/// <summary>
/// Converts a single precision floating point number to a string.
/// </summary>
/// <param name="result">The location where the result will be placed.</param>
/// <param name="value">The value to format.</param>
/// <param name="precision">The precision to output when formatting.</param>
/// <param name="options">The format mode to use.</param>
/// <param name="provider">The provider used to determine how the value will be
/// formatted.</param>
public static void ToString(StringBuilder result, float value, int precision,
RyuFormatOptions options = RyuFormatOptions.RoundtripMode,
IFormatProvider provider = null)
{
var info = RyuUtils.GetFormatInfo(provider);
// Step 1: Decode the floating-point number, and unify normalized and subnormal
// cases
bool ieeeSign = RyuFloat32.Decode(value, out uint ieeeMantissa,
out uint ieeeExponent);
// Case distinction; exit early for the easy cases
bool mZero = ieeeMantissa == 0UL;
if (ieeeExponent == RyuFloat32.EXPONENT_MASK)
{
RyuUtils.GenerateSpecial(result, ieeeSign, !mZero, info);
}
else if (mZero && ieeeExponent == 0UL)
{
RyuUtils.GenerateZero(result, ieeeSign, precision, options, info);
}
else if ((options & RyuFormatOptions.RoundtripMode) != 0)
{
new RyuFloat32(ieeeSign, ieeeMantissa, ieeeExponent).ToRoundtripString(result,
options, info);
}
}
private static bool HasTrailingZeroes(int exponent, int rexp, ulong mantissa)
{
int requiredTwos = -exponent - rexp;
return(requiredTwos <= 0 || (requiredTwos < 60 && RyuUtils.IsMultipleOf2Power(
mantissa, requiredTwos)));
}
/// <summary>
/// Decode a double into its sign, mantissa, and exponent.
/// </summary>
internal static bool Decode(double value, out ulong mantissa, out uint exponent)
{
ulong bits = RyuUtils.double_to_bits(value);
mantissa = bits & MANTISSA_MASK;
exponent = (uint)(bits >> DOUBLE_MANTISSA_BITS) & EXPONENT_MASK;
return((bits & SIGN_MASK) != 0U);
}
/// <summary>
/// Decode a float into its sign, mantissa, and exponent.
/// </summary>
internal static bool Decode(float value, out uint mantissa, out uint exponent)
{
uint bits = RyuUtils.float_to_bits(value);
mantissa = bits & MANTISSA_MASK;
exponent = (bits >> FLOAT_MANTISSA_BITS) & EXPONENT_MASK;
return((bits & SIGN_MASK) != 0U);
}
/// <summary>
/// Convert a 32-bit Ryu floating point number to a roundtrip notation string.
/// </summary>
public void ToRoundtripString(StringBuilder result, RyuFormatOptions options,
NumberFormatInfo info = null)
{
// Step 5: Print the decimal representation
if (info == null)
{
info = CultureInfo.CurrentCulture.NumberFormat;
}
if (sign)
{
result.Append(info.NegativeSign);
}
#if DEBUG
if (info.NumberDecimalSeparator.Length > 1)
{
throw new ArgumentException("Requires a single character decimal point");
}
#endif
// Print the decimal digits
uint mantissa = this.mantissa;
int olength = RyuUtils.DecimalLength9(mantissa), start = result.Length, index =
olength + start;
result.Length = index + 1;
index = RyuUtils.PrintGroups42(result, ref mantissa, index);
// Group of 1
if (mantissa >= 10U)
{
string digits = RyuTables.DIGIT_TABLE[mantissa];
// We can't use memcpy here: the decimal dot goes between these two digits
result[index--] = digits[1];
result[start] = digits[0];
}
else
{
result[start] = mantissa.DigitToChar();
}
// Print decimal point if needed
if (olength > 1)
{
result[start + 1] = info.NumberDecimalSeparator[0];
index += olength;
}
result.Length = index;
RyuUtils.AppendExponent(result, exponent + olength - 1, options, info);
}
public RyuFloat64(bool sign, ulong ieeeMantissa, uint ieeeExponent)
{
// Subtract 2 more so that the bounds computation has 2 additional bits
const int DOUBLE_EXP_DIFF_P2 = DOUBLE_BIAS + DOUBLE_MANTISSA_BITS + 2;
int exponent;
ulong mantissa;
if (ieeeExponent == 0)
{
exponent = 1 - DOUBLE_EXP_DIFF_P2;
mantissa = ieeeMantissa;
}
else
{
exponent = (int)ieeeExponent - DOUBLE_EXP_DIFF_P2;
mantissa = (1UL << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
}
// Step 2: Determine the interval of valid decimal representations
bool even = (mantissa & 1UL) == 0UL, acceptBounds = even, mmShift =
ieeeMantissa != 0U || ieeeExponent <= 1U;
ulong mv = mantissa << 2;
// Step 3: Convert to a decimal power base using 128-bit arithmetic
