/// <summary>
/// Convert a 64-bit floating point number to an exponential notation string.
/// </summary>
internal static void ToExponentialString(StringBuilder result, ulong ieeeMantissa,
uint ieeeExponent, int precision, RyuFormatOptions options,
NumberFormatInfo info)
{
bool printDP = precision > 0, soft = (options & RyuFormatOptions.SoftPrecision) !=
0;
uint digits = 0U;
int printedDigits = 0, availDigits = 0, exp = 0, exponent = Decode(ieeeMantissa,
ieeeExponent, out ulong mantissa), start = result.Length;
ulong mantShift = mantissa << MANTISSA_SHIFT;
++precision;
if (exponent >= -RyuFloat64.DOUBLE_MANTISSA_BITS)
{
int idx = (exponent < 0) ? 0 : RyuUtils.IndexForExponent(exponent), i =
RyuUtils.LengthForIndex(idx) - 1, j = Pow10BitsForIndex(idx) - exponent +
MANTISSA_SHIFT, p = RyuTables.POW10_OFFSET_D[idx] + i;
for (; i >= 0; i--)
{
// Temporary: j is usually around 128, and by shifting a bit, we push it
// to 128 or above, which is a slightly faster code path in
// MulShiftMod1E9. Instead, we can just increase the multipliers
digits = RyuUtils.MulShiftMod1E9(mantShift, RyuTables.POW10_SPLIT_D[p, 0],
RyuTables.POW10_SPLIT_D[p, 1], RyuTables.POW10_SPLIT_D[p, 2], j);
if (printedDigits > 0)
{
if (printedDigits + 9 > precision)
{
availDigits = 9;
break;
}
RyuUtils.Append9Digits(result, digits);
printedDigits += 9;
}
else if (digits != 0U)
{
availDigits = RyuUtils.DecimalLength9(digits);
exp = i * 9 + availDigits - 1;
if (availDigits > precision)
{
break;
}
RyuUtils.AppendDDigits(result, digits, availDigits + 1, printDP, info);
printedDigits = availDigits;
availDigits = 0;
}
p--;
}
}
if (exponent < 0 && availDigits == 0)
{
int idx = (-exponent) >> 4, pMax = RyuTables.POW10_OFFSET_2_D[idx + 1], p =
RyuTables.POW10_OFFSET_2_D[idx], j = MANTISSA_SHIFT +
POW10_ADDITIONAL_BITS - exponent - (idx << 4);
for (int i = RyuTables.MIN_BLOCK_2_D[idx]; i < 200; i++)
{
digits = (p >= pMax) ? 0U : RyuUtils.MulShiftMod1E9(mantShift,
RyuTables.POW10_SPLIT_2_D[p, 0], RyuTables.POW10_SPLIT_2_D[p, 1],
RyuTables.POW10_SPLIT_2_D[p, 2], j);
if (printedDigits > 0)
{
if (printedDigits + 9 > precision)
{
availDigits = 9;
break;
}
RyuUtils.Append9Digits(result, digits);
printedDigits += 9;
}
else if (digits != 0)
{
availDigits = RyuUtils.DecimalLength9(digits);
exp = (i + 1) * -9 + availDigits - 1;
if (availDigits > precision)
{
break;
}
RyuUtils.AppendDDigits(result, digits, availDigits + 1, printDP, info);
printedDigits = availDigits;
availDigits = 0;
}
p++;
}
}
// 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd
int maxDigits = precision - printedDigits, roundFlag;
uint lastDigit = 0U;
if (availDigits == 0)
{
digits = 0U;
}
if (availDigits > maxDigits)
{
lastDigit = RyuUtils.LastDigit(ref digits, availDigits - maxDigits);
}
if (lastDigit != 5U)
{
roundFlag = (lastDigit > 5U) ? 1 : 0;
}
else
{
// Is m * 2^e2 * 10^(precision + 1 - exp) integer?
// precision was already increased by 1, so we don't need to write + 1 here.
int rexp = precision - exp;
bool trailingZeroes = HasTrailingZeroes(exponent, rexp, mantissa);
if (rexp < 0 && trailingZeroes)
{
trailingZeroes = RyuUtils.IsMultipleOf5Power(mantissa, -rexp);
}
roundFlag = trailingZeroes ? 2 : 1;
}
if (printedDigits > 0)
{
if (digits == 0U)
{
if (!soft)
{
RyuUtils.Append0(result, maxDigits);
}
}
else
{
RyuUtils.AppendCDigits(result, digits, maxDigits);
}
}
else
{
RyuUtils.AppendDDigits(result, digits, maxDigits + 1, printDP, info);
}
if (roundFlag != 0 && RyuUtils.RoundResult(result, start, roundFlag, out _, info))
{
exp++;
}
if (soft)
{
RyuUtils.SoftenResult(result, info);
}
RyuUtils.AppendExponent(result, exp, options, info);
}
/// <summary>
/// Convert a 64-bit floating point number to a fixed notation string.
