|
public Sub ( int &sign, |
||
| sign | int | |
| reg | ||
| return | void | |
/// <summary>Adds the values of two specified <see cref="BigInteger" /> objects.</summary>
/// <returns>The sum of <paramref name="left" /> and <paramref name="right" />.</returns>
/// <param name="left">The first value to add.</param>
/// <param name="right">The second value to add.</param>
public static BigInteger operator +(BigInteger left, BigInteger right)
{
if (right.IsZero)
{
return(left);
}
if (left.IsZero)
{
return(right);
}
var signLeft = 1;
var signRight = 1;
var regLeft = new BigIntegerBuilder(left, ref signLeft);
var regRight = new BigIntegerBuilder(right, ref signRight);
if (signLeft != signRight)
{
regLeft.Sub(ref signLeft, ref regRight);
}
else
{
regLeft.Add(ref regRight);
}
return(regLeft.GetInteger(signLeft));
}
/// <summary>
/// Subtracts a <see cref="BigInteger" /> value from another
/// <see cref="BigInteger" /> value.
/// </summary>
/// <returns>The result of subtracting <paramref name="right" /> from <paramref name="left" />.</returns>
/// <param name="left">The value to subtract from (the minuend).</param>
/// <param name="right">The value to subtract (the subtrahend).</param>
public static BigInteger operator -(BigInteger left, BigInteger right)
{
if (right.IsZero)
{
return(left);
}
if (left.IsZero)
{
return(-right);
}
var leftSign = 1;
var rightSign = -1;
var regLeft = new BigIntegerBuilder(left, ref leftSign);
var regRight = new BigIntegerBuilder(right, ref rightSign);
if (leftSign != rightSign)
{
regLeft.Sub(ref leftSign, ref regRight);
}
else
{
regLeft.Add(ref regRight);
}
return(regLeft.GetInteger(leftSign));
}
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
{
int num2;
uint num11;
int sign = 1;
Label_0002:
num2 = reg1._iuLast + 1;
int b = reg2._iuLast + 1;
if (num2 < b)
{
#if !(dotNET10 || dotNET11 || dotNETCF10)
NumericsHelpers.Swap <BigIntegerBuilder>(ref reg1, ref reg2);
NumericsHelpers.Swap <int>(ref num2, ref b);
#else
NumericsHelpers.Swap(ref reg1, ref reg2);
NumericsHelpers.Swap(ref num2, ref b);
#endif
}
if (b == 1)
{
if (num2 == 1)
{
reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
return;
}
if (reg2._uSmall != 0)
{
reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
}
return;
}
if (num2 == 2)
{
reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
return;
}
if (b <= (num2 - 2))
{
reg1.Mod(ref reg2);
goto Label_0002;
}
ulong a = reg1.GetHigh2(num2);
ulong num5 = reg2.GetHigh2(num2);
int num6 = NumericsHelpers.CbitHighZero((ulong)(a | num5));
if (num6 > 0)
{
a = (a << num6) | (reg1._rgu[num2 - 3] >> (0x20 - num6));
num5 = (num5 << num6) | (reg2._rgu[num2 - 3] >> (0x20 - num6));
}
if (a < num5)
{
#if !(dotNET10 || dotNET11 || dotNETCF10)
NumericsHelpers.Swap <ulong>(ref a, ref num5);
NumericsHelpers.Swap <BigIntegerBuilder>(ref reg1, ref reg2);
#else
NumericsHelpers.Swap(ref a, ref num5);
NumericsHelpers.Swap(ref reg1, ref reg2);
#endif
}
if ((a == ulong.MaxValue) || (num5 == ulong.MaxValue))
{
a = a >> 1;
num5 = num5 >> 1;
}
if (a == num5)
{
reg1.Sub(ref sign, ref reg2);
goto Label_0002;
}
if (NumericsHelpers.GetHi(num5) == 0)
{
