155ee80713569ab0324fc8dcedcb5518501daa6a6ricow@chromium.org// Copyright 2011 the V8 project authors. All rights reserved. 23484964a86451e86dcf04be9bd8c0d76ee04f081rossberg@chromium.org// Use of this source code is governed by a BSD-style license that can be 33484964a86451e86dcf04be9bd8c0d76ee04f081rossberg@chromium.org// found in the LICENSE file. 44a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 577ca49ac05d25684c89442029c22f5b2bce94395ulan@chromium.org#include <cmath> 64a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 7196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "include/v8stdint.h" 85de0074a922429f5e0ec2cf140c2d2989bf88140yangguo@chromium.org#include "src/base/logging.h" 9196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "src/utils.h" 1055ee80713569ab0324fc8dcedcb5518501daa6a6ricow@chromium.org 11196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "src/bignum-dtoa.h" 124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 13196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "src/bignum.h" 14196eb601290dc49c3754da728dc58700dff2de1bmachenbach@chromium.org#include "src/double.h" 154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comnamespace v8 { 174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comnamespace internal { 184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic int NormalizedExponent(uint64_t significand, int exponent) { 20e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(significand != 0); 214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com while ((significand & Double::kHiddenBit) == 0) { 224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com significand = significand << 1; 234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com exponent = exponent - 1; 244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return exponent; 264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Forward declarations: 304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Returns an estimation of k such that 10^(k-1) <= v < 10^k. 314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic int EstimatePower(int exponent); 324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator 334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// and denominator. 344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void InitialScaledStartValues(double v, 354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int estimated_power, 364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool need_boundary_deltas, 374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, 384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* denominator, 394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, 404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_plus); 414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Multiplies numerator/denominator so that its values lies in the range 1-10. 424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Returns decimal_point s.t. 434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v = numerator'/denominator' * 10^(decimal_point-1) 444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// where numerator' and denominator' are the values of numerator and 454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// denominator after the call to this function. 464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void FixupMultiply10(int estimated_power, bool is_even, 474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int* decimal_point, 484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus); 504a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Generates digits from the left to the right and stops when the generated 514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// digits yield the shortest decimal representation of v. 524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void GenerateShortestDigits(Bignum* numerator, Bignum* denominator, 534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus, 544a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool is_even, 554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char> buffer, int* length); 564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Generates 'requested_digits' after the decimal point. 574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void BignumToFixed(int requested_digits, int* decimal_point, 584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char>(buffer), int* length); 604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Generates 'count' digits of numerator/denominator. 614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Once 'count' digits have been produced rounds the result depending on the 624a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// remainder (remainders of exactly .5 round upwards). Might update the 634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// decimal_point when rounding up (for example for 0.9999). 644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void GenerateCountedDigits(int count, int* decimal_point, 654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char>(buffer), int* length); 674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comvoid BignumDtoa(double v, BignumDtoaMode mode, int requested_digits, 704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char> buffer, int* length, int* decimal_point) { 71e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(v > 0); 72e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(!Double(v).IsSpecial()); 734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t significand = Double(v).Significand(); 744a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool is_even = (significand & 1) == 0; 754a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int exponent = Double(v).Exponent(); 764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int normalized_exponent = NormalizedExponent(significand, exponent); 774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // estimated_power might be too low by 1. 784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int estimated_power = EstimatePower(normalized_exponent); 794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Shortcut for Fixed. 814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The requested digits correspond to the digits after the point. If the 824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // number is much too small, then there is no need in trying to get any 834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // digits. 844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) { 854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[0] = '\0'; 864a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = 0; 874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Set decimal-point to -requested_digits. This is what Gay does. 884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that it should not have any effect anyways since the string is 894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // empty. 904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *decimal_point = -requested_digits; 914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum numerator; 954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum denominator; 964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum delta_minus; 974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum delta_plus; 984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Make sure the bignum can grow large enough. The smallest double equals 994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 4e-324. In this case the denominator needs fewer than 324*4 binary digits. 1004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The maximum double is 1.7976931348623157e308 which needs fewer than 1014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 308*4 binary digits. 102e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(Bignum::kMaxSignificantBits >= 324*4); 1034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST); 1044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com InitialScaledStartValues(v, estimated_power, need_boundary_deltas, 1054a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &numerator, &denominator, 1064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &delta_minus, &delta_plus); 1074a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // We now have v = (numerator / denominator) * 10^estimated_power. 