Kristian Monsen | 25f6136 | 2010-05-21 11:50:48 +0100 | [diff] [blame] | 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 <math.h> |
| 29 | |
| 30 | #include "v8.h" |
| 31 | |
| 32 | #include "double.h" |
| 33 | #include "fixed-dtoa.h" |
| 34 | |
| 35 | namespace v8 { |
| 36 | namespace internal { |
| 37 | |
| 38 | // Represents a 128bit type. This class should be replaced by a native type on |
| 39 | // platforms that support 128bit integers. |
| 40 | class UInt128 { |
| 41 | public: |
| 42 | UInt128() : high_bits_(0), low_bits_(0) { } |
| 43 | UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { } |
| 44 | |
| 45 | void Multiply(uint32_t multiplicand) { |
| 46 | uint64_t accumulator; |
| 47 | |
| 48 | accumulator = (low_bits_ & kMask32) * multiplicand; |
| 49 | uint32_t part = static_cast<uint32_t>(accumulator & kMask32); |
| 50 | accumulator >>= 32; |
| 51 | accumulator = accumulator + (low_bits_ >> 32) * multiplicand; |
| 52 | low_bits_ = (accumulator << 32) + part; |
| 53 | accumulator >>= 32; |
| 54 | accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; |
| 55 | part = static_cast<uint32_t>(accumulator & kMask32); |
| 56 | accumulator >>= 32; |
| 57 | accumulator = accumulator + (high_bits_ >> 32) * multiplicand; |
| 58 | high_bits_ = (accumulator << 32) + part; |
| 59 | ASSERT((accumulator >> 32) == 0); |
| 60 | } |
| 61 | |
| 62 | void Shift(int shift_amount) { |
| 63 | ASSERT(-64 <= shift_amount && shift_amount <= 64); |
| 64 | if (shift_amount == 0) { |
| 65 | return; |
| 66 | } else if (shift_amount == -64) { |
| 67 | high_bits_ = low_bits_; |
| 68 | low_bits_ = 0; |
| 69 | } else if (shift_amount == 64) { |
| 70 | low_bits_ = high_bits_; |
| 71 | high_bits_ = 0; |
| 72 | } else if (shift_amount <= 0) { |
| 73 | high_bits_ <<= -shift_amount; |
| 74 | high_bits_ += low_bits_ >> (64 + shift_amount); |
| 75 | low_bits_ <<= -shift_amount; |
| 76 | } else { |
| 77 | low_bits_ >>= shift_amount; |
| 78 | low_bits_ += high_bits_ << (64 - shift_amount); |
| 79 | high_bits_ >>= shift_amount; |
| 80 | } |
| 81 | } |
| 82 | |
| 83 | // Modifies *this to *this MOD (2^power). |
| 84 | // Returns *this DIV (2^power). |
| 85 | int DivModPowerOf2(int power) { |
| 86 | if (power >= 64) { |
| 87 | int result = static_cast<int>(high_bits_ >> (power - 64)); |
| 88 | high_bits_ -= static_cast<uint64_t>(result) << (power - 64); |
| 89 | return result; |
| 90 | } else { |
| 91 | uint64_t part_low = low_bits_ >> power; |
| 92 | uint64_t part_high = high_bits_ << (64 - power); |
| 93 | int result = static_cast<int>(part_low + part_high); |
| 94 | high_bits_ = 0; |
| 95 | low_bits_ -= part_low << power; |
| 96 | return result; |
| 97 | } |
| 98 | } |
| 99 | |
| 100 | bool IsZero() const { |
| 101 | return high_bits_ == 0 && low_bits_ == 0; |
| 102 | } |
| 103 | |
| 104 | int BitAt(int position) { |
| 105 | if (position >= 64) { |
| 106 | return static_cast<int>(high_bits_ >> (position - 64)) & 1; |
| 107 | } else { |
| 108 | return static_cast<int>(low_bits_ >> position) & 1; |
| 109 | } |
| 110 | } |
| 111 | |
| 112 | private: |
| 113 | static const uint64_t kMask32 = 0xFFFFFFFF; |
| 114 | // Value == (high_bits_ << 64) + low_bits_ |
| 115 | uint64_t high_bits_; |
| 116 | uint64_t low_bits_; |
| 117 | }; |
| 118 | |
| 119 | |
| 120 | static const int kDoubleSignificandSize = 53; // Includes the hidden bit. |
| 121 | |
| 122 | |
| 123 | static void FillDigits32FixedLength(uint32_t number, int requested_length, |
| 124 | Vector<char> buffer, int* length) { |
| 125 | for (int i = requested_length - 1; i >= 0; --i) { |
| 126 | buffer[(*length) + i] = '0' + number % 10; |
| 127 | number /= 10; |
| 128 | } |
| 129 | *length += requested_length; |
| 130 | } |
| 131 | |
| 132 | |
| 133 | static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) { |
| 134 | int number_length = 0; |
| 135 | // We fill the digits in reverse order and exchange them afterwards. |