reg1.Mod(ref reg2);
goto Label_0002;
}
uint num7 = 1;
uint num8 = 0;
uint num9 = 0;
uint num10 = 1;
Label_0159:
num11 = 1;
ulong num12 = a - num5;
while ((num12 >= num5) && (num11 < 0x20))
{
num12 -= num5;
num11++;
}
if (num12 >= num5)
{
ulong num13 = a / num5;
if (num13 > 0xffffffffL)
{
goto Label_029E;
}
num11 = (uint)num13;
num12 = a - (num11 * num5);
}
ulong num14 = (ulong)num7 + (ulong)num11 * (ulong)num9;
ulong num15 = (ulong)num8 + (ulong)num11 * (ulong)num10;
if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (num5 - num9))))
{
num7 = (uint)num14;
num8 = (uint)num15;
a = num12;
if (a > num8)
{
num11 = 1;
num12 = num5 - a;
while ((num12 >= a) && (num11 < 0x20))
{
num12 -= a;
num11++;
}
if (num12 >= a)
{
ulong num16 = num5 / a;
if (num16 > 0xffffffffL)
{
goto Label_029E;
}
num11 = (uint)num16;
num12 = num5 - (num11 * a);
}
num14 = (ulong)num10 + (ulong)num11 * (ulong)num8;
num15 = (ulong)num9 + (ulong)num11 * (ulong)num7;
if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (a - num8))))
{
num10 = (uint)num14;
num9 = (uint)num15;
num5 = num12;
if (num5 > num9)
{
goto Label_0159;
}
}
}
}
Label_029E:
if (num8 == 0)
{
if ((a / ((ulong)2L)) >= num5)
{
reg1.Mod(ref reg2);
}
else
{
reg1.Sub(ref sign, ref reg2);
}
}
else
{
reg1.SetSizeKeep(b, 0);
reg2.SetSizeKeep(b, 0);
int num17 = 0;
int num18 = 0;
for (int i = 0; i < b; i++)
{
uint num20 = reg1._rgu[i];
uint num21 = reg2._rgu[i];
long num22 = (long)num20 * (long)num7 - (long)num21 * (long)num8 + (long)num17;
long num23 = (long)num21 * (long)num10 - (long)num20 * (long)num9 + (long)num18;
num17 = (int)(num22 >> 0x20);
num18 = (int)(num23 >> 0x20);
reg1._rgu[i] = (uint)num22;
reg2._rgu[i] = (uint)num23;
}
reg1.Trim();
reg2.Trim();
}
goto Label_0002;
}
// This leaves the GCD in reg1 and trash in reg2.
// This uses Lehmer's method, with test due to Jebelean / Belnkiy and Vidunas.
// See Knuth, vol 2, page 345; Jebelean (1993) "Improving the Multiprecision Euclidean Algorithm";
// and Belenkiy & Vidunas (1998) "A Greatest Common Divisor Algorithm".
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
{
// This value has no real significance. Occ----ionally we want to subtract
// the two registers and keep the absolute value of the difference. To do
// so we need to pass a ref sign to Sub.
int signTmp = +1;
for (; ;)
{
int cuMax = reg1._iuLast + 1;
int cuMin = reg2._iuLast + 1;
if (cuMax < cuMin)
{
NumericsHelpers.Swap(ref reg1, ref reg2);
NumericsHelpers.Swap(ref cuMax, ref cuMin);
}
if (cuMin == 1)
{
if (cuMax == 1)
{
reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
}
else if (reg2._uSmall != 0)
{
reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
}
return;
}
if (cuMax == 2)
{
reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
return;
}
if (cuMin <= cuMax - 2)
{
// reg1 is much larger than reg2, so just mod.
reg1.Mod(ref reg2);
continue;
}
ulong uu1 = reg1.GetHigh2(cuMax);
ulong uu2 = reg2.GetHigh2(cuMax);
int cbit = NumericsHelpers.CbitHighZero(uu1 | uu2);
if (cbit > 0)
{
uu1 = (uu1 << cbit) | (reg1._rgu[cuMax - 3] >> (kcbitUint - cbit));
// Note that [cuMax - 3] is correct, NOT [cuMin - 3].