1084a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com FixupMultiply10(estimated_power, is_even, decimal_point, 1094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &numerator, &denominator, 1104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &delta_minus, &delta_plus); 1114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // We now have v = (numerator / denominator) * 10^(decimal_point-1), and 1124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 1 <= (numerator + delta_plus) / denominator < 10 1134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com switch (mode) { 1144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com case BIGNUM_DTOA_SHORTEST: 1154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com GenerateShortestDigits(&numerator, &denominator, 1164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &delta_minus, &delta_plus, 1174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com is_even, buffer, length); 1184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com break; 1194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com case BIGNUM_DTOA_FIXED: 1204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com BignumToFixed(requested_digits, decimal_point, 1214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &numerator, &denominator, 1224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer, length); 1234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com break; 1244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com case BIGNUM_DTOA_PRECISION: 1254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com GenerateCountedDigits(requested_digits, decimal_point, 1264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com &numerator, &denominator, 1274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer, length); 1284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com break; 1294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com default: 1304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com UNREACHABLE(); 1314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 1324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[*length] = '\0'; 1334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 1344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 1354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 1364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// The procedure starts generating digits from the left to the right and stops 1374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// when the generated digits yield the shortest decimal representation of v. A 1384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// decimal representation of v is a number lying closer to v than to any other 1394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// double, so it converts to v when read. 1404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 1414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// This is true if d, the decimal representation, is between m- and m+, the 1424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// upper and lower boundaries. d must be strictly between them if !is_even. 1434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m- := (numerator - delta_minus) / denominator 1444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m+ := (numerator + delta_plus) / denominator 1454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 1464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Precondition: 0 <= (numerator+delta_plus) / denominator < 10. 1474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit 1484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// will be produced. This should be the standard precondition. 1494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void GenerateShortestDigits(Bignum* numerator, Bignum* denominator, 1504a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus, 1514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool is_even, 1524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char> buffer, int* length) { 1534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Small optimization: if delta_minus and delta_plus are the same just reuse 1544a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // one of the two bignums. 1554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (Bignum::Equal(*delta_minus, *delta_plus)) { 1564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus = delta_minus; 1574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 1584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = 0; 1594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com while (true) { 1604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint16_t digit; 1614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com digit = numerator->DivideModuloIntBignum(*denominator); 162e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(digit <= 9); // digit is a uint16_t and therefore always positive. 1634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // digit = numerator / denominator (integer division). 1644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = numerator % denominator. 1654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[(*length)++] = digit + '0'; 1664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 1674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Can we stop already? 1684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // If the remainder of the division is less than the distance to the lower 1694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // boundary we can stop. In this case we simply round down (discarding the 1704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // remainder). 1714a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Similarly we test if we can round up (using the upper boundary). 1724a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool in_delta_room_minus; 1734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool in_delta_room_plus; 1744a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (is_even) { 1754a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus); 1764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 1774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_delta_room_minus = Bignum::Less(*numerator, *delta_minus); 1784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 1794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (is_even) { 1804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_delta_room_plus = 1814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0; 1824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 1834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_delta_room_plus = 1844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0; 1854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 1864a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (!in_delta_room_minus && !in_delta_room_plus) { 1874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Prepare for next iteration. 1884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->Times10(); 1894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->Times10(); 1904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // We optimized delta_plus to be equal to delta_minus (if they share the 1914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // same value). So don't multiply delta_plus if they point to the same 1924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // object. 1934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (delta_minus != delta_plus) { 1944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->Times10(); 1954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 1964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else if (in_delta_room_minus && in_delta_room_plus) { 1974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Let's see if 2*numerator < denominator. 1984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // If yes, then the next digit would be < 5 and we can round down. 1994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator); 2004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (compare < 0) { 2014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Remaining digits are less than .5. -> Round down (== do nothing). 2024a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else if (compare > 0) { 2034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Remaining digits are more than .5 of denominator. -> Round up. 2044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that the last digit could not be a '9' as otherwise the whole 2054a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // loop would have stopped earlier. 2064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // We still have an assert here in case the preconditions were not 2074a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // satisfied. 208e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(buffer[(*length) - 1] != '9'); 2094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[(*length) - 1]++; 2104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 2114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Halfway case. 2124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // TODO(floitsch): need a way to solve half-way cases. 2134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // For now let's round towards even (since this is what Gay seems to 2144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // do). 