public Fraction(Fraction/*!*/ copyFrom, int maxPrecision)
: this(maxPrecision, maxPrecision)
{
// Copy the fraction
int length = System.Math.Min(maxPrecision, copyFrom.MaxPrecision);
Array.Copy(copyFrom._words, _words, length);
}
private static Fraction/*!*/ Normalize(Fraction/*!*/ f, out int digitOffset)
{
// Count leading zero words
int leadingZeroWords = 0;
while (leadingZeroWords < f.MaxPrecision && f._words[leadingZeroWords] == 0)
{
leadingZeroWords++;
}
if (leadingZeroWords == f.MaxPrecision)
{
// The fraction is just all zeros
digitOffset = 0;
return f;
}
// Count trailing zero words
int trailingZeroWords = 0;
while (f._words[f.Precision - 1 - trailingZeroWords] == 0)
{
trailingZeroWords++;
}
// Count leading zero digits (within the first non-zero word)
// and also calculate up and down factors for masking
int leadingZeroDigits = BASE_FIG;
uint firstWord = f._words[leadingZeroWords];
uint downFactor = 1;
while (firstWord != 0)
{
firstWord /= 10;
leadingZeroDigits--;
downFactor *= 10;
}
uint upFactor = BASE / downFactor;
int newPrecision = f.Precision - leadingZeroWords - trailingZeroWords;
Fraction n = new Fraction(newPrecision);
// Copy the non-zero words across
Array.Copy(f._words, leadingZeroWords, n._words, 0, n.MaxPrecision);
if (leadingZeroDigits > 0)
{
// Scroll the digits within the non-zero words to trim off the first zero digits
uint bottomDigits = n._words[0] * upFactor;
uint topDigits = 0;
int wordIndex = 1;
while (wordIndex < n.Precision)
{
topDigits = n._words[wordIndex] / downFactor;
n._words[wordIndex - 1] = bottomDigits + topDigits;
bottomDigits = (n._words[wordIndex] % downFactor) * upFactor;
wordIndex++;
}
// Fix up the last word
n._words[wordIndex - 1] = bottomDigits;
// and the Precision
n.Precision = wordIndex;
}
// Return the offset in digits caused by the normalization.
digitOffset = -(leadingZeroWords * BASE_FIG + leadingZeroDigits);
return n;
}
private static Fraction/*!*/ Parse(string/*!*/ digits, out int digitOffset)
{
// Trim off any trailing zeros
digits = digits.TrimEnd('0');
if (digits == "")
{
digitOffset = 0;
return Zero;
}
// Create the new fraction
int precision = digits.Length / BASE_FIG;
int finalDigits = digits.Length % BASE_FIG;
if (finalDigits > 0) { ++precision; }
Fraction/*!*/ fraction = new Fraction(precision);
// Iterate through groups of BASE_FIG digits
int digitIndex;
int wordIndex = 0;
for (digitIndex = 0; digitIndex + BASE_FIG <= digits.Length; digitIndex += BASE_FIG)
{
fraction._words[wordIndex] = uint.Parse(digits.Substring(digitIndex, BASE_FIG), CultureInfo.InvariantCulture);
wordIndex++;
}
// Add on the last few digits, adding extra zeros as necessary
if (finalDigits > 0)
{
uint lastWord = uint.Parse(digits.Substring(digitIndex), CultureInfo.InvariantCulture);
while (finalDigits < BASE_FIG)
{
lastWord *= 10;
++finalDigits;
}
fraction._words[wordIndex] = lastWord;
}
fraction = Fraction.Normalize(fraction, out digitOffset);
return fraction;
}
/// <summary>
/// Limits the precision of the given Fraction.
/// </summary>
/// <param name="sign">The sign of the BigDecimal</param>
/// <param name="fraction">The fraction to limit</param>
/// <param name="digits">The number of digits to which we are limiting</param>
/// <param name="mode">The rounding mode to use when limiting</param>
/// <returns>A new fraction that has no more than <paramref name="digits"/> digits.</returns>
/// <example>
/// Consider a fraction of 123456789 using default HalfUp rounding.