uu2 = (uu2 << cbit) | (reg2._rgu[cuMax - 3] >> (kcbitUint - cbit));
}
if (uu1 < uu2)
{
NumericsHelpers.Swap(ref uu1, ref uu2);
NumericsHelpers.Swap(ref reg1, ref reg2);
}
// Make sure we don't overflow.
if (uu1 == ulong.MaxValue || uu2 == ulong.MaxValue)
{
uu1 >>= 1;
uu2 >>= 1;
}
if (uu1 == uu2)
{
// The high bits are the same, so we don't know which
// is larger. No matter, just subtract one from the other
// and keep the absolute value of the result.
reg1.Sub(ref signTmp, ref reg2);
continue;
}
if (NumericsHelpers.GetHi(uu2) == 0)
{
// reg1 is much larger than reg2, so just mod.
reg1.Mod(ref reg2);
continue;
}
// These are the coefficients to apply to reg1 and reg2 to get
// the new values, using: a * reg1 - b * reg2 and -c * reg1 + d * reg2.
uint a = 1, b = 0;
uint c = 0, d = 1;
for (; ;)
{
uint uQuo = 1;
ulong uuNew = uu1 - uu2;
while (uuNew >= uu2 && uQuo < 32)
{
uuNew -= uu2;
uQuo++;
}
if (uuNew >= uu2)
{
ulong uuQuo = uu1 / uu2;
if (uuQuo > uint.MaxValue)
{
break;
}
uQuo = (uint)uuQuo;
uuNew = uu1 - uQuo * uu2;
}
ulong uuAdNew = a + (ulong)uQuo * c;
ulong uuBcNew = b + (ulong)uQuo * d;
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
{
break;
}
// Jebelean / Belenkiy-Vidunas conditions
if (uuNew < uuBcNew || uuNew + uuAdNew > uu2 - c)
{
break;
}
a = (uint)uuAdNew;
b = (uint)uuBcNew;
uu1 = uuNew;
if (uu1 <= b)
{
break;
}
uQuo = 1;
uuNew = uu2 - uu1;
while (uuNew >= uu1 && uQuo < 32)
{
uuNew -= uu1;
uQuo++;
}
if (uuNew >= uu1)
{
ulong uuQuo = uu2 / uu1;
if (uuQuo > uint.MaxValue)
{
break;
}
uQuo = (uint)uuQuo;
uuNew = uu2 - uQuo * uu1;
}
uuAdNew = d + (ulong)uQuo * b;
uuBcNew = c + (ulong)uQuo * a;
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
{
break;
}
// Jebelean / Belenkiy-Vidunas conditions
if (uuNew < uuBcNew || uuNew + uuAdNew > uu1 - b)
{
break;
}
d = (uint)uuAdNew;
c = (uint)uuBcNew;
uu2 = uuNew;
if (uu2 <= c)
{
break;
}
}
if (b == 0)
{
if (uu1 / 2 >= uu2)
{
reg1.Mod(ref reg2);
}
else
{
reg1.Sub(ref signTmp, ref reg2);
}
}
else
{
// Replace reg1 with a * reg1 - b * reg2.
// Replace reg2 with -c * reg1 + d * reg2.
// Do everything mod cuMin uint's.
