// 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(ref GrisuDouble v,
Span <char> buffer,
out int length,
out int decimal_exponent)
{
DiyFp w = 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 boundary_minus, boundary_plus;
v.NormalizedBoundaries(out boundary_minus, out boundary_plus);
Debug.Assert(boundary_plus.E == w.E);
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
int ten_mk_minimal_binary_exponent =
kMinimalTargetExponent - (w.E + DiyFp.kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.E + DiyFp.kSignificandSize);
PowersOfTenCache.GetCachedPowerForBinaryExponentRange(
ten_mk_minimal_binary_exponent,
ten_mk_maximal_binary_exponent,
out ten_mk, out mk);
Debug.Assert((kMinimalTargetExponent <= w.E + ten_mk.E +
DiyFp.kSignificandSize) &&
(kMaximalTargetExponent >= w.E + ten_mk.E +
DiyFp.kSignificandSize));
// 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
//DiyFp scaled_w = DiyFp.Times(ref w, ref ten_mk);
w.Multiply(ref ten_mk);
Debug.Assert(w.E ==
boundary_plus.E + ten_mk.E + DiyFp.kSignificandSize);
// 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 terriffic.
//DiyFp scaled_boundary_minus = DiyFp.Times(ref boundary_minus, ref ten_mk);
boundary_minus.Multiply(ref ten_mk);
//DiyFp scaled_boundary_plus = DiyFp.Times(ref boundary_plus, ref ten_mk);
boundary_plus.Multiply(ref ten_mk);
// 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.
int kappa;
bool result = DigitGen(ref boundary_minus, ref w, ref boundary_plus,
buffer, out length, out kappa);
decimal_exponent = -mk + kappa;
return(result);
}
// 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(ref GrisuDouble v,
char[] buffer,
out int length,
out int decimal_exponent)
{
DiyFp w = 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 boundary_minus, boundary_plus;
v.NormalizedBoundaries(out boundary_minus, out boundary_plus);
Debug.Assert(boundary_plus.E == w.E);
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
int ten_mk_minimal_binary_exponent =
kMinimalTargetExponent - (w.E + DiyFp.kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.E + DiyFp.kSignificandSize);
PowersOfTenCache.GetCachedPowerForBinaryExponentRange(
ten_mk_minimal_binary_exponent,
ten_mk_maximal_binary_exponent,
out ten_mk, out mk);
Debug.Assert((kMinimalTargetExponent <= w.E + ten_mk.E +
DiyFp.kSignificandSize) &&
(kMaximalTargetExponent >= w.E + ten_mk.E +
DiyFp.kSignificandSize));
// 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
//DiyFp scaled_w = DiyFp.Times(ref w, ref ten_mk);
w.Multiply(ref ten_mk);
Debug.Assert(w.E ==
boundary_plus.E + ten_mk.E + DiyFp.kSignificandSize);
// 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 terriffic.
//DiyFp scaled_boundary_minus = DiyFp.Times(ref boundary_minus, ref ten_mk);
boundary_minus.Multiply(ref ten_mk);
//DiyFp scaled_boundary_plus = DiyFp.Times(ref boundary_plus, ref ten_mk);
boundary_plus.Multiply(ref ten_mk);
// 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.
int kappa;
bool result = DigitGen(ref boundary_minus, ref w, ref boundary_plus,
buffer, out length, out kappa);
decimal_exponent = -mk + kappa;
return result;
}