| 136 | while (number != 0) { |
| 137 | int digit = number % 10; |
| 138 | number /= 10; |
| 139 | buffer[(*length) + number_length] = '0' + digit; |
| 140 | number_length++; |
| 141 | } |
| 142 | // Exchange the digits. |
| 143 | int i = *length; |
| 144 | int j = *length + number_length - 1; |
| 145 | while (i < j) { |
| 146 | char tmp = buffer[i]; |
| 147 | buffer[i] = buffer[j]; |
| 148 | buffer[j] = tmp; |
| 149 | i++; |
| 150 | j--; |
| 151 | } |
| 152 | *length += number_length; |
| 153 | } |
| 154 | |
| 155 | |
| 156 | static void FillDigits64FixedLength(uint64_t number, int requested_length, |
| 157 | Vector<char> buffer, int* length) { |
| 158 | const uint32_t kTen7 = 10000000; |
| 159 | // For efficiency cut the number into 3 uint32_t parts, and print those. |
| 160 | uint32_t part2 = static_cast<uint32_t>(number % kTen7); |
| 161 | number /= kTen7; |
| 162 | uint32_t part1 = static_cast<uint32_t>(number % kTen7); |
| 163 | uint32_t part0 = static_cast<uint32_t>(number / kTen7); |
| 164 | |
| 165 | FillDigits32FixedLength(part0, 3, buffer, length); |
| 166 | FillDigits32FixedLength(part1, 7, buffer, length); |
| 167 | FillDigits32FixedLength(part2, 7, buffer, length); |
| 168 | } |
| 169 | |
| 170 | |
| 171 | static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) { |
| 172 | const uint32_t kTen7 = 10000000; |
| 173 | // For efficiency cut the number into 3 uint32_t parts, and print those. |
| 174 | uint32_t part2 = static_cast<uint32_t>(number % kTen7); |
| 175 | number /= kTen7; |
| 176 | uint32_t part1 = static_cast<uint32_t>(number % kTen7); |
| 177 | uint32_t part0 = static_cast<uint32_t>(number / kTen7); |
| 178 | |
| 179 | if (part0 != 0) { |
| 180 | FillDigits32(part0, buffer, length); |
| 181 | FillDigits32FixedLength(part1, 7, buffer, length); |
| 182 | FillDigits32FixedLength(part2, 7, buffer, length); |
| 183 | } else if (part1 != 0) { |
| 184 | FillDigits32(part1, buffer, length); |
| 185 | FillDigits32FixedLength(part2, 7, buffer, length); |
| 186 | } else { |
| 187 | FillDigits32(part2, buffer, length); |
| 188 | } |
| 189 | } |
| 190 | |
| 191 | |
| 192 | static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { |
| 193 | // An empty buffer represents 0. |
| 194 | if (*length == 0) { |
| 195 | buffer[0] = '1'; |
| 196 | *decimal_point = 1; |
| 197 | *length = 1; |
| 198 | return; |
| 199 | } |
| 200 | // Round the last digit until we either have a digit that was not '9' or until |
| 201 | // we reached the first digit. |
| 202 | buffer[(*length) - 1]++; |
| 203 | for (int i = (*length) - 1; i > 0; --i) { |
| 204 | if (buffer[i] != '0' + 10) { |
| 205 | return; |
| 206 | } |
| 207 | buffer[i] = '0'; |
| 208 | buffer[i - 1]++; |
| 209 | } |
| 210 | // If the first digit is now '0' + 10, we would need to set it to '0' and add |
| 211 | // a '1' in front. However we reach the first digit only if all following |
| 212 | // digits had been '9' before rounding up. Now all trailing digits are '0' and |
| 213 | // we simply switch the first digit to '1' and update the decimal-point |
| 214 | // (indicating that the point is now one digit to the right). |
| 215 | if (buffer[0] == '0' + 10) { |
| 216 | buffer[0] = '1'; |
| 217 | (*decimal_point)++; |
| 218 | } |
| 219 | } |
| 220 | |
| 221 | |
| 222 | // The given fractionals number represents a fixed-point number with binary |
| 223 | // point at bit (-exponent). |
| 224 | // Preconditions: |
| 225 | // -128 <= exponent <= 0. |
| 226 | // 0 <= fractionals * 2^exponent < 1 |
| 227 | // The buffer holds the result. |
| 228 | // The function will round its result. During the rounding-process digits not |
| 229 | // generated by this function might be updated, and the decimal-point variable |
| 230 | // might be updated. If this function generates the digits 99 and the buffer |
| 231 | // already contained "199" (thus yielding a buffer of "19999") then a |
