private void UpdateMxLarge(long x1, long x2, int[] r)
{
for (var l = 0; l < r.Length; l++)
{
var i = r[l];
var x = niLarge[i];
var sqrt = (long)UInt128.FloorSqrt(x);
var xover = (long)UInt128.Min((ulong)(sqrt * C3 / C4), x);
xover = (long)(x / (x / (ulong)xover));
var s = (Int128)0;
var jmin = UpToOdd(Math.Max(imax / i + 1, (long)UInt128.Min((ulong)xover + 1, x / ((ulong)x2 + 1) + 1)));
var jmax = DownToOdd((long)UInt128.Min((ulong)xover, x / (ulong)x1));
s += JSumLarge1(x, jmin, ref jmax, x1);
s += JSumLarge2(x, jmin, jmax, x1);
var kmin = Math.Max(1, x1);
var kmax = (long)UInt128.Min(x / (ulong)xover - 1, (ulong)x2);
s += KSumLarge1Mu(x, kmin, ref kmax, x1);
//s += KSumLarge1M(x, kmin, ref kmax, x1);
s += KSumLarge2(x, kmin, kmax, x1);
mx[i] -= s;
}
}
private UInt128 EvaluateInternal(UInt128 n, UInt128 x0, UInt128 xmax)
{
this.n = n;
x0 = T1(x0 + 1);
xmax = T1(xmax);
if (x0 > xmax)
{
return(0);
}
var ymin = YFloor(xmax);
var xmin = UInt128.Max(x0, UInt128.Min(T1(C1 * UInt128.CeilingCbrt(2 * n)), xmax));
#if DIAG
Console.WriteLine("n = {0}, xmin = {1}, xmax = {2}", n, xmin, xmax);
#endif
var s = (UInt128)0;
var a2 = (ulong)1;
var x2 = xmax;
var y2 = ymin;
var c2 = a2 * x2 + y2;
while (true)
{
var a1 = a2 + 1;
var x4 = YTan(a1);
var y4 = YFloor(x4);
var c4 = a1 * x4 + y4;
var x5 = x4 + 1;
var y5 = YFloor(x5);
var c5 = a1 * x5 + y5;
if (x4 <= xmin)
{
break;
}
s += Triangle(c4 - c2 - x0) - Triangle(c4 - c2 - x5) + Triangle(c5 - c2 - x5);
if (threads == 0)
{
s += ProcessRegion(0, (ulong)(a1 * x2 + y2 - c5), (ulong)(a2 * x5 + y5 - c2), a1, 1, c5, a2, 1, c2);
while (stack.Count > 0)
{
var r = stack.Pop();
s += ProcessRegion(0, r.w, r.h, r.a1, r.b1, r.c1, r.a2, r.b2, r.c2);
}
}
else
{
Enqueue(new Region((ulong)(a1 * x2 + y2 - c5), (ulong)(a2 * x5 + y5 - c2), a1, 1, c5, a2, 1, c2));
}
a2 = a1;
x2 = x4;
y2 = y4;
c2 = c4;
}
s += (xmax - x0 + 1) * ymin + Triangle(xmax - x0);
var rest = x2 - x0;
s -= y2 * rest + a2 * Triangle(rest);
xmanual = x2;
return(s);
}
private void SetValue(Node <T> node, UInt128 start, UInt128 length, UInt128 ip_from, UInt128 ip_to, T value)
{
if (ip_from > ip_to)
{
throw new ArgumentException("Invalid range", nameof(ip_from));
}
if (node != null)
{
UInt128 l_start = start;
UInt128 l_end = l_start + length - 1;
if (l_start <= ip_from && l_end >= ip_from)
{
if (l_start == ip_from && l_end <= ip_to)
{
node.LValue = value;
node.LPtr = null;
}
else
{
if (node.LValue != null)
{
node.LPtr = new Node <T> {
LValue = node.LValue,
LPtr = null,
RValue = node.LValue,
RPtr = null
};
node.LValue = default;
}
SetValue(node.LPtr, l_start, length >> 1, ip_from, UInt128.Min(l_end, ip_to), value);
}
}
UInt128 r_start = start + length;
UInt128 r_end = r_start + length - 1;
if (r_start <= ip_to && r_end >= ip_to)
{
if (r_start >= ip_from && r_end == ip_to)
{
node.RValue = value;
node.RPtr = null;
}
else
{
if (node.RValue != null)
{
node.RPtr = new Node <T> {
LValue = node.RValue,
LPtr = null,
RValue = node.RValue,
RPtr = null
};
node.RValue = default;
}
SetValue(node.RPtr, r_start, length >> 1, UInt128.Max(r_start, ip_from), ip_to, value);
}
}
}
else
{
throw new IPFilterException("Can't find node. IPFilter seems to be corrupted");
}
}
// [DataRow(uint.MaxValue, uint.MaxValue)]
// [DataRow(ulong.MaxValue, ulong.MaxValue)]
public void UInt128Test(ulong factorMax, ulong modulusMax)
{
