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Diffstat (limited to 'src/3rdparty/double-conversion')
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diff --git a/src/3rdparty/double-conversion/LICENSE b/src/3rdparty/double-conversion/LICENSE new file mode 100644 index 0000000000..933718a9ef --- /dev/null +++ b/src/3rdparty/double-conversion/LICENSE @@ -0,0 +1,26 @@ +Copyright 2006-2011, 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. diff --git a/src/3rdparty/double-conversion/README b/src/3rdparty/double-conversion/README new file mode 100644 index 0000000000..75d08df5fe --- /dev/null +++ b/src/3rdparty/double-conversion/README @@ -0,0 +1,8 @@ +This is a copy of the library for binary-decimal and decimal-binary +conversion routines for IEEE doubles, available from + + https://github.com/google/double-conversion + +commit 2fb03de56faa32bbba5e02222528e7b760f71d77 + +See the LICENSE file for license information. diff --git a/src/3rdparty/double-conversion/bignum-dtoa.cc b/src/3rdparty/double-conversion/bignum-dtoa.cc new file mode 100644 index 0000000000..f1ad7a5ae8 --- /dev/null +++ b/src/3rdparty/double-conversion/bignum-dtoa.cc @@ -0,0 +1,641 @@ +// 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 <math.h> + +#include "bignum-dtoa.h" + +#include "bignum.h" +#include "ieee.h" + +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(uint64_t significand, + int exponent, + bool lower_boundary_is_closer, + 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; + int exponent; + bool lower_boundary_is_closer; + if (mode == BIGNUM_DTOA_SHORTEST_SINGLE) { + float f = static_cast<float>(v); + ASSERT(f == v); + significand = Single(f).Significand(); + exponent = Single(f).Exponent(); + lower_boundary_is_closer = Single(f).LowerBoundaryIsCloser(); + } else { + significand = Double(v).Significand(); + exponent = Double(v).Exponent(); + lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser(); + } + bool need_boundary_deltas = + (mode == BIGNUM_DTOA_SHORTEST || mode == BIGNUM_DTOA_SHORTEST_SINGLE); + + bool is_even = (significand & 1) == 0; + 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); + InitialScaledStartValues(significand, exponent, lower_boundary_is_closer, + 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: + case BIGNUM_DTOA_SHORTEST_SINGLE: + 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; + for (;;) { + 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++; + } + ASSERT(digit <= 10); + 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 = Double::kSignificandSize; + double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10); + return static_cast<int>(estimate); +} + + +// See comments for InitialScaledStartValues. +static void InitialScaledStartValuesPositiveExponent( + uint64_t significand, int exponent, + 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(significand); + numerator->ShiftLeft(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(exponent); + // Same for delta_minus. The adjustments if f == 2^p-1 are done later. + delta_minus->AssignUInt16(1); + delta_minus->ShiftLeft(exponent); + } +} + + +// See comments for InitialScaledStartValues +static void InitialScaledStartValuesNegativeExponentPositivePower( + uint64_t significand, int exponent, + int estimated_power, bool need_boundary_deltas, + Bignum* numerator, Bignum* denominator, + Bignum* delta_minus, Bignum* delta_plus) { + // 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. The adjustments if f == 2^p-1 are done later. + delta_minus->AssignUInt16(1); + } +} + + +// See comments for InitialScaledStartValues +static void InitialScaledStartValuesNegativeExponentNegativePower( + uint64_t significand, int exponent, + int estimated_power, bool need_boundary_deltas, + Bignum* numerator, Bignum* denominator, + Bignum* delta_minus, Bignum* delta_plus) { + // 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 adjustments if f == 2^p-1 (lower boundary is closer) are done later. + } +} + + +// 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 the mode equals BIGNUM_DTOA_SHORTEST +// or BIGNUM_DTOA_SHORTEST_SINGLE. + +static void InitialScaledStartValues(uint64_t significand, + int exponent, + bool lower_boundary_is_closer, + int estimated_power, + bool need_boundary_deltas, + Bignum* numerator, + Bignum* denominator, + Bignum* delta_minus, + Bignum* delta_plus) { + if (exponent >= 0) { + InitialScaledStartValuesPositiveExponent( + significand, exponent, estimated_power, need_boundary_deltas, + numerator, denominator, delta_minus, delta_plus); + } else if (estimated_power >= 0) { + InitialScaledStartValuesNegativeExponentPositivePower( + significand, exponent, estimated_power, need_boundary_deltas, + numerator, denominator, delta_minus, delta_plus); + } else { + InitialScaledStartValuesNegativeExponentNegativePower( + significand, exponent, estimated_power, need_boundary_deltas, + numerator, denominator, delta_minus, delta_plus); + } + + if (need_boundary_deltas && lower_boundary_is_closer) { + // 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 + } +} + + +// 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 diff --git a/src/3rdparty/double-conversion/bignum-dtoa.h b/src/3rdparty/double-conversion/bignum-dtoa.h new file mode 100644 index 0000000000..34b961992d --- /dev/null +++ b/src/3rdparty/double-conversion/bignum-dtoa.h @@ -0,0 +1,84 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_BIGNUM_DTOA_H_ +#define DOUBLE_CONVERSION_BIGNUM_DTOA_H_ + +#include "utils.h" + +namespace double_conversion { + +enum BignumDtoaMode { + // Return the shortest correct representation. + // For example the output of 0.299999999999999988897 is (the less accurate but + // correct) 0.3. + BIGNUM_DTOA_SHORTEST, + // Same as BIGNUM_DTOA_SHORTEST but for single-precision floats. + BIGNUM_DTOA_SHORTEST_SINGLE, + // Return a fixed number of digits after the decimal point. + // For instance fixed(0.1, 4) becomes 0.1000 + // If the input number is big, the output will be big. + BIGNUM_DTOA_FIXED, + // Return a fixed number of digits, no matter what the exponent is. + BIGNUM_DTOA_PRECISION +}; + +// Converts the given double 'v' to ascii. +// The result should be interpreted as buffer * 10^(point-length). +// The buffer will be null-terminated. +// +// The input v must be > 0 and different from NaN, and Infinity. +// +// The output depends on the given mode: +// - SHORTEST: produce the least amount of digits for which the internal +// identity requirement is still satisfied. If the digits are printed +// (together with the correct exponent) then reading this number will give +// 'v' again. The buffer will choose the representation that is closest to +// 'v'. If there are two at the same distance, than the number is round up. +// In this mode the 'requested_digits' parameter is ignored. +// - FIXED: produces digits necessary to print a given number with +// 'requested_digits' digits after the decimal point. The produced digits +// might be too short in which case the caller has to fill the gaps with '0's. +// Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2. +// Halfway cases are rounded up. The call toFixed(0.15, 2) thus returns +// buffer="2", point=0. +// Note: the length of the returned buffer has no meaning wrt the significance +// of its digits. That is, just because it contains '0's does not mean that +// any other digit would not satisfy the internal identity requirement. +// - PRECISION: produces 'requested_digits' where the first digit is not '0'. +// Even though the length of produced digits usually equals +// 'requested_digits', the function is allowed to return fewer digits, in +// which case the caller has to fill the missing digits with '0's. +// Halfway cases are again rounded up. +// 'BignumDtoa' expects the given buffer to be big enough to hold all digits +// and a terminating null-character. +void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits, + Vector<char> buffer, int* length, int* point); + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_BIGNUM_DTOA_H_ diff --git a/src/3rdparty/double-conversion/bignum.cc b/src/3rdparty/double-conversion/bignum.cc new file mode 100644 index 0000000000..2743d67e8d --- /dev/null +++ b/src/3rdparty/double-conversion/bignum.cc @@ -0,0 +1,766 @@ +// 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.h" +#include "utils.h" + +namespace double_conversion { + +Bignum::Bignum() + : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { + for (int i = 0; i < kBigitCapacity; ++i) { + bigits_[i] = 0; + } +} + + +template<typename S> +static int BitSize(S value) { + (void) value; // Mark variable as used. + return 8 * sizeof(value); +} + +// Guaranteed to lie in one Bigit. +void Bignum::AssignUInt16(uint16_t value) { + ASSERT(kBigitSize >= BitSize(value)); + Zero(); + if (value == 0) return; + + EnsureCapacity(1); + bigits_[0] = value; + used_digits_ = 1; +} + + +void Bignum::AssignUInt64(uint64_t value) { + const int kUInt64Size = 64; + + Zero(); + if (value == 0) return; + + int needed_bigits = kUInt64Size / kBigitSize + 1; + EnsureCapacity(needed_bigits); + for (int i = 0; i < needed_bigits; ++i) { + bigits_[i] = value & kBigitMask; + value = value >> kBigitSize; + } + used_digits_ = needed_bigits; + Clamp(); +} + + +void Bignum::AssignBignum(const Bignum& other) { + exponent_ = other.exponent_; + for (int i = 0; i < other.used_digits_; ++i) { + bigits_[i] = other.bigits_[i]; + } + // Clear the excess digits (if there were any). + for (int i = other.used_digits_; i < used_digits_; ++i) { + bigits_[i] = 0; + } + used_digits_ = other.used_digits_; +} + + +static uint64_t ReadUInt64(Vector<const char> buffer, + int from, + int digits_to_read) { + uint64_t result = 0; + for (int i = from; i < from + digits_to_read; ++i) { + int digit = buffer[i] - '0'; + ASSERT(0 <= digit && digit <= 9); + result = result * 10 + digit; + } + return result; +} + + +void Bignum::AssignDecimalString(Vector<const char> value) { + // 2^64 = 18446744073709551616 > 10^19 + const int kMaxUint64DecimalDigits = 19; + Zero(); + int length = value.length(); + int pos = 0; + // Let's just say that each digit needs 4 bits. + while (length >= kMaxUint64DecimalDigits) { + uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); + pos += kMaxUint64DecimalDigits; + length -= kMaxUint64DecimalDigits; + MultiplyByPowerOfTen(kMaxUint64DecimalDigits); + AddUInt64(digits); + } + uint64_t digits = ReadUInt64(value, pos, length); + MultiplyByPowerOfTen(length); + AddUInt64(digits); + Clamp(); +} + + +static int HexCharValue(char c) { + if ('0' <= c && c <= '9') return c - '0'; + if ('a' <= c && c <= 'f') return 10 + c - 'a'; + ASSERT('A' <= c && c <= 'F'); + return 10 + c - 'A'; +} + + +void Bignum::AssignHexString(Vector<const char> value) { + Zero(); + int length = value.length(); + + int needed_bigits = length * 4 / kBigitSize + 1; + EnsureCapacity(needed_bigits); + int string_index = length - 1; + for (int i = 0; i < needed_bigits - 1; ++i) { + // These bigits are guaranteed to be "full". + Chunk current_bigit = 0; + for (int j = 0; j < kBigitSize / 4; j++) { + current_bigit += HexCharValue(value[string_index--]) << (j * 4); + } + bigits_[i] = current_bigit; + } + used_digits_ = needed_bigits - 1; + + Chunk most_significant_bigit = 0; // Could be = 0; + for (int j = 0; j <= string_index; ++j) { + most_significant_bigit <<= 4; + most_significant_bigit += HexCharValue(value[j]); + } + if (most_significant_bigit != 0) { + bigits_[used_digits_] = most_significant_bigit; + used_digits_++; + } + Clamp(); +} + + +void Bignum::AddUInt64(uint64_t operand) { + if (operand == 0) return; + Bignum other; + other.AssignUInt64(operand); + AddBignum(other); +} + + +void Bignum::AddBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + + // If this has a greater exponent than other append zero-bigits to this. + // After this call exponent_ <= other.exponent_. + Align(other); + + // There are two possibilities: + // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) + // bbbbb 00000000 + // ---------------- + // ccccccccccc 0000 + // or + // aaaaaaaaaa 0000 + // bbbbbbbbb 0000000 + // ----------------- + // cccccccccccc 0000 + // In both cases we might need a carry bigit. + + EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); + Chunk carry = 0; + int bigit_pos = other.exponent_ - exponent_; + ASSERT(bigit_pos >= 0); + for (int i = 0; i < other.used_digits_; ++i) { + Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; + bigits_[bigit_pos] = sum & kBigitMask; + carry = sum >> kBigitSize; + bigit_pos++; + } + + while (carry != 0) { + Chunk sum = bigits_[bigit_pos] + carry; + bigits_[bigit_pos] = sum & kBigitMask; + carry = sum >> kBigitSize; + bigit_pos++; + } + used_digits_ = Max(bigit_pos, used_digits_); + ASSERT(IsClamped()); +} + + +void Bignum::SubtractBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + // We require this to be bigger than other. + ASSERT(LessEqual(other, *this)); + + Align(other); + + int offset = other.exponent_ - exponent_; + Chunk borrow = 0; + int i; + for (i = 0; i < other.used_digits_; ++i) { + ASSERT((borrow == 0) || (borrow == 1)); + Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; + bigits_[i + offset] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + } + while (borrow != 0) { + Chunk difference = bigits_[i + offset] - borrow; + bigits_[i + offset] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + ++i; + } + Clamp(); +} + + +void Bignum::ShiftLeft(int shift_amount) { + if (used_digits_ == 0) return; + exponent_ += shift_amount / kBigitSize; + int local_shift = shift_amount % kBigitSize; + EnsureCapacity(used_digits_ + 1); + BigitsShiftLeft(local_shift); +} + + +void Bignum::MultiplyByUInt32(uint32_t factor) { + if (factor == 1) return; + if (factor == 0) { + Zero(); + return; + } + if (used_digits_ == 0) return; + + // The product of a bigit with the factor is of size kBigitSize + 32. + // Assert that this number + 1 (for the carry) fits into double chunk. + ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); + DoubleChunk carry = 0; + for (int i = 0; i < used_digits_; ++i) { + DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; + bigits_[i] = static_cast<Chunk>(product & kBigitMask); + carry = (product >> kBigitSize); + } + while (carry != 0) { + EnsureCapacity(used_digits_ + 1); + bigits_[used_digits_] = carry & kBigitMask; + used_digits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByUInt64(uint64_t factor) { + if (factor == 1) return; + if (factor == 0) { + Zero(); + return; + } + ASSERT(kBigitSize < 32); + uint64_t carry = 0; + uint64_t low = factor & 0xFFFFFFFF; + uint64_t high = factor >> 32; + for (int i = 0; i < used_digits_; ++i) { + uint64_t product_low = low * bigits_[i]; + uint64_t product_high = high * bigits_[i]; + uint64_t tmp = (carry & kBigitMask) + product_low; + bigits_[i] = tmp & kBigitMask; + carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + + (product_high << (32 - kBigitSize)); + } + while (carry != 0) { + EnsureCapacity(used_digits_ + 1); + bigits_[used_digits_] = carry & kBigitMask; + used_digits_++; + carry >>= kBigitSize; + } +} + + +void Bignum::MultiplyByPowerOfTen(int exponent) { + const uint64_t kFive27 = UINT64_2PART_C(0x6765c793, fa10079d); + const uint16_t kFive1 = 5; + const uint16_t kFive2 = kFive1 * 5; + const uint16_t kFive3 = kFive2 * 5; + const uint16_t kFive4 = kFive3 * 5; + const uint16_t kFive5 = kFive4 * 5; + const uint16_t kFive6 = kFive5 * 5; + const uint32_t kFive7 = kFive6 * 5; + const uint32_t kFive8 = kFive7 * 5; + const uint32_t kFive9 = kFive8 * 5; + const uint32_t kFive10 = kFive9 * 5; + const uint32_t kFive11 = kFive10 * 5; + const uint32_t kFive12 = kFive11 * 5; + const uint32_t kFive13 = kFive12 * 5; + const uint32_t kFive1_to_12[] = + { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, + kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; + + ASSERT(exponent >= 0); + if (exponent == 0) return; + if (used_digits_ == 0) return; + + // We shift by exponent at the end just before returning. + int remaining_exponent = exponent; + while (remaining_exponent >= 27) { + MultiplyByUInt64(kFive27); + remaining_exponent -= 27; + } + while (remaining_exponent >= 13) { + MultiplyByUInt32(kFive13); + remaining_exponent -= 13; + } + if (remaining_exponent > 0) { + MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); + } + ShiftLeft(exponent); +} + + +void Bignum::Square() { + ASSERT(IsClamped()); + int product_length = 2 * used_digits_; + EnsureCapacity(product_length); + + // Comba multiplication: compute each column separately. + // Example: r = a2a1a0 * b2b1b0. + // r = 1 * a0b0 + + // 10 * (a1b0 + a0b1) + + // 100 * (a2b0 + a1b1 + a0b2) + + // 1000 * (a2b1 + a1b2) + + // 10000 * a2b2 + // + // In the worst case we have to accumulate nb-digits products of digit*digit. + // + // Assert that the additional number of bits in a DoubleChunk are enough to + // sum up used_digits of Bigit*Bigit. + if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { + UNIMPLEMENTED(); + } + DoubleChunk accumulator = 0; + // First shift the digits so we don't overwrite them. + int copy_offset = used_digits_; + for (int i = 0; i < used_digits_; ++i) { + bigits_[copy_offset + i] = bigits_[i]; + } + // We have two loops to avoid some 'if's in the loop. + for (int i = 0; i < used_digits_; ++i) { + // Process temporary digit i with power i. + // The sum of the two indices must be equal to i. + int bigit_index1 = i; + int bigit_index2 = 0; + // Sum all of the sub-products. + while (bigit_index1 >= 0) { + Chunk chunk1 = bigits_[copy_offset + bigit_index1]; + Chunk chunk2 = bigits_[copy_offset + bigit_index2]; + accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + for (int i = used_digits_; i < product_length; ++i) { + int bigit_index1 = used_digits_ - 1; + int bigit_index2 = i - bigit_index1; + // Invariant: sum of both indices is again equal to i. + // Inner loop runs 0 times on last iteration, emptying accumulator. + while (bigit_index2 < used_digits_) { + Chunk chunk1 = bigits_[copy_offset + bigit_index1]; + Chunk chunk2 = bigits_[copy_offset + bigit_index2]; + accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; + bigit_index1--; + bigit_index2++; + } + // The overwritten bigits_[i] will never be read in further loop iterations, + // because bigit_index1 and bigit_index2 are always greater + // than i - used_digits_. + bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; + accumulator >>= kBigitSize; + } + // Since the result was guaranteed to lie inside the number the + // accumulator must be 0 now. + ASSERT(accumulator == 0); + + // Don't forget to update the used_digits and the exponent. + used_digits_ = product_length; + exponent_ *= 2; + Clamp(); +} + + +void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { + ASSERT(base != 0); + ASSERT(power_exponent >= 0); + if (power_exponent == 0) { + AssignUInt16(1); + return; + } + Zero(); + int shifts = 0; + // We expect base to be in range 2-32, and most often to be 10. + // It does not make much sense to implement different algorithms for counting + // the bits. + while ((base & 1) == 0) { + base >>= 1; + shifts++; + } + int bit_size = 0; + int tmp_base = base; + while (tmp_base != 0) { + tmp_base >>= 1; + bit_size++; + } + int final_size = bit_size * power_exponent; + // 1 extra bigit for the shifting, and one for rounded final_size. + EnsureCapacity(final_size / kBigitSize + 2); + + // Left to Right exponentiation. + int mask = 1; + while (power_exponent >= mask) mask <<= 1; + + // The mask is now pointing to the bit above the most significant 1-bit of + // power_exponent. + // Get rid of first 1-bit; + mask >>= 2; + uint64_t this_value = base; + + bool delayed_multipliciation = false; + const uint64_t max_32bits = 0xFFFFFFFF; + while (mask != 0 && this_value <= max_32bits) { + this_value = this_value * this_value; + // Verify that there is enough space in this_value to perform the + // multiplication. The first bit_size bits must be 0. + if ((power_exponent & mask) != 0) { + uint64_t base_bits_mask = + ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); + bool high_bits_zero = (this_value & base_bits_mask) == 0; + if (high_bits_zero) { + this_value *= base; + } else { + delayed_multipliciation = true; + } + } + mask >>= 1; + } + AssignUInt64(this_value); + if (delayed_multipliciation) { + MultiplyByUInt32(base); + } + + // Now do the same thing as a bignum. + while (mask != 0) { + Square(); + if ((power_exponent & mask) != 0) { + MultiplyByUInt32(base); + } + mask >>= 1; + } + + // And finally add the saved shifts. + ShiftLeft(shifts * power_exponent); +} + + +// Precondition: this/other < 16bit. +uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { + ASSERT(IsClamped()); + ASSERT(other.IsClamped()); + ASSERT(other.used_digits_ > 0); + + // Easy case: if we have less digits than the divisor than the result is 0. + // Note: this handles the case where this == 0, too. + if (BigitLength() < other.BigitLength()) { + return 0; + } + + Align(other); + + uint16_t result = 0; + + // Start by removing multiples of 'other' until both numbers have the same + // number of digits. + while (BigitLength() > other.BigitLength()) { + // This