| 232 | // rounding-up will change the contents of the buffer to "20000". |
| 233 | static void FillFractionals(uint64_t fractionals, int exponent, |
| 234 | int fractional_count, Vector<char> buffer, |
| 235 | int* length, int* decimal_point) { |
| 236 | ASSERT(-128 <= exponent && exponent <= 0); |
| 237 | // 'fractionals' is a fixed-point number, with binary point at bit |
| 238 | // (-exponent). Inside the function the non-converted remainder of fractionals |
| 239 | // is a fixed-point number, with binary point at bit 'point'. |
| 240 | if (-exponent <= 64) { |
| 241 | // One 64 bit number is sufficient. |
| 242 | ASSERT(fractionals >> 56 == 0); |
| 243 | int point = -exponent; |
| 244 | for (int i = 0; i < fractional_count; ++i) { |
| 245 | if (fractionals == 0) break; |
| 246 | // Instead of multiplying by 10 we multiply by 5 and adjust the point |
| 247 | // location. This way the fractionals variable will not overflow. |
| 248 | // Invariant at the beginning of the loop: fractionals < 2^point. |
| 249 | // Initially we have: point <= 64 and fractionals < 2^56 |
| 250 | // After each iteration the point is decremented by one. |
| 251 | // Note that 5^3 = 125 < 128 = 2^7. |
| 252 | // Therefore three iterations of this loop will not overflow fractionals |
| 253 | // (even without the subtraction at the end of the loop body). At this |
| 254 | // time point will satisfy point <= 61 and therefore fractionals < 2^point |
| 255 | // and any further multiplication of fractionals by 5 will not overflow. |
| 256 | fractionals *= 5; |
| 257 | point--; |
| 258 | int digit = static_cast<int>(fractionals >> point); |
| 259 | buffer[*length] = '0' + digit; |
| 260 | (*length)++; |
| 261 | fractionals -= static_cast<uint64_t>(digit) << point; |
| 262 | } |
| 263 | // If the first bit after the point is set we have to round up. |
| 264 | if (((fractionals >> (point - 1)) & 1) == 1) { |
| 265 | RoundUp(buffer, length, decimal_point); |
| 266 | } |
| 267 | } else { // We need 128 bits. |
| 268 | ASSERT(64 < -exponent && -exponent <= 128); |
| 269 | UInt128 fractionals128 = UInt128(fractionals, 0); |
| 270 | fractionals128.Shift(-exponent - 64); |
| 271 | int point = 128; |
| 272 | for (int i = 0; i < fractional_count; ++i) { |
| 273 | if (fractionals128.IsZero()) break; |
| 274 | // As before: instead of multiplying by 10 we multiply by 5 and adjust the |
| 275 | // point location. |
| 276 | // This multiplication will not overflow for the same reasons as before. |
| 277 | fractionals128.Multiply(5); |
| 278 | point--; |
| 279 | int digit = fractionals128.DivModPowerOf2(point); |
| 280 | buffer[*length] = '0' + digit; |
| 281 | (*length)++; |
| 282 | } |
| 283 | if (fractionals128.BitAt(point - 1) == 1) { |
| 284 | RoundUp(buffer, length, decimal_point); |
| 285 | } |
| 286 | } |
| 287 | } |
| 288 | |
| 289 | |
| 290 | // Removes leading and trailing zeros. |
| 291 | // If leading zeros are removed then the decimal point position is adjusted. |
| 292 | static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) { |
| 293 | while (*length > 0 && buffer[(*length) - 1] == '0') { |
| 294 | (*length)--; |
| 295 | } |
| 296 | int first_non_zero = 0; |
| 297 | while (first_non_zero < *length && buffer[first_non_zero] == '0') { |
| 298 | first_non_zero++; |
| 299 | } |
| 300 | if (first_non_zero != 0) { |
| 301 | for (int i = first_non_zero; i < *length; ++i) { |
| 302 | buffer[i - first_non_zero] = buffer[i]; |
| 303 | } |
| 304 | *length -= first_non_zero; |
| 305 | *decimal_point -= first_non_zero; |
| 306 | } |
| 307 | } |
| 308 | |
| 309 | |
| 310 | bool FastFixedDtoa(double v, |
| 311 | int fractional_count, |
| 312 | Vector<char> buffer, |
| 313 | int* length, |
| 314 | int* decimal_point) { |
| 315 | const uint32_t kMaxUInt32 = 0xFFFFFFFF; |
| 316 | uint64_t significand = Double(v).Significand(); |
| 317 | int exponent = Double(v).Exponent(); |
| 318 | // v = significand * 2^exponent (with significand a 53bit integer). |
