Version 2.1.4.1...

src/grisu3.cc

Index: src/grisu3.cc
===================================================================
--- src/grisu3.cc	(revision 4127)
+++ src/grisu3.cc	(working copy)
@@ -1,494 +0,0 @@
-// Copyright 2010 the V8 project authors. All rights reserved.
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are
-// met:
-//
-//     * Redistributions of source code must retain the above copyright
-//       notice, this list of conditions and the following disclaimer.
-//     * Redistributions in binary form must reproduce the above
-//       copyright notice, this list of conditions and the following
-//       disclaimer in the documentation and/or other materials provided
-//       with the distribution.
-//     * Neither the name of Google Inc. nor the names of its
-//       contributors may be used to endorse or promote products derived
-//       from this software without specific prior written permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-// 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.
-
-#include "v8.h"
-
-#include "grisu3.h"
-
-#include "cached_powers.h"
-#include "diy_fp.h"
-#include "double.h"
-
-namespace v8 {
-namespace internal {
-
-template <int alpha = -60, int gamma = -32>
-class Grisu3 {
- public:
-  // Provides a decimal representation of v.
-  // Returns true if it succeeds, otherwise the result can not 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
-  // 0.099999999999 instead of 0.1.
-  // 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.
-  static bool grisu3(double v,
-                     char* buffer, int* length, int* decimal_exponent);
-
- private:
-  // Rounds the buffer according to the rest.
-  // If there is too much imprecision to round then false is returned.
-  // Similarily false is returned when the buffer is not within Delta.
-  static bool RoundWeed(char* buffer, int len, uint64_t wp_W, uint64_t Delta,
-                        uint64_t rest, uint64_t ten_kappa, uint64_t ulp);
-  // Dispatches to the a specialized digit-generation routine. The chosen
-  // routine depends on w.e (which in turn depends on alpha and gamma).
-  // Currently there is only one digit-generation routine, but it would be easy
-  // to add others.
-  static bool DigitGen(DiyFp low, DiyFp w, DiyFp high,
-                       char* buffer, int* len, int* kappa);
-  // Generates w's digits. The result is the shortest in the interval low-high.
-  // All DiyFp are assumed to be imprecise and this function takes this
-  // imprecision into account. If the function cannot compute the best
-  // representation (due to the imprecision) then false is returned.
-  static bool DigitGen_m60_m32(DiyFp low, DiyFp w, DiyFp high,
-                               char* buffer, int* length, int* kappa);
-};
-
-
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::grisu3(double v,
-                                  char* buffer,
-                                  int* length,
-                                  int* decimal_exponent) {
-  DiyFp w = Double(v).AsNormalizedDiyFp();
-  // boundary_minus and boundary_plus are the boundaries between v and its
-  // neighbors. Any number strictly between boundary_minus and boundary_plus
-  // will round to v when read as double.
-  // Grisu3 will never output representations that lie exactly on a boundary.
-  DiyFp boundary_minus, boundary_plus;
-  Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
-  ASSERT(boundary_plus.e() == w.e());
-  DiyFp ten_mk;  // Cached power of ten: 10^-k
-  int mk;        // -k
-  GetCachedPower(w.e() + DiyFp::kSignificandSize, alpha, gamma, &mk, &ten_mk);
-  ASSERT(alpha <= w.e() + ten_mk.e() + DiyFp::kSignificandSize &&
-         gamma >= 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);
-  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.
-  int kappa;
-  bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
-                         buffer, length, &kappa);
-  *decimal_exponent = -mk + kappa;
-  return result;
-}
-
-// 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 alpha and gamma. Typically alpha >= -63
-// and gamma <= 3.
-// 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~
-//  * alpha <= w.e() <= gamma
-// 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%).
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen(DiyFp low,
-                                    DiyFp w,
-                                    DiyFp high,
-                                    char* buffer,
-                                    int* len,
-                                    int* kappa) {
-  ASSERT(low.e() == w.e() && w.e() == high.e());
-  ASSERT(low.f() + 1 <= high.f() - 1);
-  ASSERT(alpha <= w.e() && w.e() <= gamma);
-  // The following tests use alpha and gamma to avoid unnecessary dynamic tests.
