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;
}
}
public UInt128 Evaluate(UInt128 n)
{
var xmax = UInt128.FloorSqrt(n);
var s = Evaluate(n, 1, xmax);
var xmax2 = T1(xmax);
return(2 * s - (UInt128)xmax2 * (UInt128)xmax2);
}
public static ulong FloorSqrt(Int128 a)
{
if (a.IsNegative)
{
throw new ArgumentException("argument must not be negative");
}
return(UInt128.FloorSqrt(a.v));
}
public static ulong FloorSquareRoot(UInt128 a)
{
return(UInt128.FloorSqrt(a));
}
private UInt128 YTan(UInt128 a)
{
return(T1(UInt128.FloorSqrt((n / a))));
}
public ulong UTan(UInt128 ab1, UInt128 abba, UInt128 ab2, UInt128 a3b3, UInt128 c1)
{
return((ulong)((ab1 + UInt128.FloorSqrt(UInt128.Square(abba + ab2) * n / a3b3) - (c1 << 1)) / 2));
}
// [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);
}
}