var random = new MersenneTwister(0).Create <ulong>();
for (int i = 0; i < 10000; i++)
{
var n = random.Next(modulusMax - 1) + 1;
var a = random.Next(factorMax) % n;
var b = random.Next(factorMax) % n;
var c = random.Next(factorMax) % n;
var d = random.Next(factorMax) % n;
var s = (int)(b % 32);
var value = (UInt128)0;
Assert.AreEqual((BigInteger)a << s, (UInt128)a << s);
Assert.AreEqual((BigInteger)a >> s, (UInt128)a >> s);
Assert.AreEqual((BigInteger)a & b, (UInt128)a & b);
Assert.AreEqual((BigInteger)a & b, a & (UInt128)b);
Assert.AreEqual((BigInteger)a & b, (UInt128)a & (UInt128)b);
Assert.AreEqual((BigInteger)a | b, (UInt128)a | b);
Assert.AreEqual((BigInteger)a | b, a | (UInt128)b);
Assert.AreEqual((BigInteger)a | b, (UInt128)a | (UInt128)b);
Assert.AreEqual((BigInteger)a ^ b, (UInt128)a ^ b);
Assert.AreEqual((BigInteger)a ^ b, a ^ (UInt128)b);
Assert.AreEqual((BigInteger)a ^ b, (UInt128)a ^ (UInt128)b);
if (a <= long.MaxValue)
{
Assert.AreEqual(~(BigInteger)a, (long)~(UInt128)a);
}
Assert.AreEqual((BigInteger)a + b, (UInt128)a + b);
Assert.AreEqual((BigInteger)a + b, a + (UInt128)b);
Assert.AreEqual((BigInteger)a + b, (UInt128)a + (UInt128)b);
Assert.AreEqual(((BigInteger)a * n + (BigInteger)b * n) % ((BigInteger)1 << 128), (UInt128)a * n + (UInt128)b * n);
if (a >= b)
{
Assert.AreEqual((BigInteger)a - b, (UInt128)a - b);
Assert.AreEqual((BigInteger)a - b, a - (UInt128)b);
Assert.AreEqual((BigInteger)a - b, (UInt128)a - (UInt128)b);
Assert.AreEqual((BigInteger)a * n - (BigInteger)b * n, (UInt128)a * n - (UInt128)b * n);
}
Assert.AreEqual(+(BigInteger)a, +(Int128)a);
value = a; Assert.AreEqual((BigInteger)a + 1, ++value);
value = a; Assert.AreEqual((BigInteger)a, value++);
value = (UInt128)a * b; Assert.AreEqual((BigInteger)a * b + 1, ++value);
value = (UInt128)a * b; Assert.AreEqual((BigInteger)a * b, value++);
if (a > 0)
{
value = a; Assert.AreEqual((BigInteger)a - 1, --value);
value = a; Assert.AreEqual((BigInteger)a, value--);
}
if (a > 0 && b > 0)
{
value = (UInt128)a * b; Assert.AreEqual((BigInteger)a * b - 1, --value);
value = (UInt128)a * b; Assert.AreEqual((BigInteger)a * b, value--);
}
if (n <= uint.MaxValue)
{
Assert.AreEqual((BigInteger)a * n, (UInt128)a * (uint)n);
Assert.AreEqual((BigInteger)b * n, (UInt128)b * (uint)n);
Assert.AreEqual((BigInteger)a * b * n % ((BigInteger)1 << 128), (UInt128)a * b * (uint)n);
Assert.AreEqual((BigInteger)n * a, (uint)n * (UInt128)a);
Assert.AreEqual((BigInteger)n * b, (uint)n * (UInt128)b);
Assert.AreEqual((BigInteger)n * a * b % ((BigInteger)1 << 128), (uint)n * ((UInt128)a * (UInt128)b));
}
Assert.AreEqual((BigInteger)a * b, a * (UInt128)b);
Assert.AreEqual((BigInteger)a * b, (UInt128)a * b);
Assert.AreEqual((BigInteger)a * b, a * (UInt128)b);
Assert.AreEqual((BigInteger)a * b, (UInt128)a * (UInt128)b);
if (b > 0)
{
Assert.AreEqual((BigInteger)a % b, (UInt128)a % b);
Assert.AreEqual((BigInteger)a % b, a % (UInt128)b);
Assert.AreEqual((BigInteger)a % b, (UInt128)a % (UInt128)b);
}
Assert.AreEqual((BigInteger)a * b % n, (UInt128)a * b % n);
Assert.AreEqual((BigInteger)a * b % n, a * (UInt128)b % n);
Assert.AreEqual((BigInteger)a * b % n, (UInt128)a * (UInt128)b % (UInt128)n);
if (c > 0 && d > 0)
{
Assert.AreEqual((BigInteger)a * b / ((BigInteger)c * d), (UInt128)a * (UInt128)b / ((UInt128)c * (UInt128)d));
