Math.Raw support for custom binary curves

- Also migrate the 'raw' stuff into Math.Raw following Java build

1 files changed, 1053 insertions, 0 deletions

diff --git a/crypto/src/math/raw/Nat.cs b/crypto/src/math/raw/Nat.cs
new file mode 100644
index 000000000..1f9ab00ec
--- /dev/null
+++ b/crypto/src/math/raw/Nat.cs
@@ -0,0 +1,1053 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.Raw
+{
+    internal abstract class Nat
+    {
+        private const ulong M = 0xFFFFFFFFUL;
+
+        public static uint Add(int len, uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[i] + y[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint Add33At(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zPos + 0] + x;
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zPos + 1] + 1;
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zPos + 2);
+        }
+
+        public static uint Add33At(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zOff + zPos] + x;
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + zPos + 1] + 1;
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2);
+        }
+
+        public static uint Add33To(int len, uint x, uint[] z)
+        {
+            ulong c = (ulong)z[0] + x;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[1] + 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 2);
+        }
+
+        public static uint Add33To(int len, uint x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)z[zOff + 0] + x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + 1] + 1;
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 2);
+        }
+
+        public static uint AddBothTo(int len, uint[] x, uint[] y, uint[] z)
+        {
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[i] + y[i] + z[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint AddBothTo(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[xOff + i] + y[yOff + i] + z[zOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint AddDWordAt(int len, ulong x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zPos + 0] + (x & M);
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zPos + 1] + (x >> 32);
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zPos + 2);
+        }
+
+        public static uint AddDWordAt(int len, ulong x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            ulong c = (ulong)z[zOff + zPos] + (x & M);
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + zPos + 1] + (x >> 32);
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 2);
+        }
+
+        public static uint AddDWordTo(int len, ulong x, uint[] z)
+        {
+            ulong c = (ulong)z[0] + (x & M);
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[1] + (x >> 32);
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 2);
+        }
+
+        public static uint AddDWordTo(int len, ulong x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)z[zOff + 0] + (x & M);
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zOff + 1] + (x >> 32);
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 2);
+        }
+
+        public static uint AddTo(int len, uint[] x, uint[] z)
+        {
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[i] + z[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint AddTo(int len, uint[] x, int xOff, uint[] z, int zOff)
+        {
+            ulong c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (ulong)x[xOff + i] + z[zOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            return (uint)c;
+        }
+
+        public static uint AddWordAt(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 1));
+            ulong c = (ulong)x + z[zPos];
+            z[zPos] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zPos + 1);
+        }
+
+        public static uint AddWordAt(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 1));
+            ulong c = (ulong)x + z[zOff + zPos];
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, zPos + 1);
+        }
+
+        public static uint AddWordTo(int len, uint x, uint[] z)
+        {
+            ulong c = (ulong)x + z[0];
+            z[0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, 1);
+        }
+
+        public static uint AddWordTo(int len, uint x, uint[] z, int zOff)
+        {
+            ulong c = (ulong)x + z[zOff];
+            z[zOff] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zOff, 1);
+        }
+
+        public static void Copy(int len, uint[] x, uint[] z)
+        {
+            Array.Copy(x, 0, z, 0, len);
+        }
+
+        public static uint[] Copy(int len, uint[] x)
+        {
+            uint[] z = new uint[len];
+            Array.Copy(x, 0, z, 0, len);
+            return z;
+        }
+
+        public static uint[] Create(int len)
+        {
+            return new uint[len];
+        }
+
+        public static ulong[] Create64(int len)
+        {
