public static bool UnitTest()
{
FourierPoint a, b;
Random random = new Random(1001);
byte[] ra = new byte[32];
BigInteger p = (BigInteger.One << 128) - (BigInteger.One << 54) + BigInteger.One;
for (int i = 20 * 1000; --i >= 0;)
{
random.NextBytes(ra);
ra[ra.Length - 1] = 0;
a = new FourierPoint(BitConverter.ToUInt64(ra, 0), BitConverter.ToUInt64(ra, 8));
b = new FourierPoint(BitConverter.ToUInt64(ra, 16), BitConverter.ToUInt64(ra, 24));
BigInteger ba = new BigInteger(ra.Take(16).Concat(Enumerable.Repeat((byte)0, 1)).ToArray());
BigInteger bb = new BigInteger(ra.Skip(16).Take(16).Concat(Enumerable.Repeat((byte)0, 1)).ToArray());
FourierPoint.mulmod(ref a, ref b);
ba = (ba * bb) % p;
byte[] rbb1 = ba.ToByteArray();
Array.Resize(ref rbb1, 16);
byte[] rbb2 = new byte[16];
BitConverter.GetBytes(a.Low).CopyTo(rbb2, 0);
BitConverter.GetBytes(a.High).CopyTo(rbb2, 8);
for (int k = 16; --k >= 0;)
{
if (rbb1[k] != rbb2[k])
{
return(false);
}
}
}
return(true);
}
private static void ifft(this FourierPoint[] list)
{
int n = list.Length;
var handle = GCHandle.Alloc(list, GCHandleType.Pinned);
try
{
IntPtr listAddress = handle.AddrOfPinnedObject();
for (int k = 1; k < n; k <<= 1)
{
FourierPoint.butterflyCore(listAddress, 0, k);
FourierPoint wpower = FourierPoint.One;
for (int j = k << 1, x = 0; j < n; x++, j += k << 1)
{
int pos = 0;
while ((x & (1 << pos)) != 0)
{
pos++;
}
FourierPoint.mulmod(ref wpower, ref FourierPoint.RootsInverters[pos]);
FourierPoint.inverseFFTCore(listAddress, j, k, ref wpower);
}
}
}
finally
{
handle.Free();
}
}
public static bool UnitTest(int seed)
{
Random random = new Random(seed);
int bits = 17;
int n = 1 << bits;
FourierPoint[] a0 = new FourierPoint[n];
FourierPoint[] a1 = new FourierPoint[n];
byte[] bytes = new byte[16];
for (int i = n; --i >= 0;)
{
random.NextBytes(bytes);
a0[i] = a1[i] = new FourierPoint(BitConverter.ToUInt64(bytes, 0), BitConverter.ToUInt64(bytes, 8));
}
a0.FFT(false);
a0.IFFT(false);
//var scale = FourierPoint.PowMod(FourierPoint.HalfOne, new FourierPoint((ulong)bits, 0));
for (int i = n; --i >= 0;)
{
//a0[i] *= scale;
a0[i] >>= bits;
}
for (int i = n; --i >= 0;)
{
if (a0[i] != a1[i])
{
return(false);
}
}
return(true);
}
public static void remodP(ref FourierPoint a)
{
if (a.High == ulong.MaxValue && a.Low >= (1023UL << 54) + 1UL)
{
a.Low -= (1023UL << 54) + 1UL;
a.High = 0;
}
}
public override bool Equals(object obj)
{
if (!(obj is FourierPoint))
{
return(false);
}
FourierPoint other = (FourierPoint)obj;
return(this == other);
}
private static void GroupDigits(ulong[] number, int bitsPerDigit, FourierPoint[] result)
{
long numberOfDigits = Math.Min(result.Length, (number.LongLength * 64 + bitsPerDigit - 1) / bitsPerDigit);
long position = numberOfDigits * bitsPerDigit;
for (long i = numberOfDigits; --i >= 0;)
{
position -= bitsPerDigit;
result[i] = new FourierPoint(ReadBits(number, position, bitsPerDigit), 0UL);
}
}
public static void Multiply(ulong[] input1, ulong[] input2, ulong[] result, int n)
