// MultNm()
//
// Multiply two numerics.
//
// Parameters:
// x - IN Multiplier
// y - IN Multiplicand
//
// Result scale and precision(same as in SQL Server Manual and Hydra):
// scale = s1 + s2
// precision = s1 + s2 + (p1 - s1) + (p2 - s2) + 1
//
// Overflow Rules:
// If scale is greater than NUMERIC_MAX_PRECISION it is set to
// NUMERIC_MAX_PRECISION. If precision is greater than NUMERIC_MAX_PRECISION
// it is set to NUMERIC_MAX_PRECISION, then scale is reduced to keep the
// integer part untruncated but keeping a minimum value of x_cNumeDivScaleMin.
// For example, if using the above formula, the resulting precision is 46 and
// scale is 10, the precision will be reduced to 38. To keep the integral part
// untruncated the scale needs be reduced to 2, but since x_cNumeDivScaleMin
// is set to 6 currently, resulting scale will be 6.
// O_OVERFLOW is returned only if the actual precision is greater than
// NUMERIC_MAX_PRECISION or the actual length is greater than x_cbNumeBuf.
//
// Algorithm:
// Starting from the lowest significant UI4, for each UI4 of the multiplier
// iterate through the UI4s of the multiplicand starting from
// the least significant UI4s, multiply the multiplier UI4 with
// multiplicand UI4, update the result buffer with the product modulo
// x_dwlBaseUI4 at the same index as the multiplicand, and carry the quotient to
// add to the next multiplicand UI4. Until the end of the multiplier data
// array is reached.
//
/// <devdoc>
/// <para>[To be supplied.]</para>
/// </devdoc>
public static SqlDecimal operator *(SqlDecimal x, SqlDecimal y)
{
x.AssertValid();
y.AssertValid();
if (x.IsNull || y.IsNull)
return Null;
//Implementation:
// I) Figure result scale,prec
// II) Perform mult.
// III) Adjust product to result scale,prec
// Local variables for actual multiplication
int iulPlier; //index of UI4 in the Multiplier
uint ulPlier; //current multiplier UI4
ulong dwlAccum; //accumulated sum
ulong dwlNextAccum; //overflow of accumulated sum
int culCand = y.m_bLen; //length of multiplicand in UI4s
//Local variables to track scale,precision
int ActualScale; // Scale after mult done
int ResScale; // Final scale we will force result to
int ResPrec; // Final precision we will force result to
int ResInteger; // # of digits in integer part of result (prec-scale)
int lScaleAdjust; //How much result scale will be adjusted
bool fResPositive; // Result sign
SqlDecimal ret;
//I) Figure result prec,scale
ActualScale = x.m_bScale + y.m_bScale;
ResScale = ActualScale;
ResInteger = (x.m_bPrec - x.m_bScale) + (y.m_bPrec - y.m_bScale) + 1;
//result precision = s1 + s2 + (p1 - s1) + (p2 - s2) + 1
ResPrec = ResScale + ResInteger;
// Downward adjust res prec,scale if either larger than NUMERIC_MAX_PRECISION
if (ResPrec > s_NUMERIC_MAX_PRECISION)
ResPrec = s_NUMERIC_MAX_PRECISION;
if (ResScale > s_NUMERIC_MAX_PRECISION)
ResScale = s_NUMERIC_MAX_PRECISION;
//
// It is possible when two large numbers are being multiplied the scale
// can be reduced to 0 to keep data untruncated; the fix here is to
// preserve a minimum scale of 6.
//
// If overflow, reduce the scale to avoid truncation of data
ResScale = Math.Min((ResPrec - ResInteger), ResScale);
// But keep a minimum scale of NUMERIC_MIN_DVSCALE
ResScale = Math.Max(ResScale, Math.Min(ActualScale, s_cNumeDivScaleMin));
lScaleAdjust = ResScale - ActualScale;
fResPositive = (x.IsPositive == y.IsPositive);//positive if both signs same.
// II) Perform multiplication
uint[] rglData1 = new uint[4] { x.m_data1, x.m_data2, x.m_data3, x.m_data4 };
uint[] rglData2 = new uint[4] { y.m_data1, y.m_data2, y.m_data3, y.m_data4 };
//Local buffer to hold the result of multiplication.
