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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 |
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29 | 29 |
30 #include <math.h> | 30 #include <math.h> |
31 | 31 |
32 #include "double.h" | 32 #include "double.h" |
33 #include "fixed-dtoa.h" | 33 #include "fixed-dtoa.h" |
34 #include "wtf/UnusedParam.h" | 34 #include "wtf/UnusedParam.h" |
35 | 35 |
36 namespace WTF { | 36 namespace WTF { |
37 | 37 |
38 namespace double_conversion { | 38 namespace double_conversion { |
39 | 39 |
40 // Represents a 128bit type. This class should be replaced by a native type
on | 40 // Represents a 128bit type. This class should be replaced by a native type
on |
41 // platforms that support 128bit integers. | 41 // platforms that support 128bit integers. |
42 class UInt128 { | 42 class UInt128 { |
43 public: | 43 public: |
44 UInt128() : high_bits_(0), low_bits_(0) { } | 44 UInt128() : high_bits_(0), low_bits_(0) { } |
45 UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low)
{ } | 45 UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low)
{ } |
46 | 46 |
47 void Multiply(uint32_t multiplicand) { | 47 void Multiply(uint32_t multiplicand) { |
48 uint64_t accumulator; | 48 uint64_t accumulator; |
49 | 49 |
50 accumulator = (low_bits_ & kMask32) * multiplicand; | 50 accumulator = (low_bits_ & kMask32) * multiplicand; |
51 uint32_t part = static_cast<uint32_t>(accumulator & kMask32); | 51 uint32_t part = static_cast<uint32_t>(accumulator & kMask32); |
52 accumulator >>= 32; | 52 accumulator >>= 32; |
53 accumulator = accumulator + (low_bits_ >> 32) * multiplicand; | 53 accumulator = accumulator + (low_bits_ >> 32) * multiplicand; |
54 low_bits_ = (accumulator << 32) + part; | 54 low_bits_ = (accumulator << 32) + part; |
55 accumulator >>= 32; | 55 accumulator >>= 32; |
56 accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; | 56 accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; |
57 part = static_cast<uint32_t>(accumulator & kMask32); | 57 part = static_cast<uint32_t>(accumulator & kMask32); |
58 accumulator >>= 32; | 58 accumulator >>= 32; |
59 accumulator = accumulator + (high_bits_ >> 32) * multiplicand; | 59 accumulator = accumulator + (high_bits_ >> 32) * multiplicand; |
60 high_bits_ = (accumulator << 32) + part; | 60 high_bits_ = (accumulator << 32) + part; |
61 ASSERT((accumulator >> 32) == 0); | 61 ASSERT((accumulator >> 32) == 0); |
62 } | 62 } |
63 | 63 |
64 void Shift(int shift_amount) { | 64 void Shift(int shift_amount) { |
65 ASSERT(-64 <= shift_amount && shift_amount <= 64); | 65 ASSERT(-64 <= shift_amount && shift_amount <= 64); |
66 if (shift_amount == 0) { | 66 if (shift_amount == 0) { |
67 return; | 67 return; |
68 } else if (shift_amount == -64) { | 68 } else if (shift_amount == -64) { |
69 high_bits_ = low_bits_; | 69 high_bits_ = low_bits_; |
70 low_bits_ = 0; | 70 low_bits_ = 0; |
71 } else if (shift_amount == 64) { | 71 } else if (shift_amount == 64) { |
72 low_bits_ = high_bits_; | 72 low_bits_ = high_bits_; |
73 high_bits_ = 0; | 73 high_bits_ = 0; |
74 } else if (shift_amount <= 0) { | 74 } else if (shift_amount <= 0) { |
75 high_bits_ <<= -shift_amount; | 75 high_bits_ <<= -shift_amount; |
76 high_bits_ += low_bits_ >> (64 + shift_amount); | 76 high_bits_ += low_bits_ >> (64 + shift_amount); |
77 low_bits_ <<= -shift_amount; | 77 low_bits_ <<= -shift_amount; |
78 } else { | 78 } else { |
79 low_bits_ >>= shift_amount; | 79 low_bits_ >>= shift_amount; |
80 low_bits_ += high_bits_ << (64 - shift_amount); | 80 low_bits_ += high_bits_ << (64 - shift_amount); |