/// Limit : Result
/// 1 1
/// 2 12
/// 3 123
/// 4 1234
/// 5 12346
/// 6 123457
/// 7 1234568
/// 8 12345679
/// 9 123456789
/// 10 123456789
/// </example>
public static Fraction/*!*/ LimitPrecision(int sign, Fraction/*!*/ fraction, int digits, BigDecimal.RoundingModes mode, out int offset)
{
Fraction result;
if (digits <= 0)
{
uint digit = (uint)(fraction.IsZero ? 0 : 1);
if (RoundDigit(sign, digit, 0, mode) > 0)
{
offset = 1 - digits;
return One;
}
else
{
offset = 0;
return Zero;
}
}
if (digits >= fraction.DigitCount)
{
offset = 0;
return fraction;
}
// Calculate offsets of relevant digits
int secondLastDigitIndex; // i.e. fraction[digits-1]
int secondLastWordIndex;
uint secondLastDigit;
int lastDigitIndex; // i.e. fraction[digits]
int lastWordIndex;
uint lastDigit;
#if SILVERLIGHT
secondLastWordIndex = DivRem(digits - 1, BASE_FIG, out secondLastDigitIndex);
#else
secondLastWordIndex = System.Math.DivRem(digits - 1, BASE_FIG, out secondLastDigitIndex);
#endif
if (secondLastDigitIndex == BASE_FIG - 1)
{
lastWordIndex = secondLastWordIndex + 1;
lastDigitIndex = 0;
}
else
{
lastWordIndex = secondLastWordIndex;
lastDigitIndex = secondLastDigitIndex + 1;
}
// TODO: Extract these calculations out into static readonly arrays
// Mask for last digit. E.g. lastDigitIndex = 3, BASE_FIG = 9 => lastFactor = 1000000
uint lastFactor = _powers[lastDigitIndex];
// Mask for second last digit
uint secondLastFactor = _powers[secondLastDigitIndex];
// Calculate the current digits and rounding direction
secondLastDigit = (fraction._words[secondLastWordIndex] / secondLastFactor) % 10;
if (lastWordIndex < fraction.MaxPrecision)
{
lastDigit = (fraction._words[lastWordIndex] / lastFactor) % 10;
}
else
{
lastDigit = 0;
}
int round = RoundDigit(sign, lastDigit, secondLastDigit, mode);
// Create a temporary fraction used to cause the rounding in the original
result = new Fraction(lastWordIndex + 1);
Array.Copy(fraction._words, 0, result._words, 0, System.Math.Min(lastWordIndex + 1, fraction.Precision));
// Clear the digits beyond the second last digit
result._words[secondLastWordIndex] = result._words[secondLastWordIndex] - (fraction._words[secondLastWordIndex] % secondLastFactor);
if (round > 0)
{
// Increment the last digit of result by 1
Fraction temp = new Fraction(secondLastWordIndex + 1);
temp._words[secondLastWordIndex] = secondLastFactor;
result = Fraction.Add(result, temp, 0, out offset);
}
else
{
offset = 0;
}
result.Precision = System.Math.Min(secondLastWordIndex + 1, result.MaxPrecision);
return result;
}
// Note: Scrolling left is just the same as scrolling right by (BASE_FIG-offset)
private static Fraction/*!*/ ScrollRight(Fraction/*!*/ fraction, int offset)
{
Debug.Assert(offset <= BASE_FIG);
Debug.Assert(offset >= 0);
// Don't do anything if offset is not going to change the internal digit layout
if (offset % BASE_FIG == 0)
{
return fraction;
}
int oldPrecision = fraction.Precision;
int newPrecision = oldPrecision + 1;
Fraction newFraction = new Fraction(newPrecision);
// Calculate masking values
// divisor is used to mask off and bring top digits down to bottom digits (TTTTTTBBBB / divisor == TTTTTT)
// also divisor is used to mask off the bottom digits (TTTTTTBBBB % divisor == BBBB)
// factor is then used to bring bottom digits up to top digits (BBBB * factor == BBBB000000)
uint downFactor = 1;
for (int i = 0; i < offset; ++i)
{
downFactor *= 10;
}
uint upFactor = BASE / downFactor;
// Scroll the digits
// We want to go from TTTTTTBBBB TTTTTTBBBB TTTTTTBBBB to 0000TTTTTT BBBBTTTTTT BBBBTTTTTT BBBB000000