ulong vr, vm, vp;
int e10;
bool vmTrailingZeroes = false, vrTrailingZeroes = false;
if (exponent >= 0)
{
// Tried special-casing q == 0, but there was no effect on performance
// This expression is slightly faster than max(0, log10Pow2(e2) - 1)
int q = RyuUtils.Log10Pow2(exponent);
if (exponent > 3)
{
q--;
}
int k = DOUBLE_POW5_INV_BITCOUNT + RyuUtils.Pow5Bits(q) - 1, i = -exponent +
q + k;
ulong a = RyuTables.double_computeInvPow5(q, out ulong b);
e10 = q;
vr = RyuUtils.MulShiftAll(mantissa, a, b, i, out vp, out vm, mmShift);
if (q <= 21U)
{
// This should use q <= 22, but I think 21 is also safe. Smaller values
// may still be safe, but it's more difficult to reason about them.
// Only one of mp, mv, and mm can be a multiple of 5, if any
uint mvMod5 = (uint)mv % 5U;
if (mvMod5 == 0U)
{
vrTrailingZeroes = RyuUtils.IsMultipleOf5Power(mv, q);
}
else if (acceptBounds)
{
// Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
// <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
// <=> true && pow5Factor(mm) >= q, since e2 >= q
vmTrailingZeroes = RyuUtils.IsMultipleOf5Power(mv - 1UL - (mmShift ?
1UL : 0UL), q);
}
else
{
// Same as min(e2 + 1, pow5Factor(mp)) >= q
vp -= RyuUtils.IsMultipleOf5Power(mv + 2UL, q) ? 1UL : 0UL;
}
}
}
else
{
// This expression is slightly faster than max(0, log10Pow5(-e2) - 1)
int q = RyuUtils.Log10Pow5(-exponent);
if (-exponent > 1)
{
q--;
}
int i = -exponent - q, k = RyuUtils.Pow5Bits(i) - DOUBLE_POW5_BITCOUNT,
j = q - k;
ulong a = RyuTables.double_computePow5(i, out ulong b);
e10 = q + exponent;
vr = RyuUtils.MulShiftAll(mantissa, a, b, j, out vp, out vm, mmShift);
if (q <= 1U)
{
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0
// bits; mv = 4 * m2, so it always has at least two trailing 0 bits
vrTrailingZeroes = true;
if (acceptBounds)
{
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1
vmTrailingZeroes = mmShift;
}
else
{
// mp = mv + 2, so it always has at least one trailing 0 bit
--vp;
}
}
else if (q < 63U)
{
// We want to know if the fUL product has at least q trailing zeros
// We need to compute min(p2(mv), p5(mv) - e2) >= q
// <=> p2(mv) >= q && p5(mv) - e2 >= q
// <=> p2(mv) >= q (because -e2 >= q)
vrTrailingZeroes = RyuUtils.IsMultipleOf2Power(mv, q);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid
// representations
int removed = 0;
uint removedDigit = 0U;
ulong output, p10, m10;
// On average, we remove ~2 digits
if (vmTrailingZeroes || vrTrailingZeroes)
{
// General case, which happens rarely (~0.7%)
while ((p10 = vp / 10UL) > (m10 = vm.DivMod(10U, out uint vmRem)))
{
if (vmRem != 0U)
{
vmTrailingZeroes = false;
}
if (removedDigit != 0U)
{
vrTrailingZeroes = false;
}
vr = vr.DivMod(10U, out removedDigit);
vp = p10;
vm = m10;
removed++;
}
if (vmTrailingZeroes)
{
while (((uint)vm - 10U * (uint)(m10 = vm / 10UL)) == 0U)
{
if (removedDigit != 0U)
{
vrTrailingZeroes = false;
}
vr = vr.DivMod(10U, out removedDigit);
vp /= 10UL;
vm = m10;
removed++;
}
}
if (vrTrailingZeroes && removedDigit == 5U && vr % 2U == 0U)
{
// Round even if the exact number is .....50..0
removedDigit = 4U;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up
output = vr;
if ((vr == vm && (!acceptBounds || !vmTrailingZeroes)) || removedDigit >= 5U)
{
output++;
}
}
else
{
// Specialized for the common case (~99.3%); percentages below are relative to
// this
bool roundUp = false;
if (RyuUtils.DivCompare(ref vp, ref vm, 100UL))
{
// Optimization: remove two digits at a time (~86.2%)
vr = vr.DivMod(100U, out uint round100);
roundUp = round100 >= 50U;
removed += 2;
}
// Loop iterations below (approximately), without optimization above:
// 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
// Loop iterations below (approximately), with optimization above:
// 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
while (RyuUtils.DivCompare(ref vp, ref vm, 10UL))
{
vr = vr.DivMod(10U, out uint vrRem);
roundUp = vrRem >= 5U;
removed++;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up
output = vr;
if (vr == vm || roundUp)
{
output++;
}
}
this.sign = sign;
this.exponent = e10 + removed;
this.mantissa = output;
}
/// <summary>
/// Convert a 64-bit Ryu floating point number to a roundtrip notation string.