81 high_bits_ >>= shift_amount; | 81 high_bits_ >>= shift_amount; |
82 } | 82 } |
83 } | 83 } |
84 | 84 |
85 // Modifies *this to *this MOD (2^power). | 85 // Modifies *this to *this MOD (2^power). |
86 // Returns *this DIV (2^power). | 86 // Returns *this DIV (2^power). |
87 int DivModPowerOf2(int power) { | 87 int DivModPowerOf2(int power) { |
88 if (power >= 64) { | 88 if (power >= 64) { |
89 int result = static_cast<int>(high_bits_ >> (power - 64)); | 89 int result = static_cast<int>(high_bits_ >> (power - 64)); |
90 high_bits_ -= static_cast<uint64_t>(result) << (power - 64); | 90 high_bits_ -= static_cast<uint64_t>(result) << (power - 64); |
91 return result; | 91 return result; |
92 } else { | 92 } else { |
93 uint64_t part_low = low_bits_ >> power; | 93 uint64_t part_low = low_bits_ >> power; |
94 uint64_t part_high = high_bits_ << (64 - power); | 94 uint64_t part_high = high_bits_ << (64 - power); |
95 int result = static_cast<int>(part_low + part_high); | 95 int result = static_cast<int>(part_low + part_high); |
96 high_bits_ = 0; | 96 high_bits_ = 0; |
97 low_bits_ -= part_low << power; | 97 low_bits_ -= part_low << power; |
98 return result; | 98 return result; |
99 } | 99 } |
100 } | 100 } |
101 | 101 |
102 bool IsZero() const { | 102 bool IsZero() const { |
103 return high_bits_ == 0 && low_bits_ == 0; | 103 return high_bits_ == 0 && low_bits_ == 0; |
104 } | 104 } |
105 | 105 |
106 int BitAt(int position) { | 106 int BitAt(int position) { |
107 if (position >= 64) { | 107 if (position >= 64) { |
108 return static_cast<int>(high_bits_ >> (position - 64)) & 1; | 108 return static_cast<int>(high_bits_ >> (position - 64)) & 1; |
109 } else { | 109 } else { |
110 return static_cast<int>(low_bits_ >> position) & 1; | 110 return static_cast<int>(low_bits_ >> position) & 1; |
111 } | 111 } |
112 } | 112 } |
113 | 113 |
114 private: | 114 private: |
115 static const uint64_t kMask32 = 0xFFFFFFFF; | 115 static const uint64_t kMask32 = 0xFFFFFFFF; |
116 // Value == (high_bits_ << 64) + low_bits_ | 116 // Value == (high_bits_ << 64) + low_bits_ |
117 uint64_t high_bits_; | 117 uint64_t high_bits_; |
118 uint64_t low_bits_; | 118 uint64_t low_bits_; |
119 }; | 119 }; |
120 | 120 |
121 | 121 |
122 static const int kDoubleSignificandSize = 53; // Includes the hidden bit. | 122 static const int kDoubleSignificandSize = 53; // Includes the hidden bit. |
123 | 123 |
124 | 124 |
125 static void FillDigits32FixedLength(uint32_t number, int requested_length, | 125 static void FillDigits32FixedLength(uint32_t number, int requested_length, |
126 Vector<char> buffer, int* length) { | 126 Vector<char> buffer, int* length) { |
127 for (int i = requested_length - 1; i >= 0; --i) { | 127 for (int i = requested_length - 1; i >= 0; --i) { |
128 buffer[(*length) + i] = '0' + number % 10; | 128 buffer[(*length) + i] = '0' + number % 10; |
129 number /= 10; | 129 number /= 10; |
130 } | 130 } |
131 *length += requested_length; | 131 *length += requested_length; |
132 } | 132 } |
133 | 133 |
134 | 134 |
135 static void FillDigits32(uint32_t number, Vector<char> buffer, int* length)
{ | 135 static void FillDigits32(uint32_t number, Vector<char> buffer, int* length)
{ |
136 int number_length = 0; | 136 int number_length = 0; |
137 // We fill the digits in reverse order and exchange them afterwards. | 137 // We fill the digits in reverse order and exchange them afterwards. |
138 while (number != 0) { | 138 while (number != 0) { |
139 int digit = number % 10; | 139 int digit = number % 10; |