naive approach is extremely inefficient if `this` divided by other + // is big. This function is implemented for doubleToString where + // the result should be small (less than 10). + ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); + ASSERT(bigits_[used_digits_ - 1] < 0x10000); + // Remove the multiples of the first digit. + // Example this = 23 and other equals 9. -> Remove 2 multiples. + result += static_cast<uint16_t>(bigits_[used_digits_ - 1]); + SubtractTimes(other, bigits_[used_digits_ - 1]); + } + + ASSERT(BigitLength() == other.BigitLength()); + + // Both bignums are at the same length now. + // Since other has more than 0 digits we know that the access to + // bigits_[used_digits_ - 1] is safe. + Chunk this_bigit = bigits_[used_digits_ - 1]; + Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; + + if (other.used_digits_ == 1) { + // Shortcut for easy (and common) case. + int quotient = this_bigit / other_bigit; + bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; + ASSERT(quotient < 0x10000); + result += static_cast<uint16_t>(quotient); + Clamp(); + return result; + } + + int division_estimate = this_bigit / (other_bigit + 1); + ASSERT(division_estimate < 0x10000); + result += static_cast<uint16_t>(division_estimate); + SubtractTimes(other, division_estimate); + + if (other_bigit * (division_estimate + 1) > this_bigit) { + // No need to even try to subtract. Even if other's remaining digits were 0 + // another subtraction would be too much. + return result; + } + + while (LessEqual(other, *this)) { + SubtractBignum(other); + result++; + } + return result; +} + + +template<typename S> +static int SizeInHexChars(S number) { + ASSERT(number > 0); + int result = 0; + while (number != 0) { + number >>= 4; + result++; + } + return result; +} + + +static char HexCharOfValue(int value) { + ASSERT(0 <= value && value <= 16); + if (value < 10) return static_cast<char>(value + '0'); + return static_cast<char>(value - 10 + 'A'); +} + + +bool Bignum::ToHexString(char* buffer, int buffer_size) const { + ASSERT(IsClamped()); + // Each bigit must be printable as separate hex-character. + ASSERT(kBigitSize % 4 == 0); + const int kHexCharsPerBigit = kBigitSize / 4; + + if (used_digits_ == 0) { + if (buffer_size < 2) return false; + buffer[0] = '0'; + buffer[1] = '\0'; + return true; + } + // We add 1 for the terminating '\0' character. + int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + + SizeInHexChars(bigits_[used_digits_ - 1]) + 1; + if (needed_chars > buffer_size) return false; + int string_index = needed_chars - 1; + buffer[string_index--] = '\0'; + for (int i = 0; i < exponent_; ++i) { + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = '0'; + } + } + for (int i = 0; i < used_digits_ - 1; ++i) { + Chunk current_bigit = bigits_[i]; + for (int j = 0; j < kHexCharsPerBigit; ++j) { + buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); + current_bigit >>= 4; + } + } + // And finally the last bigit. + Chunk most_significant_bigit = bigits_[used_digits_ - 1]; + while (most_significant_bigit != 0) { + buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); + most_significant_bigit >>= 4; + } + return true; +} + + +Bignum::Chunk Bignum::BigitAt(int index) const { + if (index >= BigitLength()) return 0; + if (index < exponent_) return 0; + return bigits_[index - exponent_]; +} + + +int Bignum::Compare(const Bignum& a, const Bignum& b) { + ASSERT(a.IsClamped()); + ASSERT(b.IsClamped()); + int bigit_length_a = a.BigitLength(); + int bigit_length_b = b.BigitLength(); + if (bigit_length_a < bigit_length_b) return -1; + if (bigit_length_a > bigit_length_b) return +1; + for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { + Chunk bigit_a = a.BigitAt(i); + Chunk bigit_b = b.BigitAt(i); + if (bigit_a < bigit_b) return -1; + if (bigit_a > bigit_b) return +1; + // Otherwise they are equal up to this digit. Try the next digit. + } + return 0; +} + + +int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { + ASSERT(a.IsClamped()); + ASSERT(b.IsClamped()); + ASSERT(c.IsClamped()); + if (a.BigitLength() < b.BigitLength()) { + return PlusCompare(b, a, c); + } + if (a.BigitLength() + 1 < c.BigitLength()) return -1; + if (a.BigitLength() > c.BigitLength()) return +1; + // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than + // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one + // of 'a'. + if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { + return -1; + } + + Chunk borrow = 0; + // Starting at min_exponent all digits are == 0. So no need to compare them. + int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); + for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { + Chunk chunk_a = a.BigitAt(i); + Chunk chunk_b = b.BigitAt(i); + Chunk chunk_c = c.BigitAt(i); + Chunk sum = chunk_a + chunk_b; + if (sum > chunk_c + borrow) { + return +1; + } else { + borrow = chunk_c + borrow - sum; + if (borrow > 1) return -1; + borrow <<= kBigitSize; + } + } + if (borrow == 0) return 0; + return -1; +} + + +void Bignum::Clamp() { + while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { + used_digits_--; + } + if (used_digits_ == 0) { + // Zero. + exponent_ = 0; + } +} + + +bool Bignum::IsClamped() const { + return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; +} + + +void Bignum::Zero() { + for (int i = 0; i < used_digits_; ++i) { + bigits_[i] = 0; + } + used_digits_ = 0; + exponent_ = 0; +} + + +void Bignum::Align(const Bignum& other) { + if (exponent_ > other.exponent_) { + // If "X" represents a "hidden" digit (by the exponent) then we are in the + // following case (a == this, b == other): + // a: aaaaaaXXXX or a: aaaaaXXX + // b: bbbbbbX b: bbbbbbbbXX + // We replace some of the hidden digits (X) of a with 0 digits. + // a: aaaaaa000X or a: aaaaa0XX + int zero_digits = exponent_ - other.exponent_; + EnsureCapacity(used_digits_ + zero_digits); + for (int i = used_digits_ - 1; i >= 0; --i) { + bigits_[i + zero_digits] = bigits_[i]; + } + for (int i = 0; i < zero_digits; ++i) { + bigits_[i] = 0; + } + used_digits_ += zero_digits; + exponent_ -= zero_digits; + ASSERT(used_digits_ >= 0); + ASSERT(exponent_ >= 0); + } +} + + +void Bignum::BigitsShiftLeft(int shift_amount) { + ASSERT(shift_amount < kBigitSize); + ASSERT(shift_amount >= 0); + Chunk carry = 0; + for (int i = 0; i < used_digits_; ++i) { + Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); + bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; + carry = new_carry; + } + if (carry != 0) { + bigits_[used_digits_] = carry; + used_digits_++; + } +} + + +void Bignum::SubtractTimes(const Bignum& other, int factor) { + ASSERT(exponent_ <= other.exponent_); + if (factor < 3) { + for (int i = 0; i < factor; ++i) { + SubtractBignum(other); + } + return; + } + Chunk borrow = 0; + int exponent_diff = other.exponent_ - exponent_; + for (int i = 0; i < other.used_digits_; ++i) { + DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; + DoubleChunk remove = borrow + product; + Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask); + bigits_[i + exponent_diff] = difference & kBigitMask; + borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + + (remove >> kBigitSize)); + } + for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { + if (borrow == 0) return; + Chunk difference = bigits_[i] - borrow; + bigits_[i] = difference & kBigitMask; + borrow = difference >> (kChunkSize - 1); + } + Clamp(); +} + + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/bignum.h b/src/3rdparty/double-conversion/bignum.h new file mode 100644 index 0000000000..5ec3544f57 --- /dev/null +++ b/src/3rdparty/double-conversion/bignum.h @@ -0,0 +1,145 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_BIGNUM_H_ +#define DOUBLE_CONVERSION_BIGNUM_H_ + +#include "utils.h" + +namespace double_conversion { + +class Bignum { + public: + // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately. + // This bignum can encode much bigger numbers, since it contains an + // exponent. + static const int kMaxSignificantBits = 3584; + + Bignum(); + void AssignUInt16(uint16_t value); + void AssignUInt64(uint64_t value); + void AssignBignum(const Bignum& other); + + void AssignDecimalString(Vector<const char> value); + void AssignHexString(Vector<const char> value); + + void AssignPowerUInt16(uint16_t base, int exponent); + + void AddUInt16(uint16_t operand); + void AddUInt64(uint64_t operand); + void AddBignum(const Bignum& other); + // Precondition: this >= other. + void SubtractBignum(const Bignum& other); + + void Square(); + void ShiftLeft(int shift_amount); + void MultiplyByUInt32(uint32_t factor); + void MultiplyByUInt64(uint64_t factor); + void MultiplyByPowerOfTen(int exponent); + void Times10() { return MultiplyByUInt32(10); } + // Pseudocode: + // int result = this / other; + // this = this % other; + // In the worst case this function is in O(this/other). + uint16_t DivideModuloIntBignum(const Bignum& other); + + bool ToHexString(char* buffer, int buffer_size) const; + + // Returns + // -1 if a < b, + // 0 if a == b, and + // +1 if a > b. + static int Compare(const Bignum& a, const Bignum& b); + static bool Equal(const Bignum& a, const Bignum& b) { + return Compare(a, b) == 0; + } + static bool LessEqual(const Bignum& a, const Bignum& b) { + return Compare(a, b) <= 0; + } + static bool Less(const Bignum& a, const Bignum& b) { + return Compare(a, b) < 0; + } + // Returns Compare(a + b, c); + static int PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c); + // Returns a + b == c + static bool PlusEqual(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) == 0; + } + // Returns a + b <= c + static bool PlusLessEqual(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) <= 0; + } + // Returns a + b < c + static bool PlusLess(const Bignum& a, const Bignum& b, const Bignum& c) { + return PlusCompare(a, b, c) < 0; + } + private: + typedef uint32_t Chunk; + typedef uint64_t DoubleChunk; + + static const int kChunkSize = sizeof(Chunk) * 8; + static const int kDoubleChunkSize = sizeof(DoubleChunk) * 8; + // With bigit size of 28 we loose some bits, but a double still fits easily + // into two chunks, and more importantly we can use the Comba multiplication. + static const int kBigitSize = 28; + static const Chunk kBigitMask = (1 << kBigitSize) - 1; + // Every instance allocates kBigitLength chunks on the stack. Bignums cannot + // grow. There are no checks if the stack-allocated space is sufficient. + static const int kBigitCapacity = kMaxSignificantBits / kBigitSize; + + void EnsureCapacity(int size) { + if (size > kBigitCapacity) { + UNREACHABLE(); + } + } + void Align(const Bignum& other); + void Clamp(); + bool IsClamped() const; + void Zero(); + // Requires this to have enough capacity (no tests done). + // Updates used_digits_ if necessary. + // shift_amount must be < kBigitSize. + void BigitsShiftLeft(int shift_amount); + // BigitLength includes the "hidden" digits encoded in the exponent. + int BigitLength() const { return used_digits_ + exponent_; } + Chunk BigitAt(int index) const; + void SubtractTimes(const Bignum& other, int factor); + + Chunk bigits_buffer_[kBigitCapacity]; + // A vector backed by bigits_buffer_. This way accesses to the array are + // checked for out-of-bounds errors. + Vector<Chunk> bigits_; + int used_digits_; + // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize). + int exponent_; + + DISALLOW_COPY_AND_ASSIGN(Bignum); +}; + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_BIGNUM_H_ diff --git a/src/3rdparty/double-conversion/cached-powers.cc b/src/3rdparty/double-conversion/cached-powers.cc new file mode 100644 index 0000000000..9536f26927 --- /dev/null +++ b/src/3rdparty/double-conversion/cached-powers.cc @@ -0,0 +1,178 @@ +// Copyright 2006-2008 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 <stdarg.h> +#include <limits.h> +#include <math.h> + +#include "utils.h" + +#include "cached-powers.h" + +namespace double_conversion { + +struct CachedPower { + uint64_t significand; + int16_t binary_exponent; + int16_t decimal_exponent; +}; + +static const CachedPower kCachedPowers[] = { + {UINT64_2PART_C(0xfa8fd5a0, 081c0288), -1220, -348}, + {UINT64_2PART_C(0xbaaee17f, a23ebf76), -1193, -340}, + {UINT64_2PART_C(0x8b16fb20, 3055ac76), -1166, -332}, + {UINT64_2PART_C(0xcf42894a, 5dce35ea), -1140, -324}, + {UINT64_2PART_C(0x9a6bb0aa, 55653b2d), -1113, -316}, + {UINT64_2PART_C(0xe61acf03, 3d1a45df), -1087, -308}, + {UINT64_2PART_C(0xab70fe17, c79ac6ca), -1060, -300}, + {UINT64_2PART_C(0xff77b1fc, bebcdc4f), -1034, -292}, + {UINT64_2PART_C(0xbe5691ef, 416bd60c), -1007, -284}, + {UINT64_2PART_C(0x8dd01fad, 907ffc3c), -980, -276}, + {UINT64_2PART_C(0xd3515c28, 31559a83), -954, -268}, + {UINT64_2PART_C(0x9d71ac8f, ada6c9b5), -927, -260}, + {UINT64_2PART_C(0xea9c2277, 23ee8bcb), -901, -252}, + {UINT64_2PART_C(0xaecc4991, 4078536d), -874, -244}, + {UINT64_2PART_C(0x823c1279, 5db6ce57), -847, -236}, + {UINT64_2PART_C(0xc2109436, 4dfb5637), -821, -228}, + {UINT64_2PART_C(0x9096ea6f, 3848984f), -794, -220}, + {UINT64_2PART_C(0xd77485cb, 25823ac7), -768, -212}, + {UINT64_2PART_C(0xa086cfcd, 97bf97f4), -741, -204}, + {UINT64_2PART_C(0xef340a98, 172aace5), -715, -196}, + {UINT64_2PART_C(0xb23867fb, 2a35b28e), -688, -188}, + {UINT64_2PART_C(0x84c8d4df, d2c63f3b), -661, -180}, + {UINT64_2PART_C(0xc5dd4427, 1ad3cdba), -635, -172}, + {UINT64_2PART_C(0x936b9fce, bb25c996), -608, -164}, + {UINT64_2PART_C(0xdbac6c24, 7d62a584), -582, -156}, + {UINT64_2PART_C(0xa3ab6658, 0d5fdaf6), -555, -148}, + {UINT64_2PART_C(0xf3e2f893, dec3f126), -529, -140}, + {UINT64_2PART_C(0xb5b5ada8, aaff80b8), -502, -132}, + {UINT64_2PART_C(0x87625f05, 6c7c4a8b), -475, -124}, + {UINT64_2PART_C(0xc9bcff60, 34c13053), -449, -116}, + {UINT64_2PART_C(0x964e858c, 91ba2655), -422, -108}, + {UINT64_2PART_C(0xdff97724, 70297ebd), -396, -100}, + {UINT64_2PART_C(0xa6dfbd9f, b8e5b88f), -369, -92}, + {UINT64_2PART_C(0xf8a95fcf, 88747d94), -343, -84}, + {UINT64_2PART_C(0xb9447093, 8fa89bcf), -316, -76}, + {UINT64_2PART_C(0x8a08f0f8, bf0f156b), -289, -68}, + {UINT64_2PART_C(0xcdb02555, 653131b6), -263, -60}, + {UINT64_2PART_C(0x993fe2c6, d07b7fac), -236, -52}, + {UINT64_2PART_C(0xe45c10c4, 2a2b3b06), -210, -44}, + {UINT64_2PART_C(0xaa242499, 697392d3), -183, -36}, + {UINT64_2PART_C(0xfd87b5f2, 8300ca0e), -157, -28}, + {UINT64_2PART_C(0xbce50864, 92111aeb), -130, -20}, + {UINT64_2PART_C(0x8cbccc09, 6f5088cc), -103, -12}, + {UINT64_2PART_C(0xd1b71758, e219652c), -77, -4}, + {UINT64_2PART_C(0x9c400000, 00000000), -50, 4}, + {UINT64_2PART_C(0xe8d4a510, 00000000), -24, 12}, + {UINT64_2PART_C(0xad78ebc5, ac620000), 3, 20}, + {UINT64_2PART_C(0x813f3978, f8940984), 30, 28}, + {UINT64_2PART_C(0xc097ce7b, c90715b3), 56, 36}, + {UINT64_2PART_C(0x8f7e32ce, 7bea5c70), 83, 44}, + {UINT64_2PART_C(0xd5d238a4, abe98068), 109, 52}, + {UINT64_2PART_C(0x9f4f2726, 179a2245), 136, 60}, + {UINT64_2PART_C(0xed63a231, d4c4fb27), 162, 68}, + {UINT64_2PART_C(0xb0de6538, 8cc8ada8), 189, 76}, + {UINT64_2PART_C(0x83c7088e, 1aab65db), 216, 84}, + {UINT64_2PART_C(0xc45d1df9, 42711d9a), 242, 92}, + {UINT64_2PART_C(0x924d692c, a61be758), 269, 100}, + {UINT64_2PART_C(0xda01ee64, 1a708dea), 295, 108}, + {UINT64_2PART_C(0xa26da399, 9aef774a), 322, 116}, + {UINT64_2PART_C(0xf209787b, b47d6b85), 348, 124}, + {UINT64_2PART_C(0xb454e4a1, 79dd1877), 375, 132}, + {UINT64_2PART_C(0x865b8692, 5b9bc5c2), 402, 140}, + {UINT64_2PART_C(0xc83553c5, c8965d3d), 428, 148}, + {UINT64_2PART_C(0x952ab45c, fa97a0b3), 455, 156}, + {UINT64_2PART_C(0xde469fbd, 99a05fe3), 481, 164}, + {UINT64_2PART_C(0xa59bc234, db398c25), 508, 172}, + {UINT64_2PART_C(0xf6c69a72, a3989f5c), 534, 180}, + {UINT64_2PART_C(0xb7dcbf53, 54e9bece), 561, 188}, + {UINT64_2PART_C(0x88fcf317, f22241e2), 588, 196}, + {UINT64_2PART_C(0xcc20ce9b, d35c78a5), 614, 204}, + {UINT64_2PART_C(0x98165af3, 7b2153df), 641, 212}, + {UINT64_2PART_C(0xe2a0b5dc, 971f303a), 667, 220}, + {UINT64_2PART_C(0xa8d9d153, 5ce3b396), 694, 228}, + {UINT64_2PART_C(0xfb9b7cd9, a4a7443c), 720, 236}, + {UINT64_2PART_C(0xbb764c4c, a7a44410), 747, 244}, + {UINT64_2PART_C(0x8bab8eef, b6409c1a), 774, 252}, + {UINT64_2PART_C(0xd01fef10, a657842c), 800, 260}, + {UINT64_2PART_C(0x9b10a4e5, e9913129), 827, 268}, + {UINT64_2PART_C(0xe7109bfb, a19c0c9d), 853, 276}, + {UINT64_2PART_C(0xac2820d9, 623bf429), 880, 284}, + {UINT64_2PART_C(0x80444b5e, 7aa7cf85), 907, 292}, + {UINT64_2PART_C(0xbf21e440, 03acdd2d), 933, 300}, + {UINT64_2PART_C(0x8e679c2f, 5e44ff8f), 960, 308}, + {UINT64_2PART_C(0xd433179d, 9c8cb841), 986, 316}, + {UINT64_2PART_C(0x9e19db92, b4e31ba9), 1013, 324}, + {UINT64_2PART_C(0xeb96bf6e, badf77d9), 1039, 332}, + {UINT64_2PART_C(0xaf87023b, 9bf0ee6b), 1066, 340}, +}; + +static const int kCachedPowersLength = ARRAY_SIZE(kCachedPowers); +static const int kCachedPowersOffset = 348; // -1 * the first decimal_exponent. +static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10) +// Difference between the decimal exponents in the table above. +const int PowersOfTenCache::kDecimalExponentDistance = 8; +const int PowersOfTenCache::kMinDecimalExponent = -348; +const int PowersOfTenCache::kMaxDecimalExponent = 340; + +void PowersOfTenCache::GetCachedPowerForBinaryExponentRange( + int min_exponent, + int max_exponent, + DiyFp* power, + int* decimal_exponent) { + (void)max_exponent; // Silence unused parameter warning in release builds + (void)kCachedPowersLength; // Silence unused parameter warning in release builds + int kQ = DiyFp::kSignificandSize; + double k = ceil((min_exponent + kQ - 1) * kD_1_LOG2_10); + int foo = kCachedPowersOffset; + int index = + (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1; + ASSERT(0 <= index && index < kCachedPowersLength); + CachedPower cached_power = kCachedPowers[index]; + ASSERT(min_exponent <= cached_power.binary_exponent); + (void) max_exponent; // Mark variable as used. + ASSERT(cached_power.binary_exponent <= max_exponent); + *decimal_exponent = cached_power.decimal_exponent; + *power = DiyFp(cached_power.significand, cached_power.binary_exponent); +} + + +void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent, + DiyFp* power, + int* found_exponent) { + ASSERT(kMinDecimalExponent <= requested_exponent); + ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance); + int index = + (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance; + CachedPower cached_power = kCachedPowers[index]; + *power = DiyFp(cached_power.significand, cached_power.binary_exponent); + *found_exponent = cached_power.decimal_exponent; + ASSERT(*found_exponent <= requested_exponent); + ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance); +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/cached-powers.h b/src/3rdparty/double-conversion/cached-powers.h new file mode 100644 index 0000000000..61a50614cf --- /dev/null +++ b/src/3rdparty/double-conversion/cached-powers.h @@ -0,0 +1,64 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_CACHED_POWERS_H_ +#define DOUBLE_CONVERSION_CACHED_POWERS_H_ + +#include "diy-fp.h" + +namespace double_conversion { + +class PowersOfTenCache { + public: + + // Not all powers of ten are cached. The decimal exponent of two neighboring + // cached numbers will differ by kDecimalExponentDistance. + static const int kDecimalExponentDistance; + + static const int kMinDecimalExponent; + static const int kMaxDecimalExponent; + + // Returns a cached power-of-ten with a binary exponent in the range + // [min_exponent; max_exponent] (boundaries included). + static void GetCachedPowerForBinaryExponentRange(int min_exponent, + int max_exponent, + DiyFp* power, + int* decimal_exponent); + + // Returns a cached power of ten x ~= 10^k such that + // k <= decimal_exponent < k + kCachedPowersDecimalDistance. + // The given decimal_exponent must satisfy + // kMinDecimalExponent <= requested_exponent, and + // requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance. + static void GetCachedPowerForDecimalExponent(int requested_exponent, + DiyFp* power, + int* found_exponent); +}; + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_CACHED_POWERS_H_ diff --git a/src/3rdparty/double-conversion/diy-fp.cc b/src/3rdparty/double-conversion/diy-fp.cc new file mode 100644 index 0000000000..ddd1891b16 --- /dev/null +++ b/src/3rdparty/double-conversion/diy-fp.cc @@ -0,0 +1,57 @@ +// 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 "diy-fp.h" +#include "utils.h" + +namespace double_conversion { + +void DiyFp::Multiply(const DiyFp& other) { + // Simply "emulates" a 128 bit multiplication. + // However: the resulting number only contains 64 bits. The least + // significant 64 bits are only used for rounding the most significant 64 + // bits. + const uint64_t kM32 = 0xFFFFFFFFU; + uint64_t a = f_ >> 32; + uint64_t b = f_ & kM32; + uint64_t c = other.f_ >> 32; + uint64_t d = other.f_ & kM32; + uint64_t ac = a * c; + uint64_t bc = b * c; + uint64_t ad = a * d; + uint64_t bd = b * d; + uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32); + // By adding 1U << 31 to tmp we round the final result. + // Halfway cases will be round up. + tmp += 1U << 31; + uint64_t result_f = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32); + e_ += other.e_ + 64; + f_ = result_f; +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/diy-fp.h b/src/3rdparty/double-conversion/diy-fp.h new file mode 100644 index 0000000000..9dcf8fbdba --- /dev/null +++ b/src/3rdparty/double-conversion/diy-fp.h @@ -0,0 +1,118 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_DIY_FP_H_ +#define DOUBLE_CONVERSION_DIY_FP_H_ + +#include "utils.h" + +namespace double_conversion { + +// This "Do It Yourself Floating Point" class implements a floating-point number +// with a uint64 significand and an int exponent. Normalized DiyFp numbers will +// have the most significant bit of the significand set. +// Multiplication and Subtraction do not normalize their results. +// DiyFp are not designed to contain special doubles (NaN and Infinity). +class DiyFp { + public: + static const int kSignificandSize = 64; + + DiyFp() : f_(0), e_(0) {} + DiyFp(uint64_t f, int e) : f_(f), e_(e) {} + + // this = this - other. + // The exponents of both numbers must be the same and the significand of this + // must be bigger than the significand of other. + // The result will not be normalized. + void Subtract(const DiyFp& other) { + ASSERT(e_ == other.e_); + ASSERT(f_ >= other.f_); + f_ -= other.f_; + } + + // Returns a - b. + // The exponents of both numbers must be the same and this must be bigger + // than other. The result will not be normalized. + static DiyFp Minus(const DiyFp& a, const DiyFp& b) { + DiyFp result = a; + result.Subtract(b); + return result; + } + + + // this = this * other. + void Multiply(const DiyFp& other); + + // returns a * b; + static DiyFp Times(const DiyFp& a, const DiyFp& b) { + DiyFp result = a; + result.Multiply(b); + return result; + } + + void Normalize() { + ASSERT(f_ != 0); + uint64_t f = f_; + int e = e_; + + // This method is mainly called for normalizing boundaries. In general + // boundaries need to be shifted by 10 bits. We thus optimize for this case. + const uint64_t k10MSBits = UINT64_2PART_C(0xFFC00000, 00000000); + while ((f & k10MSBits) == 0) { + f <<= 10; + e -= 10; + } + while ((f & kUint64MSB) == 0) { + f <<= 1; + e--; + } + f_ = f; + e_ = e; + } + + static DiyFp Normalize(const DiyFp& a) { + DiyFp result = a; + result.Normalize(); + return result; + } + + uint64_t f() const { return f_; } + int e() const { return e_; } + + void set_f(uint64_t new_value) { f_ = new_value; } + void set_e(int new_value) { e_ = new_value; } + + private: + static const uint64_t kUint64MSB = UINT64_2PART_C(0x80000000, 00000000); + + uint64_t f_; + int e_; +}; + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_DIY_FP_H_ diff --git a/src/3rdparty/double-conversion/double-conversion.cc b/src/3rdparty/double-conversion/double-conversion.cc new file mode 100644 index 0000000000..909985be82 --- /dev/null +++ b/src/3rdparty/double-conversion/double-conversion.cc @@ -0,0 +1,975 @@ +// 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 <limits.h> +#include <math.h> + +#include "double-conversion.h" + +#include "bignum-dtoa.h" +#include "fast-dtoa.h" +#include "fixed-dtoa.h" +#include "ieee.h" +#include "strtod.h" +#include "utils.h" + +namespace double_conversion { + +const DoubleToStringConverter& DoubleToStringConverter::EcmaScriptConverter() { + int flags = UNIQUE_ZERO | EMIT_POSITIVE_EXPONENT_SIGN; + static DoubleToStringConverter converter(flags, + "Infinity", + "NaN", + 'e', + -6, 21, + 6, 0); + return converter; +} + + +bool DoubleToStringConverter::HandleSpecialValues( + double value, + StringBuilder* result_builder) const { + Double double_inspect(value); + if (double_inspect.IsInfinite()) { + if (infinity_symbol_ == NULL) return false; + if (value < 0) { + result_builder->AddCharacter('-'); + } + result_builder->AddString(infinity_symbol_); + return true; + } + if (double_inspect.IsNan()) { + if (nan_symbol_ == NULL) return false; + result_builder->AddString(nan_symbol_); + return true; + } + return false; +} + + +void DoubleToStringConverter::CreateExponentialRepresentation( + const char* decimal_digits, + int length, + int exponent, + StringBuilder* result_builder) const { + ASSERT(length != 0); + result_builder->AddCharacter(decimal_digits[0]); + if (length != 1) { + result_builder->AddCharacter('.'); + result_builder->AddSubstring(&decimal_digits[1], length-1); + } + result_builder->AddCharacter(exponent_character_); + if (exponent < 0) { + result_builder->AddCharacter('-'); + exponent = -exponent; + } else { + if ((flags_ & EMIT_POSITIVE_EXPONENT_SIGN) != 0) { + result_builder->AddCharacter('+'); + } + } + if (exponent == 0) { + result_builder->AddCharacter('0'); + return; + } + ASSERT(exponent < 1e4); + const int kMaxExponentLength = 5; + char buffer[kMaxExponentLength + 1]; + buffer[kMaxExponentLength] = '\0'; + int first_char_pos = kMaxExponentLength; + while (exponent > 0) { + buffer[--first_char_pos] = '0' + (exponent % 10); + exponent /= 10; + } + result_builder->AddSubstring(&buffer[first_char_pos], + kMaxExponentLength - first_char_pos); +} + + +void DoubleToStringConverter::CreateDecimalRepresentation( + const char* decimal_digits, + int length, + int decimal_point, + int digits_after_point, + StringBuilder* result_builder) const { + // Create a representation that is padded with zeros if needed. + if (decimal_point <= 0) { + // "0.00000decimal_rep". + result_builder->AddCharacter('0'); + if (digits_after_point > 0) { + result_builder->AddCharacter('.'); + result_builder->AddPadding('0', -decimal_point); + ASSERT(length <= digits_after_point - (-decimal_point)); + result_builder->AddSubstring(decimal_digits, length); + int remaining_digits = digits_after_point - (-decimal_point) - length; + result_builder->AddPadding('0', remaining_digits); + } + } else if (decimal_point >= length) { + // "decimal_rep0000.00000" or "decimal_rep.0000" + result_builder->AddSubstring(decimal_digits, length); + result_builder->AddPadding('0', decimal_point - length); + if (digits_after_point > 0) { + result_builder->AddCharacter('.'); + result_builder->AddPadding('0', digits_after_point); + } + } else { + // "decima.l_rep000" + ASSERT(digits_after_point > 0); + result_builder->AddSubstring(decimal_digits, decimal_point); + result_builder->AddCharacter('.'); + ASSERT(length - decimal_point <= digits_after_point); + result_builder->AddSubstring(&decimal_digits[decimal_point], + length - decimal_point); + int remaining_digits = digits_after_point - (length - decimal_point); + result_builder->AddPadding('0', remaining_digits); + } + if (digits_after_point == 0) { + if ((flags_ & EMIT_TRAILING_DECIMAL_POINT) != 0) { + result_builder->AddCharacter('.'); + } + if ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) { + result_builder->AddCharacter('0'); + } + } +} + + +bool DoubleToStringConverter::ToShortestIeeeNumber( + double value, + StringBuilder* result_builder, + DoubleToStringConverter::DtoaMode mode) const { + ASSERT(mode == SHORTEST || mode == SHORTEST_SINGLE); + if (Double(value).IsSpecial()) { + return HandleSpecialValues(value, result_builder); + } + + int decimal_point; + bool sign; + const int kDecimalRepCapacity = kBase10MaximalLength + 1; + char decimal_rep[kDecimalRepCapacity]; + int decimal_rep_length; + + DoubleToAscii(value, mode, 0, decimal_rep, kDecimalRepCapacity, + &sign, &decimal_rep_length, &decimal_point); + + bool unique_zero = (flags_ & UNIQUE_ZERO) != 0; + if (sign && (value != 0.0 || !unique_zero)) { + result_builder->AddCharacter('-'); + } + + int exponent = decimal_point - 1; + if ((decimal_in_shortest_low_ <= exponent) && + (exponent < decimal_in_shortest_high_)) { + CreateDecimalRepresentation(decimal_rep, decimal_rep_length, + decimal_point, + Max(0, decimal_rep_length - decimal_point), + result_builder); + } else { + CreateExponentialRepresentation(decimal_rep, decimal_rep_length, exponent, + result_builder); + } + return true; +} + + +bool DoubleToStringConverter::ToFixed(double value, + int requested_digits, + StringBuilder* result_builder) const { + ASSERT(kMaxFixedDigitsBeforePoint == 60); + const double kFirstNonFixed = 1e60; + + if (Double(value).IsSpecial()) { + return HandleSpecialValues(value, result_builder); + } + + if (requested_digits > kMaxFixedDigitsAfterPoint) return false; + if (value >= kFirstNonFixed || value <= -kFirstNonFixed) return false; + + // Find a sufficiently precise decimal representation of n. + int decimal_point; + bool sign; + // Add space for the '\0' byte. + const int kDecimalRepCapacity = + kMaxFixedDigitsBeforePoint + kMaxFixedDigitsAfterPoint + 1; + char decimal_rep[kDecimalRepCapacity]; + int decimal_rep_length; + DoubleToAscii(value, FIXED, requested_digits, + decimal_rep, kDecimalRepCapacity, + &sign, &decimal_rep_length, &decimal_point); + + bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0); + if (sign && (value != 0.0 || !unique_zero)) { + result_builder->AddCharacter('-'); + } + + CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point, + requested_digits, result_builder); + return true; +} + + +bool DoubleToStringConverter::ToExponential( + double value, + int requested_digits, + StringBuilder* result_builder) const { + if (Double(value).IsSpecial()) { + return HandleSpecialValues(value, result_builder); + } + + if (requested_digits < -1) return false; + if (requested_digits > kMaxExponentialDigits) return false; + + int decimal_point; + bool sign; + // Add space for digit before the decimal point and the '\0' character. + const int kDecimalRepCapacity = kMaxExponentialDigits + 2; + ASSERT(kDecimalRepCapacity > kBase10MaximalLength); + char decimal_rep[kDecimalRepCapacity]; + int decimal_rep_length; + + if (requested_digits == -1) { + DoubleToAscii(value, SHORTEST, 0, + decimal_rep, kDecimalRepCapacity, + &sign, &decimal_rep_length, &decimal_point); + } else { + DoubleToAscii(value, PRECISION, requested_digits + 1, + decimal_rep, kDecimalRepCapacity, + &sign, &decimal_rep_length, &decimal_point); + ASSERT(decimal_rep_length <= requested_digits + 1); + + for (int i = decimal_rep_length; i < requested_digits + 1; ++i) { + decimal_rep[i] = '0'; + } + decimal_rep_length = requested_digits + 1; + } + + bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0); + if (sign && (value != 0.0 || !unique_zero)) { + result_builder->AddCharacter('-'); + } + + int exponent = decimal_point - 1; + CreateExponentialRepresentation(decimal_rep, + decimal_rep_length, + exponent, + result_builder); + return true; +} + + +bool DoubleToStringConverter::ToPrecision(double value, + int precision, + StringBuilder* result_builder) const { + if (Double(value).IsSpecial()) { + return HandleSpecialValues(value, result_builder); + } + + if (precision < kMinPrecisionDigits || precision > kMaxPrecisionDigits) { + return false; + } + + // Find a sufficiently precise decimal representation of n. + int decimal_point; + bool sign; + // Add one for the terminating null character. + const int kDecimalRepCapacity = kMaxPrecisionDigits + 1; + char decimal_rep[kDecimalRepCapacity]; + int decimal_rep_length; + + DoubleToAscii(value, PRECISION, precision, + decimal_rep, kDecimalRepCapacity, + &sign, &decimal_rep_length, &decimal_point); + ASSERT(decimal_rep_length <= precision); + + bool unique_zero = ((flags_ & UNIQUE_ZERO) != 0); + if (sign && (value != 0.0 || !unique_zero)) { + result_builder->AddCharacter('-'); + } + + // The exponent if we print the number as x.xxeyyy. That is with the + // decimal point after the first digit. + int exponent = decimal_point - 1; + + int extra_zero = ((flags_ & EMIT_TRAILING_ZERO_AFTER_POINT) != 0) ? 1 : 0; + if ((-decimal_point + 1 > max_leading_padding_zeroes_in_precision_mode_) || + (decimal_point - precision + extra_zero > + max_trailing_padding_zeroes_in_precision_mode_)) { + // Fill buffer to contain 'precision' digits. + // Usually the buffer is already at the correct length, but 'DoubleToAscii' + // is allowed to return less characters. + for (int i = decimal_rep_length; i < precision; ++i) { + decimal_rep[i] = '0'; + } + + CreateExponentialRepresentation(decimal_rep, + precision, + exponent, + result_builder); + } else { + CreateDecimalRepresentation(decimal_rep, decimal_rep_length, decimal_point, + Max(0, precision - decimal_point), + result_builder); + } + return true; +} + + +static BignumDtoaMode DtoaToBignumDtoaMode( + DoubleToStringConverter::DtoaMode dtoa_mode) { + switch (dtoa_mode) { + case DoubleToStringConverter::SHORTEST: return BIGNUM_DTOA_SHORTEST; + case DoubleToStringConverter::SHORTEST_SINGLE: + return BIGNUM_DTOA_SHORTEST_SINGLE; + case DoubleToStringConverter::FIXED: return BIGNUM_DTOA_FIXED; + case DoubleToStringConverter::PRECISION: return BIGNUM_DTOA_PRECISION; + default: + UNREACHABLE(); + } +} + + +void DoubleToStringConverter::DoubleToAscii(double v, + DtoaMode mode, + int requested_digits, + char* buffer, + int buffer_length, + bool* sign, + int* length, + int* point) { + Vector<char> vector(buffer, buffer_length); + ASSERT(!Double(v).IsSpecial()); + ASSERT(mode == SHORTEST || mode == SHORTEST_SINGLE || requested_digits >= 0); + + if (Double(v).Sign() < 0) { + *sign = true; + v = -v; + } else { + *sign = false; + } + + if (mode == PRECISION && requested_digits == 0) { + vector[0] = '\0'; + *length = 0; + return; + } + + if (v == 0) { + vector[0] = '0'; + vector[1] = '\0'; + *length = 1; + *point = 1; + return; + } + + bool fast_worked; + switch (mode) { + case SHORTEST: + fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST, 0, vector, length, point); + break; + case SHORTEST_SINGLE: + fast_worked = FastDtoa(v, FAST_DTOA_SHORTEST_SINGLE, 0, + vector, length, point); + break; + case FIXED: + fast_worked = FastFixedDtoa(v, requested_digits, vector, length, point); + break; + case PRECISION: + fast_worked = FastDtoa(v, FAST_DTOA_PRECISION, requested_digits, + vector, length, point); + break; + default: + fast_worked = false; + UNREACHABLE(); + } + if (fast_worked) return; + + // If the fast dtoa didn't succeed use the slower bignum version. + BignumDtoaMode bignum_mode = DtoaToBignumDtoaMode(mode); + BignumDtoa(v, bignum_mode, requested_digits, vector, length, point); + vector[*length] = '\0'; +} + + +// Consumes the given substring from the iterator. +// Returns false, if the substring does not match. +template <class Iterator> +static bool ConsumeSubString(Iterator* current, + Iterator end, + const char* substring) { + ASSERT(**current == *substring); + for (substring++; *substring != '\0'; substring++) { + ++*current; + if (*current == end || **current != *substring) return false; + } + ++*current; + return true; +} + + +// Maximum number of significant digits in decimal representation. +// The longest possible double in decimal representation is +// (2^53 - 1) * 2 ^ -1074 that is (2 ^ 53 - 1) * 5 ^ 1074 / 10 ^ 1074 +// (768 digits). If we parse a number whose first digits are equal to a +// mean of 2 adjacent doubles (that could have up to 769 digits) the result +// must be rounded to the bigger one unless the tail consists of zeros, so +// we don't need to preserve all the digits. +const int kMaxSignificantDigits = 772; + + +static const char kWhitespaceTable7[] = { 32, 13, 10, 9, 11, 12 }; +static const int kWhitespaceTable7Length = ARRAY_SIZE(kWhitespaceTable7); + + +static const uc16 kWhitespaceTable16[] = { + 160, 8232, 8233, 5760, 6158, 8192, 8193, 8194, 8195, + 8196, 8197, 8198, 8199, 8200, 8201, 8202, 8239, 8287, 12288, 65279 +}; +static const int kWhitespaceTable16Length = ARRAY_SIZE(kWhitespaceTable16); + + +static bool isWhitespace(int x) { + if (x < 128) { + for (int i = 0; i < kWhitespaceTable7Length; i++) { + if (kWhitespaceTable7[i] == x) return true; + } + } else { + for (int i = 0; i < kWhitespaceTable16Length; i++) { + if (kWhitespaceTable16[i] == x) return true; + } + } + return false; +} + + +// Returns true if a nonspace found and false if the end has reached. +template <class Iterator> +static inline bool AdvanceToNonspace(Iterator* current, Iterator end) { + while (*current != end) { + if (!isWhitespace(**current)) return true; + ++*current; + } + return false; +} + + +static bool isDigit(int x, int radix) { + return (x >= '0' && x <= '9' && x < '0' + radix) + || (radix > 10 && x >= 'a' && x < 'a' + radix - 10) + || (radix > 10 && x >= 'A' && x < 'A' + radix - 10); +} + + +static double SignedZero(bool sign) { + return sign ? -0.0 : 0.0; +} + + +// Returns true if 'c' is a decimal digit that is valid for the given radix. +// +// The function is small and could be inlined, but VS2012 emitted a warning +// because it constant-propagated the radix and concluded that the last +// condition was always true. By moving it into a separate function the +// compiler wouldn't warn anymore. +static bool IsDecimalDigitForRadix(int c, int radix) { + return '0' <= c && c <= '9' && (c - '0') < radix; +} + +// Returns true if 'c' is a character digit that is valid for the given radix. +// The 'a_character' should be 'a' or 'A'. +// +// The function is small and could be inlined, but VS2012 emitted a warning +// because it constant-propagated the radix and concluded that the first +// condition was always false. By moving it into a separate function the +// compiler wouldn't warn anymore. +static bool IsCharacterDigitForRadix(int c, int radix, char a_character) { + return radix > 10 && c >= a_character && c < a_character + radix - 10; +} + + +// Parsing integers with radix 2, 4, 8, 16, 32. Assumes current != end. +template <int radix_log_2, class Iterator> +static double RadixStringToIeee(Iterator* current, + Iterator end, + bool sign, + bool allow_trailing_junk, + double junk_string_value, + bool read_as_double, + bool* result_is_junk) { + ASSERT(*current != end); + + const int kDoubleSize = Double::kSignificandSize; + const int kSingleSize = Single::kSignificandSize; + const int kSignificandSize = read_as_double? kDoubleSize: kSingleSize; + + *result_is_junk = true; + + // Skip leading 0s. + while (**current == '0') { + ++(*current); + if (*current == end) { + *result_is_junk = false; + return SignedZero(sign); + } + } + + int64_t number = 0; + int exponent = 0; + const int radix = (1 << radix_log_2); + + do { + int digit; + if (IsDecimalDigitForRadix(**current, radix)) { + digit = static_cast<char>(**current) - '0'; + } else if (IsCharacterDigitForRadix(**current, radix, 'a')) { + digit = static_cast<char>(**current) - 'a' + 10; + } else if (IsCharacterDigitForRadix(**current, radix, 'A')) { + digit = static_cast<char>(**current) - 'A' + 10; + } else { + if (allow_trailing_junk || !AdvanceToNonspace(current, end)) { + break; + } else { + return junk_string_value; + } + } + + number = number * radix + digit; + int overflow = static_cast<int>(number >> kSignificandSize); + if (overflow != 0) { + // Overflow occurred. Need to determine which direction to round the + // result. + int overflow_bits_count = 1; + while (overflow > 1) { + overflow_bits_count++; + overflow >>= 1; + } + + int dropped_bits_mask = ((1 << overflow_bits_count) - 1); + int dropped_bits = static_cast<int>(number) & dropped_bits_mask; + number >>= overflow_bits_count; + exponent = overflow_bits_count; + + bool zero_tail = true; + for (;;) { + ++(*current); + if (*current == end || !isDigit(**current, radix)) break; + zero_tail = zero_tail && **current == '0'; + exponent += radix_log_2; + } + + if (!allow_trailing_junk && AdvanceToNonspace(current, end)) { + return junk_string_value; + } + + int middle_value = (1 << (overflow_bits_count - 1)); + if (dropped_bits > middle_value) { + number++; // Rounding up. + } else if (dropped_bits == middle_value) { + // Rounding to even to consistency with decimals: half-way case rounds + // up if significant part is odd and down otherwise. + if ((number & 1) != 0 || !zero_tail) { + number++; // Rounding up. + } + } + + // Rounding up may cause overflow. + if ((number & ((int64_t)1 << kSignificandSize)) != 0) { + exponent++; + number >>= 1; + } + break; + } + ++(*current); + } while (*current != end); + + ASSERT(number < ((int64_t)1 << kSignificandSize)); + ASSERT(static_cast<int64_t>(static_cast<double>(number)) == number); + + *result_is_junk = false; + + if (exponent == 0) { + if (sign) { + if (number == 0) return -0.0; + number = -number; + } + return static_cast<double>(number); + } + + ASSERT(number != 0); + return Double(DiyFp(number, exponent)).value(); +} + + +template <class Iterator> +double StringToDoubleConverter::StringToIeee( + Iterator input, + int length, + bool read_as_double, + int* processed_characters_count) const { + Iterator current = input; + Iterator end = input + length; + + *processed_characters_count = 0; + + const bool allow_trailing_junk = (flags_ & ALLOW_TRAILING_JUNK) != 0; + const bool allow_leading_spaces = (flags_ & ALLOW_LEADING_SPACES) != 0; + const bool allow_trailing_spaces = (flags_ & ALLOW_TRAILING_SPACES) != 0; + const bool allow_spaces_after_sign = (flags_ & ALLOW_SPACES_AFTER_SIGN) != 0; + + // To make sure that iterator dereferencing is valid the following + // convention is used: + // 1. Each '++current' statement is followed by check for equality to 'end'. + // 2. If AdvanceToNonspace returned false then current == end. + // 3. If 'current' becomes equal to 'end' the function returns or goes to + // 'parsing_done'. + // 4. 