1// Copyright 2010 the V8 project authors. All rights reserved. 2// Redistribution and use in source and binary forms, with or without 3// modification, are permitted provided that the following conditions are 4// met: 5// 6// * Redistributions of source code must retain the above copyright 7// notice, this list of conditions and the following disclaimer. 8// * Redistributions in binary form must reproduce the above 9// copyright notice, this list of conditions and the following 10// disclaimer in the documentation and/or other materials provided 11// with the distribution. 12// * Neither the name of Google Inc. nor the names of its 13// contributors may be used to endorse or promote products derived 14// from this software without specific prior written permission. 15// 16// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 17// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 18// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 19// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 20// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 21// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 22// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 26// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 28#include "config.h" 29 30#include <math.h> 31 32#include "fixed-dtoa.h" 33#include "double.h" 34 35namespace WTF { 36 37namespace double_conversion { 38 39 // Represents a 128bit type. This class should be replaced by a native type on 40 // platforms that support 128bit integers. 41 class UInt128 { 42 public: 43 UInt128() : high_bits_(0), low_bits_(0) { } 44 UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { } 45 46 void Multiply(uint32_t multiplicand) { 47 uint64_t accumulator; 48 49 accumulator = (low_bits_ & kMask32) * multiplicand; 50 uint32_t part = static_cast<uint32_t>(accumulator & kMask32); 51 accumulator >>= 32; 52 accumulator = accumulator + (low_bits_ >> 32) * multiplicand; 53 low_bits_ = (accumulator << 32) + part; 54 accumulator >>= 32; 55 accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; 56 part = static_cast<uint32_t>(accumulator & kMask32); 57 accumulator >>= 32; 58 accumulator = accumulator + (high_bits_ >> 32) * multiplicand; 59 high_bits_ = (accumulator << 32) + part; 60 ASSERT((accumulator >> 32) == 0); 61 } 62 63 void Shift(int shift_amount) { 64 ASSERT(-64 <= shift_amount && shift_amount <= 64); 65 if (shift_amount == 0) { 66 return; 67 } else if (shift_amount == -64) { 68 high_bits_ = low_bits_; 69 low_bits_ = 0; 70 } else if (shift_amount == 64) { 71 low_bits_ = high_bits_; 72 high_bits_ = 0; 73 } else if (shift_amount <= 0) { 74 high_bits_ <<= -shift_amount; 75 high_bits_ += low_bits_ >> (64 + shift_amount); 76 low_bits_ <<= -shift_amount; 77 } else { 78 low_bits_ >>= shift_amount; 79 low_bits_ += high_bits_ << (64 - shift_amount); 80 high_bits_ >>= shift_amount; 81 } 82 } 83 84 // Modifies *this to *this MOD (2^power). 85 // Returns *this DIV (2^power). 86 int DivModPowerOf2(int power) { 87 if (power >= 64) { 88 int result = static_cast<int>(high_bits_ >> (power - 64)); 89 high_bits_ -= static_cast<uint64_t>(result) << (power - 64); 90 return result; 91 } else { 92 uint64_t part_low = low_bits_ >> power; 93 uint64_t part_high = high_bits_ << (64 - power); 94 int result = static_cast<int>(part_low + part_high); 95 high_bits_ = 0; 96 low_bits_ -= part_low << power; 97 return result; 98 } 99 } 100 101 bool IsZero() const { 102 return high_bits_ == 0 && low_bits_ == 0; 103 } 104 105 int BitAt(int position) { 106 if (position >= 64) { 107 return static_cast<int>(high_bits_ >> (position - 64)) & 1; 108 } else { 109 return static_cast<int>(low_bits_ >> position) & 1; 110 } 