+            return new ulong[len];
+        }
+
+        public static int Dec(int len, uint[] z)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                if (--z[i] != uint.MaxValue)
+                {
+                    return 0;
+                }
+            }
+            return -1;
+        }
+
+        public static int Dec(int len, uint[] x, uint[] z)
+        {
+            int i = 0;
+            while (i < len)
+            {
+                uint c = x[i] - 1;
+                z[i] = c;
+                ++i;
+                if (c != uint.MaxValue)
+                {
+                    while (i < len)
+                    {
+                        z[i] = x[i];
+                        ++i;
+                    }
+                    return 0;
+                }
+            }
+            return -1;
+        }
+
+        public static int DecAt(int len, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= len);
+            for (int i = zPos; i < len; ++i)
+            {
+                if (--z[i] != uint.MaxValue)
+                {
+                    return 0;
+                }
+            }
+            return -1;
+        }
+
+        public static int DecAt(int len, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= len);
+            for (int i = zPos; i < len; ++i)
+            {
+                if (--z[zOff + i] != uint.MaxValue)
+                {
+                    return 0;
+                }
+            }
+            return -1;
+        }
+
+        public static bool Eq(int len, uint[] x, uint[] y)
+        {
+            for (int i = len - 1; i >= 0; --i)
+            {
+                if (x[i] != y[i])
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static uint[] FromBigInteger(int bits, BigInteger x)
+        {
+            if (x.SignValue < 0 || x.BitLength > bits)
+                throw new ArgumentException();
+
+            int len = (bits + 31) >> 5;
+            uint[] z = Create(len);
+            int i = 0;
+            while (x.SignValue != 0)
+            {
+                z[i++] = (uint)x.IntValue;
+                x = x.ShiftRight(32);
+            }
+            return z;
+        }
+
+        public static uint GetBit(uint[] x, int bit)
+        {
+            if (bit == 0)
+            {
+                return x[0] & 1;
+            }
+            int w = bit >> 5;
+            if (w < 0 || w >= x.Length)
+            {
+                return 0;
+            }
+            int b = bit & 31;
+            return (x[w] >> b) & 1;
+        }
+
+        public static bool Gte(int len, uint[] x, uint[] y)
+        {
+            for (int i = len - 1; i >= 0; --i)
+            {
+                uint x_i = x[i], y_i = y[i];
+                if (x_i < y_i)
+                    return false;
+                if (x_i > y_i)
+                    return true;
+            }
+            return true;
+        }
+
+        public static uint Inc(int len, uint[] z)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                if (++z[i] != uint.MinValue)
+                {
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static uint Inc(int len, uint[] x, uint[] z)
+        {
+            int i = 0;
+            while (i < len)
+            {
+                uint c = x[i] + 1;
+                z[i] = c;
+                ++i;
+                if (c != 0)
+                {
+                    while (i < len)
+                    {
+                        z[i] = x[i];
+                        ++i;
+                    }
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static uint IncAt(int len, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= len);
+            for (int i = zPos; i < len; ++i)
+            {
+                if (++z[i] != uint.MinValue)
+                {
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static uint IncAt(int len, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= len);
+            for (int i = zPos; i < len; ++i)
+            {
+                if (++z[zOff + i] != uint.MinValue)
+                {
+                    return 0;
+                }
+            }
+            return 1;
+        }
+
+        public static bool IsOne(int len, uint[] x)
+        {
+            if (x[0] != 1)
+            {
+                return false;
+            }
+            for (int i = 1; i < len; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static bool IsZero(int len, uint[] x)
+        {
+            if (x[0] != 0)
+            {
+                return false;
+            }
+            for (int i = 1; i < len; ++i)
+            {
+                if (x[i] != 0)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        public static void Mul(int len, uint[] x, uint[] y, uint[] zz)
+        {
+            zz[len] = (uint)MulWord(len, x[0], y, zz);
+
+            for (int i = 1; i < len; ++i)
+            {