140 number /= 10; | 140 number /= 10; |
141 buffer[(*length) + number_length] = '0' + digit; | 141 buffer[(*length) + number_length] = '0' + digit; |
142 number_length++; | 142 number_length++; |
143 } | 143 } |
144 // Exchange the digits. | 144 // Exchange the digits. |
145 int i = *length; | 145 int i = *length; |
146 int j = *length + number_length - 1; | 146 int j = *length + number_length - 1; |
147 while (i < j) { | 147 while (i < j) { |
148 char tmp = buffer[i]; | 148 char tmp = buffer[i]; |
149 buffer[i] = buffer[j]; | 149 buffer[i] = buffer[j]; |
150 buffer[j] = tmp; | 150 buffer[j] = tmp; |
151 i++; | 151 i++; |
152 j--; | 152 j--; |
153 } | 153 } |
154 *length += number_length; | 154 *length += number_length; |
155 } | 155 } |
156 | 156 |
157 | 157 |
158 static void FillDigits64FixedLength(uint64_t number, int requested_length, | 158 static void FillDigits64FixedLength(uint64_t number, int requested_length, |
159 Vector<char> buffer, int* length) { | 159 Vector<char> buffer, int* length) { |
160 UNUSED_PARAM(requested_length); | 160 UNUSED_PARAM(requested_length); |
161 const uint32_t kTen7 = 10000000; | 161 const uint32_t kTen7 = 10000000; |
162 // For efficiency cut the number into 3 uint32_t parts, and print those. | 162 // For efficiency cut the number into 3 uint32_t parts, and print those. |
163 uint32_t part2 = static_cast<uint32_t>(number % kTen7); | 163 uint32_t part2 = static_cast<uint32_t>(number % kTen7); |
164 number /= kTen7; | 164 number /= kTen7; |
165 uint32_t part1 = static_cast<uint32_t>(number % kTen7); | 165 uint32_t part1 = static_cast<uint32_t>(number % kTen7); |
166 uint32_t part0 = static_cast<uint32_t>(number / kTen7); | 166 uint32_t part0 = static_cast<uint32_t>(number / kTen7); |
167 | 167 |
168 FillDigits32FixedLength(part0, 3, buffer, length); | 168 FillDigits32FixedLength(part0, 3, buffer, length); |
169 FillDigits32FixedLength(part1, 7, buffer, length); | 169 FillDigits32FixedLength(part1, 7, buffer, length); |
170 FillDigits32FixedLength(part2, 7, buffer, length); | 170 FillDigits32FixedLength(part2, 7, buffer, length); |
171 } | 171 } |
172 | 172 |
173 | 173 |
174 static void FillDigits64(uint64_t number, Vector<char> buffer, int* length)
{ | 174 static void FillDigits64(uint64_t number, Vector<char> buffer, int* length)
{ |
175 const uint32_t kTen7 = 10000000; | 175 const uint32_t kTen7 = 10000000; |
176 // For efficiency cut the number into 3 uint32_t parts, and print those. | 176 // For efficiency cut the number into 3 uint32_t parts, and print those. |
177 uint32_t part2 = static_cast<uint32_t>(number % kTen7); | 177 uint32_t part2 = static_cast<uint32_t>(number % kTen7); |
178 number /= kTen7; | 178 number /= kTen7; |
179 uint32_t part1 = static_cast<uint32_t>(number % kTen7); | 179 uint32_t part1 = static_cast<uint32_t>(number % kTen7); |
180 uint32_t part0 = static_cast<uint32_t>(number / kTen7); | 180 uint32_t part0 = static_cast<uint32_t>(number / kTen7); |
181 | 181 |
182 if (part0 != 0) { | 182 if (part0 != 0) { |
183 FillDigits32(part0, buffer, length); | 183 FillDigits32(part0, buffer, length); |
184 FillDigits32FixedLength(part1, 7, buffer, length); | 184 FillDigits32FixedLength(part1, 7, buffer, length); |
185 FillDigits32FixedLength(part2, 7, buffer, length); | 185 FillDigits32FixedLength(part2, 7, buffer, length); |
186 } else if (part1 != 0) { | 186 } else if (part1 != 0) { |
187 FillDigits32(part1, buffer, length); | 187 FillDigits32(part1, buffer, length); |
188 FillDigits32FixedLength(part2, 7, buffer, length); | 188 FillDigits32FixedLength(part2, 7, buffer, length); |