-  if ((alpha >= -60 && gamma <= -32) ||  // -60 <= w.e() <= -32
-      (alpha <= -32 && gamma >= -60 &&   // Alpha/gamma overlaps -60/-32 region.
-       -60 <= w.e() && w.e() <= -32)) {
-    return DigitGen_m60_m32(low, w, high, buffer, len, kappa);
-  } else {
-    // A simple adaption of the special case -60/-32 would allow greater ranges
-    // of alpha/gamma and thus reduce the number of precomputed cached powers of
-    // ten.
-    UNIMPLEMENTED();
-    return false;
-  }
-}
-
-static const uint32_t kTen4 = 10000;
-static const uint32_t kTen5 = 100000;
-static const uint32_t kTen6 = 1000000;
-static const uint32_t kTen7 = 10000000;
-static const uint32_t kTen8 = 100000000;
-static const uint32_t kTen9 = 1000000000;
-
-// Returns the biggest power of ten that is <= than the given number. We
-// furthermore receive the maximum number of bits 'number' has.
-// If number_bits == 0 then 0^-1 is returned
-// The number of bits must be <= 32.
-static void BiggestPowerTen(uint32_t number,
-                            int number_bits,
-                            uint32_t* power,
-                            int* exponent) {
-  switch (number_bits) {
-    case 32:
-    case 31:
-    case 30:
-      if (kTen9 <= number) {
-        *power = kTen9;
-        *exponent = 9;
-        break;
-      }  // else fallthrough
-    case 29:
-    case 28:
-    case 27:
-      if (kTen8 <= number) {
-        *power = kTen8;
-        *exponent = 8;
-        break;
-      }  // else fallthrough
-    case 26:
-    case 25:
-    case 24:
-      if (kTen7 <= number) {
-        *power = kTen7;
-        *exponent = 7;
-        break;
-      }  // else fallthrough
-    case 23:
-    case 22:
-    case 21:
-    case 20:
-      if (kTen6 <= number) {
-        *power = kTen6;
-        *exponent = 6;
-        break;
-      }  // else fallthrough
-    case 19:
-    case 18:
-    case 17:
-      if (kTen5 <= number) {
-        *power = kTen5;
-        *exponent = 5;
-        break;
-      }  // else fallthrough
-    case 16:
-    case 15:
-    case 14:
-      if (kTen4 <= number) {
-        *power = kTen4;
-        *exponent = 4;
-        break;
-      }  // else fallthrough
-    case 13:
-    case 12:
-    case 11:
-    case 10:
-      if (1000 <= number) {
-        *power = 1000;
-        *exponent = 3;
-        break;
-      }  // else fallthrough
-    case 9:
-    case 8:
-    case 7:
-      if (100 <= number) {
-        *power = 100;
-        *exponent = 2;
-        break;
-      }  // else fallthrough
-    case 6:
-    case 5:
-    case 4:
-      if (10 <= number) {
-        *power = 10;
-        *exponent = 1;
-        break;
-      }  // else fallthrough
-    case 3:
-    case 2:
-    case 1:
-      if (1 <= number) {
-        *power = 1;
-        *exponent = 0;
-        break;
-      }  // else fallthrough
-    case 0:
-      *power = 0;
-      *exponent = -1;
-      break;
-    default:
-      // Following assignments are here to silence compiler warnings.
-      *power = 0;
-      *exponent = 0;
-      UNREACHABLE();
-  }
-}
-
-
-// Same comments as for DigitGen but with additional precondition:
-//    -60 <= w.e() <= -32
-//
-// 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 comma 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.
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen_m60_m32(DiyFp low,
-                                            DiyFp w,
-                                            DiyFp high,
-                                            char* buffer,
-                                            int* length,
-                                            int* kappa) {
-  // 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.