+                zz[i + len] = (uint)MulWordAddTo(len, x[i], y, 0, zz, i);
+            }
+        }
+
+        public static void Mul(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] zz, int zzOff)
+        {
+            zz[zzOff + len] = (uint)MulWord(len, x[xOff], y, yOff, zz, zzOff);
+
+            for (int i = 1; i < len; ++i)
+            {
+                zz[zzOff + i + len] = (uint)MulWordAddTo(len, x[xOff + i], y, yOff, zz, zzOff + i);
+            }
+        }
+
+        public static uint Mul31BothAdd(int len, uint a, uint[] x, uint b, uint[] y, uint[] z, int zOff)
+        {
+            ulong c = 0, aVal = (ulong)a, bVal = (ulong)b;
+            int i = 0;
+            do
+            {
+                c += aVal * x[i] + bVal * y[i] + z[zOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < len);
+            return (uint)c;
+        }
+
+        public static uint MulWord(int len, uint x, uint[] y, uint[] z)
+        {
+            ulong c = 0, xVal = (ulong)x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < len);
+            return (uint)c;
+        }
+
+        public static uint MulWord(int len, uint x, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = (ulong)x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[yOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < len);
+            return (uint)c;
+        }
+
+        public static uint MulWordAddTo(int len, uint x, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = (ulong)x;
+            int i = 0;
+            do
+            {
+                c += xVal * y[yOff + i] + z[zOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < len);
+            return (uint)c;
+        }
+
+        public static uint MulWordDwordAddAt(int len, uint x, ulong y, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 3));
+            ulong c = 0, xVal = (ulong)x;
+            c += xVal * (uint)y + z[zPos + 0];
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += xVal * (y >> 32) + z[zPos + 1];
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            c += (ulong)z[zPos + 2];
+            z[zPos + 2] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : IncAt(len, z, zPos + 3);
+        }
+
+        public static uint ShiftDownBit(int len, uint[] z, uint c)
+        {
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = z[i];
+                z[i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBit(int len, uint[] z, int zOff, uint c)
+        {
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = z[zOff + i];
+                z[zOff + i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBit(int len, uint[] x, uint c, uint[] z)
+        {
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                z[i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBit(int len, uint[] x, int xOff, uint c, uint[] z, int zOff)
+        {
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = x[xOff + i];
+                z[zOff + i] = (next >> 1) | (c << 31);
+                c = next;
+            }
+            return c << 31;
+        }
+
+        public static uint ShiftDownBits(int len, uint[] z, int bits, uint c)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = z[i];
+                z[i] = (next >> bits) | (c << -bits);
+                c = next;
+            }
+            return c << -bits;
+        }
+
+        public static uint ShiftDownBits(int len, uint[] z, int zOff, int bits, uint c)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = z[zOff + i];
+                z[zOff + i] = (next >> bits) | (c << -bits);
+                c = next;
+            }
+            return c << -bits;
+        }
+
+        public static uint ShiftDownBits(int len, uint[] x, int bits, uint c, uint[] z)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = x[i];
+                z[i] = (next >> bits) | (c << -bits);
+                c = next;
+            }
+            return c << -bits;
+        }
+
+        public static uint ShiftDownBits(int len, uint[] x, int xOff, int bits, uint c, uint[] z, int zOff)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = x[xOff + i];
+                z[zOff + i] = (next >> bits) | (c << -bits);
+                c = next;
+            }
+            return c << -bits;
+        }
+
+        public static uint ShiftDownWord(int len, uint[] z, uint c)
+        {
+            int i = len;
+            while (--i >= 0)
+            {
+                uint next = z[i];
+                z[i] = c;
+                c = next;
+            }
+            return c;
+        }
+
+        public static uint ShiftUpBit(int len, uint[] z, uint c)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = z[i];
+                z[i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static uint ShiftUpBit(int len, uint[] z, int zOff, uint c)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = z[zOff + i];
