOverflowMidpoint(bool below)
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{
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// An exact M = (2^54 - 1)*2^970 quotient is impossible with a finite
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// binary64 numerator and dyadic denominator: its odd numerator would
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// need all 54 bits. Instead use adjacent low components bracketing
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// 2^1023/M = 1/2 + 2^-55 + 2^-109 + ... .
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double low = Math.ScaleB(1.0, -55);
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DoubleDouble denominator = DoubleDouble.FromComponents(0.5, below ? Math.BitIncrement(low) : low);
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BigInteger midpointUnits = Units(double.MaxValue) + Units(Math.ScaleB(1.0, 970));
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BigInteger numeratorUnits = Units(Math.ScaleB(1.0, 1023));
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((numeratorUnits << 1074) < midpointUnits * Units(denominator)).ShouldBe(below);
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// Exact rational residual rounding gives BitDecrement(2^970) below M.
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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double numerator = sign * Math.ScaleB(1.0, 1023);
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double high = sign * (below ? double.MaxValue : double.PositiveInfinity);
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double residual = below ? sign * Math.BitDecrement(Math.ScaleB(1.0, 970)) : 0.0;
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CheckBoundary(numerator / denominator, high, residual);
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CheckBoundary(new DoubleDouble(numerator) / denominator, high, residual);
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CheckBoundary((-numerator) / (-denominator), high, residual);
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}
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}
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[Theory]
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[InlineData(-1)]
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[InlineData(0)]
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[InlineData(1)]
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public void ProductAndQuotientRoundUnderflowTiesToSignedZero(int side)
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{
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// (2^-1022 + side*2^-1074)*2^-53 = epsilon/2 + side*2^-1127.
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// The low component is stepped by its smallest possible increment.
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// Ties select even zero, retaining the exact nonzero result's sign.
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foreach (double sign in new[] { -1.0, 1.0 })
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{
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DoubleDouble value = DoubleDouble.FromComponents(sign * Math.ScaleB(1.0, -1022), sign * side * double.Epsilon);
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double multiplier = Math.ScaleB(1.0, -53);
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double divisor = Math.ScaleB(1.0, 53);
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double expected = Math.CopySign(side > 0 ? double.Epsilon : 0.0, sign);
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CheckBits(value * new DoubleDouble(multiplier), expected);
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CheckBits(new DoubleDouble(multiplier) * value, expected);
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CheckBits(value * multiplier, expected);
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CheckBits(multiplier * value, expected);
|
|
CheckBits(value / new DoubleDouble(divisor), expected);
|
|
CheckBits(value / divisor, expected);
|
|
|
|
// epsilon/(2 - side*epsilon) brackets the same tie; the nonzero
|
|
// denominator residual is essential despite being invisible in double.
|
|
DoubleDouble denominator = DoubleDouble.FromComponents(2.0, -side * double.Epsilon);
|
|
CheckBits((sign * double.Epsilon) / denominator, expected);
|
|
CheckBits(new DoubleDouble(sign * double.Epsilon) / denominator, expected);
|
|
CheckBits((-sign * double.Epsilon) / (-denominator), expected);
|
|
}
|
|
}
|
|
|
|
[Theory]
|
|
[InlineData(0)]
|
|
[InlineData(1)]
|
|
[InlineData(2)]
|
|
[InlineData(3)]
|
|
[InlineData(4)]
|
|
[InlineData(5)]
|
|
[InlineData(6)]
|
|
[InlineData(7)]
|
|
[InlineData(8)]
|
|
[InlineData(9)]
|
|
[InlineData(10)]
|
|
[InlineData(11)]
|
|
public void WarmedFiniteArithmeticAllocatesSubstantiallyLessThanBoundaryFallback(int operation)
|
|
{
|
|
DoubleDouble ordinary = DoubleDouble.FromComponents(1.25, Math.ScaleB(1.0, -70));
|
|
DoubleDouble boundary = DoubleDouble.FromComponents(Math.ScaleB(1.0, 1022), Math.ScaleB(1.0, 968));
|
|
DoubleDouble right = DoubleDouble.FromComponents(1.5, Math.ScaleB(1.0, -55));
|
|
// Synchronous per-thread counters exclude other parallel tests. Warm both
|
|
// branches, keep setup/assertions outside measurement, and consume results.