| 319 | // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we |
| 320 | // don't know how to compute the representation. 2^73 ~= 9.5*10^21. |
| 321 | // If necessary this limit could probably be increased, but we don't need |
| 322 | // more. |
| 323 | if (exponent > 20) return false; |
| 324 | if (fractional_count > 20) return false; |
| 325 | *length = 0; |
| 326 | // At most kDoubleSignificandSize bits of the significand are non-zero. |
| 327 | // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero |
| 328 | // bits: 0..11*..0xxx..53*..xx |
| 329 | if (exponent + kDoubleSignificandSize > 64) { |
| 330 | // The exponent must be > 11. |
| 331 | // |
| 332 | // We know that v = significand * 2^exponent. |
| 333 | // And the exponent > 11. |
| 334 | // We simplify the task by dividing v by 10^17. |
| 335 | // The quotient delivers the first digits, and the remainder fits into a 64 |
| 336 | // bit number. |
| 337 | // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. |
| 338 | const uint64_t kFive17 = V8_2PART_UINT64_C(0xB1, A2BC2EC5); // 5^17 |
| 339 | uint64_t divisor = kFive17; |
| 340 | int divisor_power = 17; |
| 341 | uint64_t dividend = significand; |
| 342 | uint32_t quotient; |
| 343 | uint64_t remainder; |
| 344 | // Let v = f * 2^e with f == significand and e == exponent. |
| 345 | // Then need q (quotient) and r (remainder) as follows: |
| 346 | // v = q * 10^17 + r |
| 347 | // f * 2^e = q * 10^17 + r |
| 348 | // f * 2^e = q * 5^17 * 2^17 + r |
| 349 | // If e > 17 then |
| 350 | // f * 2^(e-17) = q * 5^17 + r/2^17 |
| 351 | // else |
| 352 | // f = q * 5^17 * 2^(17-e) + r/2^e |
| 353 | if (exponent > divisor_power) { |
| 354 | // We only allow exponents of up to 20 and therefore (17 - e) <= 3 |
| 355 | dividend <<= exponent - divisor_power; |
| 356 | quotient = static_cast<uint32_t>(dividend / divisor); |
| 357 | remainder = (dividend % divisor) << divisor_power; |
| 358 | } else { |
| 359 | divisor <<= divisor_power - exponent; |
| 360 | quotient = static_cast<uint32_t>(dividend / divisor); |
| 361 | remainder = (dividend % divisor) << exponent; |
| 362 | } |
| 363 | FillDigits32(quotient, buffer, length); |
| 364 | FillDigits64FixedLength(remainder, divisor_power, buffer, length); |
| 365 | *decimal_point = *length; |
| 366 | } else if (exponent >= 0) { |
| 367 | // 0 <= exponent <= 11 |
| 368 | significand <<= exponent; |
| 369 | FillDigits64(significand, buffer, length); |
| 370 | *decimal_point = *length; |
| 371 | } else if (exponent > -kDoubleSignificandSize) { |
| 372 | // We have to cut the number. |
| 373 | uint64_t integrals = significand >> -exponent; |
| 374 | uint64_t fractionals = significand - (integrals << -exponent); |
| 375 | if (integrals > kMaxUInt32) { |
| 376 | FillDigits64(integrals, buffer, length); |
| 377 | } else { |
| 378 | FillDigits32(static_cast<uint32_t>(integrals), buffer, length); |
| 379 | } |
| 380 | *decimal_point = *length; |
| 381 | FillFractionals(fractionals, exponent, fractional_count, |
| 382 | buffer, length, decimal_point); |
| 383 | } else if (exponent < -128) { |
| 384 | // This configuration (with at most 20 digits) means that all digits must be |
| 385 | // 0. |
| 386 | ASSERT(fractional_count <= 20); |
| 387 | buffer[0] = '\0'; |
| 388 | *length = 0; |
| 389 | *decimal_point = -fractional_count; |
| 390 | } else { |
| 391 | *decimal_point = 0; |
| 392 | FillFractionals(significand, exponent, fractional_count, |
| 393 | buffer, length, decimal_point); |
| 394 | } |
| 395 | TrimZeros(buffer, length, decimal_point); |
| 396 | buffer[*length] = '\0'; |
| 397 | if ((*length) == 0) { |
| 398 | // The string is empty and the decimal_point thus has no importance. Mimick |
| 399 | // Gay's dtoa and and set it to -fractional_count. |
| 400 | *decimal_point = -fractional_count; |
| 401 | } |
| 402 | return true; |
| 403 | } |
| 404 | |
| 405 | } } // namespace v8::internal |