2154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 2164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if ((buffer[(*length) - 1] - '0') % 2 == 0) { 2174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Round down => Do nothing. 2184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 219e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(buffer[(*length) - 1] != '9'); 2204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[(*length) - 1]++; 2214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 2244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else if (in_delta_room_minus) { 2254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Round down (== do nothing). 2264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 2274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { // in_delta_room_plus 2284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Round up. 2294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note again that the last digit could not be '9' since this would have 2304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // stopped the loop earlier. 231e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org // We still have an DCHECK here, in case the preconditions were not 2324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // satisfied. 233e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(buffer[(*length) -1] != '9'); 2344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[(*length) - 1]++; 2354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 2364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 2394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 2404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 2414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Let v = numerator / denominator < 10. 2424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point) 2434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// from left to right. Once 'count' digits have been produced we decide wether 2444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// to round up or down. Remainders of exactly .5 round upwards. Numbers such 2454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// as 9.999999 propagate a carry all the way, and change the 2464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// exponent (decimal_point), when rounding upwards. 2474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void GenerateCountedDigits(int count, int* decimal_point, 2484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 2494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char>(buffer), int* length) { 250e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(count >= 0); 2514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com for (int i = 0; i < count - 1; ++i) { 2524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint16_t digit; 2534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com digit = numerator->DivideModuloIntBignum(*denominator); 254e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(digit <= 9); // digit is a uint16_t and therefore always positive. 2554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // digit = numerator / denominator (integer division). 2564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = numerator % denominator. 2574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[i] = digit + '0'; 2584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Prepare for next iteration. 2594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->Times10(); 2604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Generate the last digit. 2624a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint16_t digit; 2634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com digit = numerator->DivideModuloIntBignum(*denominator); 2644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) { 2654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com digit++; 2664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[count - 1] = digit + '0'; 2684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Correct bad digits (in case we had a sequence of '9's). Propagate the 2694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // carry until we hat a non-'9' or til we reach the first digit. 2704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com for (int i = count - 1; i > 0; --i) { 2714a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (buffer[i] != '0' + 10) break; 2724a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[i] = '0'; 2734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[i - 1]++; 2744a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2754a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (buffer[0] == '0' + 10) { 2764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Propagate a carry past the top place. 2774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[0] = '1'; 2784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com (*decimal_point)++; 2794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 2804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = count; 2814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 2824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 2834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 2844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Generates 'requested_digits' after the decimal point. It might omit 2854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// trailing '0's. If the input number is too small then no digits at all are 2864a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// generated (ex.: 2 fixed digits for 0.00001). 2874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 2884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Input verifies: 1 <= (numerator + delta) / denominator < 10. 2894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void BignumToFixed(int requested_digits, int* decimal_point, 2904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 2914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Vector<char>(buffer), int* length) { 2924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that we have to look at more than just the requested_digits, since 2934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // a number could be rounded up. Example: v=0.5 with requested_digits=0. 2944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Even though the power of v equals 0 we can't just stop here. 2954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (-(*decimal_point) > requested_digits) { 2964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The number is definitively too small. 2974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Ex: 0.001 with requested_digits == 1. 2984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Set decimal-point to -requested_digits. This is what Gay does. 2994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that it should not have any effect anyways since the string is 3004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // empty. 3014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *decimal_point = -requested_digits; 3024a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = 0; 3034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 3044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else if (-(*decimal_point) == requested_digits) { 3054a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // We only need to verify if the number rounds down or up. 3064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Ex: 0.04 and 0.06 with requested_digits == 1. 307e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(*decimal_point == -requested_digits); 3084a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Initially the fraction lies in range (1, 10]. Multiply the denominator 3094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // by 10 so that we can compare more easily. 3104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->Times10(); 3114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) { 3124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // If the fraction is >= 0.5 then we have to include the rounded 3134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // digit. 3144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer[0] = '1'; 3154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = 1; 3164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com (*decimal_point)++; 3174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 3184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that we caught most of similar cases earlier. 3194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *length = 0; 3204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 3214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return; 3224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 3234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The requested digits correspond to the digits after the point. 3244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The variable 'needed_digits' includes the digits before the point. 