コード例 #1
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		// Copyright 2010 the V8 project authors. All rights reserved.
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		// modification, are permitted provided that the following conditions are
		// met:
		//
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		//       with the distribution.
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		//       contributors may be used to endorse or promote products derived
		//       from this software without specific prior written permission.
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		// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
		// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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		// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
		// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
		// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
		// Ported to Java from Mozilla's version of V8-dtoa by Hannes Wallnoefer.
		// The original revision was 67d1049b0bf9 from the mozilla-central tree.
		// FastDtoa will produce at most kFastDtoaMaximalLength digits.
		// The minimal and maximal target exponent define the range of w's binary
		// exponent, where 'w' is the result of multiplying the input by a cached power
		// of ten.
		//
		// A different range might be chosen on a different platform, to optimize digit
		// generation, but a smaller range requires more powers of ten to be cached.
		// Adjusts the last digit of the generated number, and screens out generated
		// solutions that may be inaccurate. A solution may be inaccurate if it is
		// outside the safe interval, or if we ctannot prove that it is closer to the
		// input than a neighboring representation of the same length.
		//
		// Input: * buffer containing the digits of too_high / 10^kappa
		//        * distance_too_high_w == (too_high - w).f() * unit
		//        * unsafe_interval == (too_high - too_low).f() * unit
		//        * rest = (too_high - buffer * 10^kappa).f() * unit
		//        * ten_kappa = 10^kappa * unit
		//        * unit = the common multiplier
		// Output: returns true if the buffer is guaranteed to contain the closest
		//    representable number to the input.
		//  Modifies the generated digits in the buffer to approach (round towards) w.
		internal static bool RoundWeed(FastDtoaBuilder buffer, long distance_too_high_w, long unsafe_interval, long rest, long ten_kappa, long unit)
		{
			long small_distance = distance_too_high_w - unit;
			long big_distance = distance_too_high_w + unit;
			// Let w_low  = too_high - big_distance, and
			//     w_high = too_high - small_distance.
			// Note: w_low < w < w_high
			//
			// The real w (* unit) must lie somewhere inside the interval
			// ]w_low; w_low[ (often written as "(w_low; w_low)")
			// Basically the buffer currently contains a number in the unsafe interval
			// ]too_low; too_high[ with too_low < w < too_high
			//
			//  too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
			//                     ^v 1 unit            ^      ^                 ^      ^
			//  boundary_high ---------------------     .      .                 .      .
			//                     ^v 1 unit            .      .                 .      .
			//   - - - - - - - - - - - - - - - - - - -  +  - - + - - - - - -     .      .
			//                                          .      .         ^       .      .
			//                                          .  big_distance  .       .      .
			//                                          .      .         .       .    rest
			//                              small_distance     .         .       .      .
			//                                          v      .         .       .      .
			//  w_high - - - - - - - - - - - - - - - - - -     .         .       .      .
			//                     ^v 1 unit                   .         .       .      .
			//  w ----------------------------------------     .         .       .      .
			//                     ^v 1 unit                   v         .       .      .
			//  w_low  - - - - - - - - - - - - - - - - - - - - -         .       .      .
			//                                                           .       .      v
			//  buffer --------------------------------------------------+-------+--------
			//                                                           .       .
			//                                                  safe_interval    .
			//                                                           v       .
			//   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -     .
			//                     ^v 1 unit                                     .
			//  boundary_low -------------------------                     unsafe_interval
			//                     ^v 1 unit                                     v
			//  too_low  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
			//
			//
			// Note that the value of buffer could lie anywhere inside the range too_low
			// to too_high.
			//
			// boundary_low, boundary_high and w are approximations of the real boundaries
			// and v (the input number). They are guaranteed to be precise up to one unit.
			// In fact the error is guaranteed to be strictly less than one unit.
			//
			// Anything that lies outside the unsafe interval is guaranteed not to round
			// to v when read again.
			// Anything that lies inside the safe interval is guaranteed to round to v
			// when read again.
			// If the number inside the buffer lies inside the unsafe interval but not
			// inside the safe interval then we simply do not know and bail out (returning
			// false).
			//
			// Similarly we have to take into account the imprecision of 'w' when rounding
			// the buffer. If we have two potential representations we need to make sure
			// that the chosen one is closer to w_low and w_high since v can be anywhere
			// between them.
			//
			// By generating the digits of too_high we got the largest (closest to
			// too_high) buffer that is still in the unsafe interval. In the case where
			// w_high < buffer < too_high we try to decrement the buffer.
			// This way the buffer approaches (rounds towards) w.
			// There are 3 conditions that stop the decrementation process:
			//   1) the buffer is already below w_high
			//   2) decrementing the buffer would make it leave the unsafe interval
			//   3) decrementing the buffer would yield a number below w_high and farther
			//      away than the current number. In other words:
			//              (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
			// Instead of using the buffer directly we use its distance to too_high.
