| Index: third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
|
| diff --git a/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc b/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
|
| deleted file mode 100644
|
| index 0d79df4c3daf7febd5b87bce000a45261cd234ca..0000000000000000000000000000000000000000
|
| --- a/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
|
| +++ /dev/null
|
| @@ -1,656 +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 "bignum-dtoa.h"
|
| -
|
| -#include "bignum.h"
|
| -#include "double.h"
|
| -#include <math.h>
|
| -
|
| -namespace WTF {
|
| -
|
| -namespace double_conversion {
|
| -
|
| - static int NormalizedExponent(uint64_t significand, int exponent) {
|
| - ASSERT(significand != 0);
|
| - while ((significand & Double::kHiddenBit) == 0) {
|
| - significand = significand << 1;
|
| - exponent = exponent - 1;
|
| - }
|
| - return exponent;
|
| - }
|
| -
|
| -
|
| - // Forward declarations:
|
| - // Returns an estimation of k such that 10^(k-1) <= v < 10^k.
|
| - static int EstimatePower(int exponent);
|
| - // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
|
| - // and denominator.
|
| - static void InitialScaledStartValues(double v,
|
| - int estimated_power,
|
| - bool need_boundary_deltas,
|
| - Bignum* numerator,
|
| - Bignum* denominator,
|
| - Bignum* delta_minus,
|
| - Bignum* delta_plus);
|
| - // Multiplies numerator/denominator so that its values lies in the range 1-10.
|
| - // Returns decimal_point s.t.
|
| - // v = numerator'/denominator' * 10^(decimal_point-1)
|
| - // where numerator' and denominator' are the values of numerator and
|
| - // denominator after the call to this function.
|
| - static void FixupMultiply10(int estimated_power, bool is_even,
|
| - int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus);
|
| - // Generates digits from the left to the right and stops when the generated
|
| - // digits yield the shortest decimal representation of v.
|
| - static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus,
|
| - bool is_even,
|
| - Vector<char> buffer, int* length);
|
| - // Generates 'requested_digits' after the decimal point.
|
| - static void BignumToFixed(int requested_digits, int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Vector<char>(buffer), int* length);
|
| - // Generates 'count' digits of numerator/denominator.
|
| - // Once 'count' digits have been produced rounds the result depending on the
|
| - // remainder (remainders of exactly .5 round upwards). Might update the
|
| - // decimal_point when rounding up (for example for 0.9999).
|
| - static void GenerateCountedDigits(int count, int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Vector<char>(buffer), int* length);
|
| -
|
| -
|
| - void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
|
| - Vector<char> buffer, int* length, int* decimal_point) {
|
| - ASSERT(v > 0);
|
| - ASSERT(!Double(v).IsSpecial());
|
| - uint64_t significand = Double(v).Significand();
|
| - bool is_even = (significand & 1) == 0;
|
| - int exponent = Double(v).Exponent();
|
| - int normalized_exponent = NormalizedExponent(significand, exponent);
|
| - // estimated_power might be too low by 1.
|
| - int estimated_power = EstimatePower(normalized_exponent);
|
| -
|
| - // Shortcut for Fixed.
|
| - // The requested digits correspond to the digits after the point. If the
|
| - // number is much too small, then there is no need in trying to get any
|
| - // digits.
|
| - if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
|
| - buffer[0] = '\0';
|
| - *length = 0;
|
| - // Set decimal-point to -requested_digits. This is what Gay does.
|
| - // Note that it should not have any effect anyways since the string is
|
| - // empty.
|
| - *decimal_point = -requested_digits;
|
| - return;
|
| - }
|
| -
|
| - Bignum numerator;
|
| - Bignum denominator;
|
| - Bignum delta_minus;
|
| - Bignum delta_plus;
|
| - // Make sure the bignum can grow large enough. The smallest double equals
|
| - // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
|
| - // The maximum double is 1.7976931348623157e308 which needs fewer than
|
| - // 308*4 binary digits.
