// © 2018 and later: Unicode, Inc. and others. // License & terms of use: http://www.unicode.org/copyright.html // // From the double-conversion library. Original license: // // 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. // ICU PATCH: ifdef around UCONFIG_NO_FORMATTING #include "unicode/utypes.h" #if !UCONFIG_NO_FORMATTING #include <cmath> // ICU PATCH: Customize header file paths for ICU. #include "double-conversion-bignum-dtoa.h" #include "double-conversion-bignum.h" #include "double-conversion-ieee.h" // ICU PATCH: Wrap in ICU namespace U_NAMESPACE_BEGIN namespace double_conversion { static int NormalizedExponent(uint64_t significand, int 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) { … } // 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) { … } // 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 whether // 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) { … } // 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) { … } // 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 approximation .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) { … } // 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) { … } // 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) { … } // 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) { … } // 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 boundaries 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) { … } // 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) { … } } // namespace double_conversion // ICU PATCH: Close ICU namespace U_NAMESPACE_END #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
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