/// </summary>
public void ToRoundtripString(StringBuilder result, RyuFormatOptions options,
NumberFormatInfo info = null)
{
// Step 5: Print the decimal representation
if (info == null)
{
info = CultureInfo.CurrentCulture.NumberFormat;
}
if (sign)
{
result.Append(info.NegativeSign);
}
#if DEBUG
if (info.NumberDecimalSeparator.Length > 1)
{
throw new ArgumentException("Requires a single character decimal point");
}
#endif
ulong mantissa = this.mantissa;
uint mantissaShort;
int olength = RyuUtils.DecimalLength17(mantissa), start = result.Length, index =
olength + start;
result.Length = index + 1;
// Print the decimal digits: group of 8
if ((mantissa >> 32) != 0U)
{
// We prefer 32-bit operations, even on 64-bit platforms.
// We have at most 17 digits, and uint can store 9 digits.
// If output doesn't fit into uint, we cut off 8 digits,
// so the rest will fit into uint
ulong q = mantissa / 100000000UL;
mantissaShort = (uint)mantissa - 100000000U * (uint)q;
uint o10000 = mantissaShort / 10000U;
uint c0 = mantissaShort - 10000U * o10000, d0 = o10000 % 10000U;
uint c1 = c0 / 100U, d1 = d0 / 100U;
mantissa = q;
index = result.WriteDigits(index, c0 - 100U * c1);
index = result.WriteDigits(index, c1);
index = result.WriteDigits(index, d0 - 100U * d1);
index = result.WriteDigits(index, d1);
}
mantissaShort = (uint)mantissa;
index = RyuUtils.PrintGroups42(result, ref mantissaShort, index);
// Group of 1
if (mantissaShort >= 10U)
{
string digits = RyuTables.DIGIT_TABLE[mantissaShort];
// We can't use memcpy here: the decimal dot goes between these two digits
result[index--] = digits[1];
result[start] = digits[0];
}
else
{
result[start] = mantissaShort.DigitToChar();
}
// Print decimal point if needed
if (olength > 1)
{
result[start + 1] = info.NumberDecimalSeparator[0];
index += olength;
}
result.Length = index;
RyuUtils.AppendExponent(result, exponent + olength - 1, options, info);
}
/// <summary>
/// Creates a Ryu float from an IEEE 32 bit float.
/// </summary>
public RyuFloat32(bool fSign, uint ieeeMantissa, uint ieeeExponent)
{
const int FLOAT_EXP_DIFF_P2 = FLOAT_BIAS + FLOAT_MANTISSA_BITS + 2;
int exponent;
uint mantissa;
if (ieeeExponent == 0U)
{
// Subtract 2 so that the bounds computation has 2 additional bits
exponent = 1 - FLOAT_EXP_DIFF_P2;
mantissa = ieeeMantissa;
}
else
{
exponent = (int)ieeeExponent - FLOAT_EXP_DIFF_P2;
mantissa = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
}
bool even = (mantissa & 1U) == 0U, acceptBounds = even, mmShift =
ieeeMantissa != 0 || ieeeExponent <= 1;
// Step 2: Determine the interval of valid decimal representations
uint mv = mantissa << 2, mp = mv + 2U, mm = mv - 1U - (mmShift ? 1U : 0U);
// Step 3: Convert to a decimal power base using 64-bit arithmetic
uint vr, vp, vm;
int e10;
bool vmTrailingZeroes = false, vrTrailingZeroes = false;
uint removedDigit = 0U;
if (exponent >= 0)
{
int q = RyuUtils.Log10Pow2(exponent), k = FLOAT_POW5_INV_BITCOUNT + RyuUtils.
