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 |