'current' is not dereferenced after the 'parsing_done' label. + // 5. Code before 'parsing_done' may rely on 'current != end'. + if (current == end) return empty_string_value_; + + if (allow_leading_spaces || allow_trailing_spaces) { + if (!AdvanceToNonspace(¤t, end)) { + *processed_characters_count = static_cast<int>(current - input); + return empty_string_value_; + } + if (!allow_leading_spaces && (input != current)) { + // No leading spaces allowed, but AdvanceToNonspace moved forward. + return junk_string_value_; + } + } + + // The longest form of simplified number is: "-<significant digits>.1eXXX\0". + const int kBufferSize = kMaxSignificantDigits + 10; + char buffer[kBufferSize]; // NOLINT: size is known at compile time. + int buffer_pos = 0; + + // Exponent will be adjusted if insignificant digits of the integer part + // or insignificant leading zeros of the fractional part are dropped. + int exponent = 0; + int significant_digits = 0; + int insignificant_digits = 0; + bool nonzero_digit_dropped = false; + + bool sign = false; + + if (*current == '+' || *current == '-') { + sign = (*current == '-'); + ++current; + Iterator next_non_space = current; + // Skip following spaces (if allowed). + if (!AdvanceToNonspace(&next_non_space, end)) return junk_string_value_; + if (!allow_spaces_after_sign && (current != next_non_space)) { + return junk_string_value_; + } + current = next_non_space; + } + + if (infinity_symbol_ != NULL) { + if (*current == infinity_symbol_[0]) { + if (!ConsumeSubString(¤t, end, infinity_symbol_)) { + return junk_string_value_; + } + + if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) { + return junk_string_value_; + } + if (!allow_trailing_junk && AdvanceToNonspace(¤t, end)) { + return junk_string_value_; + } + + ASSERT(buffer_pos == 0); + *processed_characters_count = static_cast<int>(current - input); + return sign ? -Double::Infinity() : Double::Infinity(); + } + } + + if (nan_symbol_ != NULL) { + if (*current == nan_symbol_[0]) { + if (!ConsumeSubString(¤t, end, nan_symbol_)) { + return junk_string_value_; + } + + if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) { + return junk_string_value_; + } + if (!allow_trailing_junk && AdvanceToNonspace(¤t, end)) { + return junk_string_value_; + } + + ASSERT(buffer_pos == 0); + *processed_characters_count = static_cast<int>(current - input); + return sign ? -Double::NaN() : Double::NaN(); + } + } + + bool leading_zero = false; + if (*current == '0') { + ++current; + if (current == end) { + *processed_characters_count = static_cast<int>(current - input); + return SignedZero(sign); + } + + leading_zero = true; + + // It could be hexadecimal value. + if ((flags_ & ALLOW_HEX) && (*current == 'x' || *current == 'X')) { + ++current; + if (current == end || !isDigit(*current, 16)) { + return junk_string_value_; // "0x". + } + + bool result_is_junk; + double result = RadixStringToIeee<4>(¤t, + end, + sign, + allow_trailing_junk, + junk_string_value_, + read_as_double, + &result_is_junk); + if (!result_is_junk) { + if (allow_trailing_spaces) AdvanceToNonspace(¤t, end); + *processed_characters_count = static_cast<int>(current - input); + } + return result; + } + + // Ignore leading zeros in the integer part. + while (*current == '0') { + ++current; + if (current == end) { + *processed_characters_count = static_cast<int>(current - input); + return SignedZero(sign); + } + } + } + + bool octal = leading_zero && (flags_ & ALLOW_OCTALS) != 0; + + // Copy significant digits of the integer part (if any) to the buffer. + while (*current >= '0' && *current <= '9') { + if (significant_digits < kMaxSignificantDigits) { + ASSERT(buffer_pos < kBufferSize); + buffer[buffer_pos++] = static_cast<char>(*current); + significant_digits++; + // Will later check if it's an octal in the buffer. + } else { + insignificant_digits++; // Move the digit into the exponential part. + nonzero_digit_dropped = nonzero_digit_dropped || *current != '0'; + } + octal = octal && *current < '8'; + ++current; + if (current == end) goto parsing_done; + } + + if (significant_digits == 0) { + octal = false; + } + + if (*current == '.') { + if (octal && !allow_trailing_junk) return junk_string_value_; + if (octal) goto parsing_done; + + ++current; + if (current == end) { + if (significant_digits == 0 && !leading_zero) { + return junk_string_value_; + } else { + goto parsing_done; + } + } + + if (significant_digits == 0) { + // octal = false; + // Integer part consists of 0 or is absent. Significant digits start after + // leading zeros (if any). + while (*current == '0') { + ++current; + if (current == end) { + *processed_characters_count = static_cast<int>(current - input); + return SignedZero(sign); + } + exponent--; // Move this 0 into the exponent. + } + } + + // There is a fractional part. + // We don't emit a '.', but adjust the exponent instead. + while (*current >= '0' && *current <= '9') { + if (significant_digits < kMaxSignificantDigits) { + ASSERT(buffer_pos < kBufferSize); + buffer[buffer_pos++] = static_cast<char>(*current); + significant_digits++; + exponent--; + } else { + // Ignore insignificant digits in the fractional part. + nonzero_digit_dropped = nonzero_digit_dropped || *current != '0'; + } + ++current; + if (current == end) goto parsing_done; + } + } + + if (!leading_zero && exponent == 0 && significant_digits == 0) { + // If leading_zeros is true then the string contains zeros. + // If exponent < 0 then string was [+-]\.0*... + // If significant_digits != 0 the string is not equal to 0. + // Otherwise there are no digits in the string. + return junk_string_value_; + } + + // Parse exponential part. + if (*current == 'e' || *current == 'E') { + if (octal && !allow_trailing_junk) return junk_string_value_; + if (octal) goto parsing_done; + ++current; + if (current == end) { + if (allow_trailing_junk) { + goto parsing_done; + } else { + return junk_string_value_; + } + } + char sign = '+'; + if (*current == '+' || *current == '-') { + sign = static_cast<char>(*current); + ++current; + if (current == end) { + if (allow_trailing_junk) { + goto parsing_done; + } else { + return junk_string_value_; + } + } + } + + if (current == end || *current < '0' || *current > '9') { + if (allow_trailing_junk) { + goto parsing_done; + } else { + return junk_string_value_; + } + } + + const int max_exponent = INT_MAX / 2; + ASSERT(-max_exponent / 2 <= exponent && exponent <= max_exponent / 2); + int num = 0; + do { + // Check overflow. + int digit = *current - '0'; + if (num >= max_exponent / 10 + && !(num == max_exponent / 10 && digit <= max_exponent % 10)) { + num = max_exponent; + } else { + num = num * 10 + digit; + } + ++current; + } while (current != end && *current >= '0' && *current <= '9'); + + exponent += (sign == '-' ? -num : num); + } + + if (!(allow_trailing_spaces || allow_trailing_junk) && (current != end)) { + return junk_string_value_; + } + if (!allow_trailing_junk && AdvanceToNonspace(¤t, end)) { + return junk_string_value_; + } + if (allow_trailing_spaces) { + AdvanceToNonspace(¤t, end); + } + + parsing_done: + exponent += insignificant_digits; + + if (octal) { + double result; + bool result_is_junk; + char* start = buffer; + result = RadixStringToIeee<3>(&start, + buffer + buffer_pos, + sign, + allow_trailing_junk, + junk_string_value_, + read_as_double, + &result_is_junk); + ASSERT(!result_is_junk); + *processed_characters_count = static_cast<int>(current - input); + return result; + } + + if (nonzero_digit_dropped) { + buffer[buffer_pos++] = '1'; + exponent--; + } + + ASSERT(buffer_pos < kBufferSize); + buffer[buffer_pos] = '\0'; + + double converted; + if (read_as_double) { + converted = Strtod(Vector<const char>(buffer, buffer_pos), exponent); + } else { + converted = Strtof(Vector<const char>(buffer, buffer_pos), exponent); + } + *processed_characters_count = static_cast<int>(current - input); + return sign? -converted: converted; +} + + +double StringToDoubleConverter::StringToDouble( + const char* buffer, + int length, + int* processed_characters_count) const { + return StringToIeee(buffer, length, true, processed_characters_count); +} + + +double StringToDoubleConverter::StringToDouble( + const uc16* buffer, + int length, + int* processed_characters_count) const { + return StringToIeee(buffer, length, true, processed_characters_count); +} + + +float StringToDoubleConverter::StringToFloat( + const char* buffer, + int length, + int* processed_characters_count) const { + return static_cast<float>(StringToIeee(buffer, length, false, + processed_characters_count)); +} + + +float StringToDoubleConverter::StringToFloat( + const uc16* buffer, + int length, + int* processed_characters_count) const { + return static_cast<float>(StringToIeee(buffer, length, false, + processed_characters_count)); +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/double-conversion.pri b/src/3rdparty/double-conversion/double-conversion.pri new file mode 100644 index 0000000000..3207169689 --- /dev/null +++ b/src/3rdparty/double-conversion/double-conversion.pri @@ -0,0 +1,24 @@ +INCLUDEPATH += $$PWD/include $$PWD/include/double-conversion +SOURCES += \ + $$PWD/bignum.cc \ + $$PWD/bignum-dtoa.cc \ + $$PWD/cached-powers.cc \ + $$PWD/diy-fp.cc \ + $$PWD/double-conversion.cc \ + $$PWD/fast-dtoa.cc \ + $$PWD/fixed-dtoa.cc \ + $$PWD/strtod.cc + +HEADERS += \ + $$PWD/bignum-dtoa.h \ + $$PWD/bignum.h \ + $$PWD/cached-powers.h \ + $$PWD/diy-fp.h \ + $$PWD/include/double-conversion/double-conversion.h \ + $$PWD/fast-dtoa.h \ + $$PWD/fixed-dtoa.h \ + $$PWD/ieee.h \ + $$PWD/strtod.h \ + $$PWD/include/double-conversion/utils.h + +OTHER_FILES += README diff --git a/src/3rdparty/double-conversion/fast-dtoa.cc b/src/3rdparty/double-conversion/fast-dtoa.cc new file mode 100644 index 0000000000..61350383a9 --- /dev/null +++ b/src/3rdparty/double-conversion/fast-dtoa.cc @@ -0,0 +1,665 @@ +// Copyright 2012 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 "fast-dtoa.h" + +#include "cached-powers.h" +#include "diy-fp.h" +#include "ieee.h" + +namespace double_conversion { + +// 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. +static const int kMinimalTargetExponent = -60; +static const int kMaximalTargetExponent = -32; + + +// 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 cannot 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 +// * 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 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. +static bool RoundWeed(Vector<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_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_high[ (often written as "(w_low; w_high)") + + // 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 finding + // the closest representation of 'w'. If we have two potential + // representations, and one is closer to both w_low and w_high, then we know + // it is closer to the actual value v. + // + // 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 + // We need to do the following tests in this order to avoid over- and + // underflows. + ASSERT(rest <= unsafe_interval); + while (rest < small_distance && // Negated condition 1 + unsafe_interval - rest >= ten_kappa && // Negated condition 2 + (rest + ten_kappa < small_distance || // buffer{-1} > w_high + 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 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); +} + + +// Rounds the buffer upwards if the result is closer to v by possibly adding +// 1 to the buffer. If the precision of the calculation is not sufficient to +// round correctly, return false. +// The rounding might shift the whole buffer in which case the kappa is +// adjusted. For example "99", kappa = 3 might become "10", kappa = 4. +// +// If 2*rest > ten_kappa then the buffer needs to be round up. +// rest can have an error of +/- 1 unit. This function accounts for the +// imprecision and returns false, if the rounding direction cannot be +// unambiguously determined. +// +// Precondition: rest < ten_kappa. +static bool RoundWeedCounted(Vector<char> buffer, + int length, + uint64_t rest, + uint64_t ten_kappa, + uint64_t unit, + int* kappa) { + ASSERT(rest < ten_kappa); + // The following tests are done in a specific order to avoid overflows. They + // will work correctly with any uint64 values of rest < ten_kappa and unit. + // + // If the unit is too big, then we don't know which way to round. For example + // a unit of 50 means that the real number lies within rest +/- 50. If + // 10^kappa == 40 then there is no way to tell which way to round. + if (unit >= ten_kappa) return false; + // Even if unit is just half the size of 10^kappa we are already completely + // lost. (And after the previous test we know that the expression will not + // over/underflow.) + if (ten_kappa - unit <= unit) return false; + // If 2 * (rest + unit) <= 10^kappa we can safely round down. + if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) { + return true; + } + // If 2 * (rest - unit) >= 10^kappa, then we can safely round up. + if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) { + // Increment the last digit recursively until we find a non '9' digit. + buffer[length - 1]++; + for (int i = length - 1; i > 0; --i) { + if (buffer[i] != '0' + 10) break; + buffer[i] = '0'; + buffer[i - 1]++; + } + // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the + // exception of the first digit all digits are now '0'. Simply switch the + // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and + // the power (the kappa) is increased. + if (buffer[0] == '0' + 10) { + buffer[0] = '1'; + (*kappa) += 1; + } + return true; + } + return false; +} + +// Returns the biggest power of ten that is less than or equal to the given +// number. We furthermore receive the maximum number of bits 'number' has. +// +// Returns power == 10^(exponent_plus_one-1) such that +// power <= number < power * 10. +// If number_bits == 0 then 0^(0-1) is returned. +// The number of bits must be <= 32. +// Precondition: number < (1 << (number_bits + 1)). + +// Inspired by the method for finding an integer log base 10 from here: +// http://graphics.stanford.edu/~seander/bithacks.html#IntegerLog10 +static unsigned int const kSmallPowersOfTen[] = + {0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, + 1000000000}; + +static void BiggestPowerTen(uint32_t number, + int number_bits, + uint32_t* power, + int* exponent_plus_one) { + ASSERT(number < (1u << (number_bits + 1))); + // 1233/4096 is approximately 1/lg(10). + int exponent_plus_one_guess = ((number_bits + 1) * 1233 >> 12); + // We increment to skip over the first entry in the kPowersOf10 table. + // Note: kPowersOf10[i] == 10^(i-1). + exponent_plus_one_guess++; + // We don't have any guarantees that 2^number_bits <= number. + if (number < kSmallPowersOfTen[exponent_plus_one_guess]) { + exponent_plus_one_guess--; + } + *power = kSmallPowersOfTen[exponent_plus_one_guess]; + *exponent_plus_one = exponent_plus_one_guess; +} + +// 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 kMinimalTargetExponent and +// kMaximalTargetExponent. +// 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 than a unit of their last digits. +// * low.e() == w.e() == high.e() +// * low < w < high, and taking into account their error: low~ <= high~ +// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent +// 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. +static bool DigitGen(DiyFp low, + DiyFp w, + DiyFp high, + Vector<char> buffer, + int* length, + int* kappa) { + ASSERT(low.e() == w.e() && w.e() == high.e()); + ASSERT(low.f() + 1 <= high.f() - 1); + ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent); + // 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 divisor; + int divisor_exponent_plus_one; + BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), + &divisor, &divisor_exponent_plus_one); + *kappa = divisor_exponent_plus_one; + *length = 0; + // Loop invariant: buffer = too_high / 10^kappa (integer division) + // The invariant holds for the first iteration: kappa has been initialized + // with the divisor exponent + 1. And the divisor is the biggest power of ten + // that is smaller than integrals. + while (*kappa > 0) { + int digit = integrals / divisor; + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('0' + digit); + (*length)++; + integrals %= divisor; + (*kappa)--; + // Note that kappa now equals the exponent of the divisor 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>(divisor) << -one.e(), unit); + } + divisor /= 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. + // Note that the multiplication by 10 does not overflow, because w.e >= -60 + // and thus one.e >= -60. + ASSERT(one.e() >= -60); + ASSERT(fractionals < one.f()); + ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f()); + for (;;) { + fractionals *= 10; + unit *= 10; + unsafe_interval.set_f(unsafe_interval.f() * 10); + // Integer division by one. + int digit = static_cast<int>(fractionals >> -one.e()); + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('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); + } + } +} + + + +// Generates (at most) requested_digits digits of input number w. +// w is a floating-point number (DiyFp), consisting of a significand and an +// exponent. Its exponent is bounded by kMinimalTargetExponent and +// kMaximalTargetExponent. +// Hence -60 <= w.e() <= -32. +// +// Returns false if it fails, in which case the generated digits in the buffer +// should not be used. +// Preconditions: +// * w is correct up to 1 ulp (unit in the last place). That +// is, its error must be strictly less than a unit of its last digit. +// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent +// +// Postconditions: returns false if procedure fails. +// otherwise: +// * buffer is not null-terminated, but length contains the number of +// digits. +// * the representation in buffer is the most precise representation of +// requested_digits digits. +// * buffer contains at most requested_digits digits of w. If there are less +// than requested_digits digits then some trailing '0's have been removed. +// * kappa is such that +// w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2. +// +// 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, but the failure-rate +// increases with higher requested_digits. +static bool DigitGenCounted(DiyFp w, + int requested_digits, + Vector<char> buffer, + int* length, + int* kappa) { + ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent); + ASSERT(kMinimalTargetExponent >= -60); + ASSERT(kMaximalTargetExponent <= -32); + // w is assumed to have an error less than 1 unit. Whenever w is scaled we + // also scale its error. + uint64_t w_error = 1; + // We cut the input number into two parts: the integral digits and the + // fractional digits. We don't emit any decimal separator, but adapt kappa + // instead. Example: instead of writing "1.2" we put "12" into the buffer and + // increase kappa by 1. + 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>(w.f() >> -one.e()); + // Modulo by one is an and. + uint64_t fractionals = w.f() & (one.f() - 1); + uint32_t divisor; + int divisor_exponent_plus_one; + BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()), + &divisor, &divisor_exponent_plus_one); + *kappa = divisor_exponent_plus_one; + *length = 0; + + // Loop invariant: buffer = w / 10^kappa (integer division) + // The invariant holds for the first iteration: kappa has been initialized + // with the divisor exponent + 1. And the divisor is the biggest power of ten + // that is smaller than 'integrals'. + while (*kappa > 0) { + int digit = integrals / divisor; + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('0' + digit); + (*length)++; + requested_digits--; + integrals %= divisor; + (*kappa)--; + // Note that kappa now equals the exponent of the divisor and that the + // invariant thus holds again. + if (requested_digits == 0) break; + divisor /= 10; + } + + if (requested_digits == 0) { + uint64_t rest = + (static_cast<uint64_t>(integrals) << -one.e()) + fractionals; + return RoundWeedCounted(buffer, *length, rest, + static_cast<uint64_t>(divisor) << -one.e(), w_error, + kappa); + } + + // 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 (the 'unit'), too. + // Note that the multiplication by 10 does not overflow, because w.e >= -60 + // and thus one.e >= -60. + ASSERT(one.e() >= -60); + ASSERT(fractionals < one.f()); + ASSERT(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f()); + while (requested_digits > 0 && fractionals > w_error) { + fractionals *= 10; + w_error *= 10; + // Integer division by one. + int digit = static_cast<int>(fractionals >> -one.e()); + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('0' + digit); + (*length)++; + requested_digits--; + fractionals &= one.f() - 1; // Modulo by one. + (*kappa)--; + } + if (requested_digits != 0) return false; + return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error, + kappa); +} + + +// 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. +static bool Grisu3(double v, + FastDtoaMode