//Longer than CReNumeBuf because full precision of multiplication is carried out
const int x_culNumeMultRes = 9; // Maximum # UI4s in result buffer in multiplication
uint[] rgulRes = new uint[x_culNumeMultRes]; //new [] are already initialized to zero
int culRes; // # of UI4s in result
int idRes = 0;
//Iterate over the bytes of multiplier
for (iulPlier = 0; iulPlier < x.m_bLen; iulPlier++)
{
ulPlier = rglData1[iulPlier];
dwlAccum = 0;
//Multiply each UI4 of multiCand by ulPliear and accumulate into result buffer
// Start on correct place in result
idRes = iulPlier;
for (int iulCand = 0; iulCand < culCand; iulCand++)
{
// dwlAccum = dwlAccum + rgulRes[idRes] + ulPlier*rglData2[iulCand]
// use dwlNextAccum to detect overflow of DWORDLONG
dwlNextAccum = dwlAccum + rgulRes[idRes];
ulong ulTemp = (ulong)rglData2[iulCand];
dwlAccum = (ulong)ulPlier * ulTemp;
dwlAccum += dwlNextAccum;
if (dwlAccum < dwlNextAccum) // indicates dwl addition overflowed
dwlNextAccum = s_ulInt32Base; // = maxUI64/x_dwlBaseUI4
else
dwlNextAccum = 0;
// Update result and accum
rgulRes[idRes++] = (uint)(dwlAccum);// & x_ulInt32BaseForMod); // equiv to mod x_lInt32Base
dwlAccum = (dwlAccum >> 32) + dwlNextAccum; // equiv to div BaseUI4 + dwlNAccum
// dwlNextAccum can't overflow next iteration
Debug.Assert(dwlAccum < s_ulInt32Base * 2);
}
Debug.Assert(dwlAccum < s_ulInt32Base); // can never final accum > 1 more UI4
if (dwlAccum != 0)
rgulRes[idRes++] = (uint)dwlAccum;
}
// Skip leading 0s (may exist if we are multiplying by 0)
for (; (rgulRes[idRes] == 0) && (idRes > 0); idRes--)
;
// Calculate actual result length
culRes = idRes + 1;
// III) Adjust precision,scale to result prec,scale
if (lScaleAdjust != 0)
{
// If need to decrease scale
if (lScaleAdjust < 0)
{
Debug.Assert(s_NUMERIC_MAX_PRECISION == ResPrec);
// have to adjust - might yet end up fitting.
// Cannot call AdjustScale - number cannot fit in a numeric, so
// have to duplicate code here
uint ulRem; //Remainder when downshifting
uint ulShiftBase; //What to multiply by to effect scale adjust
do
{
if (lScaleAdjust <= -9)
{
ulShiftBase = s_rgulShiftBase[8];
lScaleAdjust += 9;
}
else
{
ulShiftBase = s_rgulShiftBase[-lScaleAdjust - 1];
lScaleAdjust = 0;
}
MpDiv1(rgulRes, ref culRes, ulShiftBase, out ulRem);
}
while (lScaleAdjust != 0);
// Still do not fit?
if (culRes > s_cNumeMax)
throw new OverflowException(SQLResource.ArithOverflowMessage);
for (idRes = culRes; idRes < s_cNumeMax; idRes++)
rgulRes[idRes] = 0;
ret = new SqlDecimal(rgulRes, (byte)culRes, (byte)ResPrec, (byte)ResScale, fResPositive);
// Is it greater than 10**38?
if (ret.FGt10_38())
throw new OverflowException(SQLResource.ArithOverflowMessage);
ret.AssertValid();
// If remainder is 5 or above, increment/decrement by 1.
