public void TestSubnormal()
{
ExpandedDouble hd = new ExpandedDouble(0x0000000000000001L);
if (hd.GetBinaryExponent() == -1023)
{
throw new AssertionException("identified bug - subnormal numbers not decoded properly");
}
Assert.AreEqual(-1086, hd.GetBinaryExponent());
BigInteger frac = hd.GetSignificand();
Assert.AreEqual(64, frac.BitLength());
Assert.AreEqual(1, frac.BitCount());
}
public void TestNegative()
{
ExpandedDouble hd = new ExpandedDouble(unchecked((long)0xC010000000000000L));
if (hd.GetBinaryExponent() == -2046)
{
throw new AssertionException("identified bug - sign bit not masked out of exponent");
}
Assert.AreEqual(2, hd.GetBinaryExponent());
BigInteger frac = hd.GetSignificand();
Assert.AreEqual(64, frac.BitLength());
Assert.AreEqual(1, frac.BitCount());
}
/* namespace */
public static String RawDoubleBitsToText(long pRawBits)
{
long rawBits = pRawBits;
bool isNegative = rawBits < 0; // sign bit is in the same place for long and double
if (isNegative)
{
rawBits &= 0x7FFFFFFFFFFFFFFFL;
}
if (rawBits == 0)
{
return(isNegative ? "-0" : "0");
}
ExpandedDouble ed = new ExpandedDouble(rawBits);
if (ed.GetBinaryExponent() < -1022)
{
// value is 'denormalised' which means it is less than 2^-1022
// excel displays all these numbers as zero, even though calculations work OK
return(isNegative ? "-0" : "0");
}
if (ed.GetBinaryExponent() == 1024)
{
// Special number NaN /InfInity
// Normally one would not create HybridDecimal objects from these values
// except in these cases Excel really tries to render them as if they were normal numbers
if (rawBits == EXCEL_NAN_BITS)
{
return("3.484840871308E+308");
}
// This is where excel really Gets it wrong
// Special numbers like InfInity and NaN are interpreted according to
// the standard rules below.
isNegative = false; // except that the sign bit is ignored
}
NormalisedDecimal nd = ed.NormaliseBaseTen();
StringBuilder sb = new StringBuilder(MAX_TEXT_LEN + 1);
if (isNegative)
{
sb.Append('-');
}
ConvertToText(sb, nd);
return(sb.ToString());
}
public static bool ConfirmRoundTrip(int i, long rawBitsA)
{
double a = BitConverter.Int64BitsToDouble(rawBitsA);
if (a == 0.0)
{
// Can't represent 0.0 or -0.0 with NormalisedDecimal
return true;
}
ExpandedDouble ed1;
NormalisedDecimal nd2;
ExpandedDouble ed3;
try
{
ed1 = new ExpandedDouble(rawBitsA);
nd2 = ed1.NormaliseBaseTen();
CheckNormaliseBaseTenResult(ed1, nd2);
ed3 = nd2.NormaliseBaseTwo();
}
catch (Exception e)
{
Console.WriteLine("example[" + i + "] ("
+ FormatDoubleAsHex(a) + ") exception: " + e.Message);
return false;
}
if (ed3.GetBinaryExponent() != ed1.GetBinaryExponent())
{
Console.WriteLine("example[" + i + "] ("
+ FormatDoubleAsHex(a) + ") bin exp mismatch");
return false;
}
BigInteger diff = ed3.GetSignificand() - (ed1.GetSignificand()).Abs();
if (diff.Signum() == 0)
{
return true;
}
// original quantity only has 53 bits of precision
// these quantities may have errors in the 64th bit, which hopefully don't make any difference
if (diff.BitCount() < 2)
{
// errors in the 64th bit happen from time to time
// this is well below the 53 bits of precision required
return true;
}
// but bigger errors are a concern
Console.WriteLine("example[" + i + "] ("
+ FormatDoubleAsHex(a) + ") frac mismatch: " + diff.ToString());
for (int j = -2; j < 3; j++)