|
| - ASSERT(Bignum::kMaxSignificantBits >= 324*4);
|
| - bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST);
|
| - InitialScaledStartValues(v, estimated_power, need_boundary_deltas,
|
| - &numerator, &denominator,
|
| - &delta_minus, &delta_plus);
|
| - // We now have v = (numerator / denominator) * 10^estimated_power.
|
| - FixupMultiply10(estimated_power, is_even, decimal_point,
|
| - &numerator, &denominator,
|
| - &delta_minus, &delta_plus);
|
| - // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
|
| - // 1 <= (numerator + delta_plus) / denominator < 10
|
| - switch (mode) {
|
| - case BIGNUM_DTOA_SHORTEST:
|
| - GenerateShortestDigits(&numerator, &denominator,
|
| - &delta_minus, &delta_plus,
|
| - is_even, buffer, length);
|
| - break;
|
| - case BIGNUM_DTOA_FIXED:
|
| - BignumToFixed(requested_digits, decimal_point,
|
| - &numerator, &denominator,
|
| - buffer, length);
|
| - break;
|
| - case BIGNUM_DTOA_PRECISION:
|
| - GenerateCountedDigits(requested_digits, decimal_point,
|
| - &numerator, &denominator,
|
| - buffer, length);
|
| - break;
|
| - default:
|
| - UNREACHABLE();
|
| - }
|
| - buffer[*length] = '\0';
|
| - }
|
| -
|
| -
|
| - // The procedure starts generating digits from the left to the right and stops
|
| - // when the generated digits yield the shortest decimal representation of v. A
|
| - // decimal representation of v is a number lying closer to v than to any other
|
| - // double, so it converts to v when read.
|
| - //
|
| - // This is true if d, the decimal representation, is between m- and m+, the
|
| - // upper and lower boundaries. d must be strictly between them if !is_even.
|
| - // m- := (numerator - delta_minus) / denominator
|
| - // m+ := (numerator + delta_plus) / denominator
|
| - //
|
| - // Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
|
| - // If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
|
| - // will be produced. This should be the standard precondition.
|
| - static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus,
|
| - bool is_even,
|
| - Vector<char> buffer, int* length) {
|
| - // Small optimization: if delta_minus and delta_plus are the same just reuse
|
| - // one of the two bignums.
|
| - if (Bignum::Equal(*delta_minus, *delta_plus)) {
|
| - delta_plus = delta_minus;
|
| - }
|
| - *length = 0;
|
| - while (true) {
|
| - uint16_t digit;
|
| - digit = numerator->DivideModuloIntBignum(*denominator);
|
| - ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
|
| - // digit = numerator / denominator (integer division).
|
| - // numerator = numerator % denominator.
|
| - buffer[(*length)++] = static_cast<char>(digit + '0');
|
| -
|
| - // Can we stop already?
|
| - // If the remainder of the division is less than the distance to the lower
|
| - // boundary we can stop. In this case we simply round down (discarding the
|
| - // remainder).
|
| - // Similarly we test if we can round up (using the upper boundary).
|
| - bool in_delta_room_minus;
|
| - bool in_delta_room_plus;
|
| - if (is_even) {
|
| - in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
|
| - } else {
|
| - in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
|
| - }
|
| - if (is_even) {
|
| - in_delta_room_plus =
|
| - Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
|
| - } else {
|
| - in_delta_room_plus =
|
| - Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
|
| - }
|
| - if (!in_delta_room_minus && !in_delta_room_plus) {
|
| - // Prepare for next iteration.
|
| - numerator->Times10();
|
| - delta_minus->Times10();
|
| - // We optimized delta_plus to be equal to delta_minus (if they share the
|
| - // same value). So don't multiply delta_plus if they point to the same
|
| - // object.
|
| - if (delta_minus != delta_plus) {
|
| - delta_plus->Times10();
|
| - }
|
| - } else if (in_delta_room_minus && in_delta_room_plus) {
|
| - // Let's see if 2*numerator < denominator.