if (ulRem >= ulShiftBase / 2)
ret.AddULong(1);
// After adjusting, if the result is 0 and remainder is less than 5,
// set the sign to be positive
if (ret.FZero())
ret.SetPositive();
return ret;
}
// Otherwise call AdjustScale
if (culRes > s_cNumeMax) // Do not fit now, so will not fit after adjustment
throw new OverflowException(SQLResource.ArithOverflowMessage);
// NOTE: Have not check for value in the range (10**38..2**128),
// as we'll call AdjustScale with positive argument, and it'll
// return "normal" overflow
for (idRes = culRes; idRes < s_cNumeMax; idRes++)
rgulRes[idRes] = 0;
ret = new SqlDecimal(rgulRes, (byte)culRes, (byte)ResPrec, (byte)ActualScale, fResPositive);
if (ret.FZero())
ret.SetPositive();
ret.AssertValid();
ret.AdjustScale(lScaleAdjust, true);
return ret;
}
else
{
if (culRes > s_cNumeMax)
throw new OverflowException(SQLResource.ArithOverflowMessage);
for (idRes = culRes; idRes < s_cNumeMax; idRes++)
rgulRes[idRes] = 0;
ret = new SqlDecimal(rgulRes, (byte)culRes, (byte)ResPrec, (byte)ResScale, fResPositive);
// Is it greater than 10**38?
if (ret.FGt10_38())
throw new OverflowException(SQLResource.ArithOverflowMessage);
if (ret.FZero())
ret.SetPositive();
ret.AssertValid();
return ret;
}
}
public static SqlDecimal operator *(SqlDecimal x, SqlDecimal y)
{
SqlDecimal num11;
if (x.IsNull || y.IsNull)
{
return Null;
}
int bLen = y.m_bLen;
int num10 = x.m_bScale + y.m_bScale;
int num3 = num10;
int num13 = ((x.m_bPrec - x.m_bScale) + (y.m_bPrec - y.m_bScale)) + 1;
int num6 = num3 + num13;
if (num6 > NUMERIC_MAX_PRECISION)
{
num6 = NUMERIC_MAX_PRECISION;
}
if (num3 > NUMERIC_MAX_PRECISION)
{
num3 = NUMERIC_MAX_PRECISION;
}
num3 = Math.Max(Math.Min(num6 - num13, num3), Math.Min(num10, x_cNumeDivScaleMin));
int digits = num3 - num10;
bool fPositive = x.IsPositive == y.IsPositive;
uint[] numArray5 = new uint[] { x.m_data1, x.m_data2, x.m_data3, x.m_data4 };
uint[] numArray4 = new uint[] { y.m_data1, y.m_data2, y.m_data3, y.m_data4 };
uint[] rgulU = new uint[9];
int index = 0;
for (int i = 0; i < x.m_bLen; i++)
{
uint num16 = numArray5[i];
ulong num2 = 0L;
index = i;
for (int j = 0; j < bLen; j++)
{
ulong num7 = num2 + rgulU[index];
ulong num15 = numArray4[j];
num2 = num16 * num15;
num2 += num7;
if (num2 < num7)
{
num7 = x_ulInt32Base;
}
else
{
num7 = 0L;
}
rgulU[index++] = (uint) num2;
num2 = (num2 >> 0x20) + num7;
}
if (num2 != 0L)
{
rgulU[index++] = (uint) num2;
}
}
while ((rgulU[index] == 0) && (index > 0))
{
index--;
}
int ciulU = index + 1;
if (digits != 0)
{
if (digits < 0)
{
uint num12;
uint num14;
do
{
if (digits <= -9)
{
num12 = x_rgulShiftBase[8];
digits += 9;
}
else
{
num12 = x_rgulShiftBase[-digits - 1];
digits = 0;
}
MpDiv1(rgulU, ref ciulU, num12, out num14);
}
while (digits != 0);
if (ciulU > x_cNumeMax)
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
for (index = ciulU; index < x_cNumeMax; index++)
{
rgulU[index] = 0;
}
num11 = new SqlDecimal(rgulU, (byte) ciulU, (byte) num6, (byte) num3, fPositive);
if (num11.FGt10_38())
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
if (num14 >= (num12 / 2))
{
num11.AddULong(1);
}
if (num11.FZero())
{
num11.SetPositive();
}
return num11;
}
if (ciulU > x_cNumeMax)
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
for (index = ciulU; index < x_cNumeMax; index++)
{
rgulU[index] = 0;
}
num11 = new SqlDecimal(rgulU, (byte) ciulU, (byte) num6, (byte) num10, fPositive);