-  uint64_t unit = 1;
-  DiyFp too_low = DiyFp(low.f() - unit, low.e());
-  DiyFp too_high = 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 = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
-  // Division by one is a shift.
-  uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
-  // Modulo by one is an and.
-  uint64_t fractionals = too_high.f() & (one.f() - 1);
-  uint32_t divider;
-  int divider_exponent;
-  BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
-                  &divider, &divider_exponent);
-  *kappa = divider_exponent + 1;
-  *length = 0;
-  // 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[*length] = '0' + digit;
-    (*length)++;
-    integrals %= divider;
-    (*kappa)--;
-    // Note that kappa now equals the exponent of the divider and that the
-    // invariant thus holds again.
-    uint64_t rest =
-        (static_cast<uint64_t>(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.
-      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
-                       unsafe_interval.f(), rest,
-                       static_cast<uint64_t>(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.set_f(unsafe_interval.f() * 5);
-    unsafe_interval.set_e(unsafe_interval.e() + 1);  // Will be optimized out.
-    one.set_f(one.f() >> 1);
-    one.set_e(one.e() + 1);
-    // Integer division by one.
-    int digit = static_cast<int>(fractionals >> -one.e());
-    buffer[*length] = '0' + digit;
-    (*length)++;
-    fractionals &= one.f() - 1;  // Modulo by one.
-    (*kappa)--;
-    if (fractionals < unsafe_interval.f()) {
-      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
-                       unsafe_interval.f(), fractionals, one.f(), unit);
-    }
-  }
-}
-
-
-// Rounds the given generated digits in the buffer and weeds out generated
-// digits that are not in the safe interval, or where we cannot find a rounded
-// representation.
-// Input: * buffer containing the digits of too_high / 10^kappa
-//        * the buffer's length
-//        * 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 on success.
-//    Modifies the generated digits in the buffer to approach (round towards) w.
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::RoundWeed(char* buffer,
-                                     int length,
-                                     uint64_t distance_too_high_w,
-                                     uint64_t unsafe_interval,
-                                     uint64_t rest,
-                                     uint64_t ten_kappa,
-                                     uint64_t unit) {
-  uint64_t small_distance = distance_too_high_w - unit;
-  uint64_t big_distance = distance_too_high_w + unit;
-  // Let w- = too_high - big_distance, and
-  //     w+ = too_high - small_distance.
-  // Note: w- < w < w+
-  //
-  // The real w (* unit) must lie somewhere inside the interval
-  // ]w-; w+[ (often written as "(w-; w+)")
-
-  // Basically the buffer currently contains a number in the unsafe interval
-  // ]too_low; too_high[ with too_low < w < too_high
-  //
-  // By generating the digits of too_high we got the biggest last digit.
-  // In the case that w+ < 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+
-  //   2) decrementing the buffer would make it leave the unsafe interval
-  //   3) decrementing the buffer would yield a number below w+ and farther away
-  //      than the current number. In other words:
-  //                       (buffer{-1} < w+) && w+ - buffer{-1} > buffer - w+
-  // Instead of using the buffer directly we use its distance to too_high.
-  // Conceptually rest ~= too_high - buffer
-  while (rest < small_distance &&  // Negated condition 1
-         unsafe_interval - rest >= ten_kappa &&  // Negated condition 2
-         (rest + ten_kappa < small_distance ||  // buffer{-1} > w+
-          small_distance - rest >= rest + ten_kappa - small_distance)) {
-    buffer[length - 1]--;
-    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 too
-  //      [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);
-}
-
-
-bool grisu3(double v, char* buffer, int* sign, int* length, int* point) {
-  ASSERT(v != 0);
-  ASSERT(!Double(v).IsSpecial());
-
-  if (v < 0) {
-    v = -v;
-    *sign = 1;
-  } else {
-    *sign = 0;
-  }
-  int decimal_exponent;
-  bool result = Grisu3<-60, -32>::grisu3(v, buffer, length, &decimal_exponent);
-  *point = *length + decimal_exponent;
-  buffer[*length] = '\0';
-  return result;
-}
-
-} }  // namespace v8::internal