|
| - // If yes, then the next digit would be < 5 and we can round down.
|
| - int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
|
| - if (compare < 0) {
|
| - // Remaining digits are less than .5. -> Round down (== do nothing).
|
| - } else if (compare > 0) {
|
| - // Remaining digits are more than .5 of denominator. -> Round up.
|
| - // Note that the last digit could not be a '9' as otherwise the whole
|
| - // loop would have stopped earlier.
|
| - // We still have an assert here in case the preconditions were not
|
| - // satisfied.
|
| - ASSERT(buffer[(*length) - 1] != '9');
|
| - buffer[(*length) - 1]++;
|
| - } else {
|
| - // Halfway case.
|
| - // TODO(floitsch): need a way to solve half-way cases.
|
| - // For now let's round towards even (since this is what Gay seems to
|
| - // do).
|
| -
|
| - if ((buffer[(*length) - 1] - '0') % 2 == 0) {
|
| - // Round down => Do nothing.
|
| - } else {
|
| - ASSERT(buffer[(*length) - 1] != '9');
|
| - buffer[(*length) - 1]++;
|
| - }
|
| - }
|
| - return;
|
| - } else if (in_delta_room_minus) {
|
| - // Round down (== do nothing).
|
| - return;
|
| - } else { // in_delta_room_plus
|
| - // Round up.
|
| - // Note again that the last digit could not be '9' since this would have
|
| - // stopped the loop earlier.
|
| - // We still have an ASSERT here, in case the preconditions were not
|
| - // satisfied.
|
| - ASSERT(buffer[(*length) -1] != '9');
|
| - buffer[(*length) - 1]++;
|
| - return;
|
| - }
|
| - }
|
| - }
|
| -
|
| -
|
| - // Let v = numerator / denominator < 10.
|
| - // Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
|
| - // from left to right. Once 'count' digits have been produced we decide wether
|
| - // to round up or down. Remainders of exactly .5 round upwards. Numbers such
|
| - // as 9.999999 propagate a carry all the way, and change the
|
| - // exponent (decimal_point), when rounding upwards.
|
| - static void GenerateCountedDigits(int count, int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Vector<char>(buffer), int* length) {
|
| - ASSERT(count >= 0);
|
| - for (int i = 0; i < count - 1; ++i) {
|
| - uint16_t digit;
|
| - digit = numerator->DivideModuloIntBignum(*denominator);
|
| - ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
|
| - // digit = numerator / denominator (integer division).
|
| - // numerator = numerator % denominator.
|
| - buffer[i] = static_cast<char>(digit + '0');
|
| - // Prepare for next iteration.
|
| - numerator->Times10();
|
| - }
|
| - // Generate the last digit.
|
| - uint16_t digit;
|
| - digit = numerator->DivideModuloIntBignum(*denominator);
|
| - if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
|
| - digit++;
|
| - }
|
| - buffer[count - 1] = static_cast<char>(digit + '0');
|
| - // Correct bad digits (in case we had a sequence of '9's). Propagate the
|
| - // carry until we hat a non-'9' or til we reach the first digit.
|
| - for (int i = count - 1; i > 0; --i) {
|
| - if (buffer[i] != '0' + 10) break;
|
| - buffer[i] = '0';
|
| - buffer[i - 1]++;
|
| - }
|
| - if (buffer[0] == '0' + 10) {
|
| - // Propagate a carry past the top place.
|
| - buffer[0] = '1';
|
| - (*decimal_point)++;
|
| - }
|
| - *length = count;
|
| - }
|
| -
|
| -
|
| - // Generates 'requested_digits' after the decimal point. It might omit
|
| - // trailing '0's. If the input number is too small then no digits at all are
|
| - // generated (ex.: 2 fixed digits for 0.00001).
|
| - //
|
| - // Input verifies: 1 <= (numerator + delta) / denominator < 10.