3254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int needed_digits = (*decimal_point) + requested_digits; 3264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com GenerateCountedDigits(needed_digits, decimal_point, 3274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator, denominator, 3284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com buffer, length); 3294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 3304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 3314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Returns an estimation of k such that 10^(k-1) <= v < 10^k where 3344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v = f * 2^exponent and 2^52 <= f < 2^53. 3354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v is hence a normalized double with the given exponent. The output is an 3364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// approximation for the exponent of the decimal approimation .digits * 10^k. 3374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 3384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// The result might undershoot by 1 in which case 10^k <= v < 10^k+1. 3394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Note: this property holds for v's upper boundary m+ too. 3404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 10^k <= m+ < 10^k+1. 3414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// (see explanation below). 3424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 3434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Examples: 3444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// EstimatePower(0) => 16 3454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// EstimatePower(-52) => 0 3464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 3474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0. 3484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic int EstimatePower(int exponent) { 3494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // This function estimates log10 of v where v = f*2^e (with e == exponent). 3504a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)). 3514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Note that f is bounded by its container size. Let p = 53 (the double's 3524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // significand size). Then 2^(p-1) <= f < 2^p. 3534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 3544a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close 3554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)). 3564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The computed number undershoots by less than 0.631 (when we compute log3 3574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // and not log10). 3584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 3594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Optimization: since we only need an approximated result this computation 3604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // can be performed on 64 bit integers. On x86/x64 architecture the speedup is 3614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // not really measurable, though. 3624a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 3634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Since we want to avoid overshooting we decrement by 1e10 so that 3644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // floating-point imprecisions don't affect us. 3654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 3664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Explanation for v's boundary m+: the computation takes advantage of 3674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement 3684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // (even for denormals where the delta can be much more important). 3694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com const double k1Log10 = 0.30102999566398114; // 1/lg(10) 3714a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3724a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // For doubles len(f) == 53 (don't forget the hidden bit). 3734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com const int kSignificandSize = 53; 374e31286d471eb2e656a1809383fa16b76053dd673machenbach@chromium.org double estimate = 375e31286d471eb2e656a1809383fa16b76053dd673machenbach@chromium.org std::ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10); 3764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com return static_cast<int>(estimate); 3774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 3784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// See comments for InitialScaledStartValues. 3814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void InitialScaledStartValuesPositiveExponent( 3824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com double v, int estimated_power, bool need_boundary_deltas, 3834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 3844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus) { 3854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // A positive exponent implies a positive power. 386e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(estimated_power >= 0); 3874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Since the estimated_power is positive we simply multiply the denominator 3884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // by 10^estimated_power. 3894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = v. 3914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->AssignUInt64(Double(v).Significand()); 3924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(Double(v).Exponent()); 3934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // denominator = 10^estimated_power. 3944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->AssignPowerUInt16(10, estimated_power); 3954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 3964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (need_boundary_deltas) { 3974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Introduce a common denominator so that the deltas to the boundaries are 3984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // integers. 3994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); 4004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); 4014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common 4024a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // denominator (of 2) delta_plus equals 2^e. 4034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->AssignUInt16(1); 4044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->ShiftLeft(Double(v).Exponent()); 4054a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Same for delta_minus (with adjustments below if f == 2^p-1). 4064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->AssignUInt16(1); 4074a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->ShiftLeft(Double(v).Exponent()); 4084a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // If the significand (without the hidden bit) is 0, then the lower 4104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // boundary is closer than just half a ulp (unit in the last place). 4114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // There is only one exception: if the next lower number is a denormal then 4124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we 4134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // have to test it in the other function where exponent < 0). 4144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t v_bits = Double(v).AsUint64(); 4154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if ((v_bits & Double::kSignificandMask) == 0) { 4164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The lower boundary is closer at half the distance of "normal" numbers. 4174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Increase the common denominator and adapt all but the delta_minus. 4184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); // *2 4194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); // *2 4204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->ShiftLeft(1); // *2 4214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 4224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 4234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 4244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// See comments for InitialScaledStartValues 4274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void InitialScaledStartValuesNegativeExponentPositivePower( 4284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com double v, int estimated_power, bool need_boundary_deltas, 4294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 4304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus) { 4314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t significand = Double(v).Significand(); 4324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int exponent = Double(v).Exponent(); 4334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // v = f * 2^e with e < 0, and with estimated_power >= 0. 