public static int f2s_buffered_n(float f, Span <char> result)
{
// Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
uint32_t bits = float_to_bits(f);
// Decode bits into sign, mantissa, and exponent.
bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
uint32_t ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
uint32_t ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
// Case distinction; exit early for the easy cases.
if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
{
return(copy_special_str(result, ieeeSign, ieeeExponent != 0, ieeeMantissa != 0));
}
floating_decimal_32 v = f2d(ieeeMantissa, ieeeExponent);
return(to_chars(v, ieeeSign, result));
}
static floating_decimal_32 f2d(uint32_t ieeeMantissa, uint32_t ieeeExponent)
{
int32_t e2;
uint32_t m2;
if (ieeeExponent == 0)
{
// We subtract 2 so that the bounds computation has 2 additional bits.
e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
m2 = ieeeMantissa;
}
else
{
e2 = (int32_t)ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
}
bool even = (m2 & 1) == 0;
bool acceptBounds = even;
// Step 2: Determine the interval of valid decimal representations.
uint32_t mv = 4 * m2;
uint32_t mp = 4 * m2 + 2;
// Implicit bool -> int32_t conversion. True is 1, false is 0.
uint32_t mmShift = (ieeeMantissa != 0 || ieeeExponent <= 1) ? 1U : 0;
uint32_t mm = 4 * m2 - 1 - mmShift;
// Step 3: Convert to a decimal power base using 64-bit arithmetic.
uint32_t vr, vp, vm;
int32_t e10;
bool vmIsTrailingZeros = false;
bool vrIsTrailingZeros = false;
uint8_t lastRemovedDigit = 0;
if (e2 >= 0)
{
int32_t q = (int32_t)log10Pow2(e2);
e10 = q;
int32_t k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
int32_t i = -e2 + q + k;
vr = mulPow5InvDivPow2(mv, q, i);
vp = mulPow5InvDivPow2(mp, q, i);
vm = mulPow5InvDivPow2(mm, q, i);
if (q != 0 && (vp - 1) / 10 <= vm / 10)
{
// 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.
int32_t l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
lastRemovedDigit = (uint8_t)(mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
}
if (q <= 9)
{
// 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 % 5 == 0)
{
vrIsTrailingZeros = multipleOfPowerOf5_32(mv, q);
}
else if (acceptBounds)
{
vmIsTrailingZeros = multipleOfPowerOf5_32(mm, q);
}
else
{
if (multipleOfPowerOf5_32(mp, q))
{
--vp;
}
}
}
}
else
{
int32_t q = (int32_t)log10Pow5(-e2);
e10 = q + e2;
int32_t i = -e2 - q;
int32_t k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
int32_t j = q - k;
vr = mulPow5divPow2(mv, i, j);
vp = mulPow5divPow2(mp, i, j);
vm = mulPow5divPow2(mm, i, j);
if (q != 0 && (vp - 1) / 10 <= vm / 10)
{
j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
lastRemovedDigit = (uint8_t)(mulPow5divPow2(mv, i + 1, j) % 10);
}
if (q <= 1)
{
// {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.
vrIsTrailingZeros = true;
if (acceptBounds)
{
// mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
vmIsTrailingZeros = mmShift == 1;
}
else
{
// mp = mv + 2, so it always has at least one trailing 0 bit.
--vp;
}
}
else if (q < 31)
{ // TODO(ulfjack): Use a tighter bound here.
vrIsTrailingZeros = multipleOfPowerOf2_32(mv, q - 1);
}
}
// Step 4: Find the shortest decimal representation in the interval of valid representations.
int32_t removed = 0;
uint32_t output;
if (vmIsTrailingZeros || vrIsTrailingZeros)
{
// General case, which happens rarely (~4.0%).
while (vp / 10 > Math.DivRem((int32_t)vm, 10, out int32_t rem))
{
vmIsTrailingZeros &= rem == 0;
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t)(vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
if (vmIsTrailingZeros)
{
while (vm % 10 == 0)
{
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8_t)(vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
}
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
{
// Round even if the exact number is .....50..0.
lastRemovedDigit = 4;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr;
if ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5)
{
++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 (vp / 10 > vm / 10)
{
lastRemovedDigit = (uint8_t)(vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
// We need to take vr + 1 if vr is outside bounds or we need to round up.
output = vr;
if (vr == vm || lastRemovedDigit >= 5)
{
++output;
}
}
int32_t exp = e10 + removed;
floating_decimal_32 fd = new floating_decimal_32
{
exponent = exp,
mantissa = output,
};
return(fd);
}
static int to_chars(floating_decimal_32 v, bool sign, Span <char> result)
{
// Step 5: Print the decimal representation.
int index = 0;
if (sign)
{
result[index++] = '-';
}
int32_t output = (int)v.mantissa;
int32_t olength = decimalLength9((uint)output);
// Print the decimal digits.