189 } else { | 189 } else { |
190 FillDigits32(part2, buffer, length); | 190 FillDigits32(part2, buffer, length); |
191 } | 191 } |
192 } | 192 } |
193 | 193 |
194 | 194 |
195 static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { | 195 static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { |
196 // An empty buffer represents 0. | 196 // An empty buffer represents 0. |
197 if (*length == 0) { | 197 if (*length == 0) { |
198 buffer[0] = '1'; | 198 buffer[0] = '1'; |
199 *decimal_point = 1; | 199 *decimal_point = 1; |
200 *length = 1; | 200 *length = 1; |
201 return; | 201 return; |
202 } | 202 } |
203 // Round the last digit until we either have a digit that was not '9' or
until | 203 // Round the last digit until we either have a digit that was not '9' or
until |
204 // we reached the first digit. | 204 // we reached the first digit. |
205 buffer[(*length) - 1]++; | 205 buffer[(*length) - 1]++; |
206 for (int i = (*length) - 1; i > 0; --i) { | 206 for (int i = (*length) - 1; i > 0; --i) { |
207 if (buffer[i] != '0' + 10) { | 207 if (buffer[i] != '0' + 10) { |
208 return; | 208 return; |
209 } | 209 } |
210 buffer[i] = '0'; | 210 buffer[i] = '0'; |
211 buffer[i - 1]++; | 211 buffer[i - 1]++; |
212 } | 212 } |
213 // If the first digit is now '0' + 10, we would need to set it to '0' an
d add | 213 // If the first digit is now '0' + 10, we would need to set it to '0' an
d add |
214 // a '1' in front. However we reach the first digit only if all followin
g | 214 // a '1' in front. However we reach the first digit only if all followin
g |
215 // digits had been '9' before rounding up. Now all trailing digits are '
0' and | 215 // digits had been '9' before rounding up. Now all trailing digits are '
0' and |
216 // we simply switch the first digit to '1' and update the decimal-point | 216 // we simply switch the first digit to '1' and update the decimal-point |
217 // (indicating that the point is now one digit to the right). | 217 // (indicating that the point is now one digit to the right). |
218 if (buffer[0] == '0' + 10) { | 218 if (buffer[0] == '0' + 10) { |
219 buffer[0] = '1'; | 219 buffer[0] = '1'; |
220 (*decimal_point)++; | 220 (*decimal_point)++; |
221 } | 221 } |
222 } | 222 } |
223 | 223 |
224 | 224 |
225 // The given fractionals number represents a fixed-point number with binary | 225 // The given fractionals number represents a fixed-point number with binary |
226 // point at bit (-exponent). | 226 // point at bit (-exponent). |
227 // Preconditions: | 227 // Preconditions: |
228 // -128 <= exponent <= 0. | 228 // -128 <= exponent <= 0. |
229 // 0 <= fractionals * 2^exponent < 1 | 229 // 0 <= fractionals * 2^exponent < 1 |
230 // The buffer holds the result. | 230 // The buffer holds the result. |
231 // The function will round its result. During the rounding-process digits no
t | 231 // The function will round its result. During the rounding-process digits no
t |
232 // generated by this function might be updated, and the decimal-point variab
le | 232 // generated by this function might be updated, and the decimal-point variab
le |
233 // might be updated. If this function generates the digits 99 and the buffer | 233 // might be updated. If this function generates the digits 99 and the buffer |
234 // already contained "199" (thus yielding a buffer of "19999") then a | 234 // already contained "199" (thus yielding a buffer of "19999") then a |
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281 point--; | 281 point--; |
282 int digit = fractionals128.DivModPowerOf2(point); | 282 int digit = fractionals128.DivModPowerOf2(point); |