111 } 112 113 private: 114 static const uint64_t kMask32 = 0xFFFFFFFF; 115 // Value == (high_bits_ << 64) + low_bits_ 116 uint64_t high_bits_; 117 uint64_t low_bits_; 118 }; 119 120 121 static const int kDoubleSignificandSize = 53; // Includes the hidden bit. 122 123 124 static void FillDigits32FixedLength(uint32_t number, int requested_length, 125 BufferReference<char> buffer, int* length) { 126 for (int i = requested_length - 1; i >= 0; --i) { 127 buffer[(*length) + i] = '0' + number % 10; 128 number /= 10; 129 } 130 *length += requested_length; 131 } 132 133 134 static void FillDigits32(uint32_t number, BufferReference<char> buffer, int* length) { 135 int number_length = 0; 136 // We fill the digits in reverse order and exchange them afterwards. 137 while (number != 0) { 138 int digit = number % 10; 139 number /= 10; 140 buffer[(*length) + number_length] = '0' + digit; 141 number_length++; 142 } 143 // Exchange the digits. 144 int i = *length; 145 int j = *length + number_length - 1; 146 while (i < j) { 147 char tmp = buffer[i]; 148 buffer[i] = buffer[j]; 149 buffer[j] = tmp; 150 i++; 151 j--; 152 } 153 *length += number_length; 154 } 155 156 157 static void FillDigits64FixedLength(uint64_t number, int requested_length, 158 BufferReference<char> buffer, int* length) { 159 UNUSED_PARAM(requested_length); 160 const uint32_t kTen7 = 10000000; 161 // For efficiency cut the number into 3 uint32_t parts, and print those. 162 uint32_t part2 = static_cast<uint32_t>(number % kTen7); 163 number /= kTen7; 164 uint32_t part1 = static_cast<uint32_t>(number % kTen7); 165 uint32_t part0 = static_cast<uint32_t>(number / kTen7); 166 167 FillDigits32FixedLength(part0, 3, buffer, length); 168 FillDigits32FixedLength(part1, 7, buffer, length); 169 FillDigits32FixedLength(part2, 7, buffer, length); 170 } 171 172 173 static void FillDigits64(uint64_t number, BufferReference<char> buffer, int* length) { 174 const uint32_t kTen7 = 10000000; 175 // For efficiency cut the number into 3 uint32_t parts, and print those. 176 uint32_t part2 = static_cast<uint32_t>(number % kTen7); 177 number /= kTen7; 178 uint32_t part1 = static_cast<uint32_t>(number % kTen7); 179 uint32_t part0 = static_cast<uint32_t>(number / kTen7); 180 181 if (part0 != 0) { 182 FillDigits32(part0, buffer, length); 183 FillDigits32FixedLength(part1, 7, buffer, length); 184 FillDigits32FixedLength(part2, 7, buffer, length); 185 } else if (part1 != 0) { 186 FillDigits32(part1, buffer, length); 187 FillDigits32FixedLength(part2, 7, buffer, length); 188 } else { 189 FillDigits32(part2, buffer, length); 190 } 191 } 192 193 194 static void RoundUp(BufferReference<char> buffer, int* length, int* decimal_point) { 195 // An empty buffer represents 0. 196 if (*length == 0) { 197 buffer[0] = '1'; 198 *decimal_point = 1; 199 *length = 1; 200 return; 201 } 202 // Round the last digit until we either have a digit that was not '9' or until 203 // we reached the first digit. 204 buffer[(*length) - 1]++; 205 for (int i = (*length) - 1; i > 0; --i) { 206 if (buffer[i] != '0' + 10) { 207 return; 208 } 209 buffer[i] = '0'; 210 buffer[i - 1]++; 211 } 212 // If the first digit is now '0' + 10, we would need to set it to '0' and add 213 // a '1' in front. However we reach the first digit only if all following 214 // digits had been '9' before rounding up. Now all trailing digits are '0' and 215 // we simply switch the first digit to '1' and update the decimal-point 216 // (indicating that the point is now one digit to the right). 217 if (buffer[0] == '0' + 10) { 218 buffer[0] = '1'; 219 (*decimal_point)++; 220 } 221 } 222 223 224 // The given fractionals number represents a fixed-point number with binary 225 // point at bit (-exponent). 