Assert.AreEqual((BigInteger)a * b % ((BigInteger)c * d), (UInt128)a * (UInt128)b % ((UInt128)c * (UInt128)d));
}
if (b > 0)
{
Assert.AreEqual((BigInteger)a / b, (UInt128)a / b);
Assert.AreEqual((BigInteger)a / b, a / (UInt128)b);
Assert.AreEqual((BigInteger)a / b, (UInt128)a / (UInt128)b);
}
Assert.AreEqual((BigInteger)a * b / n, (UInt128)a * b / n);
Assert.AreEqual((BigInteger)a * b / n, a * (UInt128)b / n);
Assert.AreEqual((BigInteger)a * b / n, (UInt128)a * (UInt128)b / (UInt128)n);
Assert.AreEqual((BigInteger)a < b, (UInt128)a < b);
Assert.AreEqual((BigInteger)a < b, a < (UInt128)b);
Assert.AreEqual((BigInteger)a < b, (UInt128)a < (UInt128)b);
Assert.AreEqual((BigInteger)a <= b, (UInt128)a <= b);
Assert.AreEqual((BigInteger)a <= b, a <= (UInt128)b);
Assert.AreEqual((BigInteger)a <= b, (UInt128)a <= (UInt128)b);
Assert.AreEqual((BigInteger)a > b, (UInt128)a > b);
Assert.AreEqual((BigInteger)a > b, a > (UInt128)b);
Assert.AreEqual((BigInteger)a > b, (UInt128)a > (UInt128)b);
Assert.AreEqual((BigInteger)a >= b, (UInt128)a >= b);
Assert.AreEqual((BigInteger)a >= b, a >= (UInt128)b);
Assert.AreEqual((BigInteger)a >= b, (UInt128)a >= (UInt128)b);
Assert.AreEqual((BigInteger)a == b, (UInt128)a == b);
Assert.AreEqual((BigInteger)a == b, a == (UInt128)b);
Assert.AreEqual((BigInteger)a == b, (UInt128)a == (UInt128)b);
Assert.AreEqual((BigInteger)a != b, (UInt128)a != b);
Assert.AreEqual((BigInteger)a != b, a != (UInt128)b);
Assert.AreEqual((BigInteger)a != b, (UInt128)a != (UInt128)b);
Assert.AreEqual((BigInteger)a * a, UInt128.Square(a));
Assert.AreEqual(BigInteger.Abs(a), UInt128.Abs(a));
Assert.AreEqual(BigInteger.Abs((BigInteger)a * b), UInt128.Abs((UInt128)a * b));
Assert.AreEqual(BigInteger.Min(a, b), UInt128.Min(a, b));
Assert.AreEqual(BigInteger.Min((BigInteger)a * n, (BigInteger)b * n), UInt128.Min((UInt128)a * n, (UInt128)b * n));
Assert.AreEqual(BigInteger.Max(a, b), UInt128.Max(a, b));
Assert.AreEqual(BigInteger.Max((BigInteger)a * n, (BigInteger)b * n), UInt128.Max((UInt128)a * n, (UInt128)b * n));
for (var j = 0; j < 2; j++)
{
var m = UInt128.Abs(j == 0 ? (UInt128)a * (UInt128)b : (UInt128)n * (UInt128)n);
var floorsqrt = UInt128.FloorSqrt(m);
Assert.IsTrue((BigInteger)floorsqrt * floorsqrt <= m && (BigInteger)(floorsqrt + 1) * (floorsqrt + 1) > m);
var ceilingsqrt = UInt128.CeilingSqrt(m);
Assert.IsTrue((BigInteger)(ceilingsqrt - 1) * (ceilingsqrt - 1) < m && (BigInteger)ceilingsqrt * ceilingsqrt >= m);
}
for (var j = 0; j < 2; j++)
{
var m = j == 0 ? (UInt128)a * (UInt128)b : (UInt128)BigInteger.Pow((BigInteger)Math.Floor(Math.Pow((double)((BigInteger)a * b), (double)1 / 3)), 3);
var floorcbrt = UInt128.FloorCbrt(m);
Assert.IsTrue((BigInteger)floorcbrt * floorcbrt * floorcbrt <= m && (BigInteger)(floorcbrt + 1) * (floorcbrt + 1) * (floorcbrt + 1) > m);
var ceilingcbrt = UInt128.CeilingCbrt(m);
Assert.IsTrue((BigInteger)(ceilingcbrt - 1) * (ceilingcbrt - 1) * (ceilingcbrt - 1) < m && (BigInteger)ceilingcbrt * ceilingcbrt * ceilingcbrt >= m);
}
Assert.AreEqual(BigInteger.GreatestCommonDivisor((BigInteger)a, (BigInteger)b), UInt128.GreatestCommonDivisor((UInt128)a, (UInt128)b));
Assert.AreEqual(BigInteger.GreatestCommonDivisor((BigInteger)a * b, (BigInteger)c * d), UInt128.GreatestCommonDivisor((UInt128)a * b, (UInt128)c * d));
Assert.AreEqual(0, 0);
}
}
public static UInt128 Min(UInt128 a, UInt128 b)
{
return(UInt128.Min(a, b));
}