mode, + Vector<char> buffer, + int* length, + int* decimal_exponent) { + DiyFp w = Double(v).AsNormalizedDiyFp(); + // 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, boundary_plus; + if (mode == FAST_DTOA_SHORTEST) { + Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus); + } else { + ASSERT(mode == FAST_DTOA_SHORTEST_SINGLE); + float single_v = static_cast<float>(v); + Single(single_v).NormalizedBoundaries(&boundary_minus, &boundary_plus); + } + ASSERT(boundary_plus.e() == w.e()); + DiyFp ten_mk; // Cached power of ten: 10^-k + int mk; // -k + int ten_mk_minimal_binary_exponent = + kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize); + int ten_mk_maximal_binary_exponent = + kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize); + PowersOfTenCache::GetCachedPowerForBinaryExponentRange( + ten_mk_minimal_binary_exponent, + ten_mk_maximal_binary_exponent, + &ten_mk, &mk); + ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() + + DiyFp::kSignificandSize) && + (kMaximalTargetExponent >= 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; +} + + +// The "counted" version of grisu3 (see above) only generates requested_digits +// number of digits. This version does not generate the shortest representation, +// and with enough requested digits 0.1 will at some point print as 0.9999999... +// Grisu3 is too imprecise for real halfway cases (1.5 will not work) and +// therefore the rounding strategy for halfway cases is irrelevant. +static bool Grisu3Counted(double v, + int requested_digits, + Vector<char> buffer, + int* length, + int* decimal_exponent) { + DiyFp w = Double(v).AsNormalizedDiyFp(); + DiyFp ten_mk; // Cached power of ten: 10^-k + int mk; // -k + int ten_mk_minimal_binary_exponent = + kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize); + int ten_mk_maximal_binary_exponent = + kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize); + PowersOfTenCache::GetCachedPowerForBinaryExponentRange( + ten_mk_minimal_binary_exponent, + ten_mk_maximal_binary_exponent, + &ten_mk, &mk); + ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() + + DiyFp::kSignificandSize) && + (kMaximalTargetExponent >= 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); + + // We now have (double) (scaled_w * 10^-mk). + // DigitGen will generate the first requested_digits digits of scaled_w and + // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It + // will not always be exactly the same since DigitGenCounted only produces a + // limited number of digits.) + int kappa; + bool result = DigitGenCounted(scaled_w, requested_digits, + buffer, length, &kappa); + *decimal_exponent = -mk + kappa; + return result; +} + + +bool FastDtoa(double v, + FastDtoaMode mode, + int requested_digits, + Vector<char> buffer, + int* length, + int* decimal_point) { + ASSERT(v > 0); + ASSERT(!Double(v).IsSpecial()); + + bool result = false; + int decimal_exponent = 0; + switch (mode) { + case FAST_DTOA_SHORTEST: + case FAST_DTOA_SHORTEST_SINGLE: + result = Grisu3(v, mode, buffer, length, &decimal_exponent); + break; + case FAST_DTOA_PRECISION: + result = Grisu3Counted(v, requested_digits, + buffer, length, &decimal_exponent); + break; + default: + UNREACHABLE(); + } + if (result) { + *decimal_point = *length + decimal_exponent; + buffer[*length] = '\0'; + } + return result; +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/fast-dtoa.h b/src/3rdparty/double-conversion/fast-dtoa.h new file mode 100644 index 0000000000..5f1e8eee5e --- /dev/null +++ b/src/3rdparty/double-conversion/fast-dtoa.h @@ -0,0 +1,88 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_FAST_DTOA_H_ +#define DOUBLE_CONVERSION_FAST_DTOA_H_ + +#include "utils.h" + +namespace double_conversion { + +enum FastDtoaMode { + // Computes the shortest representation of the given input. The returned + // result will be the most accurate number of this length. Longer + // representations might be more accurate. + FAST_DTOA_SHORTEST, + // Same as FAST_DTOA_SHORTEST but for single-precision floats. + FAST_DTOA_SHORTEST_SINGLE, + // Computes a representation where the precision (number of digits) is + // given as input. The precision is independent of the decimal point. + FAST_DTOA_PRECISION +}; + +// FastDtoa will produce at most kFastDtoaMaximalLength digits. This does not +// include the terminating '\0' character. +static const int kFastDtoaMaximalLength = 17; +// Same for single-precision numbers. +static const int kFastDtoaMaximalSingleLength = 9; + +// Provides a decimal representation of v. +// The result should be interpreted as buffer * 10^(point - length). +// +// Precondition: +// * v must be a strictly positive finite double. +// +// Returns true if it succeeds, otherwise the result can not be trusted. +// There will be *length digits inside the buffer followed by a null terminator. +// If the function returns true and mode equals +// - FAST_DTOA_SHORTEST, then +// the parameter requested_digits is ignored. +// The result satisfies +// v == (double) (buffer * 10^(point - length)). +// The digits in the buffer are the shortest representation possible. E.g. +// if 0.099999999999 and 0.1 represent the same double then "1" is returned +// with point = 0. +// The last digit will be closest to the actual v. That is, even if several +// digits might correctly yield 'v' when read again, the buffer will contain +// the one closest to v. +// - FAST_DTOA_PRECISION, then +// the buffer contains requested_digits digits. +// the difference v - (buffer * 10^(point-length)) is closest to zero for +// all possible representations of requested_digits digits. +// If there are two values that are equally close, then FastDtoa returns +// false. +// For both modes the buffer must be large enough to hold the result. +bool FastDtoa(double d, + FastDtoaMode mode, + int requested_digits, + Vector<char> buffer, + int* length, + int* decimal_point); + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_FAST_DTOA_H_ diff --git a/src/3rdparty/double-conversion/fixed-dtoa.cc b/src/3rdparty/double-conversion/fixed-dtoa.cc new file mode 100644 index 0000000000..aef65fdc21 --- /dev/null +++ b/src/3rdparty/double-conversion/fixed-dtoa.cc @@ -0,0 +1,404 @@ +// 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 <math.h> + +#include "fixed-dtoa.h" +#include "ieee.h" + +namespace double_conversion { + +// Represents a 128bit type. This class should be replaced by a native type on +// platforms that support 128bit integers. +class UInt128 { + public: + UInt128() : high_bits_(0), low_bits_(0) { } + UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { } + + void Multiply(uint32_t multiplicand) { + uint64_t accumulator; + + accumulator = (low_bits_ & kMask32) * multiplicand; + uint32_t part = static_cast<uint32_t>(accumulator & kMask32); + accumulator >>= 32; + accumulator = accumulator + (low_bits_ >> 32) * multiplicand; + low_bits_ = (accumulator << 32) + part; + accumulator >>= 32; + accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; + part = static_cast<uint32_t>(accumulator & kMask32); + accumulator >>= 32; + accumulator = accumulator + (high_bits_ >> 32) * multiplicand; + high_bits_ = (accumulator << 32) + part; + ASSERT((accumulator >> 32) == 0); + } + + void Shift(int shift_amount) { + ASSERT(-64 <= shift_amount && shift_amount <= 64); + if (shift_amount == 0) { + return; + } else if (shift_amount == -64) { + high_bits_ = low_bits_; + low_bits_ = 0; + } else if (shift_amount == 64) { + low_bits_ = high_bits_; + high_bits_ = 0; + } else if (shift_amount <= 0) { + high_bits_ <<= -shift_amount; + high_bits_ += low_bits_ >> (64 + shift_amount); + low_bits_ <<= -shift_amount; + } else { + low_bits_ >>= shift_amount; + low_bits_ += high_bits_ << (64 - shift_amount); + high_bits_ >>= shift_amount; + } + } + + // Modifies *this to *this MOD (2^power). + // Returns *this DIV (2^power). + int DivModPowerOf2(int power) { + if (power >= 64) { + int result = static_cast<int>(high_bits_ >> (power - 64)); + high_bits_ -= static_cast<uint64_t>(result) << (power - 64); + return result; + } else { + uint64_t part_low = low_bits_ >> power; + uint64_t part_high = high_bits_ << (64 - power); + int result = static_cast<int>(part_low + part_high); + high_bits_ = 0; + low_bits_ -= part_low << power; + return result; + } + } + + bool IsZero() const { + return high_bits_ == 0 && low_bits_ == 0; + } + + int BitAt(int position) { + if (position >= 64) { + return static_cast<int>(high_bits_ >> (position - 64)) & 1; + } else { + return static_cast<int>(low_bits_ >> position) & 1; + } + } + + private: + static const uint64_t kMask32 = 0xFFFFFFFF; + // Value == (high_bits_ << 64) + low_bits_ + uint64_t high_bits_; + uint64_t low_bits_; +}; + + +static const int kDoubleSignificandSize = 53; // Includes the hidden bit. + + +static void FillDigits32FixedLength(uint32_t number, int requested_length, + Vector<char> buffer, int* length) { + for (int i = requested_length - 1; i >= 0; --i) { + buffer[(*length) + i] = '0' + number % 10; + number /= 10; + } + *length += requested_length; +} + + +static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) { + int number_length = 0; + // We fill the digits in reverse order and exchange them afterwards. + while (number != 0) { + int digit = number % 10; + number /= 10; + buffer[(*length) + number_length] = static_cast<char>('0' + digit); + number_length++; + } + // Exchange the digits. + int i = *length; + int j = *length + number_length - 1; + while (i < j) { + char tmp = buffer[i]; + buffer[i] = buffer[j]; + buffer[j] = tmp; + i++; + j--; + } + *length += number_length; +} + + +static void FillDigits64FixedLength(uint64_t number, + Vector<char> buffer, int* length) { + const uint32_t kTen7 = 10000000; + // For efficiency cut the number into 3 uint32_t parts, and print those. + uint32_t part2 = static_cast<uint32_t>(number % kTen7); + number /= kTen7; + uint32_t part1 = static_cast<uint32_t>(number % kTen7); + uint32_t part0 = static_cast<uint32_t>(number / kTen7); + + FillDigits32FixedLength(part0, 3, buffer, length); + FillDigits32FixedLength(part1, 7, buffer, length); + FillDigits32FixedLength(part2, 7, buffer, length); +} + + +static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) { + const uint32_t kTen7 = 10000000; + // For efficiency cut the number into 3 uint32_t parts, and print those. + uint32_t part2 = static_cast<uint32_t>(number % kTen7); + number /= kTen7; + uint32_t part1 = static_cast<uint32_t>(number % kTen7); + uint32_t part0 = static_cast<uint32_t>(number / kTen7); + + if (part0 != 0) { + FillDigits32(part0, buffer, length); + FillDigits32FixedLength(part1, 7, buffer, length); + FillDigits32FixedLength(part2, 7, buffer, length); + } else if (part1 != 0) { + FillDigits32(part1, buffer, length); + FillDigits32FixedLength(part2, 7, buffer, length); + } else { + FillDigits32(part2, buffer, length); + } +} + + +static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { + // An empty buffer represents 0. + if (*length == 0) { + buffer[0] = '1'; + *decimal_point = 1; + *length = 1; + return; + } + // Round the last digit until we either have a digit that was not '9' or until + // we reached the first digit. + buffer[(*length) - 1]++; + for (int i = (*length) - 1; i > 0; --i) { + if (buffer[i] != '0' + 10) { + return; + } + buffer[i] = '0'; + buffer[i - 1]++; + } + // If the first digit is now '0' + 10, we would need to set it to '0' and add + // a '1' in front. However we reach the first digit only if all following + // digits had been '9' before rounding up. Now all trailing digits are '0' and + // we simply switch the first digit to '1' and update the decimal-point + // (indicating that the point is now one digit to the right). + if (buffer[0] == '0' + 10) { + buffer[0] = '1'; + (*decimal_point)++; + } +} + + +// The given fractionals number represents a fixed-point number with binary +// point at bit (-exponent). +// Preconditions: +// -128 <= exponent <= 0. +// 0 <= fractionals * 2^exponent < 1 +// The buffer holds the result. +// The function will round its result. During the rounding-process digits not +// generated by this function might be updated, and the decimal-point variable +// might be updated. If this function generates the digits 99 and the buffer +// already contained "199" (thus yielding a buffer of "19999") then a +// rounding-up will change the contents of the buffer to "20000". +static void FillFractionals(uint64_t fractionals, int exponent, + int fractional_count, Vector<char> buffer, + int* length, int* decimal_point) { + ASSERT(-128 <= exponent && exponent <= 0); + // 'fractionals' is a fixed-point number, with binary point at bit + // (-exponent). Inside the function the non-converted remainder of fractionals + // is a fixed-point number, with binary point at bit 'point'. + if (-exponent <= 64) { + // One 64 bit number is sufficient. + ASSERT(fractionals >> 56 == 0); + int point = -exponent; + for (int i = 0; i < fractional_count; ++i) { + if (fractionals == 0) break; + // Instead of multiplying by 10 we multiply by 5 and adjust the point + // location. This way the fractionals variable will not overflow. + // Invariant at the beginning of the loop: fractionals < 2^point. + // Initially we have: point <= 64 and fractionals < 2^56 + // After each iteration the point is decremented by one. + // Note that 5^3 = 125 < 128 = 2^7. + // Therefore three iterations of this loop will not overflow fractionals + // (even without the subtraction at the end of the loop body). At this + // time point will satisfy point <= 61 and therefore fractionals < 2^point + // and any further multiplication of fractionals by 5 will not overflow. + fractionals *= 5; + point--; + int digit = static_cast<int>(fractionals >> point); + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('0' + digit); + (*length)++; + fractionals -= static_cast<uint64_t>(digit) << point; + } + // If the first bit after the point is set we have to round up. + if (((fractionals >> (point - 1)) & 1) == 1) { + RoundUp(buffer, length, decimal_point); + } + } else { // We need 128 bits. + ASSERT(64 < -exponent && -exponent <= 128); + UInt128 fractionals128 = UInt128(fractionals, 0); + fractionals128.Shift(-exponent - 64); + int point = 128; + for (int i = 0; i < fractional_count; ++i) { + if (fractionals128.IsZero()) break; + // As before: instead of multiplying by 10 we multiply by 5 and adjust the + // point location. + // This multiplication will not overflow for the same reasons as before. + fractionals128.Multiply(5); + point--; + int digit = fractionals128.DivModPowerOf2(point); + ASSERT(digit <= 9); + buffer[*length] = static_cast<char>('0' + digit); + (*length)++; + } + if (fractionals128.BitAt(point - 1) == 1) { + RoundUp(buffer, length, decimal_point); + } + } +} + + +// Removes leading and trailing zeros. +// If leading zeros are removed then the decimal point position is adjusted. +static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) { + while (*length > 0 && buffer[(*length) - 1] == '0') { + (*length)--; + } + int first_non_zero = 0; + while (first_non_zero < *length && buffer[first_non_zero] == '0') { + first_non_zero++; + } + if (first_non_zero != 0) { + for (int i = first_non_zero; i < *length; ++i) { + buffer[i - first_non_zero] = buffer[i]; + } + *length -= first_non_zero; + *decimal_point -= first_non_zero; + } +} + + +bool FastFixedDtoa(double v, + int fractional_count, + Vector<char> buffer, + int* length, + int* decimal_point) { + const uint32_t kMaxUInt32 = 0xFFFFFFFF; + uint64_t significand = Double(v).Significand(); + int exponent = Double(v).Exponent(); + // v = significand * 2^exponent (with significand a 53bit integer). + // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we + // don't know how to compute the representation. 2^73 ~= 9.5*10^21. + // If necessary this limit could probably be increased, but we don't need + // more. + if (exponent > 20) return false; + if (fractional_count > 20) return false; + *length = 0; + // At most kDoubleSignificandSize bits of the significand are non-zero. + // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero + // bits: 0..11*..0xxx..53*..xx + if (exponent + kDoubleSignificandSize > 64) { + // The exponent must be > 11. + // + // We know that v = significand * 2^exponent. + // And the exponent > 11. + // We simplify the task by dividing v by 10^17. + // The quotient delivers the first digits, and the remainder fits into a 64 + // bit number. + // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. + const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17 + uint64_t divisor = kFive17; + int divisor_power = 17; + uint64_t dividend = significand; + uint32_t quotient; + uint64_t remainder; + // Let v = f * 2^e with f == significand and e == exponent. + // Then need q (quotient) and r (remainder) as follows: + // v = q * 10^17 + r + // f * 2^e = q * 10^17 + r + // f * 2^e = q * 5^17 * 2^17 + r + // If e > 17 then + // f * 2^(e-17) = q * 5^17 + r/2^17 + // else + // f = q * 5^17 * 2^(17-e) + r/2^e + if (exponent > divisor_power) { + // We only allow exponents of up to 20 and therefore (17 - e) <= 3 + dividend <<= exponent - divisor_power; + quotient = static_cast<uint32_t>(dividend / divisor); + remainder = (dividend % divisor) << divisor_power; + } else { + divisor <<= divisor_power - exponent; + quotient = static_cast<uint32_t>(dividend / divisor); + remainder = (dividend % divisor) << exponent; + } + FillDigits32(quotient, buffer, length); + FillDigits64FixedLength(remainder, buffer, length); + *decimal_point = *length; + } else if (exponent >= 0) { + // 0 <= exponent <= 11 + significand <<= exponent; + FillDigits64(significand, buffer, length); + *decimal_point = *length; + } else if (exponent > -kDoubleSignificandSize) { + // We have to cut the number. + uint64_t integrals = significand >> -exponent; + uint64_t fractionals = significand - (integrals << -exponent); + if (integrals > kMaxUInt32) { + FillDigits64(integrals, buffer, length); + } else { + FillDigits32(static_cast<uint32_t>(integrals), buffer, length); + } + *decimal_point = *length; + FillFractionals(fractionals, exponent, fractional_count, + buffer, length, decimal_point); + } else if (exponent < -128) { + // This configuration (with at most 20 digits) means that all digits must be + // 0. + ASSERT(fractional_count <= 20); + buffer[0] = '\0'; + *length = 0; + *decimal_point = -fractional_count; + } else { + *decimal_point = 0; + FillFractionals(significand, exponent, fractional_count, + buffer, length, decimal_point); + } + TrimZeros(buffer, length, decimal_point); + buffer[*length] = '\0'; + if ((*length) == 0) { + // The string is empty and the decimal_point thus has no importance. Mimick + // Gay's dtoa and and set it to -fractional_count. + *decimal_point = -fractional_count; + } + return true; +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/fixed-dtoa.h b/src/3rdparty/double-conversion/fixed-dtoa.h new file mode 100644 index 0000000000..3bdd08e21f --- /dev/null +++ b/src/3rdparty/double-conversion/fixed-dtoa.h @@ -0,0 +1,56 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_FIXED_DTOA_H_ +#define DOUBLE_CONVERSION_FIXED_DTOA_H_ + +#include "utils.h" + +namespace double_conversion { + +// Produces digits necessary to print a given number with +// 'fractional_count' digits after the decimal point. +// The buffer must be big enough to hold the result plus one terminating null +// character. +// +// The produced digits might be too short in which case the caller has to fill +// the gaps with '0's. +// Example: FastFixedDtoa(0.001, 5, ...) is allowed to return buffer = "1", and +// decimal_point = -2. +// Halfway cases are rounded towards +/-Infinity (away from 0). The call +// FastFixedDtoa(0.15, 2, ...) thus returns buffer = "2", decimal_point = 0. +// The returned buffer may contain digits that would be truncated from the +// shortest representation of the input. +// +// This method only works for some parameters. If it can't handle the input it +// returns false. The output is null-terminated when the function succeeds. +bool FastFixedDtoa(double v, int fractional_count, + Vector<char> buffer, int* length, int* decimal_point); + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_FIXED_DTOA_H_ diff --git a/src/3rdparty/double-conversion/ieee.h b/src/3rdparty/double-conversion/ieee.h new file mode 100644 index 0000000000..661141d1a8 --- /dev/null +++ b/src/3rdparty/double-conversion/ieee.h @@ -0,0 +1,402 @@ +// Copyright 2012 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. + +#ifndef DOUBLE_CONVERSION_DOUBLE_H_ +#define DOUBLE_CONVERSION_DOUBLE_H_ + +#include "diy-fp.h" + +namespace double_conversion { + +// We assume that doubles and uint64_t have the same endianness. +static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } +static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } +static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); } +static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); } + +// Helper functions for doubles. +class Double { + public: + static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); + static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); + static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); + static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); + static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. + static const int kSignificandSize = 53; + + Double() : d64_(0) {} + explicit Double(double d) : d64_(double_to_uint64(d)) {} + explicit Double(uint64_t d64) : d64_(d64) {} + explicit Double(DiyFp diy_fp) + : d64_(DiyFpToUint64(diy_fp)) {} + + // The value encoded by this Double must be greater or equal to +0.0. + // It must not be special (infinity, or NaN). + DiyFp AsDiyFp() const { + ASSERT(Sign() > 0); + ASSERT(!IsSpecial()); + return DiyFp(Significand(), Exponent()); + } + + // The value encoded by this Double must be strictly greater than 0. + DiyFp AsNormalizedDiyFp() const { + ASSERT(value() > 0.0); + uint64_t f = Significand(); + int e = Exponent(); + + // The current double could be a denormal. + while ((f & kHiddenBit) == 0) { + f <<= 1; + e--; + } + // Do the final shifts in one go. + f <<= DiyFp::kSignificandSize - kSignificandSize; + e -= DiyFp::kSignificandSize - kSignificandSize; + return DiyFp(f, e); + } + + // Returns the double's bit as uint64. + uint64_t AsUint64() const { + return d64_; + } + + // Returns the next greater double. Returns +infinity on input +infinity. + double NextDouble() const { + if (d64_ == kInfinity) return Double(kInfinity).value(); + if (Sign() < 0 && Significand() == 0) { + // -0.0 + return 0.0; + } + if (Sign() < 0) { + return Double(d64_ - 1).value(); + } else { + return Double(d64_ + 1).value(); + } + } + + double PreviousDouble() const { + if (d64_ == (kInfinity | kSignMask)) return -Double::Infinity(); + if (Sign() < 0) { + return Double(d64_ + 1).value(); + } else { + if (Significand() == 0) return -0.0; + return Double(d64_ - 1).value(); + } + } + + int Exponent() const { + if (IsDenormal()) return kDenormalExponent; + + uint64_t d64 = AsUint64(); + int biased_e = + static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); + return biased_e - kExponentBias; + } + + uint64_t Significand() const { + uint64_t d64 = AsUint64(); + uint64_t significand = d64 & kSignificandMask; + if (!IsDenormal()) { + return significand + kHiddenBit; + } else { + return significand; + } + } + + // Returns true if the double is a denormal. + bool IsDenormal() const { + uint64_t d64 = AsUint64(); + return (d64 & kExponentMask) == 0; + } + + // We consider denormals not to be special. + // Hence only Infinity and NaN are special. + bool IsSpecial() const { + uint64_t d64 = AsUint64(); + return (d64 & kExponentMask) == kExponentMask; + } + + bool IsNan() const { + uint64_t d64 = AsUint64(); + return ((d64 & kExponentMask) == kExponentMask) && + ((d64 & kSignificandMask) != 0); + } + + bool IsInfinite() const { + uint64_t d64 = AsUint64(); + return ((d64 & kExponentMask) == kExponentMask) && + ((d64 & kSignificandMask) == 0); + } + + int Sign() const { + uint64_t d64 = AsUint64(); + return (d64 & kSignMask) == 0? 