Exemplo n.º 1
0
 public static bool NumberToString(double v, FastDtoaBuilder buffer)
 {
     buffer.Reset();
     if (v < 0)
     {
         buffer.Append('-');
         v = -v;
     }
     return(Dtoa(v, buffer));
 }
Exemplo n.º 2
0
        // 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.
        private static bool DigitGen(DiyFp low,
                                     DiyFp w,
                                     DiyFp high,
                                     FastDtoaBuilder buffer,
                                     int mk)
        {
            // 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;
            var  tooLow  = new DiyFp(low.F - unit, low.E);
            var  tooHigh = 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.
            var unsafeInterval = DiyFp.Minus(tooHigh, tooLow);
            // 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.
            var one = new DiyFp(1L << -w.E, w.E);
            // Division by one is a shift.
            var integrals = (int)(tooHigh.F.UnsignedShift(-one.E) & 0xffffffffL);
            // Modulo by one is an and.
            long fractionals     = tooHigh.F & (one.F - 1);
            long result          = BiggestPowerTen(integrals, DiyFp.KSignificandSize - (-one.E));
            var  divider         = (int)(result.UnsignedShift(32) & 0xffffffffL);
            var  dividerExponent = (int)(result & 0xffffffffL);
            var  kappa           = dividerExponent + 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 < unsafeInterval.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(tooHigh, w).F,
                                     unsafeInterval.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;
                unsafeInterval.F = unsafeInterval.F * 5;
                unsafeInterval.E = unsafeInterval.E + 1; // Will be optimized out.
                one.F            = one.F.UnsignedShift(1);
                one.E            = one.E + 1;
                // Integer division by one.
                var digit = (int)((fractionals.UnsignedShift(-one.E)) & 0xffffffffL);
                buffer.Append((char)('0' + digit));
                fractionals &= one.F - 1; // Modulo by one.
                kappa--;
                if (fractionals < unsafeInterval.F)
                {
                    buffer.Point = buffer.End - mk + kappa;
                    return(RoundWeed(buffer, DiyFp.Minus(tooHigh, w).F *unit,
                                     unsafeInterval.F, fractionals, one.F, unit));
                }
            }
        }