/// </summary>
internal static void ToFixedString(StringBuilder result, ulong ieeeMantissa,
uint ieeeExponent, int precision, RyuFormatOptions options,
NumberFormatInfo info)
{
bool zero = true, soft = (options & RyuFormatOptions.SoftPrecision) != 0;
int exponent = Decode(ieeeMantissa, ieeeExponent, out ulong mantissa), start =
result.Length;
ulong mShift = mantissa << MANTISSA_SHIFT;
uint digits;
if (exponent >= -RyuFloat64.DOUBLE_MANTISSA_BITS)
{
int idx = (exponent < 0) ? 0 : RyuUtils.IndexForExponent(exponent), p10bits =
Pow10BitsForIndex(idx), i = RyuUtils.LengthForIndex(idx) - 1, p =
RyuTables.POW10_OFFSET_D[idx] + i, j = p10bits - exponent + MANTISSA_SHIFT;
for (; i >= 0; i--)
{
digits = RyuUtils.MulShiftMod1E9(mShift, RyuTables.POW10_SPLIT_D[p, 0],
RyuTables.POW10_SPLIT_D[p, 1], RyuTables.POW10_SPLIT_D[p, 2], j);
if (!zero)
{
RyuUtils.Append9Digits(result, digits);
}
else if (digits != 0U)
{
RyuUtils.AppendNDigits(result, RyuUtils.DecimalLength9(digits),
digits);
zero = false;
}
p--;
}
}
if (zero)
{
result.Append(RyuUtils.ZERO);
}
if ((options & RyuFormatOptions.ThousandsSeparators) != 0)
{
RyuUtils.AddThousands(result, start, info);
}
if (precision > 0 && (!soft || exponent < 0))
{
result.Append(info.NumberDecimalSeparator);
}
if (exponent < 0)
{
// 0 = don't round up; 1 = round up unconditionally; 2 = round up if odd
int idx = (-exponent) >> 4, roundFlag = 0, i = 0, blocks = precision / 9 + 1,
minBlock = RyuTables.MIN_BLOCK_2_D[idx];
if (blocks <= minBlock)
{
RyuUtils.Append0(result, precision);
i = blocks;
}
else if (i < minBlock)
{
RyuUtils.Append0(result, 9 * minBlock);
i = minBlock;
}
int p = RyuTables.POW10_OFFSET_2_D[idx] + i - minBlock, pMax = RyuTables.
POW10_OFFSET_2_D[idx + 1], j = MANTISSA_SHIFT + POW10_ADDITIONAL_BITS -
exponent - (idx << 4);
for (; i < blocks; ++i)
{
if (p >= pMax)
{
// If the remaining digits are all 0, then no rounding required
if (!soft)
{
RyuUtils.Append0(result, precision - 9 * i);
}
break;
}
digits = RyuUtils.MulShiftMod1E9(mShift, RyuTables.POW10_SPLIT_2_D[p, 0],
RyuTables.POW10_SPLIT_2_D[p, 1], RyuTables.POW10_SPLIT_2_D[p, 2], j);
if (i < blocks - 1)
{
RyuUtils.Append9Digits(result, digits);
}
else
{
int maximum = precision - 9 * i;
uint lastDigit = RyuUtils.LastDigit(ref digits, 9 - maximum);
// Is m * 10^(additionalDigits + 1) / 2^(-e2) integer?
if (lastDigit > 5U)
{
roundFlag = 1;
}
else if (lastDigit < 5U)
{
roundFlag = 0;
}
else if (HasTrailingZeroes(exponent, precision + 1, mantissa))
{
roundFlag = 2;
}
else
{
roundFlag = 1;
}
if (maximum > 0)
{
RyuUtils.AppendCDigits(result, digits, maximum);
}
break;
}
p++;
}
if (roundFlag != 0 && RyuUtils.RoundResult(result, start, roundFlag,
out int decimalIndex, info))
{
if (decimalIndex > 0)
{
result[decimalIndex++] = RyuUtils.ZERO;
result[decimalIndex] = info.NumberDecimalSeparator[0];
}
result.Append(RyuUtils.ZERO);
}
if (soft && precision > 0)
{
RyuUtils.SoftenResult(result, info);
}
}
else if (!soft)
{
RyuUtils.Append0(result, precision);
}
}