Exemple #1
0
 public static ulong CeilingSqrt(Int128 a)
 {
     if (a.IsNegative)
     {
         throw new ArgumentException("argument must not be negative");
     }
     return(UInt128.CeilingSqrt(a.v));
 }
Exemple #2
0
        public void VFloor2(UInt128 u1, ulong a1, ulong b1, UInt128 c1, UInt128 c2, UInt128 abba, UInt128 ab2, out ulong v1, out ulong v2)
        {
            var uu = (u1 + c1) << 1;
            var t1 = ab2 << 1;
            var t2 = abba * uu - a1 + b1 - t1 * c2;
            var t3 = uu - a1 - b1;
            var t4 = UInt128.Square(t3) - t1 * n;

            v1 = (ulong)((t2 - UInt128.CeilingSqrt(t4)) / t1);
            v2 = (ulong)((t2 + (abba << 1) - UInt128.CeilingSqrt((t4 + ((t3 + 1) << 2)))) / t1);
        }
Exemple #3
0
        public UInt128 ProcessRegionManual(int thread, ulong w, ulong a1, ulong b1, UInt128 c1, ulong a2, ulong b2, UInt128 c2)
        {
            if (w <= 1)
            {
                return(0);
            }

            var s    = (UInt128)0;
            var umax = w - 1;
            var t1   = (a1 * b2 + b1 * a2) << 1;
            var t2   = (c1 << 1) - a1 - b1;
            var t3   = (t2 << 2) + 12;
            var t4   = (a1 * b1) << 2;
            var t5   = t1 * (1 + c1) - a1 + b1 - t4 * c2;
            var t6   = UInt128.Square(t2 + 2) - t4 * n;

            var u = (ulong)1;

            while (true)
            {
                Debug.Assert((t5 - UInt128.CeilingSqrt(t6)) / t4 == VFloor(u, a1, b1, c1, a2, b2, c2));
#if false
                s += (t5 - UInt128.CeilingSqrt(t6)) / t4;
                if (u >= umax)
                {
                    break;
                }
                t5 += t1;
                t6 += t3;
                t3 += 8;
#else
                UInt128.Add(ref s, (ulong)((t5 - UInt128.CeilingSqrt(t6)) / t4));
                if (u >= umax)
                {
                    break;
                }
                UInt128.Add(ref t5, t1);
                UInt128.Add(ref t6, ref t3);
                UInt128.Add(ref t3, 8);
#endif
                ++u;
            }

            Debug.Assert(s == ProcessRegionHorizontal(w, 0, a1, b1, c1, a2, b2, c2));
#if DIAG
            Console.WriteLine("ProcessRegionManual: s = {0}", s);
#endif
            return(s);
        }
Exemple #4
0
 public static ulong CeilingSquareRoot(UInt128 a)
 {
     return(UInt128.CeilingSqrt(a));
 }
Exemple #5
0
 public ulong VFloor(UInt128 u, ulong a1, ulong b1, UInt128 c1, ulong a2, ulong b2, UInt128 c2)
 {
     return((ulong)((2 * (a1 * b2 + b1 * a2) * (u + c1) - a1 + b1 - UInt128.CeilingSqrt(UInt128.Square(2 * (u + c1) - a1 - b1) - 4 * a1 * b1 * n)) / (4 * a1 * b1) - c2));
 }
Exemple #6
0
 public ulong UFloor(UInt128 v, ulong a1, ulong b1, UInt128 c1, ulong a2, ulong b2, UInt128 c2)
 {
     return((ulong)((2 * (a1 * b2 + b1 * a2) * (v + c2) + a2 - b2 - UInt128.CeilingSqrt(UInt128.Square(2 * (v + c2) - a2 - b2) - 4 * a2 * b2 * n)) / (4 * a2 * b2) - c1));
 }
Exemple #7
0
//        [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);
            }
        }