reg1.SetSizeKeep(cuMin, 0);
reg2.SetSizeKeep(cuMin, 0);
int nCarry1 = 0;
int nCarry2 = 0;
for (int iu = 0; iu < cuMin; iu++)
{
uint u1 = reg1._rgu[iu];
uint u2 = reg2._rgu[iu];
long nn1 = (long)u1 * a - (long)u2 * b + nCarry1;
long nn2 = (long)u2 * d - (long)u1 * c + nCarry2;
nCarry1 = (int)(nn1 >> kcbitUint);
nCarry2 = (int)(nn2 >> kcbitUint);
reg1._rgu[iu] = (uint)nn1;
reg2._rgu[iu] = (uint)nn2;
}
reg1.Trim();
reg2.Trim();
}
}
}
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2)
{
var num = 1;
while (true)
{
var num1 = reg1._iuLast + 1;
var num2 = reg2._iuLast + 1;
if (num1 < num2)
{
NumericHelper.Swap(ref reg1, ref reg2);
NumericHelper.Swap(ref num1, ref num2);
}
if (num2 == 1)
{
if (num1 == 1)
{
reg1._uSmall = NumericHelper.GCD(reg1._uSmall, reg2._uSmall);
}
else if (reg2._uSmall != 0)
{
reg1.Set(NumericHelper.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
}
return;
}
if (num1 == 2)
{
break;
}
if (num2 > num1 - 2)
{
var high2 = reg1.GetHigh2(num1);
var high21 = reg2.GetHigh2(num1);
var num3 = NumericHelper.CbitHighZero(high2 | high21);
if (num3 > 0)
{
high2 = (high2 << (num3 & 63)) | (reg1._bits[num1 - 3] >> ((32 - num3) & 31));
high21 = (high21 << (num3 & 63)) | (reg2._bits[num1 - 3] >> ((32 - num3) & 31));
}
if (high2 < high21)
{
NumericHelper.Swap(ref high2, ref high21);
NumericHelper.Swap(ref reg1, ref reg2);
}
if (high2 == ulong.MaxValue || high21 == ulong.MaxValue)
{
high2 >>= 1;
high21 >>= 1;
}
if (high2 == high21)
{
reg1.Sub(ref num, ref reg2);
}
else if (NumericHelper.GetHi(high21) != 0)
{
uint num4 = 1;
uint num5 = 0;
uint num6 = 0;
uint num7 = 1;
while (true)
{
uint num8 = 1;
var num9 = high2 - high21;
while (num9 >= high21 && num8 < 32)
{
num9 -= high21;
num8++;
}
if (num9 >= high21)
{
var num10 = high2 / high21;
if (num10 <= uint.MaxValue)
{
num8 = (uint)num10;
num9 = high2 - (num8 * high21);
}
else
{
break;
}
}
var num11 = num4 + (num8 * (ulong)num6);
var num12 = num5 + (num8 * (ulong)num7);
if (num11 > 2147483647 || num12 > 2147483647)
{
break;
}
if (num9 < num12 || num9 + num11 > high21 - num6)
{
break;
}
num4 = (uint)num11;
num5 = (uint)num12;
high2 = num9;
if (high2 > num5)
{
num8 = 1;
num9 = high21 - high2;
while (num9 >= high2 && num8 < 32)
{
num9 -= high2;
num8++;
}
if (num9 >= high2)
{
var num13 = high21 / high2;
if (num13 <= uint.MaxValue)
{
num8 = (uint)num13;
num9 = high21 - (num8 * high2);
}
else
{
break;
}
}
num11 = num7 + (num8 * (ulong)num5);
num12 = num6 + (num8 * (ulong)num4);
if (num11 > 2147483647 || num12 > 2147483647)
{
break;
}
if (num9 < num12 || num9 + num11 > high2 - num5)
{
break;
}
num7 = (uint)num11;
num6 = (uint)num12;
high21 = num9;
if (high21 <= num6)
{
break;
}
}
else
{
break;
}
}
if (num5 != 0)
{
reg1.SetSizeKeep(num2, 0);
reg2.SetSizeKeep(num2, 0);
var num14 = 0;
var num15 = 0;
for (var i = 0; i < num2; i++)
{
var num16 = reg1._bits[i];
var num17 = reg2._bits[i];
var num18 = ((long)num16 * num4) - ((long)num17 * num5) + num14;
var num19 = ((long)num17 * num7) - ((long)num16 * num6) + num15;
num14 = (int)(num18 >> 32);
num15 = (int)(num19 >> 32);
reg1._bits[i] = (uint)num18;
reg2._bits[i] = (uint)num19;
}
reg1.Trim();
reg2.Trim();
}
else if (high2 / 2 < high21)
{
reg1.Sub(ref num, ref reg2);
}
else
{
reg1.Mod(ref reg2);
}
}
else
{
reg1.Mod(ref reg2);
}
}
else
{
reg1.Mod(ref reg2);
}
}