{
Console.WriteLine((j < 0 ? "" : "+") + j + ": " + GetNearby(ed1, j));
}
for (int j = -2; j < 3; j++)
{
Console.WriteLine((j < 0 ? "" : "+") + j + ": " + GetNearby(nd2, j));
}
return false;
}
private static void CheckNormaliseBaseTenResult(ExpandedDouble orig, NormalisedDecimal result)
{
String sigDigs = result.GetSignificantDecimalDigits();
BigInteger frac = orig.GetSignificand();
while (frac.BitLength() + orig.GetBinaryExponent() < 200)
{
frac = frac * (BIG_POW_10);
}
int binaryExp = orig.GetBinaryExponent() - orig.GetSignificand().BitLength();
String origDigs = (frac << (binaryExp + 1)).ToString(10);
if (!origDigs.StartsWith(sigDigs))
{
throw new AssertionException("Expected '" + origDigs + "' but got '" + sigDigs + "'.");
}
double dO = Double.Parse("0." + origDigs.Substring(sigDigs.Length));
double d1 = Double.Parse(result.GetFractionalPart().ToString());
BigInteger subDigsO = new BigInteger((int)(dO * 32768 + 0.5));
BigInteger subDigsB = new BigInteger((int)(d1 * 32768 + 0.5));
if (subDigsO.Equals(subDigsB))
{
return;
}
BigInteger diff = (subDigsB - subDigsO).Abs();
if (diff.IntValue() > 100)
{
// 100/32768 ~= 0.003
throw new AssertionException("minor mistake");
}
}
public static BigInteger GetNearby(ExpandedDouble hd, int offset)
{
return GetNearby(hd.GetSignificand(), hd.GetBinaryExponent(), offset);
}
public static String GetBaseDecimal(ExpandedDouble hd)
{
/*int gg = 64 - hd.GetBinaryExponent() - 1;
BigDecimal bd = new BigDecimal(hd.GetSignificand()).divide(new BigDecimal(BigInteger.ONE<<gg));
int excessPrecision = bd.precision() - 23;
if (excessPrecision > 0)
{
bd = bd.SetScale(bd.scale() - excessPrecision, BigDecimal.ROUND_HALF_UP);
}
return bd.unscaledValue().ToString();*/
throw new NotImplementedException("This Method need BigDecimal class");
}
/**
* This class attempts to reproduce Excel's behaviour for comparing numbers. Results are
* mostly the same as those from {@link Double#compare(double, double)} but with some
* rounding. For numbers that are very close, this code converts to a format having 15
* decimal digits of precision and a decimal exponent, before completing the comparison.
* <p/>
* In Excel formula evaluation, expressions like "(0.06-0.01)=0.05" evaluate to "TRUE" even
* though the equivalent java expression is <c>false</c>. In examples like this,
* Excel achieves the effect by having additional logic for comparison operations.
* <p/>
* <p/>
* Note - Excel also gives special treatment to expressions like "0.06-0.01-0.05" which
* evaluates to "0" (in java, rounding anomalies give a result of 6.9E-18). The special
* behaviour here is for different reasons to the example above: If the last operator in a
* cell formula is '+' or '-' and the result is less than 2<sup>50</sup> times smaller than
* first operand, the result is rounded to zero.
* Needless to say, the two rules are not consistent and it is relatively easy to find
* examples that satisfy<br/>
* "A=B" is "TRUE" but "A-B" is not "0"<br/>
* and<br/>
* "A=B" is "FALSE" but "A-B" is "0"<br/>
* <br/>
* This rule (for rounding the result of a final addition or subtraction), has not been
* implemented in POI (as of Jul-2009).
*
* @return <code>negative, 0, or positive</code> according to the standard Excel comparison
* of values <c>a</c> and <c>b</c>.