// The following code is equivalent to:
// for (uint32_t i = 0; i < olength - 1; ++i) {
// const uint32_t c = output % 10; output /= 10;
// result[index + olength - i] = (char) ('0' + c);
// }
// result[index] = '0' + output % 10;
int32_t i = 0;
while (output >= 10000)
{
output = Math.DivRem(output, 10000, out int32_t c);
int32_t c1 = Math.DivRem(c, 100, out int32_t c0) << 1;
c0 <<= 1;
DIGIT_TABLE.AsSpan(c0, 2).CopyTo(result.Slice(index + olength - i - 1));
DIGIT_TABLE.AsSpan(c1, 2).CopyTo(result.Slice(index + olength - i - 3));
i += 4;
}
if (output >= 100)
{
output = Math.DivRem(output, 100, out int32_t c);
c <<= 1;
DIGIT_TABLE.AsSpan(c, 2).CopyTo(result.Slice(index + olength - i - 1));
i += 2;
}
if (output >= 10)
{
int32_t c = output << 1;
// We can't use memcpy here: the decimal dot goes between these two digits.
result[(int32_t)((uint32_t)index + olength - i)] = DIGIT_TABLE[c + 1];
result[index] = DIGIT_TABLE[c];
}
else
{
result[index] = (char)('0' + output);
}
// Print decimal point if needed.
if (olength > 1)
{
result[index + 1] = '.';
index += olength + 1;
}
else
{
++index;
}
// Print the exponent.
result[index++] = 'E';
int32_t exp = v.exponent + olength - 1;
if (exp < 0)
{
result[index++] = '-';
exp = -exp;
}
if (exp >= 10)
{
DIGIT_TABLE.AsSpan(2 * exp, 2).CopyTo(result.Slice(index));
index += 2;
}
else
{
result[index++] = (char)('0' + exp);
}
return(index);
}
static int to_chars(floating_decimal_32 v, bool sign, char *result)
{
// Step 5: Print the decimal representation.
int index = 0;
if (sign)
{
result[index++] = '-';
}
uint32_t output = v.mantissa;
uint32_t olength = decimalLength9(output);
// Print the decimal digits.
// The following code is equivalent to:
// for (uint32_t i = 0; i < olength - 1; ++i) {
// const uint32_t c = output % 10; output /= 10;
// result[index + olength - i] = (char) ('0' + c);
// }
// result[index] = '0' + output % 10;
uint32_t i = 0;
while (output >= 10000)
{
#if __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
uint32_t c = output - 10000 * (output / 10000);
#else
uint32_t c = output % 10000;
#endif
output /= 10000;
uint32_t c0 = (c % 100) << 1;
uint32_t c1 = (c / 100) << 1;
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
i += 4;
}
if (output >= 100)
{
uint32_t c = (output % 100) << 1;
output /= 100;
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
i += 2;
}
if (output >= 10)
{
uint32_t c = output << 1;
// We can't use memcpy here: the decimal dot goes between these two digits.
result[index + olength - i] = DIGIT_TABLE[c + 1];
result[index] = DIGIT_TABLE[c];
}
else
{
result[index] = (char)('0' + output);
}
// Print decimal point if needed.
if (olength > 1)
{
result[index + 1] = '.';
index += (int)olength + 1;
}
else
{
++index;
}
// Print the exponent.
result[index++] = 'E';
int32_t exp = v.exponent + (int32_t)olength - 1;
if (exp < 0)
{
result[index++] = '-';
exp = -exp;
}
if (exp >= 10)
{
memcpy(result + index, DIGIT_TABLE + (uint)(2 * exp), 2);
index += 2;
}
else
{
result[index++] = (char)('0' + exp);
}
return(index);
}