|
|
_ = MeasureArithmeticAllocations(operation, ordinary, right, 128, out _);
|
|
_ = MeasureArithmeticAllocations(operation, boundary, right, 128, out _);
|
|
long ordinaryBytes = long.MaxValue;
|
|
long boundaryBytes = long.MaxValue;
|
|
for (int sample = 0; sample < 3; ++sample)
|
|
{
|
|
long finite = MeasureArithmeticAllocations(operation, ordinary, right, 256, out double finiteChecksum);
|
|
long fallback = MeasureArithmeticAllocations(operation, boundary, right, 256, out double fallbackChecksum);
|
|
double.IsFinite(finiteChecksum).ShouldBeTrue();
|
|
double.IsFinite(fallbackChecksum).ShouldBeTrue();
|
|
ordinaryBytes = Math.Min(ordinaryBytes, finite);
|
|
boundaryBytes = Math.Min(boundaryBytes, fallback);
|
|
}
|
|
// A coarse relative distinction, not a runtime-dependent BigInteger byte
|
|
// count or timing benchmark. Minima discard incidental warm-up allocation.
|
|
boundaryBytes.ShouldBeGreaterThan(0L);
|
|
ordinaryBytes.ShouldBeLessThan(boundaryBytes / 16);
|
|
}
|
|
|
|
private static long MeasureArithmeticAllocations(int operation, DoubleDouble left, DoubleDouble right, int iterations, out double checksum)
|
|
{
|
|
checksum = 0.0;
|
|
long before = GC.GetAllocatedBytesForCurrentThread();
|
|
for (int i = 0; i < iterations; ++i)
|
|
{
|
|
DoubleDouble result = operation switch
|
|
{
|
|
0 => left + right,
|
|
1 => left - right,
|
|
2 => left * right,
|
|
3 => left / right,
|
|
4 => left + right.High,
|
|
5 => right.High + left,
|
|
6 => left - right.High,
|
|
7 => right.High - left,
|
|
8 => left * right.High,
|
|
9 => right.High * left,
|
|
10 => left / right.High,
|
|
11 => right.High / left,
|
|
_ => throw new ArgumentOutOfRangeException(nameof(operation))
|
|
};
|
|
// Scale before accumulation so boundary-sized results cannot overflow.
|
|
checksum += Math.ScaleB(result.High, -1023) + Math.ScaleB(result.Low, -1023);
|
|
}
|
|
return GC.GetAllocatedBytesForCurrentThread() - before;
|
|
}
|
|
|
|
private static void CheckBoundary(DoubleDouble value, double high, double low)
|
|
{
|
|
BitConverter.DoubleToInt64Bits(value.High).ShouldBe(BitConverter.DoubleToInt64Bits(high));
|
|
BitConverter.DoubleToInt64Bits(value.Low).ShouldBe(BitConverter.DoubleToInt64Bits(low));
|
|
}
|
|
|
|
[Fact]
|
|
public void SpecialValueMatrixMatchesBinary64IncludingZeroSigns()
|
|
{
|
|
double[] values = [0.0, -0.0, 1.0, -1.0, double.PositiveInfinity, double.NegativeInfinity, double.NaN];
|
|
foreach (double left in values)
|
|
{
|
|
foreach (double right in values)
|
|
{
|
|
DoubleDouble a = new(left);
|
|
DoubleDouble b = new(right);
|
|
CheckBits(a + b, left + right);
|
|
CheckBits(a - b, left - right);
|
|
CheckBits(a * b, left * right);
|
|
CheckBits(a / b, left / right);
|
|
CheckBits(a + right, left + right);