*/
public static int Compare(double a, double b)
{
long rawBitsA = BitConverter.DoubleToInt64Bits(a);
long rawBitsB = BitConverter.DoubleToInt64Bits(b);
int biasedExponentA = IEEEDouble.GetBiasedExponent(rawBitsA);
int biasedExponentB = IEEEDouble.GetBiasedExponent(rawBitsB);
if (biasedExponentA == IEEEDouble.BIASED_EXPONENT_SPECIAL_VALUE)
{
throw new ArgumentException("Special double values are not allowed: " + ToHex(a));
}
if (biasedExponentB == IEEEDouble.BIASED_EXPONENT_SPECIAL_VALUE)
{
throw new ArgumentException("Special double values are not allowed: " + ToHex(a));
}
int cmp;
// sign bit is in the same place for long and double:
bool aIsNegative = rawBitsA < 0;
bool bIsNegative = rawBitsB < 0;
// compare signs
if (aIsNegative != bIsNegative)
{
// Excel seems to have 'normal' comparison behaviour around zero (no rounding)
// even -0.0 < +0.0 (which is not quite the initial conclusion of bug 47198)
return(aIsNegative ? -1 : +1);
}
// then compare magnitudes (IEEE 754 has exponent bias specifically to allow this)
cmp = biasedExponentA - biasedExponentB;
int absExpDiff = Math.Abs(cmp);
if (absExpDiff > 1)
{
return(aIsNegative ? -cmp : cmp);
}
if (absExpDiff == 1)
{
// special case exponent differs by 1. There is still a chance that with rounding the two quantities could end up the same
}
else
{
// else - sign and exponents equal
if (rawBitsA == rawBitsB)
{
// fully equal - exit here
return(0);
}
}
if (biasedExponentA == 0)
{
if (biasedExponentB == 0)
{
return(CompareSubnormalNumbers(rawBitsA & IEEEDouble.FRAC_MASK, rawBitsB & IEEEDouble.FRAC_MASK, aIsNegative));
}
// else biasedExponentB is 1
return(-CompareAcrossSubnormalThreshold(rawBitsB, rawBitsA, aIsNegative));
}
if (biasedExponentB == 0)
{
// else biasedExponentA is 1
return(+CompareAcrossSubnormalThreshold(rawBitsA, rawBitsB, aIsNegative));
}
// sign and exponents same, but fractional bits are different
ExpandedDouble edA = ExpandedDouble.FromRawBitsAndExponent(rawBitsA, biasedExponentA - IEEEDouble.EXPONENT_BIAS);
ExpandedDouble edB = ExpandedDouble.FromRawBitsAndExponent(rawBitsB, biasedExponentB - IEEEDouble.EXPONENT_BIAS);
NormalisedDecimal ndA = edA.NormaliseBaseTen().RoundUnits();
NormalisedDecimal ndB = edB.NormaliseBaseTen().RoundUnits();
cmp = ndA.CompareNormalised(ndB);
if (aIsNegative)
{
return(-cmp);
}
return(cmp);
}
/* namespace */
public static String RawDoubleBitsToText(long pRawBits)
{
long rawBits = pRawBits;
bool isNegative = rawBits < 0; // sign bit is in the same place for long and double
if (isNegative)
{
rawBits &= 0x7FFFFFFFFFFFFFFFL;
}
if (rawBits == 0)
{
return isNegative ? "-0" : "0";
}
ExpandedDouble ed = new ExpandedDouble(rawBits);
if (ed.GetBinaryExponent() < -1022)
{
// value is 'denormalised' which means it is less than 2^-1022
// excel displays all these numbers as zero, even though calculations work OK
return isNegative ? "-0" : "0";
}
if (ed.GetBinaryExponent() == 1024)
{
// Special number NaN /InfInity
// Normally one would not create HybridDecimal objects from these values
// except in these cases Excel really tries to render them as if they were normal numbers
if (rawBits == EXCEL_NAN_BITS)
{
return "3.484840871308E+308";
}
// This is where excel really Gets it wrong
// Special numbers like InfInity and NaN are interpreted according to
// the standard rules below.
isNegative = false; // except that the sign bit is ignored
}
NormalisedDecimal nd = ed.NormaliseBaseTen();
StringBuilder sb = new StringBuilder(MAX_TEXT_LEN + 1);
if (isNegative)
{
sb.Append('-');
}
ConvertToText(sb, nd);
return sb.ToString();
}