Pow5Bits(q) - 1, i = -exponent + q + k;
e10 = q;
vr = RyuTables.MulPow5InvDivPow2(mv, q, i);
vp = RyuTables.MulPow5InvDivPow2(mp, q, i);
vm = RyuTables.MulPow5InvDivPow2(mm, q, i);
if (q != 0U && (vp - 1U) / 10U <= vm / 10U)
{
// We need to know one removed digit even if we are not going to loop
// below. We could use q = X - 1 above, except that would require 33 bits
// for the result, and we've found that 32-bit arithmetic is faster even on
// 64-bit machines
int l = FLOAT_POW5_INV_BITCOUNT + RyuUtils.Pow5Bits(q - 1) - 1;
removedDigit = RyuTables.MulPow5InvDivPow2(mv, q - 1, -exponent +
q - 1 + l) % 10U;
}
if (q <= 9U)
{
// The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to
// be safe as well. Only one of mp, mv, and mm can be a multiple of 5, if
// any
if (mv % 5U == 0U)
{
vrTrailingZeroes = RyuUtils.IsMultipleOf5Power(mv, q);
}
else if (acceptBounds)
{
vmTrailingZeroes = RyuUtils.IsMultipleOf5Power(mm, q);
}
else if (RyuUtils.IsMultipleOf5Power(mp, q))
{
vp -= 1U;
}
}
}
else
{
int q = RyuUtils.Log10Pow5(-exponent), i = -exponent - q, k = RyuUtils.
Pow5Bits(i) - FLOAT_POW5_BITCOUNT, j = q - k;
e10 = q + exponent;
vr = RyuTables.MulPow5DivPow2(mv, i, j);
vp = RyuTables.MulPow5DivPow2(mp, i, j);
vm = RyuTables.MulPow5DivPow2(mm, i, j);
if (q != 0U && (vp - 1U) / 10U <= vm / 10U)
{
j = q - 1 - (RyuUtils.Pow5Bits(i + 1) - FLOAT_POW5_BITCOUNT);
removedDigit = RyuTables.MulPow5DivPow2(mv, i + 1, j) % 10U;
}
if (q <= 1U)
{
// {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0
// bits. mv = 4 * m2, so it always has at least two trailing 0 bits
vrTrailingZeroes = true;
if (acceptBounds)
{
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1
vmTrailingZeroes = mmShift;
}
else
{
// mp = mv + 2, so it always has at least one trailing 0 bit
--vp;
}
}
else if (q < 31U)
{
vrTrailingZeroes = RyuUtils.IsMultipleOf2Power(mv, q - 1);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid
// representations
int removed = 0;
uint output, m10, p10;
if (vmTrailingZeroes || vrTrailingZeroes)
{
// General case, which happens rarely (~4.0%)
while ((p10 = vp / 10U) > (m10 = vm.DivMod(10U, out uint vmRem)))
{
if (vmRem != 0U)
{
vmTrailingZeroes = false;
}
if (removedDigit != 0U)
{
vrTrailingZeroes = false;
}
vr = vr.DivMod(10U, out removedDigit);
vp = p10;
vm = m10;
removed++;
}
if (vmTrailingZeroes)
{
while ((vm - 10U * (m10 = vm / 10U)) == 0U)
{
if (removedDigit != 0U)
{
vrTrailingZeroes = false;
}
vr = vr.DivMod(10U, out removedDigit);
vp /= 10U;
vm = m10;
removed++;
}
}
if (vrTrailingZeroes && removedDigit == 5U && vr % 2U == 0U)
{
// Round even if the exact number is .....50..0
removedDigit = 4U;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up
output = vr;
if ((vr == vm && (!acceptBounds || !vmTrailingZeroes)) || removedDigit >= 5U)
{
output++;
}
}
else
{
// Specialized for the common case (~96.0%). Percentages below are relative to
// this. Loop iterations below (approximately):
// 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
while (RyuUtils.DivCompare10(ref vp, ref vm))
{
vr = vr.DivMod(10U, out removedDigit);
removed++;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up
output = vr;
if (vr == vm || removedDigit >= 5)
{
output++;
}
}
sign = fSign;
this.mantissa = output;
this.exponent = e10 + removed;
}
/// <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);
}
}