226 // Preconditions: 227 // -128 <= exponent <= 0. 228 // 0 <= fractionals * 2^exponent < 1 229 // The buffer holds the result. 230 // The function will round its result. During the rounding-process digits not 231 // generated by this function might be updated, and the decimal-point variable 232 // might be updated. If this function generates the digits 99 and the buffer 233 // already contained "199" (thus yielding a buffer of "19999") then a 234 // rounding-up will change the contents of the buffer to "20000". 235 static void FillFractionals(uint64_t fractionals, int exponent, 236 int fractional_count, BufferReference<char> buffer, 237 int* length, int* decimal_point) { 238 ASSERT(-128 <= exponent && exponent <= 0); 239 // 'fractionals' is a fixed-point number, with binary point at bit 240 // (-exponent). Inside the function the non-converted remainder of fractionals 241 // is a fixed-point number, with binary point at bit 'point'. 242 if (-exponent <= 64) { 243 // One 64 bit number is sufficient. 244 ASSERT(fractionals >> 56 == 0); 245 int point = -exponent; 246 for (int i = 0; i < fractional_count; ++i) { 247 if (fractionals == 0) break; 248 // Instead of multiplying by 10 we multiply by 5 and adjust the point 249 // location. This way the fractionals variable will not overflow. 250 // Invariant at the beginning of the loop: fractionals < 2^point. 251 // Initially we have: point <= 64 and fractionals < 2^56 252 // After each iteration the point is decremented by one. 253 // Note that 5^3 = 125 < 128 = 2^7. 254 // Therefore three iterations of this loop will not overflow fractionals 255 // (even without the subtraction at the end of the loop body). At this 256 // time point will satisfy point <= 61 and therefore fractionals < 2^point 257 // and any further multiplication of fractionals by 5 will not overflow. 258 fractionals *= 5; 259 point--; 260 int digit = static_cast<int>(fractionals >> point); 261 buffer[*length] = '0' + digit; 262 (*length)++; 263 fractionals -= static_cast<uint64_t>(digit) << point; 264 } 265 // If the first bit after the point is set we have to round up. 266 if (((fractionals >> (point - 1)) & 1) == 1) { 267 RoundUp(buffer, length, decimal_point); 268 } 269 } else { // We need 128 bits. 270 ASSERT(64 < -exponent && -exponent <= 128); 271 UInt128 fractionals128 = UInt128(fractionals, 0); 272 fractionals128.Shift(-exponent - 64); 273 int point = 128; 274 for (int i = 0; i < fractional_count; ++i) { 275 if (fractionals128.IsZero()) break; 276 // As before: instead of multiplying by 10 we multiply by 5 and adjust the 277 // point location. 278 // This multiplication will not overflow for the same reasons as before. 279 fractionals128.Multiply(5); 280 point--; 281 int digit = fractionals128.DivModPowerOf2(point); 282 buffer[*length] = '0' + digit; 283 (*length)++; 284 } 285 if (fractionals128.BitAt(point - 1) == 1) { 286 RoundUp(buffer, length, decimal_point); 287 } 288 } 289 } 290 291 292 // Removes leading and trailing zeros. 293 // If leading zeros are removed then the decimal point position is adjusted. 294 static void TrimZeros(BufferReference<char> buffer, int* length, int* decimal_point) { 295 while (*length > 0 && buffer[(*length) - 1] == '0') { 296 (*length)--; 297 } 298 int first_non_zero = 0; 299 while (first_non_zero < *length && buffer[first_non_zero] == '0') { 300 first_non_zero++; 301 } 302 if (first_non_zero != 0) { 303 for (int i = first_non_zero; i < *length; ++i) { 304 buffer[i - first_non_zero] = buffer[i]; 305 } 306 *length -= first_non_zero; 307 *decimal_point -= first_non_zero; 308 } 309 } 310 311 312 bool FastFixedDtoa(double v, 313 int fractional_count, 314 BufferReference<char> buffer, 315 int* length, 316 int* decimal_point) { 317 const uint32_t kMaxUInt32 = 0xFFFFFFFF; 318 uint64_t significand = Double(v).Significand(); 319 int exponent = Double(v).Exponent(); 320 // v = significand * 2^exponent (with significand a 53bit integer). 