private static void SlowFFT(ComplexNumber[] input)
{
int precisionDigits = 1;
for (int i = input.Length; --i >= 0;)
{
precisionDigits = Math.Max(precisionDigits, input[i].GetPrecisionDigits());
}
RealNumber pi = RealNumber.GetPI(precisionDigits + 1);
int n = input.Length;
var result = new ComplexNumber[n];
var powers = new ComplexNumber[n];
var array = new ComplexNumber[n];
powers[0] = ComplexNumber.One;
powers[1] = ComplexNumber.FromPolarAngle((pi << 1) / n);
for (int i = 2; i < n; i++)
{
powers[i] = powers[i >> 1] * powers[(i + 1) >> 1];
}
for (int i = n; --i >= 0;)
{
ComplexNumber sum = ComplexNumber.Zero;
for (int j = n; --j >= 0;)
{
sum += input[j] * powers[i * j % n];
}
result[i] = sum;
}
for (int i = n; --i >= 0;)
{
input[i] = result[i];
}
}
public FFTRealConstants(int precisionDigits)
{
this.PrecisionDigits = precisionDigits;
RealNumber sqrt5 = new RealNumber(5, precisionDigits).GetSqrt();
this.M_SQRT_3_4 = new RealNumber(3, precisionDigits).GetSqrt() >> 1;
this.M_ROOT5_C2 = sqrt5 >> 2;
this.M_ROOT5_C3 = ((5 - sqrt5) >> 3).GetSqrt();
this.M_ROOT5_C4 = ((5 + sqrt5) >> 3).GetSqrt();
this.PI = RealNumber.GetPI(precisionDigits);
}
public void PIUnitTestMethod()
{
int decmalDigits = 10 * 1000;
int qwords = (int)Math.Ceiling(Math.Log(10, 2) * decmalDigits / 64);
RealNumber pi = RealNumber.GetPI(qwords);
string piString = pi.ToString();
string realPIDigits = @"3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983052358089330657574067954571637752542021149557615814002501262285941302164715509792592309907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111790429782856475032031986915140287080859904801094121472213179476477726224142548545403321571853061422881375850430633217518297986622371721591607716692547487389866549494501146540628433663937900397692656721463853067360965712091807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862947265473642523081770367515906735023507283540567040386743513622224771589150495309844489333096340878076932599397805419341447377441842631298608099888687413260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56";
bool ok = piString.StartsWith(realPIDigits);
Assert.IsTrue(ok);
}
public static void EvenDCTType2(this RealNumber[] data, ComplexNumber[] v = null)
{
int N = data.Length;
if ((N & 1) != 0)
{
throw new Exception("DCT operates only on even data sizes.");
}
N >>= 1; //N = number of complex numbers.
Array.Resize(ref v, N);
for (int i = N; --i >= 0;)
{
v[i] = new ComplexNumber(data[map1(i * 2, N * 2)], data[map1(i * 2 + 1, N * 2)]);
}
FullForwardFFT(v, data);
int precisionDigits = 1;
for (int i = data.Length; --i >= 0;)
{
precisionDigits = Math.Max(precisionDigits, data[i].GetPrecisionDigits());
}
RealNumber INV_SQRT_2 = new RealNumber(0.5, precisionDigits).GetSqrt();
RealNumber PI = RealNumber.GetPI(precisionDigits);
var scalej = new ComplexNumber(INV_SQRT_2, -INV_SQRT_2);
ComplexNumber firstRoot = ComplexNumber.FromPolarAngle((PI >> 2) / N);
ComplexNumber secondRoot = ComplexNumber.FromPolarAngle((PI * 5 >> 2) / N);
ComplexNumber firstIterator = INV_SQRT_2 * firstRoot;
ComplexNumber secondIterator = INV_SQRT_2 * secondRoot.MulI();
for (int i = 1, j = N - 1; i <= j; i++, j--)
{
var vi = v[i];
var vj = v[j].Conjugate;
var t1 = (vi + vj) * firstIterator;
var t2 = (vi - vj) * secondIterator;
var a = (t1 - t2);