reg1.Set(NumericHelper.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
}
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) {
int num2;
uint num11;
int sign = 1;
Label_0002:
num2 = reg1._iuLast + 1;
int b = reg2._iuLast + 1;
if (num2 < b) {
#if !(dotNET10 || dotNET11 || dotNETCF10)
NumericsHelpers.Swap<BigIntegerBuilder>(ref reg1, ref reg2);
NumericsHelpers.Swap<int>(ref num2, ref b);
#else
NumericsHelpers.Swap(ref reg1, ref reg2);
NumericsHelpers.Swap(ref num2, ref b);
#endif
}
if (b == 1) {
if (num2 == 1) {
reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
return;
}
if (reg2._uSmall != 0) {
reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
}
return;
}
if (num2 == 2) {
reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
return;
}
if (b <= (num2 - 2)) {
reg1.Mod(ref reg2);
goto Label_0002;
}
ulong a = reg1.GetHigh2(num2);
ulong num5 = reg2.GetHigh2(num2);
int num6 = NumericsHelpers.CbitHighZero((ulong)(a | num5));
if (num6 > 0) {
a = (a << num6) | (reg1._rgu[num2 - 3] >> (0x20 - num6));
num5 = (num5 << num6) | (reg2._rgu[num2 - 3] >> (0x20 - num6));
}
if (a < num5) {
#if !(dotNET10 || dotNET11 || dotNETCF10)
NumericsHelpers.Swap<ulong>(ref a, ref num5);
NumericsHelpers.Swap<BigIntegerBuilder>(ref reg1, ref reg2);
#else
NumericsHelpers.Swap(ref a, ref num5);
NumericsHelpers.Swap(ref reg1, ref reg2);
#endif
}
if ((a == ulong.MaxValue) || (num5 == ulong.MaxValue)) {
a = a >> 1;
num5 = num5 >> 1;
}
if (a == num5) {
reg1.Sub(ref sign, ref reg2);
goto Label_0002;
}
if (NumericsHelpers.GetHi(num5) == 0) {
reg1.Mod(ref reg2);
goto Label_0002;
}
uint num7 = 1;
uint num8 = 0;
uint num9 = 0;
uint num10 = 1;
Label_0159:
num11 = 1;
ulong num12 = a - num5;
while ((num12 >= num5) && (num11 < 0x20)) {
num12 -= num5;
num11++;
}
if (num12 >= num5) {
ulong num13 = a / num5;
if (num13 > 0xffffffffL) {
goto Label_029E;
}
num11 = (uint)num13;
num12 = a - (num11 * num5);
}
ulong num14 = (ulong)num7 + (ulong)num11 * (ulong)num9;
ulong num15 = (ulong)num8 + (ulong)num11 * (ulong)num10;
if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (num5 - num9)))) {
num7 = (uint)num14;
num8 = (uint)num15;
a = num12;
if (a > num8) {
num11 = 1;
num12 = num5 - a;
while ((num12 >= a) && (num11 < 0x20)) {
num12 -= a;
num11++;
}
if (num12 >= a) {
ulong num16 = num5 / a;
if (num16 > 0xffffffffL) {
goto Label_029E;
}
num11 = (uint)num16;
num12 = num5 - (num11 * a);
}
num14 = (ulong)num10 + (ulong)num11 * (ulong)num8;
num15 = (ulong)num9 + (ulong)num11 * (ulong)num7;
if (((num14 <= 0x7fffffffL) && (num15 <= 0x7fffffffL)) && ((num12 >= num15) && ((num12 + num14) <= (a - num8)))) {
num10 = (uint)num14;
num9 = (uint)num15;
num5 = num12;
if (num5 > num9) {
goto Label_0159;
}
}
}
}
Label_029E:
if (num8 == 0) {
if ((a / ((ulong)2L)) >= num5) {
reg1.Mod(ref reg2);
}
else {
reg1.Sub(ref sign, ref reg2);
}
}
else {
reg1.SetSizeKeep(b, 0);
reg2.SetSizeKeep(b, 0);
int num17 = 0;
int num18 = 0;
for (int i = 0; i < b; i++) {
uint num20 = reg1._rgu[i];
uint num21 = reg2._rgu[i];
long num22 = (long)num20 * (long)num7 - (long)num21 * (long)num8 + (long)num17;
long num23 = (long)num21 * (long)num10 - (long)num20 * (long)num9 + (long)num18;
num17 = (int)(num22 >> 0x20);
num18 = (int)(num23 >> 0x20);
reg1._rgu[i] = (uint)num22;
reg2._rgu[i] = (uint)num23;
}
reg1.Trim();
reg2.Trim();
}
goto Label_0002;
}
// This leaves the GCD in reg1 and trash in reg2.