|
| - static void BignumToFixed(int requested_digits, int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Vector<char>(buffer), int* length) {
|
| - // Note that we have to look at more than just the requested_digits, since
|
| - // a number could be rounded up. Example: v=0.5 with requested_digits=0.
|
| - // Even though the power of v equals 0 we can't just stop here.
|
| - if (-(*decimal_point) > requested_digits) {
|
| - // The number is definitively too small.
|
| - // Ex: 0.001 with requested_digits == 1.
|
| - // Set decimal-point to -requested_digits. This is what Gay does.
|
| - // Note that it should not have any effect anyways since the string is
|
| - // empty.
|
| - *decimal_point = -requested_digits;
|
| - *length = 0;
|
| - return;
|
| - } else if (-(*decimal_point) == requested_digits) {
|
| - // We only need to verify if the number rounds down or up.
|
| - // Ex: 0.04 and 0.06 with requested_digits == 1.
|
| - ASSERT(*decimal_point == -requested_digits);
|
| - // Initially the fraction lies in range (1, 10]. Multiply the denominator
|
| - // by 10 so that we can compare more easily.
|
| - denominator->Times10();
|
| - if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
|
| - // If the fraction is >= 0.5 then we have to include the rounded
|
| - // digit.
|
| - buffer[0] = '1';
|
| - *length = 1;
|
| - (*decimal_point)++;
|
| - } else {
|
| - // Note that we caught most of similar cases earlier.
|
| - *length = 0;
|
| - }
|
| - return;
|
| - } else {
|
| - // The requested digits correspond to the digits after the point.
|
| - // The variable 'needed_digits' includes the digits before the point.
|
| - int needed_digits = (*decimal_point) + requested_digits;
|
| - GenerateCountedDigits(needed_digits, decimal_point,
|
| - numerator, denominator,
|
| - buffer, length);
|
| - }
|
| - }
|
| -
|
| -
|
| - // Returns an estimation of k such that 10^(k-1) <= v < 10^k where
|
| - // v = f * 2^exponent and 2^52 <= f < 2^53.
|
| - // v is hence a normalized double with the given exponent. The output is an
|
| - // approximation for the exponent of the decimal approimation .digits * 10^k.
|
| - //
|
| - // The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
|
| - // Note: this property holds for v's upper boundary m+ too.
|
| - // 10^k <= m+ < 10^k+1.
|
| - // (see explanation below).
|
| - //
|
| - // Examples:
|
| - // EstimatePower(0) => 16
|
| - // EstimatePower(-52) => 0
|
| - //
|
| - // Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
|
| - static int EstimatePower(int exponent) {
|
| - // This function estimates log10 of v where v = f*2^e (with e == exponent).
|
| - // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
|
| - // Note that f is bounded by its container size. Let p = 53 (the double's
|
| - // significand size). Then 2^(p-1) <= f < 2^p.
|
| - //
|
| - // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
|
| - // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
|
| - // The computed number undershoots by less than 0.631 (when we compute log3
|
| - // and not log10).
|
| - //
|
| - // Optimization: since we only need an approximated result this computation
|
| - // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
|
| - // not really measurable, though.
|
| - //
|
| - // Since we want to avoid overshooting we decrement by 1e10 so that
|
| - // floating-point imprecisions don't affect us.
|
| - //
|
| - // Explanation for v's boundary m+: the computation takes advantage of
|
| - // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
|
| - // (even for denormals where the delta can be much more important).
|
| -
|
| - const double k1Log10 = 0.30102999566398114; // 1/lg(10)
|
| -
|
| - // For doubles len(f) == 53 (don't forget the hidden bit).
|
| - const int kSignificandSize = 53;
|
| - double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
|
| - return static_cast<int>(estimate);
|
| - }
|
| -
|
| -
|
| - // See comments for InitialScaledStartValues.
|
| - static void InitialScaledStartValuesPositiveExponent(
|
| - double v, int estimated_power, bool need_boundary_deltas,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus) {
|
| - // A positive exponent implies a positive power.