var b = (t1 + t2) * scalej;
data[i] = a.Real;
data[N * 2 - i] = a.Imaginary;
data[j] = b.Real;
data[N * 2 - j] = -b.Imaginary;
firstIterator *= firstRoot;
secondIterator *= secondRoot;
}
var number = v[0];
data[N] = number.Real - number.Imaginary;
data[0] = number.Real + number.Imaginary;
}
public static void EvenDCTType3(this RealNumber[] data, ComplexNumber[] v = null)
{
int N = data.Length;
if ((N & 1) != 0)
{
throw new Exception("Inverse DCT operates only on even data sizes.");
}
N >>= 1;
Array.Resize(ref v, N);
v[0] = new ComplexNumber(data[0] + data[N], data[0] - data[N]);
//A.Conjug * B = (A * B.Conjug).Conjug
int precisionDigits = 1;
for (int i = data.Length; --i >= 0;)
{
precisionDigits = Math.Max(precisionDigits, data[i].GetPrecisionDigits());
}
RealNumber INV_SQRT_2 = new RealNumber(0.5, precisionDigits).GetSqrt();
RealNumber PI = RealNumber.GetPI(precisionDigits);
var scalej = new ComplexNumber(INV_SQRT_2, INV_SQRT_2);
ComplexNumber firstRoot = ComplexNumber.FromPolarAngle((-PI >> 2) / N);
ComplexNumber secondRoot = ComplexNumber.FromPolarAngle((-PI * 5 >> 2) / N);
ComplexNumber firstIterator = INV_SQRT_2 * firstRoot;
ComplexNumber secondIterator = INV_SQRT_2 * secondRoot.DivI();
for (int i = 1, j = N - 1; i <= j; i++, j--)
{
var a = new ComplexNumber(data[i], data[N * 2 - i]);
var b = new ComplexNumber(data[j], -data[N * 2 - j]) * scalej;
var t1 = (a + b) * firstIterator;
var t2 = (a - b) * secondIterator;
v[i] = (t1 - t2);
v[j] = (t1 + t2).Conjugate;
firstIterator *= firstRoot;
secondIterator *= secondRoot;
}
FullForwardIFFT(v, data);
for (int i = N; --i >= 0;)
{
var number = v[i];
data[map1(i * 2, N * 2)] = number.Real;
data[map1(i * 2 + 1, N * 2)] = number.Imaginary;
}
}
private static void SlowDCT2(RealNumber[] data)
{
int precisionDigits = 1;
for (int i = data.Length; --i >= 0;)
{
precisionDigits = Math.Max(precisionDigits, data[i].GetPrecisionDigits());
}
RealNumber pi = RealNumber.GetPI(precisionDigits + 1);
int n = data.Length;
ComplexNumber[] roots = new ComplexNumber[n * 4];
roots[0] = ComplexNumber.One;
roots[1] = ComplexNumber.FromPolarAngle((pi << 1) / (n * 4));
for (int i = 2; i < n * 4; i++)
{
roots[i] = roots[i >> 1] * roots[(i + 1) >> 1];
}
var result = new RealNumber[n];
for (int i = n; --i >= 0;)
{
RealNumber sum = RealNumber.Zero;
for (int j = n; --j >= 0;)
{
sum += data[j] * roots[(2 * j + 1) * i % (n * 4)].Real;
}
result[i] = sum;
}
RealNumber scale = new RealNumber(2.0, precisionDigits + 1).GetSqrt();
for (int i = n; --i > 0;)
{
data[i] = result[i] * scale;
}
data[0] = result[0];
}
public void TestAll()
{
for (int digits = 1; digits < 100; digits++)
{
RealNumber b_one = new RealNumber(2L, digits);
RealNumber log1 = RealNumber.Zero, log2 = RealNumber.Zero;
Parallel.Invoke(
() =>
{
log1 = b_one.GetLog();
},
() =>
{
log2 = b_one.GetTaylorLog();
});
string log1String = log1.ToString();
string log2String = log2.ToString();
int diffs = differences(log2String, log1String);
if (diffs > 0)
{
File.WriteAllText("L1MILD.txt", log1String);
File.WriteAllText("L1MILT.txt", log2String);
Assert.IsTrue(false);
}
}
//IntegerNumber zzz = new IntegerNumber(0L);
//string ssttrr = zzz.ToString();
bool ok = true;
//testMultiplicationSpeed();
RealNumber ten = new RealNumber(10, 1000);
RealNumber logTen = ten.GetLog();
RealNumber tenExp1 = logTen.GetExp();
