public void Expm1Test()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Expm1(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(Math.Exp((double)x) - 1, y, ignore_sign: true);
}
}
public void RcpRawTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = 1 / x;
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(1 / (double)x, y);
}
}
public void AbsTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Abs(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(Math.Abs((double)x), y);
}
}
public void LdexpTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Ldexp(x, 1);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance((double)x * 2, y);
}
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Ldexp(x, -1);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance((double)x / 2, y);
}
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Ldexp(x, 2);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance((double)x * 4, y);
}
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Ldexp(x, -2);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance((double)x / 4, y);
}
}
public void ExpTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Exp(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(Math.Exp((double)x), y);
}
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(
MultiPrecision <Pow2.N8> .E,
MultiPrecision <Pow2.N8> .Exp(1), 1));
Assert.IsTrue(MultiPrecision <Pow2.N16> .NearlyEqualBits(
MultiPrecision <Pow2.N16> .E,
MultiPrecision <Pow2.N16> .Exp(1), 1));
}
public void RcpTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Rcp(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(1 / (double)x, y);
}
Assert.AreEqual(1, MultiPrecision <Pow2.N8> .Rcp(1));
Assert.AreEqual(0.5, MultiPrecision <Pow2.N8> .Rcp(2));
Assert.AreEqual(2, MultiPrecision <Pow2.N8> .Rcp(0.5));
Assert.AreEqual(1, MultiPrecision <Pow2.N16> .Rcp(1));
Assert.AreEqual(0.5, MultiPrecision <Pow2.N16> .Rcp(2));
Assert.AreEqual(2, MultiPrecision <Pow2.N16> .Rcp(0.5));
}
public void ToStringTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>().Concat(TestTool.LimitSet <Pow2.N8>()))
{
foreach (MultiPrecision <Pow2.N8> v in TestTool.EnumerateNeighbor(x, x.IsZero ? 0 : 2))
{
(Sign sign, Int64 exponent_dec, Accumulator <Pow2.N8> mantissa_dec) = v.ToStringCore(MultiPrecision <Pow2.N8> .DecimalDigits);
Console.WriteLine(sign);
Console.WriteLine(exponent_dec);
Console.WriteLine(mantissa_dec);
Console.WriteLine(v.ToString());
Console.WriteLine($"{v:E10}");
Console.WriteLine(v.ToString("e10"));
MultiPrecision <Pow2.N8> u = v.ToString();
Console.WriteLine(u.ToString());
Console.WriteLine(v.ToHexcode());
Console.WriteLine(u.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N8> .NearlyEqualBits(v, u, 14));
Assert.AreEqual((double)v, double.Parse(v.ToString()), Math.Abs((double)v) * 1e-8);
}
}
foreach (MultiPrecision <Pow2.N16> x in TestTool.AllRangeSet <Pow2.N16>().Concat(TestTool.LimitSet <Pow2.N16>()))
{
foreach (MultiPrecision <Pow2.N16> v in TestTool.EnumerateNeighbor(x, x.IsZero ? 0 : 2))
{
(Sign sign, Int64 exponent_dec, Accumulator <Pow2.N16> mantissa_dec) = v.ToStringCore(MultiPrecision <Pow2.N16> .DecimalDigits);
Console.WriteLine(sign);
Console.WriteLine(exponent_dec);
Console.WriteLine(mantissa_dec);
Console.WriteLine(v.ToString());
Console.WriteLine($"{v:E10}");
Console.WriteLine(v.ToString("e10"));
MultiPrecision <Pow2.N16> u = v.ToString();
Console.WriteLine(u.ToString());
Console.WriteLine(v.ToHexcode());
Console.WriteLine(u.ToHexcode());
Assert.IsTrue(MultiPrecision <Pow2.N16> .NearlyEqualBits(v, u, 14));
Assert.AreEqual((double)v, double.Parse(v.ToString()), Math.Abs((double)v) * 1e-8);
}
}
for (long i = int.MinValue; i < int.MinValue + 120; i++)
{
MultiPrecision <Pow2.N8> v = new MultiPrecision <Pow2.N8>(Sign.Plus, i, Mantissa <Pow2.N8> .One, round: false);
(Sign sign, Int64 exponent_dec, Accumulator <Pow2.N8> mantissa_dec) = v.ToStringCore(MultiPrecision <Pow2.N8> .DecimalDigits);
Console.WriteLine(sign);
Console.WriteLine(exponent_dec);
Console.WriteLine(mantissa_dec);
Console.WriteLine(v.ToString());
Console.WriteLine($"{v:E10}");
Console.WriteLine(v.ToString("e10"));
MultiPrecision <Pow2.N8> u = v.ToString();
Console.WriteLine(u.ToString());
Console.WriteLine(v.ToHexcode());
Console.WriteLine(u.ToHexcode());
Assert.AreEqual((double)v, double.Parse(v.ToString()), Math.Abs((double)v) * 1e-8);
}
for (long i = int.MaxValue - 120; i < int.MaxValue; i++)
{
MultiPrecision <Pow2.N8> v = new MultiPrecision <Pow2.N8>(Sign.Plus, i, Mantissa <Pow2.N8> .One, round: false);
(Sign sign, Int64 exponent_dec, Accumulator <Pow2.N8> mantissa_dec) = v.ToStringCore(MultiPrecision <Pow2.N8> .DecimalDigits);
Console.WriteLine(sign);
Console.WriteLine(exponent_dec);
Console.WriteLine(mantissa_dec);
Console.WriteLine(v.ToString());
Console.WriteLine($"{v:E10}");
Console.WriteLine(v.ToString("e10"));
MultiPrecision <Pow2.N8> u = v.ToString();
Console.WriteLine(u.ToString());
Console.WriteLine(v.ToHexcode());
Console.WriteLine(u.ToHexcode());
Assert.AreEqual((double)v, double.Parse(v.ToString()), Math.Abs((double)v) * 1e-8);
}
{
MultiPrecision <Pow2.N8> v = MultiPrecision <Pow2.N8> .PI;
(Sign sign, Int64 exponent_dec, Accumulator <Pow2.N8> mantissa_dec) = v.ToStringCore(MultiPrecision <Pow2.N8> .DecimalDigits);