// This uses Lehmer's method, with test due to Jebelean / Belnkiy and Vidunas.
// See Knuth, vol 2, page 345; Jebelean (1993) "Improving the Multiprecision Euclidean Algorithm";
// and Belenkiy & Vidunas (1998) "A Greatest Common Divisor Algorithm".
private static void LehmerGcd(ref BigIntegerBuilder reg1, ref BigIntegerBuilder reg2) {
// This value has no real significance. Occ----ionally we want to subtract
// the two registers and keep the absolute value of the difference. To do
// so we need to pass a ref sign to Sub.
int signTmp = +1;
for (; ; ) {
reg1.AssertValid(true);
reg2.AssertValid(true);
int cuMax = reg1._iuLast + 1;
int cuMin = reg2._iuLast + 1;
if (cuMax < cuMin) {
NumericsHelpers.Swap(ref reg1, ref reg2);
NumericsHelpers.Swap(ref cuMax, ref cuMin);
}
Contract.Assert(cuMax == reg1._iuLast + 1);
Contract.Assert(cuMin == reg2._iuLast + 1);
if (cuMin == 1) {
if (cuMax == 1)
reg1._uSmall = NumericsHelpers.GCD(reg1._uSmall, reg2._uSmall);
else if (reg2._uSmall != 0)
reg1.Set(NumericsHelpers.GCD(Mod(ref reg1, reg2._uSmall), reg2._uSmall));
return;
}
if (cuMax == 2) {
reg1.Set(NumericsHelpers.GCD(reg1.GetHigh2(2), reg2.GetHigh2(2)));
return;
}
if (cuMin <= cuMax - 2) {
// reg1 is much larger than reg2, so just mod.
reg1.Mod(ref reg2);
continue;
}
ulong uu1 = reg1.GetHigh2(cuMax);
ulong uu2 = reg2.GetHigh2(cuMax);
Contract.Assert(uu1 != 0 && uu2 != 0);
int cbit = NumericsHelpers.CbitHighZero(uu1 | uu2);
if (cbit > 0) {
uu1 = (uu1 << cbit) | (reg1._rgu[cuMax - 3] >> (kcbitUint - cbit));
// Note that [cuMax - 3] is correct, NOT [cuMin - 3].
uu2 = (uu2 << cbit) | (reg2._rgu[cuMax - 3] >> (kcbitUint - cbit));
}
if (uu1 < uu2) {
NumericsHelpers.Swap(ref uu1, ref uu2);
NumericsHelpers.Swap(ref reg1, ref reg2);
}
// Make sure we don't overflow.
if (uu1 == ulong.MaxValue || uu2 == ulong.MaxValue) {
uu1 >>= 1;
uu2 >>= 1;
}
Contract.Assert(uu1 >= uu2); // We ensured this above.
if (uu1 == uu2) {
// The high bits are the same, so we don't know which
// is larger. No matter, just subtract one from the other
// and keep the absolute value of the result.