RealNumber tenExp2 = logTen.GetTaylorExp();
IntegerNumber i1 = IntegerNumber.One << 100000;
IntegerNumber ia = i1.Sqrt();
IntegerNumber ib = i1.InverseSqrt();
RealNumber ssqrt10 = ten.GetRealDirectSqrt();
RealNumber sqrt10 = ten.GetSqrt();
RealNumber invSqrt10 = ten.GetInverseSqrt();
RealNumber one1 = sqrt10 * invSqrt10;
ok &= (one1 - 1).IsZero;
IntegerNumber int10 = IntegerNumber.Pow(10, 19 * 5000);
IntegerNumber t1 = int10.Inverse();
IntegerNumber t2 = (IntegerNumber.One << (int10.Digits * 128)) / int10;
ok &= t1 == t2;
IntegerNumber t3 = int10.InverseSqrt();
IntegerNumber t4 = ((IntegerNumber.One << (int10.Digits * 96 * 2)) / int10).Sqrt();
ok &= t3 == t4;
ok &= Fourier235RealUnitTest.FFTUnitTest();
ok &= Fourier235RealUnitTest.DCTUnitTest();
ok &= Fourier235DoubleUnitTest.FFTUnitTest();
ok &= Fourier235DoubleUnitTest.DCTUnitTest();
ok &= Fourier235UnitTest.FFTUnitTest();
ok &= Fourier235UnitTest.DCTUnitTest();
ok &= RealNumbersUnitTest.ComplexArcTanSinCosUnitTest();
ok &= RealNumbersUnitTest.NumericIntegerOperationsUnitTest();
ok &= RealNumbersUnitTest.SqrtUnitTest();
ok &= MemoryUnitTest.UnitTest(1001);
ok &= CarrylessMultiplication.UnitTest(1001);
int decimalDigits = 10100;
int qwords = (int)Math.Ceiling(Math.Log(10, 2) * decimalDigits / 64);
RealNumber pi = RealNumber.Zero;
RealNumber e = RealNumber.Zero;
RealNumber one = new RealNumber(1L, qwords);
var computePITime = AsmX64Operations.MeasureTime(() =>
{
pi = RealNumber.GetPI(qwords);
});
var computeETime = AsmX64Operations.MeasureTime(() =>
{
e = one.GetExp();
});
string pivalue = "";
string evalue = "";
var baseConvertTimePI = AsmX64Operations.MeasureTime(() =>
{
pivalue = pi.ToString();
});
var baseConvertTimeE = AsmX64Operations.MeasureTime(() =>
{
evalue = e.ToString();
});
File.WriteAllText(@"..\pi10k.txt", pivalue);
File.WriteAllText(@"..\e_10k.txt", evalue);
//MessageBox.Show(
// "Compute PI Time: " + computePITime.ToString() + "\r\n" +
// "Compute E Time: " + computeETime.ToString() + "\r\n" +
// "base convert time PI: " + baseConvertTimePI.ToString() + "\r\n" +
// "base convert time E : " + baseConvertTimeE.ToString() + "\r\n",
// "Info", MessageBoxButtons.OK, MessageBoxIcon.Information);
var no0 = new RealNumber(1L << 62, 2048 / 64);
var no1 = no0.GetExp();
var no2 = no1.GetLog();
ok &= (no2 - no0).IsZero;
ulong[] xx = Enumerable.Repeat(ulong.MaxValue, 1024 * 100).ToArray();
ulong[] yy = Enumerable.Repeat(ulong.MaxValue, 1024 * 100).ToArray();
ulong[] zz = Enumerable.Repeat((ulong)0, 1024 * 200).ToArray();
AsmX64Operations.FastestMultiplication(xx, yy, zz, xx.Length);
if (zz[0] != 1 || zz[zz.Length / 2 - 1] != 0 || zz[zz.Length / 2] + 2 != 0 || zz[zz.Length - 1] + 1 != 0)
{
ok = false;
}
ok &= RealNumbersUnitTest.UnitTest(1001);
ok &= FourierReal.UnitTest(10012);
ok &= FourierMultiplication.UnitTest();
ok &= IntegerNumberUnitTest.UnitTest();
ok &= FourierMultiplication.UnitTestBigMul(1001);
ok &= FastIntegerUnitTest.UnitTest();
ok &= FourierMultiplication.UnitTest(1001);
ok &= AsmX64Operations.ECCUnitTest();
ok &= AsmX64Operations.UnitTest();
ok &= HeapUnitTest.UnitTest();
ok &= FourierTransform.FFTUnitTest();
ok &= AccurateSummation.UnitTest();
ok &= BinarySearchUnitTest.UnitTest();
ok &= AVLTree <int> .UnitTest();
ok &= AVLTreeSorted <int> .UnitTest();
Assert.IsTrue(ok);
}