|
| - ASSERT(estimated_power >= 0);
|
| - // Since the estimated_power is positive we simply multiply the denominator
|
| - // by 10^estimated_power.
|
| -
|
| - // numerator = v.
|
| - numerator->AssignUInt64(Double(v).Significand());
|
| - numerator->ShiftLeft(Double(v).Exponent());
|
| - // denominator = 10^estimated_power.
|
| - denominator->AssignPowerUInt16(10, estimated_power);
|
| -
|
| - if (need_boundary_deltas) {
|
| - // Introduce a common denominator so that the deltas to the boundaries are
|
| - // integers.
|
| - denominator->ShiftLeft(1);
|
| - numerator->ShiftLeft(1);
|
| - // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
|
| - // denominator (of 2) delta_plus equals 2^e.
|
| - delta_plus->AssignUInt16(1);
|
| - delta_plus->ShiftLeft(Double(v).Exponent());
|
| - // Same for delta_minus (with adjustments below if f == 2^p-1).
|
| - delta_minus->AssignUInt16(1);
|
| - delta_minus->ShiftLeft(Double(v).Exponent());
|
| -
|
| - // If the significand (without the hidden bit) is 0, then the lower
|
| - // boundary is closer than just half a ulp (unit in the last place).
|
| - // There is only one exception: if the next lower number is a denormal then
|
| - // the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we
|
| - // have to test it in the other function where exponent < 0).
|
| - uint64_t v_bits = Double(v).AsUint64();
|
| - if ((v_bits & Double::kSignificandMask) == 0) {
|
| - // The lower boundary is closer at half the distance of "normal" numbers.
|
| - // Increase the common denominator and adapt all but the delta_minus.
|
| - denominator->ShiftLeft(1); // *2
|
| - numerator->ShiftLeft(1); // *2
|
| - delta_plus->ShiftLeft(1); // *2
|
| - }
|
| - }
|
| - }
|
| -
|
| -
|
| - // See comments for InitialScaledStartValues
|
| - static void InitialScaledStartValuesNegativeExponentPositivePower(
|
| - double v, int estimated_power, bool need_boundary_deltas,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus) {
|
| - uint64_t significand = Double(v).Significand();
|
| - int exponent = Double(v).Exponent();
|
| - // v = f * 2^e with e < 0, and with estimated_power >= 0.
|
| - // This means that e is close to 0 (have a look at how estimated_power is
|
| - // computed).
|
| -
|
| - // numerator = significand
|
| - // since v = significand * 2^exponent this is equivalent to
|
| - // numerator = v * / 2^-exponent
|
| - numerator->AssignUInt64(significand);
|
| - // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
|
| - denominator->AssignPowerUInt16(10, estimated_power);
|
| - denominator->ShiftLeft(-exponent);
|
| -
|
| - if (need_boundary_deltas) {
|
| - // Introduce a common denominator so that the deltas to the boundaries are
|
| - // integers.
|
| - denominator->ShiftLeft(1);
|
| - numerator->ShiftLeft(1);
|
| - // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
|
| - // denominator (of 2) delta_plus equals 2^e.
|
| - // Given that the denominator already includes v's exponent the distance
|
| - // to the boundaries is simply 1.
|
| - delta_plus->AssignUInt16(1);
|
| - // Same for delta_minus (with adjustments below if f == 2^p-1).
|
| - delta_minus->AssignUInt16(1);
|
| -
|
| - // If the significand (without the hidden bit) is 0, then the lower
|
| - // boundary is closer than just one ulp (unit in the last place).
|
| - // There is only one exception: if the next lower number is a denormal
|
| - // then the distance is 1 ulp. Since the exponent is close to zero
|
| - // (otherwise estimated_power would have been negative) this cannot happen
|
| - // here either.
|
| - uint64_t v_bits = Double(v).AsUint64();
|
| - if ((v_bits & Double::kSignificandMask) == 0) {
|
| - // The lower boundary is closer at half the distance of "normal" numbers.