// I.E. We are pushing all the digits to the right by "offset" amount and padding with zeros
uint topDigits = 0;
uint bottomDigits = 0;
int wordIndex = 0;
while (wordIndex < oldPrecision)
{
topDigits = fraction._words[wordIndex] / downFactor;
newFraction._words[wordIndex] = bottomDigits + topDigits;
bottomDigits = (fraction._words[wordIndex] % downFactor) * upFactor;
wordIndex++;
}
// Fix up the last word
newFraction._words[wordIndex] = bottomDigits;
return newFraction;
}
public static int Compare(Fraction/*!*/ x, Fraction/*!*/ y, int exponentDiff)
{
if (exponentDiff != 0)
{
return exponentDiff > 0 ? 1 : -1;
}
int wordIndex = 0;
while (wordIndex < x.Precision && wordIndex < y.Precision)
{
if (x._words[wordIndex] != y._words[wordIndex])
{
return x._words[wordIndex] > y._words[wordIndex] ? 1 : -1;
}
wordIndex++;
}
if (wordIndex == x.Precision)
{
while (wordIndex < y.Precision)
{
if (y._words[wordIndex] != 0)
{
return -1;
}
wordIndex++;
}
}
else
{
while (wordIndex < x.Precision)
{
if (x._words[wordIndex] != 0)
{
return 1;
}
wordIndex++;
}
}
return 0;
}
public static Fraction/*!*/ Divide(Fraction/*!*/ a, Fraction/*!*/ b, int minPrecision, out Fraction/*!*/ r, out int cOffset, out int rOffset)
{
int precision = System.Math.Max(a.MaxPrecision + b.MaxPrecision + 1, minPrecision);
Fraction c = new Fraction(precision);
r = new Fraction(precision * 2);
uint[] aWords = a._words;
uint[] bWords = b._words;
uint[] cWords = c._words;
uint[] rWords = r._words;
int aSize = a.Precision;
int bSize = b.Precision;
int cSize = c.MaxPrecision;
int rSize = r.MaxPrecision;
// Initialize remainder (we add an extra word at the front to catch the overflow
Array.Copy(aWords, 0, rWords, 1, System.Math.Min(aSize, rSize - 1));
// Setup basic values
ulong b1 = bWords[0];
ulong b1plus1 = bSize <= 1 ? b1 : b1 + 1;
ulong b1b2 = bSize <= 1 ? (ulong)bWords[0] * BASE : GetDoubleWord(bWords, 0, b.Precision);
ulong b1b2plus1 = bSize <= 2 ? b1b2 : b1b2 + 1;
// Main loop
int index = 1;
int size = System.Math.Min(cSize, rSize);
while (index < size)
{
if (rWords[index] == 0)
{
++index;
continue;
}
ulong r1r2 = GetDoubleWord(rWords, index, rSize);
if (r1r2 == b1b2)
{
// Iterate through the rest of b comparing words of r and b until they are not equal
int bIndex = 2;
int rIndex = index + 2;
FindNextNonEqual(rWords, bWords, bSize, ref rIndex, ref bIndex);
if (rIndex < rSize && bIndex < bSize && rWords[rIndex] < bWords[bIndex])
{
if (index + 1 > rSize)
{
break;
}
InternalDivide(rWords, rSize, r1r2 / b1plus1, bWords, bSize, index, cWords);
}
else
{
// Quotient is 1, just subtract b from r
SubtractInPlace(rWords, bWords, bSize, index);
cWords[index - 1]++;
Carry(cWords, index);
}
}
else if (r1r2 >= b1b2plus1)
{
InternalDivide(rWords, rSize, r1r2 / b1b2plus1, bWords, bSize, index - 1, cWords);
}
else
{
InternalDivide(rWords, rSize, r1r2 / b1plus1, bWords, bSize, index, cWords);
}
}
c = Normalize(c, out cOffset);
r = Normalize(r, out rOffset);
// We added artificially an extra word onto r and c to cope with carry overflow (so take away again now)
cOffset += BASE_FIG;
rOffset += BASE_FIG;
return c;
}
public static Fraction/*!*/ Multiply(Fraction/*!*/ x, Fraction/*!*/ y, out int offset)
{
int xPrecision = x.Precision;
int yPrecision = y.Precision;
int zPrecision = xPrecision + yPrecision;
uint[] xData = x._words;
uint[] yData = y._words;
uint[] zData = new uint[zPrecision];
Fraction z = new Fraction(zData);
for (int xIndex = xPrecision - 1; xIndex >= 0; xIndex--)
{
uint xValue = xData[xIndex];
int zIndex = zPrecision - (xPrecision - xIndex);