+                z[zOff + i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static uint ShiftUpBit(int len, uint[] x, uint c, uint[] z)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = x[i];
+                z[i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static uint ShiftUpBit(int len, uint[] x, int xOff, uint c, uint[] z, int zOff)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = x[xOff + i];
+                z[zOff + i] = (next << 1) | (c >> 31);
+                c = next;
+            }
+            return c >> 31;
+        }
+
+        public static ulong ShiftUpBit64(int len, ulong[] x, int xOff, ulong c, ulong[] z, int zOff)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = x[xOff + i];
+                z[zOff + i] = (next << 1) | (c >> 63);
+                c = next;
+            }
+            return c >> 63;
+        }
+
+        public static uint ShiftUpBits(int len, uint[] z, int bits, uint c)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = z[i];
+                z[i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static uint ShiftUpBits(int len, uint[] z, int zOff, int bits, uint c)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = z[zOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static ulong ShiftUpBits64(int len, ulong[] z, int zOff, int bits, ulong c)
+        {
+            Debug.Assert(bits > 0 && bits < 64);
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = z[zOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static uint ShiftUpBits(int len, uint[] x, int bits, uint c, uint[] z)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = x[i];
+                z[i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static uint ShiftUpBits(int len, uint[] x, int xOff, int bits, uint c, uint[] z, int zOff)
+        {
+            Debug.Assert(bits > 0 && bits < 32);
+            for (int i = 0; i < len; ++i)
+            {
+                uint next = x[xOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static ulong ShiftUpBits64(int len, ulong[] x, int xOff, int bits, ulong c, ulong[] z, int zOff)
+        {
+            Debug.Assert(bits > 0 && bits < 64);
+            for (int i = 0; i < len; ++i)
+            {
+                ulong next = x[xOff + i];
+                z[zOff + i] = (next << bits) | (c >> -bits);
+                c = next;
+            }
+            return c >> -bits;
+        }
+
+        public static void Square(int len, uint[] x, uint[] zz)
+        {
+            int extLen = len << 1;
+            uint c = 0;
+            int j = len, k = extLen;
+            do
+            {
+                ulong xVal = (ulong)x[--j];
+                ulong p = xVal * xVal;
+                zz[--k] = (c << 31) | (uint)(p >> 33);
+                zz[--k] = (uint)(p >> 1);
+                c = (uint)p;
+            }
+            while (j > 0);
+
+            for (int i = 1; i < len; ++i)
+            {
+                c = SquareWordAdd(x, i, zz);
+                AddWordAt(extLen, c, zz, i << 1);
+            }
+
+            ShiftUpBit(extLen, zz, x[0] << 31);
+        }
+
+        public static void Square(int len, uint[] x, int xOff, uint[] zz, int zzOff)
+        {
+            int extLen = len << 1;
+            uint c = 0;
+            int j = len, k = extLen;
+            do
+            {
+                ulong xVal = (ulong)x[xOff + --j];
+                ulong p = xVal * xVal;
+                zz[zzOff + --k] = (c << 31) | (uint)(p >> 33);
+                zz[zzOff + --k] = (uint)(p >> 1);
+                c = (uint)p;
+            }
+            while (j > 0);
+
+            for (int i = 1; i < len; ++i)
+            {
+                c = SquareWordAdd(x, xOff, i, zz, zzOff);
+                AddWordAt(extLen, c, zz, zzOff, i << 1);
+            }
+
+            ShiftUpBit(extLen, zz, zzOff, x[xOff] << 31);
+        }
+
+        public static uint SquareWordAdd(uint[] x, int xPos, uint[] z)
+        {
+            ulong c = 0, xVal = (ulong)x[xPos];
+            int i = 0;
+            do
+            {
+                c += xVal * x[i] + z[xPos + i];
+                z[xPos + i] = (uint)c;
+                c >>= 32;
+            }
+            while (++i < xPos);
+            return (uint)c;
+        }
+
+        public static uint SquareWordAdd(uint[] x, int xOff, int xPos, uint[] z, int zOff)
+        {
+            ulong c = 0, xVal = (ulong)x[xOff + xPos];
+            int i = 0;
+            do
+            {
+                c += xVal * (x[xOff + i] & M) + (z[xPos + zOff] & M);
+                z[xPos + zOff] = (uint)c;
+                c >>= 32;
+                ++zOff;
+            }
+            while (++i < xPos);
+            return (uint)c;
+        }
+