|
| - // Increase the denominator and adapt all but the delta_minus.
|
| - denominator->ShiftLeft(1); // *2
|
| - numerator->ShiftLeft(1); // *2
|
| - delta_plus->ShiftLeft(1); // *2
|
| - }
|
| - }
|
| - }
|
| -
|
| -
|
| - // See comments for InitialScaledStartValues
|
| - static void InitialScaledStartValuesNegativeExponentNegativePower(
|
| - double v, int estimated_power, bool need_boundary_deltas,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus) {
|
| - const uint64_t kMinimalNormalizedExponent =
|
| - UINT64_2PART_C(0x00100000, 00000000);
|
| - uint64_t significand = Double(v).Significand();
|
| - int exponent = Double(v).Exponent();
|
| - // Instead of multiplying the denominator with 10^estimated_power we
|
| - // multiply all values (numerator and deltas) by 10^-estimated_power.
|
| -
|
| - // Use numerator as temporary container for power_ten.
|
| - Bignum* power_ten = numerator;
|
| - power_ten->AssignPowerUInt16(10, -estimated_power);
|
| -
|
| - if (need_boundary_deltas) {
|
| - // Since power_ten == numerator we must make a copy of 10^estimated_power
|
| - // before we complete the computation of the numerator.
|
| - // delta_plus = delta_minus = 10^estimated_power
|
| - delta_plus->AssignBignum(*power_ten);
|
| - delta_minus->AssignBignum(*power_ten);
|
| - }
|
| -
|
| - // numerator = significand * 2 * 10^-estimated_power
|
| - // since v = significand * 2^exponent this is equivalent to
|
| - // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
|
| - // Remember: numerator has been abused as power_ten. So no need to assign it
|
| - // to itself.
|
| - ASSERT(numerator == power_ten);
|
| - numerator->MultiplyByUInt64(significand);
|
| -
|
| - // denominator = 2 * 2^-exponent with exponent < 0.
|
| - denominator->AssignUInt16(1);
|
| - denominator->ShiftLeft(-exponent);
|
| -
|
| - if (need_boundary_deltas) {
|
| - // Introduce a common denominator so that the deltas to the boundaries are
|
| - // integers.
|
| - numerator->ShiftLeft(1);
|
| - denominator->ShiftLeft(1);
|
| - // With this shift the boundaries have their correct value, since
|
| - // delta_plus = 10^-estimated_power, and
|
| - // delta_minus = 10^-estimated_power.
|
| - // These assignments have been done earlier.
|
| -
|
| - // The special case where the lower boundary is twice as close.
|
| - // This time we have to look out for the exception too.
|
| - uint64_t v_bits = Double(v).AsUint64();
|
| - if ((v_bits & Double::kSignificandMask) == 0 &&
|
| - // The only exception where a significand == 0 has its boundaries at
|
| - // "normal" distances:
|
| - (v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) {
|
| - numerator->ShiftLeft(1); // *2
|
| - denominator->ShiftLeft(1); // *2
|
| - delta_plus->ShiftLeft(1); // *2
|
| - }
|
| - }
|
| - }
|
| -
|
| -
|
| - // Let v = significand * 2^exponent.
|
| - // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
|
| - // and denominator. The functions GenerateShortestDigits and
|
| - // GenerateCountedDigits will then convert this ratio to its decimal
|
| - // representation d, with the required accuracy.
|
| - // Then d * 10^estimated_power is the representation of v.
|
| - // (Note: the fraction and the estimated_power might get adjusted before
|
| - // generating the decimal representation.)
|
| - //
|
| - // The initial start values consist of:
|
| - // - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
|
| - // - a scaled (common) denominator.
|
| - // optionally (used by GenerateShortestDigits to decide if it has the shortest
|
| - // decimal converting back to v):
|
| - // - v - m-: the distance to the lower boundary.
|
| - // - m+ - v: the distance to the upper boundary.