283 buffer[*length] = '0' + digit; | 283 buffer[*length] = '0' + digit; |
284 (*length)++; | 284 (*length)++; |
285 } | 285 } |
286 if (fractionals128.BitAt(point - 1) == 1) { | 286 if (fractionals128.BitAt(point - 1) == 1) { |
287 RoundUp(buffer, length, decimal_point); | 287 RoundUp(buffer, length, decimal_point); |
288 } | 288 } |
289 } | 289 } |
290 } | 290 } |
291 | 291 |
292 | 292 |
293 // Removes leading and trailing zeros. | 293 // Removes leading and trailing zeros. |
294 // If leading zeros are removed then the decimal point position is adjusted. | 294 // If leading zeros are removed then the decimal point position is adjusted. |
295 static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point)
{ | 295 static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point)
{ |
296 while (*length > 0 && buffer[(*length) - 1] == '0') { | 296 while (*length > 0 && buffer[(*length) - 1] == '0') { |
297 (*length)--; | 297 (*length)--; |
298 } | 298 } |
299 int first_non_zero = 0; | 299 int first_non_zero = 0; |
300 while (first_non_zero < *length && buffer[first_non_zero] == '0') { | 300 while (first_non_zero < *length && buffer[first_non_zero] == '0') { |
301 first_non_zero++; | 301 first_non_zero++; |
302 } | 302 } |
303 if (first_non_zero != 0) { | 303 if (first_non_zero != 0) { |
304 for (int i = first_non_zero; i < *length; ++i) { | 304 for (int i = first_non_zero; i < *length; ++i) { |
305 buffer[i - first_non_zero] = buffer[i]; | 305 buffer[i - first_non_zero] = buffer[i]; |
306 } | 306 } |
307 *length -= first_non_zero; | 307 *length -= first_non_zero; |
308 *decimal_point -= first_non_zero; | 308 *decimal_point -= first_non_zero; |
309 } | 309 } |
310 } | 310 } |
311 | 311 |
312 | 312 |
313 bool FastFixedDtoa(double v, | 313 bool FastFixedDtoa(double v, |
314 int fractional_count, | 314 int fractional_count, |
315 Vector<char> buffer, | 315 Vector<char> buffer, |
316 int* length, | 316 int* length, |
317 int* decimal_point) { | 317 int* decimal_point) { |
318 const uint32_t kMaxUInt32 = 0xFFFFFFFF; | 318 const uint32_t kMaxUInt32 = 0xFFFFFFFF; |
319 uint64_t significand = Double(v).Significand(); | 319 uint64_t significand = Double(v).Significand(); |
320 int exponent = Double(v).Exponent(); | 320 int exponent = Double(v).Exponent(); |
321 // v = significand * 2^exponent (with significand a 53bit integer). | 321 // v = significand * 2^exponent (with significand a 53bit integer). |
322 // If the exponent is larger than 20 (i.e. we may have a 73bit number) t
hen we | 322 // If the exponent is larger than 20 (i.e. we may have a 73bit number) t
hen we |
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397 } | 397 } |
398 TrimZeros(buffer, length, decimal_point); | 398 TrimZeros(buffer, length, decimal_point); |
399 buffer[*length] = '\0'; | 399 buffer[*length] = '\0'; |
400 if ((*length) == 0) { | 400 if ((*length) == 0) { |
401 // The string is empty and the decimal_point thus has no importance.
Mimick | 401 // The string is empty and the decimal_point thus has no importance.
Mimick |
402 // Gay's dtoa and and set it to -fractional_count. | 402 // Gay's dtoa and and set it to -fractional_count. |
403 *decimal_point = -fractional_count; | 403 *decimal_point = -fractional_count; |
404 } | 404 } |
405 return true; | 405 return true; |
406 } | 406 } |
407 | 407 |
408 } // namespace double_conversion | 408 } // namespace double_conversion |
409 | 409 |
410 } // namespace WTF | 410 } // namespace WTF |
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