321 // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we 322 // don't know how to compute the representation. 2^73 ~= 9.5*10^21. 323 // If necessary this limit could probably be increased, but we don't need 324 // more. 325 if (exponent > 20) return false; 326 if (fractional_count > 20) return false; 327 *length = 0; 328 // At most kDoubleSignificandSize bits of the significand are non-zero. 329 // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero 330 // bits: 0..11*..0xxx..53*..xx 331 if (exponent + kDoubleSignificandSize > 64) { 332 // The exponent must be > 11. 333 // 334 // We know that v = significand * 2^exponent. 335 // And the exponent > 11. 336 // We simplify the task by dividing v by 10^17. 337 // The quotient delivers the first digits, and the remainder fits into a 64 338 // bit number. 339 // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. 340 const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17 341 uint64_t divisor = kFive17; 342 int divisor_power = 17; 343 uint64_t dividend = significand; 344 uint32_t quotient; 345 uint64_t remainder; 346 // Let v = f * 2^e with f == significand and e == exponent. 347 // Then need q (quotient) and r (remainder) as follows: 348 // v = q * 10^17 + r 349 // f * 2^e = q * 10^17 + r 350 // f * 2^e = q * 5^17 * 2^17 + r 351 // If e > 17 then 352 // f * 2^(e-17) = q * 5^17 + r/2^17 353 // else 354 // f = q * 5^17 * 2^(17-e) + r/2^e 355 if (exponent > divisor_power) { 356 // We only allow exponents of up to 20 and therefore (17 - e) <= 3 357 dividend <<= exponent - divisor_power; 358 quotient = static_cast<uint32_t>(dividend / divisor); 359 remainder = (dividend % divisor) << divisor_power; 360 } else { 361 divisor <<= divisor_power - exponent; 362 quotient = static_cast<uint32_t>(dividend / divisor); 363 remainder = (dividend % divisor) << exponent; 364 } 365 FillDigits32(quotient, buffer, length); 366 FillDigits64FixedLength(remainder, divisor_power, buffer, length); 367 *decimal_point = *length; 368 } else if (exponent >= 0) { 369 // 0 <= exponent <= 11 370 significand <<= exponent; 371 FillDigits64(significand, buffer, length); 372 *decimal_point = *length; 373 } else if (exponent > -kDoubleSignificandSize) { 374 // We have to cut the number. 375 uint64_t integrals = significand >> -exponent; 376 uint64_t fractionals = significand - (integrals << -exponent); 377 if (integrals > kMaxUInt32) { 378 FillDigits64(integrals, buffer, length); 379 } else { 380 FillDigits32(static_cast<uint32_t>(integrals), buffer, length); 381 } 382 *decimal_point = *length; 383 FillFractionals(fractionals, exponent, fractional_count, 384 buffer, length, decimal_point); 385 } else if (exponent < -128) { 386 // This configuration (with at most 20 digits) means that all digits must be 387 // 0. 388 ASSERT(fractional_count <= 20); 389 buffer[0] = '\0'; 390 *length = 0; 391 *decimal_point = -fractional_count; 392 } else { 393 *decimal_point = 0; 394 FillFractionals(significand, exponent, fractional_count, 395 buffer, length, decimal_point); 396 } 397 TrimZeros(buffer, length, decimal_point); 398 buffer[*length] = '\0'; 399 if ((*length) == 0) { 400 // The string is empty and the decimal_point thus has no importance. Mimick 401 // Gay's dtoa and and set it to -fractional_count. 402 *decimal_point = -fractional_count; 403 } 404 return true; 405 } 406 407} // namespace double_conversion 408 409} // namespace WTF 410