4344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // This means that e is close to 0 (have a look at how estimated_power is 4354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // computed). 4364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = significand 4384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // since v = significand * 2^exponent this is equivalent to 4394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = v * / 2^-exponent 4404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->AssignUInt64(significand); 4414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // denominator = 10^estimated_power * 2^-exponent (with exponent < 0) 4424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->AssignPowerUInt16(10, estimated_power); 4434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(-exponent); 4444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (need_boundary_deltas) { 4464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Introduce a common denominator so that the deltas to the boundaries are 4474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // integers. 4484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); 4494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); 4504a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common 4514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // denominator (of 2) delta_plus equals 2^e. 4524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Given that the denominator already includes v's exponent the distance 4534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // to the boundaries is simply 1. 4544a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->AssignUInt16(1); 4554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Same for delta_minus (with adjustments below if f == 2^p-1). 4564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->AssignUInt16(1); 4574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // If the significand (without the hidden bit) is 0, then the lower 4594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // boundary is closer than just one ulp (unit in the last place). 4604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // There is only one exception: if the next lower number is a denormal 4614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // then the distance is 1 ulp. Since the exponent is close to zero 4624a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // (otherwise estimated_power would have been negative) this cannot happen 4634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // here either. 4644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t v_bits = Double(v).AsUint64(); 4654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if ((v_bits & Double::kSignificandMask) == 0) { 4664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The lower boundary is closer at half the distance of "normal" numbers. 4674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Increase the denominator and adapt all but the delta_minus. 4684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); // *2 4694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); // *2 4704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->ShiftLeft(1); // *2 4714a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 4724a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 4734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 4744a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4754a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// See comments for InitialScaledStartValues 4774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void InitialScaledStartValuesNegativeExponentNegativePower( 4784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com double v, int estimated_power, bool need_boundary_deltas, 4794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 4804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus) { 4814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com const uint64_t kMinimalNormalizedExponent = 4824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com V8_2PART_UINT64_C(0x00100000, 00000000); 4834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t significand = Double(v).Significand(); 4844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int exponent = Double(v).Exponent(); 4854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Instead of multiplying the denominator with 10^estimated_power we 4864a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // multiply all values (numerator and deltas) by 10^-estimated_power. 4874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Use numerator as temporary container for power_ten. 4894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* power_ten = numerator; 4904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com power_ten->AssignPowerUInt16(10, -estimated_power); 4914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 4924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (need_boundary_deltas) { 4934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Since power_ten == numerator we must make a copy of 10^estimated_power 4944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // before we complete the computation of the numerator. 4954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // delta_plus = delta_minus = 10^estimated_power 4964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->AssignBignum(*power_ten); 4974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->AssignBignum(*power_ten); 4984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 4994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = significand * 2 * 10^-estimated_power 5014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // since v = significand * 2^exponent this is equivalent to 5024a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // numerator = v * 10^-estimated_power * 2 * 2^-exponent. 5034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Remember: numerator has been abused as power_ten. So no need to assign it 5044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // to itself. 505e3c177a423baa3c30225c4e422b6f6c76d38b951machenbach@chromium.org DCHECK(numerator == power_ten); 5064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->MultiplyByUInt64(significand); 5074a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5084a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // denominator = 2 * 2^-exponent with exponent < 0. 5094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->AssignUInt16(1); 5104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(-exponent); 5114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (need_boundary_deltas) { 5134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Introduce a common denominator so that the deltas to the boundaries are 5144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // integers. 5154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); 5164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); 5174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // With this shift the boundaries have their correct value, since 5184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // delta_plus = 10^-estimated_power, and 5194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // delta_minus = 10^-estimated_power. 5204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // These assignments have been done earlier. 5214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The special case where the lower boundary is twice as close. 5234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // This time we have to look out for the exception too. 5244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com uint64_t v_bits = Double(v).AsUint64(); 5254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if ((v_bits & Double::kSignificandMask) == 0 && 5264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // The only exception where a significand == 0 has its boundaries at 5274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // "normal" distances: 5284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com (v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) { 5294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->ShiftLeft(1); // *2 5304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com denominator->ShiftLeft(1); // *2 5314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->ShiftLeft(1); // *2 5324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 5334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 5344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 5354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5374a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Let v = significand * 2^exponent. 