public static FastInteger[] DecimalDigitLengthBounds(EInteger ei)
{
long longBitLength = ei.GetUnsignedBitLengthAsInt64();
if (longBitLength < 33)
{
// Can easily be calculated without estimation
var fi = new FastInteger((int)ei.GetDigitCountAsInt64());
return(new FastInteger[] { fi, fi });
}
else if (longBitLength <= 2135)
{
var bitlen = (int)longBitLength;
int minDigits = 1 + (((bitlen - 1) * 631305) >> 21);
int maxDigits = 1 + ((bitlen * 631305) >> 21);
if (minDigits == maxDigits)
{
var fi = new FastInteger(minDigits);
return(new FastInteger[] { fi, fi });
}
else
{
return(new FastInteger[] {
new FastInteger(minDigits), // lower bound
new FastInteger(maxDigits), // upper bound
});
}
}
else if (longBitLength <= 6432162)
{
var bitlen = (int)longBitLength;
// Approximation of ln(2)/ln(10)
int minDigits = 1 + (int)(((long)(bitlen - 1) * 661971961083L) >> 41);
int maxDigits = 1 + (int)(((long)bitlen * 661971961083L) >> 41);
if (minDigits == maxDigits)
{
var fi = new FastInteger(minDigits);
return(new FastInteger[] { fi, fi });
}
else
{
return(new FastInteger[] {
new FastInteger(minDigits), // lower bound
new FastInteger(maxDigits), // upper bound
});
}
}
else
{
// Bit length is big enough that these bounds will
// overestimate or underestimate the true base-10 digit length
// as appropriate.
EInteger bigBitLength = ei.GetUnsignedBitLengthAsEInteger();
EInteger lowerBound = bigBitLength.Multiply(100).Divide(335);
EInteger upperBound = bigBitLength.Divide(3);
return(new FastInteger[] {
FastInteger.FromBig(lowerBound), // lower bound
FastInteger.FromBig(upperBound), // upper bound
});
}
}