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