if (num11.FZero())
{
num11.SetPositive();
}
num11.AdjustScale(digits, true);
return num11;
}
if (ciulU > x_cNumeMax)
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
for (index = ciulU; index < x_cNumeMax; index++)
{
rgulU[index] = 0;
}
num11 = new SqlDecimal(rgulU, (byte) ciulU, (byte) num6, (byte) num3, fPositive);
if (num11.FGt10_38())
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
if (num11.FZero())
{
num11.SetPositive();
}
return num11;
}
// Binary operators
// Arithmetic operators
/// <devdoc>
/// <para>[To be supplied.]</para>
/// </devdoc>
public static SqlDecimal operator +(SqlDecimal x, SqlDecimal y)
{
if (x.IsNull || y.IsNull)
return Null;
ulong dwlAccum; //accumulated sum
bool fMySignPos; //sign of x was positive at start
bool fOpSignPos; // sign of y positive at start
bool fResSignPos = true; //sign of result should be positive
int MyScale; //scale of x
int OpScale; //scale of y
int ResScale; //scale of result
int ResPrec; //precision of result
int ResInteger; //number of digits for the integer part of result
int culOp1; //# of UI4s in x
int culOp2; //# of UI4s in y
int iulData; //which UI4 we are operating on in x, y
byte bLen; // length for the result
x.AssertValid();
y.AssertValid();
fMySignPos = x.IsPositive;
fOpSignPos = y.IsPositive;
//result scale = max(s1,s2)
//result precision = max(s1,s2) + max(p1-s1,p2-s2)
MyScale = x.m_bScale;
OpScale = y.m_bScale;
// Calculate the integer part of the result.
ResInteger = Math.Max((int)x.m_bPrec - MyScale, (int)y.m_bPrec - OpScale);
Debug.Assert(ResInteger <= MaxPrecision);
// Calculate the scale of the result.
ResScale = Math.Max(MyScale, OpScale);
Debug.Assert(ResScale <= MaxScale);
// Calculate the precision of the result.
// Add 1 for final carry.
ResPrec = ResInteger + ResScale + 1;
ResPrec = Math.Min(MaxPrecision, ResPrec);
// If precision adjusted, scale is reduced to keep the integer part untruncated.
// But discard the extra carry, only keep the integer part as ResInteger, not ResInteger + 1.
Debug.Assert(ResPrec - ResInteger >= 0);
if (ResPrec - ResInteger < ResScale)
ResScale = ResPrec - ResInteger;
// Adjust both operands to be the same scale as ResScale.
if (MyScale != ResScale)
x.AdjustScale(ResScale - MyScale, true);
if (OpScale != ResScale)
y.AdjustScale(ResScale - OpScale, true);
// When sign of first operand is negative
// negate all operands including result.
if (!fMySignPos)
{
fMySignPos = !fMySignPos;
fOpSignPos = !fOpSignPos;
fResSignPos = !fResSignPos;
}
// Initialize operand lengths and pointer.
culOp1 = x.m_bLen;
culOp2 = y.m_bLen;
uint[] rglData1 = new uint[4] { x.m_data1, x.m_data2, x.m_data3, x.m_data4 };
uint[] rglData2 = new uint[4] { y.m_data1, y.m_data2, y.m_data3, y.m_data4 };
if (fOpSignPos)
{
dwlAccum = 0;
// CONSIDER: Call AddUlong when possible
// Loop through UI4s adding operands and putting result in *this
// of the operands and put result in *this
for (iulData = 0; iulData < culOp1 || iulData < culOp2; iulData++)
{
// None of these DWORDLONG additions can overflow, as dwlAccum comes in < x_lInt32Base
if (iulData < culOp1)
dwlAccum += rglData1[iulData];
if (iulData < culOp2)
dwlAccum += rglData2[iulData];
rglData1[iulData] = (uint)dwlAccum; // equiv to mod x_lInt32Base
dwlAccum >>= 32; // equiv to div x_lInt32Base
}
//If carry
if (dwlAccum != 0)
{
Debug.Assert(dwlAccum < s_ulInt32Base);