Contract.Assert(cuMax == cuMin);
reg1.Sub(ref signTmp, ref reg2);
Contract.Assert(reg1._iuLast < cuMin - 1);
continue;
}
if (NumericsHelpers.GetHi(uu2) == 0) {
// reg1 is much larger than reg2, so just mod.
reg1.Mod(ref reg2);
continue;
}
// These are the coefficients to apply to reg1 and reg2 to get
// the new values, using: a * reg1 - b * reg2 and -c * reg1 + d * reg2.
uint a = 1, b = 0;
uint c = 0, d = 1;
for (; ; ) {
Contract.Assert(uu1 + a > a); // no overflow
Contract.Assert(uu2 + d > d);
Contract.Assert(uu1 > b);
Contract.Assert(uu2 > c);
Contract.Assert(uu2 + d <= uu1 - b);
uint uQuo = 1;
ulong uuNew = uu1 - uu2;
while (uuNew >= uu2 && uQuo < 32) {
uuNew -= uu2;
uQuo++;
}
if (uuNew >= uu2) {
ulong uuQuo = uu1 / uu2;
if (uuQuo > uint.MaxValue)
break;
uQuo = (uint)uuQuo;
uuNew = uu1 - uQuo * uu2;
}
ulong uuAdNew = a + (ulong)uQuo * c;
ulong uuBcNew = b + (ulong)uQuo * d;
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
break;
// Jebelean / Belenkiy-Vidunas conditions
if (uuNew < uuBcNew || uuNew + uuAdNew > uu2 - c)
break;
Contract.Assert(uQuo == (uu1 + a - 1) / (uu2 - c));
Contract.Assert(uQuo == (uu1 - b) / (uu2 + d));
a = (uint)uuAdNew;
b = (uint)uuBcNew;
uu1 = uuNew;
if (uu1 <= b) {
Contract.Assert(uu1 == b);
break;
}
Contract.Assert(uu1 + a > a); // no overflow
Contract.Assert(uu2 + d > d);
Contract.Assert(uu2 > c);
Contract.Assert(uu1 > b);
Contract.Assert(uu1 + a <= uu2 - c);
uQuo = 1;
uuNew = uu2 - uu1;
while (uuNew >= uu1 && uQuo < 32) {
uuNew -= uu1;
uQuo++;
}
if (uuNew >= uu1) {
ulong uuQuo = uu2 / uu1;
if (uuQuo > uint.MaxValue)
break;
uQuo = (uint)uuQuo;
uuNew = uu2 - uQuo * uu1;
}
uuAdNew = d + (ulong)uQuo * b;
uuBcNew = c + (ulong)uQuo * a;
if (uuAdNew > int.MaxValue || uuBcNew > int.MaxValue)
break;
// Jebelean / Belenkiy-Vidunas conditions
if (uuNew < uuBcNew || uuNew + uuAdNew > uu1 - b)
break;
Contract.Assert(uQuo == (uu2 + d - 1) / (uu1 - b));
Contract.Assert(uQuo == (uu2 - c) / (uu1 + a));
d = (uint)uuAdNew;
c = (uint)uuBcNew;
uu2 = uuNew;
if (uu2 <= c) {
Contract.Assert(uu2 == c);
break;
}
}
if (b == 0) {
Contract.Assert(a == 1 && c == 0 && d == 1);
Contract.Assert(uu1 > uu2); // We ensured this above.
if (uu1 / 2 >= uu2)
reg1.Mod(ref reg2);
else
reg1.Sub(ref signTmp, ref reg2);
}
else {
// Replace reg1 with a * reg1 - b * reg2.
// Replace reg2 with -c * reg1 + d * reg2.
// Do everything mod cuMin uint's.
reg1.SetSizeKeep(cuMin, 0);
reg2.SetSizeKeep(cuMin, 0);
int nCarry1 = 0;
int nCarry2 = 0;
for (int iu = 0; iu < cuMin; iu++) {
uint u1 = reg1._rgu[iu];
uint u2 = reg2._rgu[iu];
long nn1 = (long)u1 * a - (long)u2 * b + nCarry1;
long nn2 = (long)u2 * d - (long)u1 * c + nCarry2;
nCarry1 = (int)(nn1 >> kcbitUint);
nCarry2 = (int)(nn2 >> kcbitUint);
reg1._rgu[iu] = (uint)nn1;
reg2._rgu[iu] = (uint)nn2;
}
reg1.Trim();
reg2.Trim();
}
}
}