|
| - //
|
| - // v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
|
| - //
|
| - // Let ep == estimated_power, then the returned values will satisfy:
|
| - // v / 10^ep = numerator / denominator.
|
| - // v's boundarys m- and m+:
|
| - // m- / 10^ep == v / 10^ep - delta_minus / denominator
|
| - // m+ / 10^ep == v / 10^ep + delta_plus / denominator
|
| - // Or in other words:
|
| - // m- == v - delta_minus * 10^ep / denominator;
|
| - // m+ == v + delta_plus * 10^ep / denominator;
|
| - //
|
| - // Since 10^(k-1) <= v < 10^k (with k == estimated_power)
|
| - // or 10^k <= v < 10^(k+1)
|
| - // we then have 0.1 <= numerator/denominator < 1
|
| - // or 1 <= numerator/denominator < 10
|
| - //
|
| - // It is then easy to kickstart the digit-generation routine.
|
| - //
|
| - // The boundary-deltas are only filled if need_boundary_deltas is set.
|
| - static void InitialScaledStartValues(double v,
|
| - int estimated_power,
|
| - bool need_boundary_deltas,
|
| - Bignum* numerator,
|
| - Bignum* denominator,
|
| - Bignum* delta_minus,
|
| - Bignum* delta_plus) {
|
| - if (Double(v).Exponent() >= 0) {
|
| - InitialScaledStartValuesPositiveExponent(
|
| - v, estimated_power, need_boundary_deltas,
|
| - numerator, denominator, delta_minus, delta_plus);
|
| - } else if (estimated_power >= 0) {
|
| - InitialScaledStartValuesNegativeExponentPositivePower(
|
| - v, estimated_power, need_boundary_deltas,
|
| - numerator, denominator, delta_minus, delta_plus);
|
| - } else {
|
| - InitialScaledStartValuesNegativeExponentNegativePower(
|
| - v, estimated_power, need_boundary_deltas,
|
| - numerator, denominator, delta_minus, delta_plus);
|
| - }
|
| - }
|
| -
|
| -
|
| - // This routine multiplies numerator/denominator so that its values lies in the
|
| - // range 1-10. That is after a call to this function we have:
|
| - // 1 <= (numerator + delta_plus) /denominator < 10.
|
| - // Let numerator the input before modification and numerator' the argument
|
| - // after modification, then the output-parameter decimal_point is such that
|
| - // numerator / denominator * 10^estimated_power ==
|
| - // numerator' / denominator' * 10^(decimal_point - 1)
|
| - // In some cases estimated_power was too low, and this is already the case. We
|
| - // then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
|
| - // estimated_power) but do not touch the numerator or denominator.
|
| - // Otherwise the routine multiplies the numerator and the deltas by 10.
|
| - static void FixupMultiply10(int estimated_power, bool is_even,
|
| - int* decimal_point,
|
| - Bignum* numerator, Bignum* denominator,
|
| - Bignum* delta_minus, Bignum* delta_plus) {
|
| - bool in_range;
|
| - if (is_even) {
|
| - // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
|
| - // are rounded to the closest floating-point number with even significand.
|
| - in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
|
| - } else {
|
| - in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
|
| - }
|
| - if (in_range) {
|
| - // Since numerator + delta_plus >= denominator we already have
|
| - // 1 <= numerator/denominator < 10. Simply update the estimated_power.
|
| - *decimal_point = estimated_power + 1;
|
| - } else {
|
| - *decimal_point = estimated_power;
|
| - numerator->Times10();
|
| - if (Bignum::Equal(*delta_minus, *delta_plus)) {
|
| - delta_minus->Times10();
|
| - delta_plus->AssignBignum(*delta_minus);
|
| - } else {
|
| - delta_minus->Times10();
|
| - delta_plus->Times10();
|
| - }
|
| - }
|
| - }
|
| -
|
| -} // namespace double_conversion
|
| -
|
| -} // namespace WTF
|
|
|