1: -1; + } + + // Precondition: the value encoded by this Double must be greater or equal + // than +0.0. + DiyFp UpperBoundary() const { + ASSERT(Sign() > 0); + return DiyFp(Significand() * 2 + 1, Exponent() - 1); + } + + // Computes the two boundaries of this. + // The bigger boundary (m_plus) is normalized. The lower boundary has the same + // exponent as m_plus. + // Precondition: the value encoded by this Double must be greater than 0. + void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { + ASSERT(value() > 0.0); + DiyFp v = this->AsDiyFp(); + DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); + DiyFp m_minus; + if (LowerBoundaryIsCloser()) { + m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); + } else { + m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); + } + m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); + m_minus.set_e(m_plus.e()); + *out_m_plus = m_plus; + *out_m_minus = m_minus; + } + + bool LowerBoundaryIsCloser() const { + // The boundary is closer if the significand is of the form f == 2^p-1 then + // the lower boundary is closer. + // Think of v = 1000e10 and v- = 9999e9. + // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but + // at a distance of 1e8. + // The only exception is for the smallest normal: the largest denormal is + // at the same distance as its successor. + // Note: denormals have the same exponent as the smallest normals. + bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0); + return physical_significand_is_zero && (Exponent() != kDenormalExponent); + } + + double value() const { return uint64_to_double(d64_); } + + // Returns the significand size for a given order of magnitude. + // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. + // This function returns the number of significant binary digits v will have + // once it's encoded into a double. In almost all cases this is equal to + // kSignificandSize. The only exceptions are denormals. They start with + // leading zeroes and their effective significand-size is hence smaller. + static int SignificandSizeForOrderOfMagnitude(int order) { + if (order >= (kDenormalExponent + kSignificandSize)) { + return kSignificandSize; + } + if (order <= kDenormalExponent) return 0; + return order - kDenormalExponent; + } + + static double Infinity() { + return Double(kInfinity).value(); + } + + static double NaN() { + return Double(kNaN).value(); + } + + private: + static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; + static const int kDenormalExponent = -kExponentBias + 1; + static const int kMaxExponent = 0x7FF - kExponentBias; + static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); + static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); + + const uint64_t d64_; + + static uint64_t DiyFpToUint64(DiyFp diy_fp) { + uint64_t significand = diy_fp.f(); + int exponent = diy_fp.e(); + while (significand > kHiddenBit + kSignificandMask) { + significand >>= 1; + exponent++; + } + if (exponent >= kMaxExponent) { + return kInfinity; + } + if (exponent < kDenormalExponent) { + return 0; + } + while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { + significand <<= 1; + exponent--; + } + uint64_t biased_exponent; + if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { + biased_exponent = 0; + } else { + biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); + } + return (significand & kSignificandMask) | + (biased_exponent << kPhysicalSignificandSize); + } + + DISALLOW_COPY_AND_ASSIGN(Double); +}; + +class Single { + public: + static const uint32_t kSignMask = 0x80000000; + static const uint32_t kExponentMask = 0x7F800000; + static const uint32_t kSignificandMask = 0x007FFFFF; + static const uint32_t kHiddenBit = 0x00800000; + static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit. + static const int kSignificandSize = 24; + + Single() : d32_(0) {} + explicit Single(float f) : d32_(float_to_uint32(f)) {} + explicit Single(uint32_t d32) : d32_(d32) {} + + // The value encoded by this Single must be greater or equal to +0.0. + // It must not be special (infinity, or NaN). + DiyFp AsDiyFp() const { + ASSERT(Sign() > 0); + ASSERT(!IsSpecial()); + return DiyFp(Significand(), Exponent()); + } + + // Returns the single's bit as uint64. + uint32_t AsUint32() const { + return d32_; + } + + int Exponent() const { + if (IsDenormal()) return kDenormalExponent; + + uint32_t d32 = AsUint32(); + int biased_e = + static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize); + return biased_e - kExponentBias; + } + + uint32_t Significand() const { + uint32_t d32 = AsUint32(); + uint32_t significand = d32 & kSignificandMask; + if (!IsDenormal()) { + return significand + kHiddenBit; + } else { + return significand; + } + } + + // Returns true if the single is a denormal. + bool IsDenormal() const { + uint32_t d32 = AsUint32(); + return (d32 & kExponentMask) == 0; + } + + // We consider denormals not to be special. + // Hence only Infinity and NaN are special. + bool IsSpecial() const { + uint32_t d32 = AsUint32(); + return (d32 & kExponentMask) == kExponentMask; + } + + bool IsNan() const { + uint32_t d32 = AsUint32(); + return ((d32 & kExponentMask) == kExponentMask) && + ((d32 & kSignificandMask) != 0); + } + + bool IsInfinite() const { + uint32_t d32 = AsUint32(); + return ((d32 & kExponentMask) == kExponentMask) && + ((d32 & kSignificandMask) == 0); + } + + int Sign() const { + uint32_t d32 = AsUint32(); + return (d32 & kSignMask) == 0? 1: -1; + } + + // Computes the two boundaries of this. + // The bigger boundary (m_plus) is normalized. The lower boundary has the same + // exponent as m_plus. + // Precondition: the value encoded by this Single must be greater than 0. + void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { + ASSERT(value() > 0.0); + DiyFp v = this->AsDiyFp(); + DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); + DiyFp m_minus; + if (LowerBoundaryIsCloser()) { + m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); + } else { + m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); + } + m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); + m_minus.set_e(m_plus.e()); + *out_m_plus = m_plus; + *out_m_minus = m_minus; + } + + // Precondition: the value encoded by this Single must be greater or equal + // than +0.0. + DiyFp UpperBoundary() const { + ASSERT(Sign() > 0); + return DiyFp(Significand() * 2 + 1, Exponent() - 1); + } + + bool LowerBoundaryIsCloser() const { + // The boundary is closer if the significand is of the form f == 2^p-1 then + // the lower boundary is closer. + // Think of v = 1000e10 and v- = 9999e9. + // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but + // at a distance of 1e8. + // The only exception is for the smallest normal: the largest denormal is + // at the same distance as its successor. + // Note: denormals have the same exponent as the smallest normals. + bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0); + return physical_significand_is_zero && (Exponent() != kDenormalExponent); + } + + float value() const { return uint32_to_float(d32_); } + + static float Infinity() { + return Single(kInfinity).value(); + } + + static float NaN() { + return Single(kNaN).value(); + } + + private: + static const int kExponentBias = 0x7F + kPhysicalSignificandSize; + static const int kDenormalExponent = -kExponentBias + 1; + static const int kMaxExponent = 0xFF - kExponentBias; + static const uint32_t kInfinity = 0x7F800000; + static const uint32_t kNaN = 0x7FC00000; + + const uint32_t d32_; + + DISALLOW_COPY_AND_ASSIGN(Single); +}; + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_DOUBLE_H_ diff --git a/src/3rdparty/double-conversion/include/double-conversion/double-conversion.h b/src/3rdparty/double-conversion/include/double-conversion/double-conversion.h new file mode 100644 index 0000000000..6bdfa8d25d --- /dev/null +++ b/src/3rdparty/double-conversion/include/double-conversion/double-conversion.h @@ -0,0 +1,543 @@ +// Copyright 2012 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. + +#ifndef DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_ +#define DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_ + +#include "utils.h" + +namespace double_conversion { + +class DoubleToStringConverter { + public: + // When calling ToFixed with a double > 10^kMaxFixedDigitsBeforePoint + // or a requested_digits parameter > kMaxFixedDigitsAfterPoint then the + // function returns false. + static const int kMaxFixedDigitsBeforePoint = 60; + static const int kMaxFixedDigitsAfterPoint = 60; + + // When calling ToExponential with a requested_digits + // parameter > kMaxExponentialDigits then the function returns false. + static const int kMaxExponentialDigits = 120; + + // When calling ToPrecision with a requested_digits + // parameter < kMinPrecisionDigits or requested_digits > kMaxPrecisionDigits + // then the function returns false. + static const int kMinPrecisionDigits = 1; + static const int kMaxPrecisionDigits = 120; + + enum Flags { + NO_FLAGS = 0, + EMIT_POSITIVE_EXPONENT_SIGN = 1, + EMIT_TRAILING_DECIMAL_POINT = 2, + EMIT_TRAILING_ZERO_AFTER_POINT = 4, + UNIQUE_ZERO = 8 + }; + + // Flags should be a bit-or combination of the possible Flags-enum. + // - NO_FLAGS: no special flags. + // - EMIT_POSITIVE_EXPONENT_SIGN: when the number is converted into exponent + // form, emits a '+' for positive exponents. Example: 1.2e+2. + // - EMIT_TRAILING_DECIMAL_POINT: when the input number is an integer and is + // converted into decimal format then a trailing decimal point is appended. + // Example: 2345.0 is converted to "2345.". + // - EMIT_TRAILING_ZERO_AFTER_POINT: in addition to a trailing decimal point + // emits a trailing '0'-character. This flag requires the + // EXMIT_TRAILING_DECIMAL_POINT flag. + // Example: 2345.0 is converted to "2345.0". + // - UNIQUE_ZERO: "-0.0" is converted to "0.0". + // + // Infinity symbol and nan_symbol provide the string representation for these + // special values. If the string is NULL and the special value is encountered + // then the conversion functions return false. + // + // The exponent_character is used in exponential representations. It is + // usually 'e' or 'E'. + // + // When converting to the shortest representation the converter will + // represent input numbers in decimal format if they are in the interval + // [10^decimal_in_shortest_low; 10^decimal_in_shortest_high[ + // (lower boundary included, greater boundary excluded). + // Example: with decimal_in_shortest_low = -6 and + // decimal_in_shortest_high = 21: + // ToShortest(0.000001) -> "0.000001" + // ToShortest(0.0000001) -> "1e-7" + // ToShortest(111111111111111111111.0) -> "111111111111111110000" + // ToShortest(100000000000000000000.0) -> "100000000000000000000" + // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21" + // + // When converting to precision mode the converter may add + // max_leading_padding_zeroes before returning the number in exponential + // format. + // Example with max_leading_padding_zeroes_in_precision_mode = 6. + // ToPrecision(0.0000012345, 2) -> "0.0000012" + // ToPrecision(0.00000012345, 2) -> "1.2e-7" + // Similarily the converter may add up to + // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid + // returning an exponential representation. A zero added by the + // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit. + // Examples for max_trailing_padding_zeroes_in_precision_mode = 1: + // ToPrecision(230.0, 2) -> "230" + // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT. + // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT. + DoubleToStringConverter(int flags, + const char* infinity_symbol, + const char* nan_symbol, + char exponent_character, + int decimal_in_shortest_low, + int decimal_in_shortest_high, + int max_leading_padding_zeroes_in_precision_mode, + int max_trailing_padding_zeroes_in_precision_mode) + : flags_(flags), + infinity_symbol_(infinity_symbol), + nan_symbol_(nan_symbol), + exponent_character_(exponent_character), + decimal_in_shortest_low_(decimal_in_shortest_low), + decimal_in_shortest_high_(decimal_in_shortest_high), + max_leading_padding_zeroes_in_precision_mode_( + max_leading_padding_zeroes_in_precision_mode), + max_trailing_padding_zeroes_in_precision_mode_( + max_trailing_padding_zeroes_in_precision_mode) { + // When 'trailing zero after the point' is set, then 'trailing point' + // must be set too. + ASSERT(((flags & EMIT_TRAILING_DECIMAL_POINT) != 0) || + !((flags & EMIT_TRAILING_ZERO_AFTER_POINT) != 0)); + } + + // Returns a converter following the EcmaScript specification. + static const DoubleToStringConverter& EcmaScriptConverter(); + + // Computes the shortest string of digits that correctly represent the input + // number. Depending on decimal_in_shortest_low and decimal_in_shortest_high + // (see constructor) it then either returns a decimal representation, or an + // exponential representation. + // Example with decimal_in_shortest_low = -6, + // decimal_in_shortest_high = 21, + // EMIT_POSITIVE_EXPONENT_SIGN activated, and + // EMIT_TRAILING_DECIMAL_POINT deactived: + // ToShortest(0.000001) -> "0.000001" + // ToShortest(0.0000001) -> "1e-7" + // ToShortest(111111111111111111111.0) -> "111111111111111110000" + // ToShortest(100000000000000000000.0) -> "100000000000000000000" + // ToShortest(1111111111111111111111.0) -> "1.1111111111111111e+21" + // + // Note: the conversion may round the output if the returned string + // is accurate enough to uniquely identify the input-number. + // For example the most precise representation of the double 9e59 equals + // "899999999999999918767229449717619953810131273674690656206848", but + // the converter will return the shorter (but still correct) "9e59". + // + // Returns true if the conversion succeeds. The conversion always succeeds + // except when the input value is special and no infinity_symbol or + // nan_symbol has been given to the constructor. + bool ToShortest(double value, StringBuilder* result_builder) const { + return ToShortestIeeeNumber(value, result_builder, SHORTEST); + } + + // Same as ToShortest, but for single-precision floats. + bool ToShortestSingle(float value, StringBuilder* result_builder) const { + return ToShortestIeeeNumber(value, result_builder, SHORTEST_SINGLE); + } + + + // Computes a decimal representation with a fixed number of digits after the + // decimal point. The last emitted digit is rounded. + // + // Examples: + // ToFixed(3.12, 1) -> "3.1" + // ToFixed(3.1415, 3) -> "3.142" + // ToFixed(1234.56789, 4) -> "1234.5679" + // ToFixed(1.23, 5) -> "1.23000" + // ToFixed(0.1, 4) -> "0.1000" + // ToFixed(1e30, 2) -> "1000000000000000019884624838656.00" + // ToFixed(0.1, 30) -> "0.100000000000000005551115123126" + // ToFixed(0.1, 17) -> "0.10000000000000001" + // + // If requested_digits equals 0, then the tail of the result depends on + // the EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT. + // Examples, for requested_digits == 0, + // let EMIT_TRAILING_DECIMAL_POINT and EMIT_TRAILING_ZERO_AFTER_POINT be + // - false and false: then 123.45 -> 123 + // 0.678 -> 1 + // - true and false: then 123.45 -> 123. + // 0.678 -> 1. + // - true and true: then 123.45 -> 123.0 + // 0.678 -> 1.0 + // + // Returns true if the conversion succeeds. The conversion always succeeds + // except for the following cases: + // - the input value is special and no infinity_symbol or nan_symbol has + // been provided to the constructor, + // - 'value' > 10^kMaxFixedDigitsBeforePoint, or + // - 'requested_digits' > kMaxFixedDigitsAfterPoint. + // The last two conditions imply that the result will never contain more than + // 1 + kMaxFixedDigitsBeforePoint + 1 + kMaxFixedDigitsAfterPoint characters + // (one additional character for the sign, and one for the decimal point). + bool ToFixed(double value, + int requested_digits, + StringBuilder* result_builder) const; + + // Computes a representation in exponential format with requested_digits + // after the decimal point. The last emitted digit is rounded. + // If requested_digits equals -1, then the shortest exponential representation + // is computed. + // + // Examples with EMIT_POSITIVE_EXPONENT_SIGN deactivated, and + // exponent_character set to 'e'. + // ToExponential(3.12, 1) -> "3.1e0" + // ToExponential(5.0, 3) -> "5.000e0" + // ToExponential(0.001, 2) -> "1.00e-3" + // ToExponential(3.1415, -1) -> "3.1415e0" + // ToExponential(3.1415, 4) -> "3.1415e0" + // ToExponential(3.1415, 3) -> "3.142e0" + // ToExponential(123456789000000, 3) -> "1.235e14" + // ToExponential(1000000000000000019884624838656.0, -1) -> "1e30" + // ToExponential(1000000000000000019884624838656.0, 32) -> + // "1.00000000000000001988462483865600e30" + // ToExponential(1234, 0) -> "1e3" + // + // Returns true if the conversion succeeds. The conversion always succeeds + // except for the following cases: + // - the input value is special and no infinity_symbol or nan_symbol has + // been provided to the constructor, + // - 'requested_digits' > kMaxExponentialDigits. + // The last condition implies that the result will never contain more than + // kMaxExponentialDigits + 8 characters (the sign, the digit before the + // decimal point, the decimal point, the exponent character, the + // exponent's sign, and at most 3 exponent digits). + bool ToExponential(double value, + int requested_digits, + StringBuilder* result_builder) const; + + // Computes 'precision' leading digits of the given 'value' and returns them + // either in exponential or decimal format, depending on + // max_{leading|trailing}_padding_zeroes_in_precision_mode (given to the + // constructor). + // The last computed digit is rounded. + // + // Example with max_leading_padding_zeroes_in_precision_mode = 6. + // ToPrecision(0.0000012345, 2) -> "0.0000012" + // ToPrecision(0.00000012345, 2) -> "1.2e-7" + // Similarily the converter may add up to + // max_trailing_padding_zeroes_in_precision_mode in precision mode to avoid + // returning an exponential representation. A zero added by the + // EMIT_TRAILING_ZERO_AFTER_POINT flag is counted for this limit. + // Examples for max_trailing_padding_zeroes_in_precision_mode = 1: + // ToPrecision(230.0, 2) -> "230" + // ToPrecision(230.0, 2) -> "230." with EMIT_TRAILING_DECIMAL_POINT. + // ToPrecision(230.0, 2) -> "2.3e2" with EMIT_TRAILING_ZERO_AFTER_POINT. + // Examples for max_trailing_padding_zeroes_in_precision_mode = 3, and no + // EMIT_TRAILING_ZERO_AFTER_POINT: + // ToPrecision(123450.0, 6) -> "123450" + // ToPrecision(123450.0, 5) -> "123450" + // ToPrecision(123450.0, 4) -> "123500" + // ToPrecision(123450.0, 3) -> "123000" + // ToPrecision(123450.0, 2) -> "1.2e5" + // + // Returns true if the conversion succeeds. The conversion always succeeds + // except for the following cases: + // - the input value is special and no infinity_symbol or nan_symbol has + // been provided to the constructor, + // - precision < kMinPericisionDigits + // - precision > kMaxPrecisionDigits + // The last condition implies that the result will never contain more than + // kMaxPrecisionDigits + 7 characters (the sign, the decimal point, the + // exponent character, the exponent's sign, and at most 3 exponent digits). + bool ToPrecision(double value, + int precision, + StringBuilder* result_builder) const; + + enum DtoaMode { + // Produce the shortest correct representation. + // For example the output of 0.299999999999999988897 is (the less accurate + // but correct) 0.3. + SHORTEST, + // Same as SHORTEST, but for single-precision floats. + SHORTEST_SINGLE, + // Produce a fixed number of digits after the decimal point. + // For instance fixed(0.1, 4) becomes 0.1000 + // If the input number is big, the output will be big. + FIXED, + // Fixed number of digits (independent of the decimal point). + PRECISION + }; + + // The maximal number of digits that are needed to emit a double in base 10. + // A higher precision can be achieved by using more digits, but the shortest + // accurate representation of any double will never use more digits than + // kBase10MaximalLength. + // Note that DoubleToAscii null-terminates its input. So the given buffer + // should be at least kBase10MaximalLength + 1 characters long. + static const int kBase10MaximalLength = 17; + + // Converts the given double 'v' to ascii. 