			// Conceptually rest ~= too_high - buffer
			while (rest < small_distance && unsafe_interval - rest >= ten_kappa && (rest + ten_kappa < small_distance || small_distance - rest >= rest + ten_kappa - small_distance))
			{
				// Negated condition 1
				// Negated condition 2
				// buffer{-1} > w_high
				buffer.DecreaseLast();
				rest += ten_kappa;
			}
			// We have approached w+ as much as possible. We now test if approaching w-
			// would require changing the buffer. If yes, then we have two possible
			// representations close to w, but we cannot decide which one is closer.
			if (rest < big_distance && unsafe_interval - rest >= ten_kappa && (rest + ten_kappa < big_distance || big_distance - rest > rest + ten_kappa - big_distance))
			{
				return false;
			}
			// Weeding test.
			//   The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
			//   Since too_low = too_high - unsafe_interval this is equivalent to
			//      [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
			//   Conceptually we have: rest ~= too_high - buffer
			return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
		}
コード例 #2
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		public static bool NumberToString(double v, FastDtoaBuilder buffer)
		{
			buffer.Reset();
			if (v < 0)
			{
				buffer.Append('-');
				v = -v;
			}
			return Dtoa(v, buffer);
		}
コード例 #3
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		public static string NumberToString(double v)
		{
			FastDtoaBuilder buffer = new FastDtoaBuilder();
			return NumberToString(v, buffer) ? buffer.Format() : null;
		}
コード例 #4
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		public static bool Dtoa(double v, FastDtoaBuilder buffer)
		{
			System.Diagnostics.Debug.Assert((v > 0));
			System.Diagnostics.Debug.Assert((!double.IsNaN(v)));
			System.Diagnostics.Debug.Assert((!System.Double.IsInfinity(v)));
			return Grisu3(v, buffer);
		}
コード例 #5
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		// 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.
		internal static bool Grisu3(double v, FastDtoaBuilder buffer)
		{
			long bits = System.BitConverter.DoubleToInt64Bits(v);
			DiyFp w = DoubleHelper.AsNormalizedDiyFp(bits);
			// 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 = new DiyFp();
			DiyFp boundary_plus = new DiyFp();
			DoubleHelper.NormalizedBoundaries(bits, boundary_minus, boundary_plus);
			System.Diagnostics.Debug.Assert((boundary_plus.E() == w.E()));
			DiyFp ten_mk = new DiyFp();
			// Cached power of ten: 10^-k
			int mk = CachedPowers.GetCachedPower(w.E() + DiyFp.kSignificandSize, minimal_target_exponent, maximal_target_exponent, ten_mk);
			System.Diagnostics.Debug.Assert((minimal_target_exponent <= w.E() + ten_mk.E() + DiyFp.kSignificandSize && maximal_target_exponent >= 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(w, ten_mk);
			System.Diagnostics.Debug.Assert((scaled_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(boundary_minus, ten_mk);
			DiyFp scaled_boundary_plus = DiyFp.Times(boundary_plus, 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.
			return DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus, buffer, mk);
		}
コード例 #6
0
ファイル: FastDtoa.cs プロジェクト: hazzik/Rhino.Net
		// Generates the digits of input number w.
		// w is a floating-point number (DiyFp), consisting of a significand and an
		// exponent. Its exponent is bounded by minimal_target_exponent and
		// maximal_target_exponent.
		//       Hence -60 <= w.e() <= -32.
		//
		// Returns false if it fails, in which case the generated digits in the buffer
		// should not be used.
		// Preconditions:
		//  * low, w and high are correct up to 1 ulp (unit in the last place). That
		//    is, their error must be less that a unit of their last digits.
		//  * low.e() == w.e() == high.e()
		//  * low < w < high, and taking into account their error: low~ <= high~
		//  * minimal_target_exponent <= w.e() <= maximal_target_exponent
		// Postconditions: returns false if procedure fails.
		//   otherwise:
		//     * buffer is not null-terminated, but len contains the number of digits.
		//     * buffer contains the shortest possible decimal digit-sequence
		//       such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
		//       correct values of low and high (without their error).
		//     * if more than one decimal representation gives the minimal number of
		//       decimal digits then the one closest to W (where W is the correct value
		//       of w) is chosen.
		// Remark: this procedure takes into account the imprecision of its input
		//   numbers. If the precision is not enough to guarantee all the postconditions
		//   then false is returned. This usually happens rarely (~0.5%).
		//
		// Say, for the sake of example, that
		//   w.e() == -48, and w.f() == 0x1234567890abcdef
		// w's value can be computed by w.f() * 2^w.e()
		// We can obtain w's integral digits by simply shifting w.f() by -w.e().
		//  -> w's integral part is 0x1234
		//  w's fractional part is therefore 0x567890abcdef.
		// Printing w's integral part is easy (simply print 0x1234 in decimal).