{
// AsmX64Operations.FastestMultiplication(input1, input2, result, n);
// return;
int fftBitsPerDigit, fftLog2Size;
GetFFTParameters(n, out fftBitsPerDigit, out fftLog2Size);
long fftN = 1L << fftLog2Size;
//double directComputations = (double)n * n;
//double karatsubaComputations = 4.7 * Math.Pow(n, LOG2_3);
//double fftComputations = 7.2 * (3.0 * fftLog2Size + 4.0) * fftN;
FourierPoint[] number1 = new FourierPoint[fftN];
GroupDigits(input1, fftBitsPerDigit, number1);
FourierPoint[] number2 = new FourierPoint[fftN];
GroupDigits(input2, fftBitsPerDigit, number2);
//FourierPoint scale = FourierPoint.PowMod(FourierPoint.HalfOne, new FourierPoint((ulong)fftLog2Size, 0UL));
number1.FFT(false);
number2.FFT(false);
for (int i = number1.Length; --i >= 0;)
{
FourierPoint point = number1[i];
FourierPoint.mulmod(ref point, ref number2[i]);
//FourierPoint.mulmod(ref point, ref scale);
point >>= fftLog2Size;
number1[i] = point;
}
number1.IFFT(false);
var number1Handle = GCHandle.Alloc(number1, GCHandleType.Pinned);
try
{
FourierPoint.PropagateCarries(number1Handle.AddrOfPinnedObject(), fftBitsPerDigit, number1.Length);
}
finally
{
number1Handle.Free();
}
UngroupDigits(number1, fftBitsPerDigit, result);
}
static FourierPoint()
{
FourierPoint p = PrimeModulo;
p.Low -= 1;
FourierPoint halfp = new FourierPoint((p.Low >> 1) | (p.High << 63), p.High >> 1);
var fp1 = PowMod(Generator, p);
var fp2 = PowMod(Generator, halfp);
remodP(ref fp1);
remodP(ref fp2);
var fp3 = PowMod(Root, new FourierPoint(1UL << 53, 0));
if (fp1 != One || fp2 != MinusOne || fp3 != MinusOne)
{
throw new InvalidOperationException("Generator does not pass unit test.");
}
Roots = new FourierPoint[54];
FourierPoint[] inverters = new FourierPoint[Roots.Length];
Roots[Roots.Length - 1] = Root;
inverters[Roots.Length - 1] = FourierPoint.PowMod(Root, new FourierPoint(PrimeModulo.Low - 2, PrimeModulo.High));
for (int i = Roots.Length - 1; --i >= 0;)
{
Roots[i] = Roots[i + 1] * Roots[i + 1];
remodP(ref Roots[i]);
inverters[i] = inverters[i + 1] * inverters[i + 1];
remodP(ref inverters[i]);
}
RootsMultipliers = new FourierPoint[Roots.Length - 1];
RootsInverters = new FourierPoint[Roots.Length - 1];
for (int i = 0; i < RootsMultipliers.Length; i++)
{
RootsMultipliers[i] = PrimeModulo - Roots[i] * Roots[i + 1];
RootsInverters[i] = PrimeModulo - inverters[i] * inverters[i + 1];
}
}
public static extern void PowMod(ref FourierPoint a, ref FourierPoint power);
public static extern void inverseFFTCore(IntPtr number, int startIndex, int n, ref FourierPoint wpower);
public static extern void submod(ref FourierPoint a, ref FourierPoint b);
public static void ShiftRightDirect(ref FourierPoint x, int shift)
{
x = new FourierPoint((x.Low >> shift) | (x.High << (64 - shift)), x.High >> shift);
}
public static extern void butterfly(ref FourierPoint a, ref FourierPoint b);
public static FourierPoint PowMod(FourierPoint a, FourierPoint power)
{
PowMod(ref a, ref power);
return(a);
}