'v' must not be NaN, +Infinity, or + // -Infinity. In SHORTEST_SINGLE-mode this restriction also applies to 'v' + // after it has been casted to a single-precision float. That is, in this + // mode static_cast<float>(v) must not be NaN, +Infinity or -Infinity. + // + // The result should be interpreted as buffer * 10^(point-length). + // + // The output depends on the given mode: + // - SHORTEST: produce the least amount of digits for which the internal + // identity requirement is still satisfied. If the digits are printed + // (together with the correct exponent) then reading this number will give + // 'v' again. The buffer will choose the representation that is closest to + // 'v'. If there are two at the same distance, than the one farther away + // from 0 is chosen (halfway cases - ending with 5 - are rounded up). + // In this mode the 'requested_digits' parameter is ignored. + // - SHORTEST_SINGLE: same as SHORTEST but with single-precision. + // - FIXED: produces digits necessary to print a given number with + // 'requested_digits' digits after the decimal point. The produced digits + // might be too short in which case the caller has to fill the remainder + // with '0's. + // Example: toFixed(0.001, 5) is allowed to return buffer="1", point=-2. + // Halfway cases are rounded towards +/-Infinity (away from 0). The call + // toFixed(0.15, 2) thus returns buffer="2", point=0. + // The returned buffer may contain digits that would be truncated from the + // shortest representation of the input. + // - PRECISION: produces 'requested_digits' where the first digit is not '0'. + // Even though the length of produced digits usually equals + // 'requested_digits', the function is allowed to return fewer digits, in + // which case the caller has to fill the missing digits with '0's. + // Halfway cases are again rounded away from 0. + // DoubleToAscii expects the given buffer to be big enough to hold all + // digits and a terminating null-character. In SHORTEST-mode it expects a + // buffer of at least kBase10MaximalLength + 1. In all other modes the + // requested_digits parameter and the padding-zeroes limit the size of the + // output. Don't forget the decimal point, the exponent character and the + // terminating null-character when computing the maximal output size. + // The given length is only used in debug mode to ensure the buffer is big + // enough. + static void DoubleToAscii(double v, + DtoaMode mode, + int requested_digits, + char* buffer, + int buffer_length, + bool* sign, + int* length, + int* point); + + private: + // Implementation for ToShortest and ToShortestSingle. + bool ToShortestIeeeNumber(double value, + StringBuilder* result_builder, + DtoaMode mode) const; + + // If the value is a special value (NaN or Infinity) constructs the + // corresponding string using the configured infinity/nan-symbol. + // If either of them is NULL or the value is not special then the + // function returns false. + bool HandleSpecialValues(double value, StringBuilder* result_builder) const; + // Constructs an exponential representation (i.e. 1.234e56). + // The given exponent assumes a decimal point after the first decimal digit. + void CreateExponentialRepresentation(const char* decimal_digits, + int length, + int exponent, + StringBuilder* result_builder) const; + // Creates a decimal representation (i.e 1234.5678). + void CreateDecimalRepresentation(const char* decimal_digits, + int length, + int decimal_point, + int digits_after_point, + StringBuilder* result_builder) const; + + const int flags_; + const char* const infinity_symbol_; + const char* const nan_symbol_; + const char exponent_character_; + const int decimal_in_shortest_low_; + const int decimal_in_shortest_high_; + const int max_leading_padding_zeroes_in_precision_mode_; + const int max_trailing_padding_zeroes_in_precision_mode_; + + DISALLOW_IMPLICIT_CONSTRUCTORS(DoubleToStringConverter); +}; + + +class StringToDoubleConverter { + public: + // Enumeration for allowing octals and ignoring junk when converting + // strings to numbers. + enum Flags { + NO_FLAGS = 0, + ALLOW_HEX = 1, + ALLOW_OCTALS = 2, + ALLOW_TRAILING_JUNK = 4, + ALLOW_LEADING_SPACES = 8, + ALLOW_TRAILING_SPACES = 16, + ALLOW_SPACES_AFTER_SIGN = 32 + }; + + // Flags should be a bit-or combination of the possible Flags-enum. + // - NO_FLAGS: no special flags. + // - ALLOW_HEX: recognizes the prefix "0x". Hex numbers may only be integers. + // Ex: StringToDouble("0x1234") -> 4660.0 + // In StringToDouble("0x1234.56") the characters ".56" are trailing + // junk. The result of the call is hence dependent on + // the ALLOW_TRAILING_JUNK flag and/or the junk value. + // With this flag "0x" is a junk-string. Even with ALLOW_TRAILING_JUNK, + // the string will not be parsed as "0" followed by junk. + // + // - ALLOW_OCTALS: recognizes the prefix "0" for octals: + // If a sequence of octal digits starts with '0', then the number is + // read as octal integer. Octal numbers may only be integers. + // Ex: StringToDouble("01234") -> 668.0 + // StringToDouble("012349") -> 12349.0 // Not a sequence of octal + // // digits. + // In StringToDouble("01234.56") the characters ".56" are trailing + // junk. The result of the call is hence dependent on + // the ALLOW_TRAILING_JUNK flag and/or the junk value. + // In StringToDouble("01234e56") the characters "e56" are trailing + // junk, too. + // - ALLOW_TRAILING_JUNK: ignore trailing characters that are not part of + // a double literal. + // - ALLOW_LEADING_SPACES: skip over leading whitespace, including spaces, + // new-lines, and tabs. + // - ALLOW_TRAILING_SPACES: ignore trailing whitespace. + // - ALLOW_SPACES_AFTER_SIGN: ignore whitespace after the sign. + // Ex: StringToDouble("- 123.2") -> -123.2. + // StringToDouble("+ 123.2") -> 123.2 + // + // empty_string_value is returned when an empty string is given as input. + // If ALLOW_LEADING_SPACES or ALLOW_TRAILING_SPACES are set, then a string + // containing only spaces is converted to the 'empty_string_value', too. + // + // junk_string_value is returned when + // a) ALLOW_TRAILING_JUNK is not set, and a junk character (a character not + // part of a double-literal) is found. + // b) ALLOW_TRAILING_JUNK is set, but the string does not start with a + // double literal. + // + // infinity_symbol and nan_symbol are strings that are used to detect + // inputs that represent infinity and NaN. They can be null, in which case + // they are ignored. + // The conversion routine first reads any possible signs. Then it compares the + // following character of the input-string with the first character of + // the infinity, and nan-symbol. If either matches, the function assumes, that + // a match has been found, and expects the following input characters to match + // the remaining characters of the special-value symbol. + // This means that the following restrictions apply to special-value symbols: + // - they must not start with signs ('+', or '-'), + // - they must not have the same first character. + // - they must not start with digits. + // + // Examples: + // flags = ALLOW_HEX | ALLOW_TRAILING_JUNK, + // empty_string_value = 0.0, + // junk_string_value = NaN, + // infinity_symbol = "infinity", + // nan_symbol = "nan": + // StringToDouble("0x1234") -> 4660.0. + // StringToDouble("0x1234K") -> 4660.0. + // StringToDouble("") -> 0.0 // empty_string_value. + // StringToDouble(" ") -> NaN // junk_string_value. + // StringToDouble(" 1") -> NaN // junk_string_value. + // StringToDouble("0x") -> NaN // junk_string_value. + // StringToDouble("-123.45") -> -123.45. + // StringToDouble("--123.45") -> NaN // junk_string_value. + // StringToDouble("123e45") -> 123e45. + // StringToDouble("123E45") -> 123e45. + // StringToDouble("123e+45") -> 123e45. + // StringToDouble("123E-45") -> 123e-45. + // StringToDouble("123e") -> 123.0 // trailing junk ignored. + // StringToDouble("123e-") -> 123.0 // trailing junk ignored. + // StringToDouble("+NaN") -> NaN // NaN string literal. + // StringToDouble("-infinity") -> -inf. // infinity literal. + // StringToDouble("Infinity") -> NaN // junk_string_value. + // + // flags = ALLOW_OCTAL | ALLOW_LEADING_SPACES, + // empty_string_value = 0.0, + // junk_string_value = NaN, + // infinity_symbol = NULL, + // nan_symbol = NULL: + // StringToDouble("0x1234") -> NaN // junk_string_value. + // StringToDouble("01234") -> 668.0. + // StringToDouble("") -> 0.0 // empty_string_value. + // StringToDouble(" ") -> 0.0 // empty_string_value. + // StringToDouble(" 1") -> 1.0 + // StringToDouble("0x") -> NaN // junk_string_value. + // StringToDouble("0123e45") -> NaN // junk_string_value. + // StringToDouble("01239E45") -> 1239e45. + // StringToDouble("-infinity") -> NaN // junk_string_value. + // StringToDouble("NaN") -> NaN // junk_string_value. + StringToDoubleConverter(int flags, + double empty_string_value, + double junk_string_value, + const char* infinity_symbol, + const char* nan_symbol) + : flags_(flags), + empty_string_value_(empty_string_value), + junk_string_value_(junk_string_value), + infinity_symbol_(infinity_symbol), + nan_symbol_(nan_symbol) { + } + + // Performs the conversion. + // The output parameter 'processed_characters_count' is set to the number + // of characters that have been processed to read the number. + // Spaces than are processed with ALLOW_{LEADING|TRAILING}_SPACES are included + // in the 'processed_characters_count'. Trailing junk is never included. + double StringToDouble(const char* buffer, + int length, + int* processed_characters_count) const; + + // Same as StringToDouble above but for 16 bit characters. + double StringToDouble(const uc16* buffer, + int length, + int* processed_characters_count) const; + + // Same as StringToDouble but reads a float. + // Note that this is not equivalent to static_cast<float>(StringToDouble(...)) + // due to potential double-rounding. + float StringToFloat(const char* buffer, + int length, + int* processed_characters_count) const; + + // Same as StringToFloat above but for 16 bit characters. + float StringToFloat(const uc16* buffer, + int length, + int* processed_characters_count) const; + + private: + const int flags_; + const double empty_string_value_; + const double junk_string_value_; + const char* const infinity_symbol_; + const char* const nan_symbol_; + + template <class Iterator> + double StringToIeee(Iterator start_pointer, + int length, + bool read_as_double, + int* processed_characters_count) const; + + DISALLOW_IMPLICIT_CONSTRUCTORS(StringToDoubleConverter); +}; + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_DOUBLE_CONVERSION_H_ diff --git a/src/3rdparty/double-conversion/include/double-conversion/utils.h b/src/3rdparty/double-conversion/include/double-conversion/utils.h new file mode 100644 index 0000000000..a89b284eda --- /dev/null +++ b/src/3rdparty/double-conversion/include/double-conversion/utils.h @@ -0,0 +1,333 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_UTILS_H_ +#define DOUBLE_CONVERSION_UTILS_H_ + +#include <stdlib.h> +#include <string.h> + +#include <assert.h> +#ifndef ASSERT +# if defined(WINCE) || defined(_WIN32_WCE) +# define ASSERT(condition) +# else +# define ASSERT(condition) \ + assert(condition); +# endif +#endif +#ifndef UNIMPLEMENTED +# define UNIMPLEMENTED() (exit(-1)) +#endif +#ifndef UNREACHABLE +# define UNREACHABLE() (exit(-1)) +#endif + +// Double operations detection based on target architecture. +// Linux uses a 80bit wide floating point stack on x86. This induces double +// rounding, which in turn leads to wrong results. +// An easy way to test if the floating-point operations are correct is to +// evaluate: 89255.0/1e22. If the floating-point stack is 64 bits wide then +// the result is equal to 89255e-22. +// The best way to test this, is to create a division-function and to compare +// the output of the division with the expected result. (Inlining must be +// disabled.) +// On Linux,x86 89255e-22 != Div_double(89255.0/1e22) +#if defined(_M_X64) || defined(__x86_64__) || \ + defined(__ARMEL__) || defined(__avr32__) || _M_ARM_FP || \ + defined(__hppa__) || defined(__ia64__) || \ + defined(__mips__) || \ + defined(__powerpc__) || defined(__ppc__) || defined(__ppc64__) || \ + defined(__sparc__) || defined(__sparc) || defined(__s390__) || \ + defined(__SH4__) || defined(__alpha__) || \ + defined(_MIPS_ARCH_MIPS32R2) || \ + defined(__AARCH64EL__) +#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1 +#elif defined(_M_IX86) || defined(__i386__) || defined(__i386) +#if defined(_WIN32) +// Windows uses a 64bit wide floating point stack. +#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1 +#else +#undef DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS +#endif // _WIN32 +#elif defined(WINCE) || defined(_WIN32_WCE) +#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1 +#elif defined(__ghs) +// Green Hills toolchain uses a 64bit wide floating point stack +#define DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS 1 +#else +#error Target architecture was not detected as supported by Double-Conversion. +#endif + +#if defined(__GNUC__) +#define DOUBLE_CONVERSION_UNUSED __attribute__((unused)) +#else +#define DOUBLE_CONVERSION_UNUSED +#endif + +#if defined(_WIN32) && !defined(__MINGW32__) + +typedef signed char int8_t; +typedef unsigned char uint8_t; +typedef short int16_t; // NOLINT +typedef unsigned short uint16_t; // NOLINT +typedef int int32_t; +typedef unsigned int uint32_t; +typedef __int64 int64_t; +typedef unsigned __int64 uint64_t; +// intptr_t and friends are defined in crtdefs.h through stdio.h. + +#else + +#include <stdint.h> + +#endif + +typedef uint16_t uc16; + +// The following macro works on both 32 and 64-bit platforms. +// Usage: instead of writing 0x1234567890123456 +// write UINT64_2PART_C(0x12345678,90123456); +#define UINT64_2PART_C(a, b) (((static_cast<uint64_t>(a) << 32) + 0x##b##u)) + + +// The expression ARRAY_SIZE(a) is a compile-time constant of type +// size_t which represents the number of elements of the given +// array. You should only use ARRAY_SIZE on statically allocated +// arrays. +#ifndef ARRAY_SIZE +#define ARRAY_SIZE(a) \ + ((sizeof(a) / sizeof(*(a))) / \ + static_cast<size_t>(!(sizeof(a) % sizeof(*(a))))) +#endif + +// A macro to disallow the evil copy constructor and operator= functions +// This should be used in the private: declarations for a class +#ifndef DISALLOW_COPY_AND_ASSIGN +#define DISALLOW_COPY_AND_ASSIGN(TypeName) \ + TypeName(const TypeName&); \ + void operator=(const TypeName&) +#endif + +// A macro to disallow all the implicit constructors, namely the +// default constructor, copy constructor and operator= functions. +// +// This should be used in the private: declarations for a class +// that wants to prevent anyone from instantiating it. This is +// especially useful for classes containing only static methods. +#ifndef DISALLOW_IMPLICIT_CONSTRUCTORS +#define DISALLOW_IMPLICIT_CONSTRUCTORS(TypeName) \ + TypeName(); \ + DISALLOW_COPY_AND_ASSIGN(TypeName) +#endif + +namespace double_conversion { + +static const int kCharSize = sizeof(char); + +// Returns the maximum of the two parameters. +template <typename T> +static T Max(T a, T b) { + return a < b ? b : a; +} + + +// Returns the minimum of the two parameters. +template <typename T> +static T Min(T a, T b) { + return a < b ? a : b; +} + + +inline int StrLength(const char* string) { + size_t length = strlen(string); + ASSERT(length == static_cast<size_t>(static_cast<int>(length))); + return static_cast<int>(length); +} + +// This is a simplified version of V8's Vector class. +template <typename T> +class Vector { + public: + Vector() : start_(NULL), length_(0) {} + Vector(T* data, int length) : start_(data), length_(length) { + ASSERT(length == 0 || (length > 0 && data != NULL)); + } + + // Returns a vector using the same backing storage as this one, + // spanning from and including 'from', to but not including 'to'. + Vector<T> SubVector(int from, int to) { + ASSERT(to <= length_); + ASSERT(from < to); + ASSERT(0 <= from); + return Vector<T>(start() + from, to - from); + } + + // Returns the length of the vector. + int length() const { return length_; } + + // Returns whether or not the vector is empty. + bool is_empty() const { return length_ == 0; } + + // Returns the pointer to the start of the data in the vector. + T* start() const { return start_; } + + // Access individual vector elements - checks bounds in debug mode. + T& operator[](int index) const { + ASSERT(0 <= index && index < length_); + return start_[index]; + } + + T& first() { return start_[0]; } + + T& last() { return start_[length_ - 1]; } + + private: + T* start_; + int length_; +}; + + +// Helper class for building result strings in a character buffer. The +// purpose of the class is to use safe operations that checks the +// buffer bounds on all operations in debug mode. +class StringBuilder { + public: + StringBuilder(char* buffer, int size) + : buffer_(buffer, size), position_(0) { } + + ~StringBuilder() { if (!is_finalized()) Finalize(); } + + int size() const { return buffer_.length(); } + + // Get the current position in the builder. + int position() const { + ASSERT(!is_finalized()); + return position_; + } + + // Reset the position. + void Reset() { position_ = 0; } + + // Add a single character to the builder. It is not allowed to add + // 0-characters; use the Finalize() method to terminate the string + // instead. + void AddCharacter(char c) { + ASSERT(c != '\0'); + ASSERT(!is_finalized() && position_ < buffer_.length()); + buffer_[position_++] = c; + } + + // Add an entire string to the builder. Uses strlen() internally to + // compute the length of the input string. + void AddString(const char* s) { + AddSubstring(s, StrLength(s)); + } + + // Add the first 'n' characters of the given string 's' to the + // builder. The input string must have enough characters. + void AddSubstring(const char* s, int n) { + ASSERT(!is_finalized() && position_ + n < buffer_.length()); + ASSERT(static_cast<size_t>(n) <= strlen(s)); + memmove(&buffer_[position_], s, n * kCharSize); + position_ += n; + } + + + // Add character padding to the builder. If count is non-positive, + // nothing is added to the builder. + void AddPadding(char c, int count) { + for (int i = 0; i < count; i++) { + AddCharacter(c); + } + } + + // Finalize the string by 0-terminating it and returning the buffer. + char* Finalize() { + ASSERT(!is_finalized() && position_ < buffer_.length()); + buffer_[position_] = '\0'; + // Make sure nobody managed to add a 0-character to the + // buffer while building the string. + ASSERT(strlen(buffer_.start()) == static_cast<size_t>(position_)); + position_ = -1; + ASSERT(is_finalized()); + return buffer_.start(); + } + + private: + Vector<char> buffer_; + int position_; + + bool is_finalized() const { return position_ < 0; } + + DISALLOW_IMPLICIT_CONSTRUCTORS(StringBuilder); +}; + +// The type-based aliasing rule allows the compiler to assume that pointers of +// different types (for some definition of different) never alias each other. +// Thus the following code does not work: +// +// float f = foo(); +// int fbits = *(int*)(&f); +// +// The compiler 'knows' that the int pointer can't refer to f since the types +// don't match, so the compiler may cache f in a register, leaving random data +// in fbits. Using C++ style casts makes no difference, however a pointer to +// char data is assumed to alias any other pointer. This is the 'memcpy +// exception'. +// +// Bit_cast uses the memcpy exception to move the bits from a variable of one +// type of a variable of another type. Of course the end result is likely to +// be implementation dependent. Most compilers (gcc-4.2 and MSVC 2005) +// will completely optimize BitCast away. +// +// There is an additional use for BitCast. +// Recent gccs will warn when they see casts that may result in breakage due to +// the type-based aliasing rule. If you have checked that there is no breakage +// you can use BitCast to cast one pointer type to another. This confuses gcc +// enough that it can no longer see that you have cast one pointer type to +// another thus avoiding the warning. +template <class Dest, class Source> +inline Dest BitCast(const Source& source) { + // Compile time assertion: sizeof(Dest) == sizeof(Source) + // A compile error here means your Dest and Source have different sizes. + DOUBLE_CONVERSION_UNUSED + typedef char VerifySizesAreEqual[sizeof(Dest) == sizeof(Source) ? 