5384a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator 5394a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// and denominator. The functions GenerateShortestDigits and 5404a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// GenerateCountedDigits will then convert this ratio to its decimal 5414a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// representation d, with the required accuracy. 5424a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Then d * 10^estimated_power is the representation of v. 5434a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// (Note: the fraction and the estimated_power might get adjusted before 5444a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// generating the decimal representation.) 5454a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5464a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// The initial start values consist of: 5474a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power. 5484a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// - a scaled (common) denominator. 5494a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// optionally (used by GenerateShortestDigits to decide if it has the shortest 5504a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// decimal converting back to v): 5514a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// - v - m-: the distance to the lower boundary. 5524a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// - m+ - v: the distance to the upper boundary. 5534a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5544a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator. 5554a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5564a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Let ep == estimated_power, then the returned values will satisfy: 5574a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v / 10^ep = numerator / denominator. 5584a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// v's boundarys m- and m+: 5594a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m- / 10^ep == v / 10^ep - delta_minus / denominator 5604a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m+ / 10^ep == v / 10^ep + delta_plus / denominator 5614a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Or in other words: 5624a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m- == v - delta_minus * 10^ep / denominator; 5634a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// m+ == v + delta_plus * 10^ep / denominator; 5644a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5654a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Since 10^(k-1) <= v < 10^k (with k == estimated_power) 5664a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// or 10^k <= v < 10^(k+1) 5674a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// we then have 0.1 <= numerator/denominator < 1 5684a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// or 1 <= numerator/denominator < 10 5694a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5704a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// It is then easy to kickstart the digit-generation routine. 5714a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 5724a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// The boundary-deltas are only filled if need_boundary_deltas is set. 5734a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void InitialScaledStartValues(double v, 5744a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int estimated_power, 5754a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool need_boundary_deltas, 5764a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, 5774a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* denominator, 5784a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, 5794a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_plus) { 5804a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (Double(v).Exponent() >= 0) { 5814a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com InitialScaledStartValuesPositiveExponent( 5824a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com v, estimated_power, need_boundary_deltas, 5834a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator, denominator, delta_minus, delta_plus); 5844a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else if (estimated_power >= 0) { 5854a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com InitialScaledStartValuesNegativeExponentPositivePower( 5864a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com v, estimated_power, need_boundary_deltas, 5874a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator, denominator, delta_minus, delta_plus); 5884a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 5894a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com InitialScaledStartValuesNegativeExponentNegativePower( 5904a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com v, estimated_power, need_boundary_deltas, 5914a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator, denominator, delta_minus, delta_plus); 5924a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 5934a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 5944a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5954a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 5964a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// This routine multiplies numerator/denominator so that its values lies in the 5974a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// range 1-10. That is after a call to this function we have: 5984a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// 1 <= (numerator + delta_plus) /denominator < 10. 5994a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Let numerator the input before modification and numerator' the argument 6004a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// after modification, then the output-parameter decimal_point is such that 6014a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// numerator / denominator * 10^estimated_power == 6024a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// numerator' / denominator' * 10^(decimal_point - 1) 6034a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// In some cases estimated_power was too low, and this is already the case. We 6044a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k == 6054a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// estimated_power) but do not touch the numerator or denominator. 6064a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com// Otherwise the routine multiplies the numerator and the deltas by 10. 6074a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.comstatic void FixupMultiply10(int estimated_power, bool is_even, 6084a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com int* decimal_point, 6094a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* numerator, Bignum* denominator, 6104a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com Bignum* delta_minus, Bignum* delta_plus) { 6114a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com bool in_range; 6124a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (is_even) { 6134a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // For IEEE doubles half-way cases (in decimal system numbers ending with 5) 6144a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // are rounded to the closest floating-point number with even significand. 6154a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0; 6164a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 6174a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0; 6184a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 6194a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (in_range) { 6204a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // Since numerator + delta_plus >= denominator we already have 6214a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com // 1 <= numerator/denominator < 10. Simply update the estimated_power. 6224a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *decimal_point = estimated_power + 1; 6234a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 6244a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com *decimal_point = estimated_power; 6254a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com numerator->Times10(); 6264a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com if (Bignum::Equal(*delta_minus, *delta_plus)) { 6274a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->Times10(); 6284a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->AssignBignum(*delta_minus); 6294a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } else { 6304a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_minus->Times10(); 6314a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com delta_plus->Times10(); 6324a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 6334a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com } 6344a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} 6354a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com 6364a6c3279070e8f133607a74c08d8c08ac394ab98erik.corry@gmail.com} } // namespace v8::internal 637