|
|
CheckBits(left + b, left + right);
|
|
CheckBits(a - right, left - right);
|
|
CheckBits(left - b, left - right);
|
|
CheckBits(a * right, left * right);
|
|
CheckBits(left * b, left * right);
|
|
CheckBits(a / right, left / right);
|
|
CheckBits(left / b, left / right);
|
|
}
|
|
}
|
|
}
|
|
|
|
[Fact]
|
|
public void DeterministicArithmeticMeetsConservativeErrorBound()
|
|
{
|
|
Random random = new(1729);
|
|
for (int i = 0; i < 250; ++i)
|
|
{
|
|
DoubleDouble a = DoubleDouble.FromComponents(Math.ScaleB((random.NextDouble() * 2.0) - 1.0, random.Next(-400, 401)),
|
|
Math.ScaleB(random.NextDouble(), random.Next(-500, -450)));
|
|
DoubleDouble b = DoubleDouble.FromComponents(Math.ScaleB((random.NextDouble() * 2.0) - 1.0, random.Next(-400, 401)),
|
|
Math.ScaleB(random.NextDouble(), random.Next(-500, -450)));
|
|
BigInteger x = Units(a);
|
|
BigInteger y = Units(b);
|
|
AssertRelative(a + b, x + y, BigInteger.One);
|
|
AssertRelative(a - b, x - y, BigInteger.One);
|
|
AssertRelative(a * b, x * y, BigInteger.One << 1074);
|
|
AssertRelative(a / b, x << 1074, y);
|
|
}
|
|
}
|
|
|
|
private static void Check(DoubleDouble value, double high, double low)
|
|
{
|
|
value.High.ShouldBe(high);
|
|
value.Low.ShouldBe(low);
|
|
}
|
|
|
|
private static void CheckBits(DoubleDouble value, double expected)
|
|
{
|
|
if (double.IsNaN(expected))
|
|
{
|
|
DoubleDouble.IsNaN(value).ShouldBeTrue();
|
|
}
|
|
else
|
|
{
|
|
BitConverter.DoubleToInt64Bits(value.High).ShouldBe(BitConverter.DoubleToInt64Bits(expected));
|
|
}
|
|
BitConverter.DoubleToInt64Bits(value.Low).ShouldBe(0L);
|
|
}
|
|
|
|
// Independent oracle: every finite binary64 is an integer multiple of 2^-1074.
|
|
private static BigInteger Units(DoubleDouble value)
|
|
{
|
|
return Units(value.High) + Units(value.Low);
|
|
}
|
|
|
|
private static BigInteger Units(double value)
|
|
{
|
|
long bits = BitConverter.DoubleToInt64Bits(value);
|
|
int exponent = (int)((bits >> 52) & 0x7ff);
|
|
BigInteger significand = bits & 0xfffffffffffffL;
|
|
if (exponent != 0)
|
|
{
|
|
significand += BigInteger.One << 52;
|
|
significand <<= exponent - 1;
|
|
}
|
|
return bits < 0 ? -significand : significand;
|
|
}
|
|
|
|
private static void AssertRelative(DoubleDouble actual, BigInteger numerator, BigInteger denominator)
|
|
{
|
|
DoubleDouble.IsFinite(actual).ShouldBeTrue();
|
|
BigInteger error = BigInteger.Abs((Units(actual) * denominator) - numerator);
|
|
// <= 2^-100 relative error plus one minimum subnormal (rounding floor).
|
|
(error <= (BigInteger.Abs(numerator) >> 100) + BigInteger.Abs(denominator)).ShouldBeTrue();
|
|
if (actual.High != 0.0)
|
|
{
|
|
(Math.Abs(actual.Low) <= Math.ScaleB(1.0, Math.ILogB(actual.High) - 53)).ShouldBeTrue();
|
|
}
|
|
}
|
|
}
|