1 : -1]; + + Dest dest; + memmove(&dest, &source, sizeof(dest)); + return dest; +} + +template <class Dest, class Source> +inline Dest BitCast(Source* source) { + return BitCast<Dest>(reinterpret_cast<uintptr_t>(source)); +} + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_UTILS_H_ diff --git a/src/3rdparty/double-conversion/strtod.cc b/src/3rdparty/double-conversion/strtod.cc new file mode 100644 index 0000000000..34717562bd --- /dev/null +++ b/src/3rdparty/double-conversion/strtod.cc @@ -0,0 +1,555 @@ +// 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 <stdarg.h> +#include <limits.h> + +#include "strtod.h" +#include "bignum.h" +#include "cached-powers.h" +#include "ieee.h" + +namespace double_conversion { + +// 2^53 = 9007199254740992. +// Any integer with at most 15 decimal digits will hence fit into a double +// (which has a 53bit significand) without loss of precision. +static const int kMaxExactDoubleIntegerDecimalDigits = 15; +// 2^64 = 18446744073709551616 > 10^19 +static const int kMaxUint64DecimalDigits = 19; + +// Max double: 1.7976931348623157 x 10^308 +// Min non-zero double: 4.9406564584124654 x 10^-324 +// Any x >= 10^309 is interpreted as +infinity. +// Any x <= 10^-324 is interpreted as 0. +// Note that 2.5e-324 (despite being smaller than the min double) will be read +// as non-zero (equal to the min non-zero double). +static const int kMaxDecimalPower = 309; +static const int kMinDecimalPower = -324; + +// 2^64 = 18446744073709551616 +static const uint64_t kMaxUint64 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF); + + +static const double exact_powers_of_ten[] = { + 1.0, // 10^0 + 10.0, + 100.0, + 1000.0, + 10000.0, + 100000.0, + 1000000.0, + 10000000.0, + 100000000.0, + 1000000000.0, + 10000000000.0, // 10^10 + 100000000000.0, + 1000000000000.0, + 10000000000000.0, + 100000000000000.0, + 1000000000000000.0, + 10000000000000000.0, + 100000000000000000.0, + 1000000000000000000.0, + 10000000000000000000.0, + 100000000000000000000.0, // 10^20 + 1000000000000000000000.0, + // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 + 10000000000000000000000.0 +}; +static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); + +// Maximum number of significant digits in the decimal representation. +// In fact the value is 772 (see conversions.cc), but to give us some margin +// we round up to 780. +static const int kMaxSignificantDecimalDigits = 780; + +static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { + for (int i = 0; i < buffer.length(); i++) { + if (buffer[i] != '0') { + return buffer.SubVector(i, buffer.length()); + } + } + return Vector<const char>(buffer.start(), 0); +} + + +static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { + for (int i = buffer.length() - 1; i >= 0; --i) { + if (buffer[i] != '0') { + return buffer.SubVector(0, i + 1); + } + } + return Vector<const char>(buffer.start(), 0); +} + + +static void CutToMaxSignificantDigits(Vector<const char> buffer, + int exponent, + char* significant_buffer, + int* significant_exponent) { + for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { + significant_buffer[i] = buffer[i]; + } + // The input buffer has been trimmed. Therefore the last digit must be + // different from '0'. + ASSERT(buffer[buffer.length() - 1] != '0'); + // Set the last digit to be non-zero. This is sufficient to guarantee + // correct rounding. + significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; + *significant_exponent = + exponent + (buffer.length() - kMaxSignificantDecimalDigits); +} + + +// Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits. +// If possible the input-buffer is reused, but if the buffer needs to be +// modified (due to cutting), then the input needs to be copied into the +// buffer_copy_space. +static void TrimAndCut(Vector<const char> buffer, int exponent, + char* buffer_copy_space, int space_size, + Vector<const char>* trimmed, int* updated_exponent) { + Vector<const char> left_trimmed = TrimLeadingZeros(buffer); + Vector<const char> right_trimmed = TrimTrailingZeros(left_trimmed); + exponent += left_trimmed.length() - right_trimmed.length(); + if (right_trimmed.length() > kMaxSignificantDecimalDigits) { + (void) space_size; // Mark variable as used. + ASSERT(space_size >= kMaxSignificantDecimalDigits); + CutToMaxSignificantDigits(right_trimmed, exponent, + buffer_copy_space, updated_exponent); + *trimmed = Vector<const char>(buffer_copy_space, + kMaxSignificantDecimalDigits); + } else { + *trimmed = right_trimmed; + *updated_exponent = exponent; + } +} + + +// Reads digits from the buffer and converts them to a uint64. +// Reads in as many digits as fit into a uint64. +// When the string starts with "1844674407370955161" no further digit is read. +// Since 2^64 = 18446744073709551616 it would still be possible read another +// digit if it was less or equal than 6, but this would complicate the code. +static uint64_t ReadUint64(Vector<const char> buffer, + int* number_of_read_digits) { + uint64_t result = 0; + int i = 0; + while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { + int digit = buffer[i++] - '0'; + ASSERT(0 <= digit && digit <= 9); + result = 10 * result + digit; + } + *number_of_read_digits = i; + return result; +} + + +// Reads a DiyFp from the buffer. +// The returned DiyFp is not necessarily normalized. +// If remaining_decimals is zero then the returned DiyFp is accurate. +// Otherwise it has been rounded and has error of at most 1/2 ulp. +static void ReadDiyFp(Vector<const char> buffer, + DiyFp* result, + int* remaining_decimals) { + int read_digits; + uint64_t significand = ReadUint64(buffer, &read_digits); + if (buffer.length() == read_digits) { + *result = DiyFp(significand, 0); + *remaining_decimals = 0; + } else { + // Round the significand. + if (buffer[read_digits] >= '5') { + significand++; + } + // Compute the binary exponent. + int exponent = 0; + *result = DiyFp(significand, exponent); + *remaining_decimals = buffer.length() - read_digits; + } +} + + +static bool DoubleStrtod(Vector<const char> trimmed, + int exponent, + double* result) { +#if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) + // On x86 the floating-point stack can be 64 or 80 bits wide. If it is + // 80 bits wide (as is the case on Linux) then double-rounding occurs and the + // result is not accurate. + // We know that Windows32 uses 64 bits and is therefore accurate. + // Note that the ARM simulator is compiled for 32bits. It therefore exhibits + // the same problem. + return false; +#endif + if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { + int read_digits; + // The trimmed input fits into a double. + // If the 10^exponent (resp. 10^-exponent) fits into a double too then we + // can compute the result-double simply by multiplying (resp. dividing) the + // two numbers. + // This is possible because IEEE guarantees that floating-point operations + // return the best possible approximation. + if (exponent < 0 && -exponent < kExactPowersOfTenSize) { + // 10^-exponent fits into a double. + *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); + ASSERT(read_digits == trimmed.length()); + *result /= exact_powers_of_ten[-exponent]; + return true; + } + if (0 <= exponent && exponent < kExactPowersOfTenSize) { + // 10^exponent fits into a double. + *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); + ASSERT(read_digits == trimmed.length()); + *result *= exact_powers_of_ten[exponent]; + return true; + } + int remaining_digits = + kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); + if ((0 <= exponent) && + (exponent - remaining_digits < kExactPowersOfTenSize)) { + // The trimmed string was short and we can multiply it with + // 10^remaining_digits. As a result the remaining exponent now fits + // into a double too. + *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); + ASSERT(read_digits == trimmed.length()); + *result *= exact_powers_of_ten[remaining_digits]; + *result *= exact_powers_of_ten[exponent - remaining_digits]; + return true; + } + } + return false; +} + + +// Returns 10^exponent as an exact DiyFp. +// The given exponent must be in the range [1; kDecimalExponentDistance[. +static DiyFp AdjustmentPowerOfTen(int exponent) { + ASSERT(0 < exponent); + ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); + // Simply hardcode the remaining powers for the given decimal exponent + // distance. + ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); + switch (exponent) { + case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60); + case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57); + case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54); + case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50); + case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47); + case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44); + case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40); + default: + UNREACHABLE(); + } +} + + +// If the function returns true then the result is the correct double. +// Otherwise it is either the correct double or the double that is just below +// the correct double. +static bool DiyFpStrtod(Vector<const char> buffer, + int exponent, + double* result) { + DiyFp input; + int remaining_decimals; + ReadDiyFp(buffer, &input, &remaining_decimals); + // Since we may have dropped some digits the input is not accurate. + // If remaining_decimals is different than 0 than the error is at most + // .5 ulp (unit in the last place). + // We don't want to deal with fractions and therefore keep a common + // denominator. + const int kDenominatorLog = 3; + const int kDenominator = 1 << kDenominatorLog; + // Move the remaining decimals into the exponent. + exponent += remaining_decimals; + int error = (remaining_decimals == 0 ? 0 : kDenominator / 2); + + int old_e = input.e(); + input.Normalize(); + error <<= old_e - input.e(); + + ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); + if (exponent < PowersOfTenCache::kMinDecimalExponent) { + *result = 0.0; + return true; + } + DiyFp cached_power; + int cached_decimal_exponent; + PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, + &cached_power, + &cached_decimal_exponent); + + if (cached_decimal_exponent != exponent) { + int adjustment_exponent = exponent - cached_decimal_exponent; + DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); + input.Multiply(adjustment_power); + if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { + // The product of input with the adjustment power fits into a 64 bit + // integer. + ASSERT(DiyFp::kSignificandSize == 64); + } else { + // The adjustment power is exact. There is hence only an error of 0.5. + error += kDenominator / 2; + } + } + + input.Multiply(cached_power); + // The error introduced by a multiplication of a*b equals + // error_a + error_b + error_a*error_b/2^64 + 0.5 + // Substituting a with 'input' and b with 'cached_power' we have + // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), + // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 + int error_b = kDenominator / 2; + int error_ab = (error == 0 ? 0 : 1); // We round up to 1. + int fixed_error = kDenominator / 2; + error += error_b + error_ab + fixed_error; + + old_e = input.e(); + input.Normalize(); + error <<= old_e - input.e(); + + // See if the double's significand changes if we add/subtract the error. + int order_of_magnitude = DiyFp::kSignificandSize + input.e(); + int effective_significand_size = + Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); + int precision_digits_count = + DiyFp::kSignificandSize - effective_significand_size; + if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { + // This can only happen for very small denormals. In this case the + // half-way multiplied by the denominator exceeds the range of an uint64. + // Simply shift everything to the right. + int shift_amount = (precision_digits_count + kDenominatorLog) - + DiyFp::kSignificandSize + 1; + input.set_f(input.f() >> shift_amount); + input.set_e(input.e() + shift_amount); + // We add 1 for the lost precision of error, and kDenominator for + // the lost precision of input.f(). + error = (error >> shift_amount) + 1 + kDenominator; + precision_digits_count -= shift_amount; + } + // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. + ASSERT(DiyFp::kSignificandSize == 64); + ASSERT(precision_digits_count < 64); + uint64_t one64 = 1; + uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; + uint64_t precision_bits = input.f() & precision_bits_mask; + uint64_t half_way = one64 << (precision_digits_count - 1); + precision_bits *= kDenominator; + half_way *= kDenominator; + DiyFp rounded_input(input.f() >> precision_digits_count, + input.e() + precision_digits_count); + if (precision_bits >= half_way + error) { + rounded_input.set_f(rounded_input.f() + 1); + } + // If the last_bits are too close to the half-way case than we are too + // inaccurate and round down. In this case we return false so that we can + // fall back to a more precise algorithm. + + *result = Double(rounded_input).value(); + if (half_way - error < precision_bits && precision_bits < half_way + error) { + // Too imprecise. The caller will have to fall back to a slower version. + // However the returned number is guaranteed to be either the correct + // double, or the next-lower double. + return false; + } else { + return true; + } +} + + +// Returns +// - -1 if buffer*10^exponent < diy_fp. +// - 0 if buffer*10^exponent == diy_fp. +// - +1 if buffer*10^exponent > diy_fp. +// Preconditions: +// buffer.length() + exponent <= kMaxDecimalPower + 1 +// buffer.length() + exponent > kMinDecimalPower +// buffer.length() <= kMaxDecimalSignificantDigits +static int CompareBufferWithDiyFp(Vector<const char> buffer, + int exponent, + DiyFp diy_fp) { + ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); + ASSERT(buffer.length() + exponent > kMinDecimalPower); + ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); + // Make sure that the Bignum will be able to hold all our numbers. + // Our Bignum implementation has a separate field for exponents. Shifts will + // consume at most one bigit (< 64 bits). + // ln(10) == 3.3219... + ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); + Bignum buffer_bignum; + Bignum diy_fp_bignum; + buffer_bignum.AssignDecimalString(buffer); + diy_fp_bignum.AssignUInt64(diy_fp.f()); + if (exponent >= 0) { + buffer_bignum.MultiplyByPowerOfTen(exponent); + } else { + diy_fp_bignum.MultiplyByPowerOfTen(-exponent); + } + if (diy_fp.e() > 0) { + diy_fp_bignum.ShiftLeft(diy_fp.e()); + } else { + buffer_bignum.ShiftLeft(-diy_fp.e()); + } + return Bignum::Compare(buffer_bignum, diy_fp_bignum); +} + + +// Returns true if the guess is the correct double. +// Returns false, when guess is either correct or the next-lower double. +static bool ComputeGuess(Vector<const char> trimmed, int exponent, + double* guess) { + if (trimmed.length() == 0) { + *guess = 0.0; + return true; + } + if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) { + *guess = Double::Infinity(); + return true; + } + if (exponent + trimmed.length() <= kMinDecimalPower) { + *guess = 0.0; + return true; + } + + if (DoubleStrtod(trimmed, exponent, guess) || + DiyFpStrtod(trimmed, exponent, guess)) { + return true; + } + if (*guess == Double::Infinity()) { + return true; + } + return false; +} + +double Strtod(Vector<const char> buffer, int exponent) { + char copy_buffer[kMaxSignificantDecimalDigits]; + Vector<const char> trimmed; + int updated_exponent; + TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits, + &trimmed, &updated_exponent); + exponent = updated_exponent; + + double guess; + bool is_correct = ComputeGuess(trimmed, exponent, &guess); + if (is_correct) return guess; + + DiyFp upper_boundary = Double(guess).UpperBoundary(); + int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary); + if (comparison < 0) { + return guess; + } else if (comparison > 0) { + return Double(guess).NextDouble(); + } else if ((Double(guess).Significand() & 1) == 0) { + // Round towards even. + return guess; + } else { + return Double(guess).NextDouble(); + } +} + +float Strtof(Vector<const char> buffer, int exponent) { + char copy_buffer[kMaxSignificantDecimalDigits]; + Vector<const char> trimmed; + int updated_exponent; + TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits, + &trimmed, &updated_exponent); + exponent = updated_exponent; + + double double_guess; + bool is_correct = ComputeGuess(trimmed, exponent, &double_guess); + + float float_guess = static_cast<float>(double_guess); + if (float_guess == double_guess) { + // This shortcut triggers for integer values. + return float_guess; + } + + // We must catch double-rounding. Say the double has been rounded up, and is + // now a boundary of a float, and rounds up again. This is why we have to + // look at previous too. + // Example (in decimal numbers): + // input: 12349 + // high-precision (4 digits): 1235 + // low-precision (3 digits): + // when read from input: 123 + // when rounded from high precision: 124. + // To do this we simply look at the neigbors of the correct result and see + // if they would round to the same float. If the guess is not correct we have + // to look at four values (since two different doubles could be the correct + // double). + + double double_next = Double(double_guess).NextDouble(); + double double_previous = Double(double_guess).PreviousDouble(); + + float f1 = static_cast<float>(double_previous); + float f2 = float_guess; + float f3 = static_cast<float>(double_next); + float f4; + if (is_correct) { + f4 = f3; + } else { + double double_next2 = Double(double_next).NextDouble(); + f4 = static_cast<float>(double_next2); + } + (void) f2; // Mark variable as used. + ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4); + + // If the guess doesn't lie near a single-precision boundary we can simply + // return its float-value. + if (f1 == f4) { + return float_guess; + } + + ASSERT((f1 != f2 && f2 == f3 && f3 == f4) || + (f1 == f2 && f2 != f3 && f3 == f4) || + (f1 == f2 && f2 == f3 && f3 != f4)); + + // guess and next are the two possible canditates (in the same way that + // double_guess was the lower candidate for a double-precision guess). + float guess = f1; + float next = f4; + DiyFp upper_boundary; + if (guess == 0.0f) { + float min_float = 1e-45f; + upper_boundary = Double(static_cast<double>(min_float) / 2).AsDiyFp(); + } else { + upper_boundary = Single(guess).UpperBoundary(); + } + int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary); + if (comparison < 0) { + return guess; + } else if (comparison > 0) { + return next; + } else if ((Single(guess).Significand() & 1) == 0) { + // Round towards even. + return guess; + } else { + return next; + } +} + +} // namespace double_conversion diff --git a/src/3rdparty/double-conversion/strtod.h b/src/3rdparty/double-conversion/strtod.h new file mode 100644 index 0000000000..ed0293b8f5 --- /dev/null +++ b/src/3rdparty/double-conversion/strtod.h @@ -0,0 +1,45 @@ +// 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. + +#ifndef DOUBLE_CONVERSION_STRTOD_H_ +#define DOUBLE_CONVERSION_STRTOD_H_ + +#include "utils.h" + +namespace double_conversion { + +// The buffer must only contain digits in the range [0-9]. It must not +// contain a dot or a sign. It must not start with '0', and must not be empty. +double Strtod(Vector<const char> buffer, int exponent); + +// The buffer must only contain digits in the range [0-9]. It must not +// contain a dot or a sign. It must not start with '0', and must not be empty. +float Strtof(Vector<const char> buffer, int exponent); + +} // namespace double_conversion + +#endif // DOUBLE_CONVERSION_STRTOD_H_ |