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 |