+        public static int Sub(int len, uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)x[i] - y[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int Sub(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)x[xOff + i] - y[yOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+        public static int Sub33At(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zPos + 0] - x;
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zPos + 1] - 1;
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zPos + 2);
+        }
+
+        public static int Sub33At(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zOff + zPos] - x;
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + zPos + 1] - 1;
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 2);
+        }
+
+        public static int Sub33From(int len, uint x, uint[] z)
+        {
+            long c = (long)z[0] - x;
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - 1;
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 2);
+        }
+
+        public static int Sub33From(int len, uint x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - 1;
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 2);
+        }
+
+        public static int SubBothFrom(int len, uint[] x, uint[] y, uint[] z)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)z[i] - x[i] - y[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int SubBothFrom(int len, uint[] x, int xOff, uint[] y, int yOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)z[zOff + i] - x[xOff + i] - y[yOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int SubDWordAt(int len, ulong x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zPos + 0] - (long)(x & M);
+            z[zPos + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zPos + 1] - (long)(x >> 32);
+            z[zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zPos + 2);
+        }
+
+        public static int SubDWordAt(int len, ulong x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 2));
+            long c = (long)z[zOff + zPos] - (long)(x & M);
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + zPos + 1] - (long)(x >> 32);
+            z[zOff + zPos + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z,  zOff, zPos + 2);
+        }
+
+        public static int SubDWordFrom(int len, ulong x, uint[] z)
+        {
+            long c = (long)z[0] - (long)(x & M);
+            z[0] = (uint)c;
+            c >>= 32;
+            c += (long)z[1] - (long)(x >> 32);
+            z[1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 2);
+        }
+
+        public static int SubDWordFrom(int len, ulong x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - (long)(x & M);
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            c += (long)z[zOff + 1] - (long)(x >> 32);
+            z[zOff + 1] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 2);
+        }
+
+        public static int SubFrom(int len, uint[] x, uint[] z)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)z[i] - x[i];
+                z[i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int SubFrom(int len, uint[] x, int xOff, uint[] z, int zOff)
+        {
+            long c = 0;
+            for (int i = 0; i < len; ++i)
+            {
+                c += (long)z[zOff + i] - x[xOff + i];
+                z[zOff + i] = (uint)c;
+                c >>= 32;
+            }
+            return (int)c;
+        }
+
+        public static int SubWordAt(int len, uint x, uint[] z, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 1));
+            long c = (long)z[zPos] - x;
+            z[zPos] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zPos + 1);
+        }
+
+        public static int SubWordAt(int len, uint x, uint[] z, int zOff, int zPos)
+        {
+            Debug.Assert(zPos <= (len - 1));
+            long c = (long)z[zOff + zPos] - x;
+            z[zOff + zPos] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, zPos + 1);
+        }
+
+        public static int SubWordFrom(int len, uint x, uint[] z)
+        {
+            long c = (long)z[0] - x;
+            z[0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, 1);
+        }
+
+        public static int SubWordFrom(int len, uint x, uint[] z, int zOff)
+        {
+            long c = (long)z[zOff + 0] - x;
+            z[zOff + 0] = (uint)c;
+            c >>= 32;
+            return c == 0 ? 0 : DecAt(len, z, zOff, 1);
+        }
+
+        public static BigInteger ToBigInteger(int len, uint[] x)
+        {
+            byte[] bs = new byte[len << 2];
+            for (int i = 0; i < len; ++i)
+            {
+                uint x_i = x[i];
+                if (x_i != 0)
+                {
+                    Pack.UInt32_To_BE(x_i, bs, (len - 1 - i) << 2);
+                }
+            }
+            return new BigInteger(1, bs);
+        }
+
+        public static void Zero(int len, uint[] z)
+        {
+            for (int i = 0; i < len; ++i)
+            {
+                z[i] = 0;
+            }
+        }
+    }
+}