//Either overflowed
if (iulData == s_cNumeMax)
throw new OverflowException(SQLResource.ArithOverflowMessage);
// Or extended length
rglData1[iulData] = (uint)dwlAccum;
iulData++;
}
// Set result length
bLen = (byte)iulData;
}
else
{
int iulLastNonZero = 0; // The last nonzero UI
// When second operand is negative, switch operands
// if operand2 is greater than operand1
if (x.LAbsCmp(y) < 0)
{
fResSignPos = !fResSignPos;
uint[] rguiTemp = rglData2;
rglData2 = rglData1;
rglData1 = rguiTemp;
culOp1 = culOp2;
culOp2 = x.m_bLen;
}
dwlAccum = s_ulInt32Base;
for (iulData = 0; iulData < culOp1 || iulData < culOp2; iulData++)
{
if (iulData < culOp1)
dwlAccum += rglData1[iulData];
if (iulData < culOp2)
dwlAccum -= rglData2[iulData];
rglData1[iulData] = (uint)dwlAccum; // equiv to mod BaseUI4
if (rglData1[iulData] != 0)
iulLastNonZero = iulData;
dwlAccum >>= 32; // equiv to /= BaseUI4
dwlAccum += s_ulInt32BaseForMod; // equiv to BaseUI4 - 1
}
// Set length based on highest non-zero ULONG
bLen = (byte)(iulLastNonZero + 1);
}
SqlDecimal ret = new SqlDecimal(rglData1, bLen, (byte)ResPrec, (byte)ResScale, fResSignPos);
if (ret.FGt10_38() || ret.CalculatePrecision() > s_NUMERIC_MAX_PRECISION)
throw new OverflowException(SQLResource.ArithOverflowMessage);
if (ret.FZero())
ret.SetPositive();
ret.AssertValid();
return ret;
}
public static SqlDecimal operator +(SqlDecimal x, SqlDecimal y)
{
int num;
ulong num2;
byte num11;
if (x.IsNull || y.IsNull)
{
return Null;
}
bool fPositive = true;
bool isPositive = x.IsPositive;
bool flag2 = y.IsPositive;
int bScale = x.m_bScale;
int num7 = y.m_bScale;
int num9 = Math.Max((int) (x.m_bPrec - bScale), (int) (y.m_bPrec - num7));
int num3 = Math.Max(bScale, num7);
int num6 = (num9 + num3) + 1;
num6 = Math.Min(MaxPrecision, num6);
if ((num6 - num9) < num3)
{
num3 = num6 - num9;
}
if (bScale != num3)
{
x.AdjustScale(num3 - bScale, true);
}
if (num7 != num3)
{
y.AdjustScale(num3 - num7, true);
}
if (!isPositive)
{
isPositive = !isPositive;
flag2 = !flag2;
fPositive = !fPositive;
}
int bLen = x.m_bLen;
int num4 = y.m_bLen;
uint[] rglData = new uint[] { x.m_data1, x.m_data2, x.m_data3, x.m_data4 };
uint[] numArray4 = new uint[] { y.m_data1, y.m_data2, y.m_data3, y.m_data4 };
if (flag2)
{
num2 = 0L;
num = 0;
while ((num < bLen) || (num < num4))
{
if (num < bLen)
{
num2 += rglData[num];
}
if (num < num4)
{
num2 += numArray4[num];
}
rglData[num] = (uint) num2;
num2 = num2 >> 0x20;
num++;
}
if (num2 != 0L)
{
if (num == x_cNumeMax)
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
rglData[num] = (uint) num2;
num++;
}
num11 = (byte) num;
}
else
{
int num10 = 0;
if (x.LAbsCmp(y) < 0)
{
fPositive = !fPositive;
uint[] numArray5 = numArray4;
numArray4 = rglData;
rglData = numArray5;
bLen = num4;
num4 = x.m_bLen;
}
num2 = x_ulInt32Base;
for (num = 0; (num < bLen) || (num < num4); num++)
{
if (num < bLen)
{
num2 += rglData[num];
}
if (num < num4)
{
num2 -= numArray4[num];
}
rglData[num] = (uint) num2;
if (rglData[num] != 0)
{
num10 = num;
}
num2 = num2 >> 0x20;
num2 += x_ulInt32BaseForMod;
}
num11 = (byte) (num10 + 1);
}
SqlDecimal num12 = new SqlDecimal(rglData, num11, (byte) num6, (byte) num3, fPositive);
if (num12.FGt10_38() || (num12.CalculatePrecision() > NUMERIC_MAX_PRECISION))
{
throw new OverflowException(SQLResource.ArithOverflowMessage);
}
if (num12.FZero())
{
num12.SetPositive();
}
return num12;
}
