private static bool FastDtoa(double v,
FastDtoaMode mode,
Span <byte> buffer,
out int length,
out int decimalPoint)
{
switch (mode)
{
case FastDtoaMode.FastDtoaShortest:
case FastDtoaMode.FastDtoaShortestSingle:
var result = Grisu3(v, mode, buffer, out length, out var decimalExponent);
decimalPoint = result ? length + decimalExponent : -1;
return(result);
// case FastDtoaMode.FAST_DTOA_PRECISION:
//result = Grisu3Counted(v, requested_digits, buffer, length, &decimal_exponent);
default:
throw new Exception("unreachable code.");
}
}
// Provides a decimal representation of v.
// Returns true if it succeeds, otherwise the result cannot be trusted.
// There will be *length digits inside the buffer (not null-terminated).
// If the function returns true then
// v == (double) (buffer * 10^decimal_exponent).
// The digits in the buffer are the shortest representation possible: no
// 0.09999999999999999 instead of 0.1. The shorter representation will even be
// chosen even if the longer one would be closer to v.
// The last digit will be closest to the actual v. That is, even if several
// digits might correctly yield 'v' when read again, the closest will be
// computed.
private static bool Grisu3(double v, FastDtoaMode mode, Span <byte> buffer, out int length, out int decimalExponent)
{
var w = new IeeeDouble(v).AsNormalizedDiyFp();
// boundary_minus and boundary_plus are the boundaries between v and its
// closest floating-point neighbors. Any number strictly between
// boundary_minus and boundary_plus will round to v when convert to a double.
// Grisu3 will never output representations that lie exactly on a boundary.
DiyFp boundaryMinus, boundaryPlus;
switch (mode)
{
case FastDtoaMode.FastDtoaShortest:
new IeeeDouble(v).NormalizedBoundaries(out boundaryMinus, out boundaryPlus);
break;
case FastDtoaMode.FastDtoaShortestSingle:
{
var singleV = (float)v;
new IeeeSingle(singleV).NormalizedBoundaries(out boundaryMinus, out boundaryPlus);
break;
}
default:
throw new Exception("Invalid Mode.");
}
var tenMkMinimalBinaryExponent = KMinimalTargetExponent - (w.e + DiyFp.kSignificandSize);
PowersOfTenCache.GetCachedPowerForBinaryExponentRange(tenMkMinimalBinaryExponent, out var tenMk, out var mk);
// Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
// 64 bit significand and ten_mk is thus only precise up to 64 bits.
// The DiyFp::Times procedure rounds its result, and ten_mk is approximated
// too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
// off by a small amount.
// In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
// In other words: let f = scaled_w.f() and e = scaled_w.e(), then
// (f-1) * 2^e < w*10^k < (f+1) * 2^e
var scaledW = DiyFp.Times(ref w, ref tenMk);
// In theory it would be possible to avoid some recomputations by computing
// the difference between w and boundary_minus/plus (a power of 2) and to
// compute scaled_boundary_minus/plus by subtracting/adding from
// scaled_w. However the code becomes much less readable and the speed
// enhancements are not terrific.
var scaledBoundaryMinus = DiyFp.Times(ref boundaryMinus, ref tenMk);
var scaledBoundaryPlus = DiyFp.Times(ref boundaryPlus, ref tenMk);
// DigitGen will generate the digits of scaled_w. Therefore we have
// v == (double) (scaled_w * 10^-mk).
// Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
// integer than it will be updated. For instance if scaled_w == 1.23 then
// the buffer will be filled with "123" und the decimal_exponent will be
// decreased by 2.
var result = DigitGen(scaledBoundaryMinus, scaledW, scaledBoundaryPlus,
buffer, out length, out var kappa);
decimalExponent = -mk + kappa;
return(result);
}