Console.WriteLine(sign);
Console.WriteLine(exponent_dec);
Console.WriteLine(mantissa_dec);
Console.WriteLine(v.ToString());
Console.WriteLine($"{v:E10}");
Console.WriteLine(v.ToString("e10"));
MultiPrecision <Pow2.N8> u = v.ToString();
Console.WriteLine(u.ToString());
Console.WriteLine(v.ToHexcode());
Console.WriteLine(u.ToHexcode());
Assert.AreEqual((double)v, double.Parse(v.ToString()), Math.Abs((double)v) * 1e-8);
}
string p99 = "0.999";
for (int i = 0; i < 100; i++)
{
p99 += "9";
MultiPrecision <Pow2.N8> u = p99;
Console.WriteLine(u.ToString());
Console.WriteLine(u.ToHexcode());
Assert.AreEqual(double.Parse(p99), (double)u, 1e-100);
}
}
public void ErfTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Erf(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(ErfApprox((double)x), y, minerr: 1e-2, ignore_sign: true);
}
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"-9.999999845827420997199811478403265131159514278547464108088316571e-1",
MultiPrecision <Pow2.N8> .Erf(-4),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"-9.999779095030014145586272238704176796201522929126007503427610452e-1",
MultiPrecision <Pow2.N8> .Erf(-3),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"-9.953222650189527341620692563672529286108917970400600767383523262e-1",
MultiPrecision <Pow2.N8> .Erf(-2),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"-8.427007929497148693412206350826092592960669979663029084599378978e-1",
MultiPrecision <Pow2.N8> .Erf(-1),
"1e-50"
));
Assert.AreEqual(0, MultiPrecision <Pow2.N8> .Erf(0));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"8.427007929497148693412206350826092592960669979663029084599378978e-1",
MultiPrecision <Pow2.N8> .Erf(1),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"9.953222650189527341620692563672529286108917970400600767383523262e-1",
MultiPrecision <Pow2.N8> .Erf(2),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"9.999779095030014145586272238704176796201522929126007503427610452e-1",
MultiPrecision <Pow2.N8> .Erf(3),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"9.999999845827420997199811478403265131159514278547464108088316571e-1",
MultiPrecision <Pow2.N8> .Erf(4),
"1e-50"
));
}
public void ErfcTest()
{
foreach (MultiPrecision <Pow2.N8> x in TestTool.AllRangeSet <Pow2.N8>())
{
MultiPrecision <Pow2.N8> y = MultiPrecision <Pow2.N8> .Erfc(x);
Console.WriteLine(x);
Console.WriteLine(y);
TestTool.Tolerance(ErfcApprox((double)x), y, minerr: 1e-2, ignore_sign: true);
}
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.9999999845827420997199811478403265131159514278547464108088316571e0",
MultiPrecision <Pow2.N8> .Erfc(-4),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.9999779095030014145586272238704176796201522929126007503427610452e0",
MultiPrecision <Pow2.N8> .Erfc(-3),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.9953222650189527341620692563672529286108917970400600767383523262e0",
MultiPrecision <Pow2.N8> .Erfc(-2),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.8427007929497148693412206350826092592960669979663029084599378978e0",
MultiPrecision <Pow2.N8> .Erfc(-1),
"1e-50"
));
Assert.AreEqual(1, MultiPrecision <Pow2.N8> .Erfc(0));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.572992070502851306587793649173907407039330020336970915400621022e-1",
MultiPrecision <Pow2.N8> .Erfc(1),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"4.677734981047265837930743632747071389108202959939923261647673800e-3",
MultiPrecision <Pow2.N8> .Erfc(2),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"2.209049699858544137277612958232037984770708739924965723895484294e-5",
MultiPrecision <Pow2.N8> .Erfc(3),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.541725790028001885215967348688404857214525358919116834290499421e-8",
MultiPrecision <Pow2.N8> .Erfc(4),
"1e-50"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"2.088487583762544757000786294957788611560818119321163727012213714e-45",
MultiPrecision <Pow2.N8> .Erfc(10),
"1e-95"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"2.070920778841656048448447875165788792932250920995399683766235534e-1088",
MultiPrecision <Pow2.N8> .Erfc(50),
"1e-1138"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"6.405961424921732039021339148586394148214414399460338057767107650e-4346",
MultiPrecision <Pow2.N8> .Erfc(100),
"1e-4396"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"2.703823745452247856854931734255359377805490749772707768226770978e-108577",
MultiPrecision <Pow2.N8> .Erfc(500),
"1e-108627"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.860037048632323370908471162289984373206233539926488472200712370e-434298",
MultiPrecision <Pow2.N8> .Erfc(1000),
"1e-434348"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.011285440970039477031542173737947576392096400158950800837668262e-10857366",
MultiPrecision <Pow2.N8> .Erfc(5000),
"1e-10857416"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"3.639987386564198052838435239316275600299066983050320050544858948e-43429453",
MultiPrecision <Pow2.N8> .Erfc(10000),
"1e-43429303"
));
Assert.IsTrue(
MultiPrecision <Pow2.N8> .NearlyEquals(
"1.969361711624327154389174953238654441985348792810296010912403861e-1085736210",
MultiPrecision <Pow2.N8> .Erfc(50000),
"1e-1085736260"
));
}