		// In order to print its fraction we repeatedly multiply the fraction by 10 and
		// get each digit. Example the first digit after the point would be computed by
		//   (0x567890abcdef * 10) >> 48. -> 3
		// The whole thing becomes slightly more complicated because we want to stop
		// once we have enough digits. That is, once the digits inside the buffer
		// represent 'w' we can stop. Everything inside the interval low - high
		// represents w. However we have to pay attention to low, high and w's
		// imprecision.
		internal static bool DigitGen(DiyFp low, DiyFp w, DiyFp high, FastDtoaBuilder buffer, int mk)
		{
			System.Diagnostics.Debug.Assert((low.E() == w.E() && w.E() == high.E()));
			System.Diagnostics.Debug.Assert(Uint64_lte(low.F() + 1, high.F() - 1));
			System.Diagnostics.Debug.Assert((minimal_target_exponent <= w.E() && w.E() <= maximal_target_exponent));
			// low, w and high are imprecise, but by less than one ulp (unit in the last
			// place).
			// If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
			// the new numbers are outside of the interval we want the final
			// representation to lie in.
			// Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
			// numbers that are certain to lie in the interval. We will use this fact
			// later on.
			// We will now start by generating the digits within the uncertain
			// interval. Later we will weed out representations that lie outside the safe
			// interval and thus _might_ lie outside the correct interval.
			long unit = 1;
			DiyFp too_low = new DiyFp(low.F() - unit, low.E());
			DiyFp too_high = new DiyFp(high.F() + unit, high.E());
			// too_low and too_high are guaranteed to lie outside the interval we want the
			// generated number in.
			DiyFp unsafe_interval = DiyFp.Minus(too_high, too_low);
			// We now cut the input number into two parts: the integral digits and the
			// fractionals. We will not write any decimal separator though, but adapt
			// kappa instead.
			// Reminder: we are currently computing the digits (stored inside the buffer)
			// such that:   too_low < buffer * 10^kappa < too_high
			// We use too_high for the digit_generation and stop as soon as possible.
			// If we stop early we effectively round down.
			DiyFp one = new DiyFp(1l << -w.E(), w.E());
			// Division by one is a shift.
			int integrals = (int)(((long)(((ulong)too_high.F()) >> -one.E())) & unchecked((long)(0xffffffffL)));
			// Modulo by one is an and.
			long fractionals = too_high.F() & (one.F() - 1);
			long result = BiggestPowerTen(integrals, DiyFp.kSignificandSize - (-one.E()));
			int divider = (int)(((long)(((ulong)result) >> 32)) & unchecked((long)(0xffffffffL)));
			int divider_exponent = (int)(result & unchecked((long)(0xffffffffL)));
			int kappa = divider_exponent + 1;
			// Loop invariant: buffer = too_high / 10^kappa  (integer division)
			// The invariant holds for the first iteration: kappa has been initialized
			// with the divider exponent + 1. And the divider is the biggest power of ten
			// that is smaller than integrals.
			while (kappa > 0)
			{
				int digit = integrals / divider;
				buffer.Append((char)('0' + digit));
				integrals %= divider;
				kappa--;
				// Note that kappa now equals the exponent of the divider and that the
				// invariant thus holds again.
				long rest = ((long)integrals << -one.E()) + fractionals;
				// Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
				// Reminder: unsafe_interval.e() == one.e()
				if (rest < unsafe_interval.F())
				{
					// Rounding down (by not emitting the remaining digits) yields a number
					// that lies within the unsafe interval.
					buffer.point = buffer.end - mk + kappa;
					return RoundWeed(buffer, DiyFp.Minus(too_high, w).F(), unsafe_interval.F(), rest, (long)divider << -one.E(), unit);
				}
				divider /= 10;
			}
			// The integrals have been generated. We are at the point of the decimal
			// separator. In the following loop we simply multiply the remaining digits by
			// 10 and divide by one. We just need to pay attention to multiply associated
			// data (like the interval or 'unit'), too.
			// Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
			// increase its (imaginary) exponent. At the same time we decrease the
			// divider's (one's) exponent and shift its significand.
			// Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
			//      fractionals.f *= 10;
			//      fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
			//      one.f >>= 1; one.e++;                 // value remains unchanged.
			//      and we have again fractionals.e == one.e which allows us to divide
			//           fractionals.f() by one.f()
			// We simply combine the *= 10 and the >>= 1.
			while (true)
			{
				fractionals *= 5;
				unit *= 5;
				unsafe_interval.SetF(unsafe_interval.F() * 5);
				unsafe_interval.SetE(unsafe_interval.E() + 1);
				// Will be optimized out.
				one.SetF((long)(((ulong)one.F()) >> 1));
				one.SetE(one.E() + 1);
				// Integer division by one.
				int digit = (int)(((long)(((ulong)fractionals) >> -one.E())) & unchecked((long)(0xffffffffL)));
				buffer.Append((char)('0' + digit));
				fractionals &= one.F() - 1;
				// Modulo by one.
				kappa--;
				if (fractionals < unsafe_interval.F())
				{
					buffer.point = buffer.end - mk + kappa;
					return RoundWeed(buffer, DiyFp.Minus(too_high, w).F() * unit, unsafe_interval.F(), fractionals, one.F(), unit);
				}
			}
		}