ulong carry = 0;
for (int yIndex = yPrecision - 1; yIndex >= 0; yIndex--)
{
carry = carry + ((ulong)xValue) * yData[yIndex] + zData[zIndex];
zData[zIndex--] = (uint)(carry % BASE);
carry /= BASE;
}
while (carry != 0)
{
carry += zData[zIndex];
zData[zIndex--] = (uint)carry;
carry /= BASE;
}
}
z = Fraction.Normalize(z, out offset);
return z;
}
public static Fraction/*!*/ Subtract(Fraction/*!*/ x, Fraction/*!*/ y, int exponentDiff, out int exponentOffset, out int sign)
{
Fraction upper = x;
Fraction lower = y;
sign = Compare(x, y, exponentDiff);
if (sign == 0)
{
exponentOffset = 0;
return new Fraction(1);
}
else if (sign < 0)
{
exponentDiff = -exponentDiff;
upper = y;
lower = x;
}
// Calculate the word and digit offsets between upper and lower
int wordOffset = exponentDiff / BASE_FIG;
int digitOffset = exponentDiff % BASE_FIG;
// If necessary we need to scroll one of the arrays
if (digitOffset != 0)
{
lower = ScrollRight(lower, digitOffset);
}
int lowerStart = wordOffset;
// We should now have something like:
// UUU UUU UU0 000 000 000 (upperStart=0, upperLength=8)
// 000 0LL LLL LLL LLL LL0 (lowerStart=4, lowerLength=13)
// assuming that exponentDiff is 4 (or -4) and BASE_FIG is 3
// where each character above is a decimal digit and a space indicates a word boundary
// Also, upper should be larger than lower
int zPrecision = System.Math.Max(upper.Precision, lower.Precision + lowerStart);
Fraction z = new Fraction(zPrecision);
uint[] upperWords = upper._words;
uint[] lowerWords = lower._words;
uint[] zWords = z._words;
// Copy words of upper straight into z
Array.Copy(upperWords, 0, zWords, 0, upper.Precision);
//// Subtract words of lower from z, borrowing as necessary
SubtractInPlace(zWords, lowerWords, lower.Precision, lowerStart);
z = Fraction.Normalize(z, out exponentOffset);
return z;
}
public static Fraction/*!*/ Add(Fraction/*!*/ x, Fraction/*!*/y, int exponentDiff, out int exponentOffset)
{
Fraction upper = x;
Fraction lower = y;
// Switch x and y around if the exponentDiff is negative
bool swap = exponentDiff < 0;
if (swap)
{
exponentDiff = -exponentDiff;
upper = y;
lower = x;
}
// Calculate the word and digit offsets between upper and lower
int wordOffset = exponentDiff / BASE_FIG;
int digitOffset = exponentDiff % BASE_FIG;
// If necessary we need to scroll one of the arrays
if (digitOffset != 0)
{
lower = ScrollRight(lower, digitOffset);
}
int upperStart = 0;
int lowerStart = wordOffset;
// We should now have something like:
// UUU UUU UU0 000 000 000 (upperStart=0, upperLength=8)
// 000 0LL LLL LLL LLL LL0 (lowerStart=4, lowerLength=13)
// assuming that exponentDiff is 4 (or -4) and BASE_FIG is 3
// where each character above is a decimal digit and a space indicates a word boundary
int zPrecision = System.Math.Max(upper.Precision, lower.Precision + wordOffset) + 1;
Fraction z = new Fraction(zPrecision);
uint[] upperWords = upper._words;
uint[] lowerWords = lower._words;
uint[] zWords = z._words;
// Copy words of lower straight into z
Array.Copy(lowerWords, 0, zWords, lowerStart + 1, lower.Precision);
// Add words of upper into z, carrying as necessary
ulong carry = 0;
for (int i = upper.Precision - 1; i >= upperStart; i--)
{
carry += upperWords[i] + zWords[i + 1];
zWords[i + 1] = (uint)(carry % BASE);
carry /= BASE;
}
Debug.Assert(carry / BASE == 0);
zWords[0] = (uint)(carry % BASE);
// We expect there to be BASE_FIG offset when normalizing unless
// the carry overflowed into the top word.
z = Fraction.Normalize(z, out exponentOffset);
exponentOffset += BASE_FIG;
return z;
}
