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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 (high_bits_ >> (position - 64)) & 1; | |
107 } else { | |
108 return (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++; j--; | |
150 } | |
151 *length += number_length; | |
152 } | |
153 | |
154 | |
155 static void FillDigits64FixedLength(uint64_t number, int requested_length, | |
156 Vector<char> buffer, int* length) { | |
157 const uint32_t kTen7 = 10000000; | |
158 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
159 uint32_t part2 = number % kTen7; | |
160 number /= kTen7; | |
161 uint32_t part1 = number % kTen7; | |
162 uint32_t part0 = number / kTen7; | |
163 | |
164 FillDigits32FixedLength(part0, 3, buffer, length); | |
165 FillDigits32FixedLength(part1, 7, buffer, length); | |
166 FillDigits32FixedLength(part2, 7, buffer, length); | |
167 } | |
168 | |
169 | |
170 static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) { | |
171 const uint32_t kTen7 = 10000000; | |
172 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
173 uint32_t part2 = number % kTen7; | |
174 number /= kTen7; | |
175 uint32_t part1 = number % kTen7; | |
176 uint32_t part0 = number / kTen7; | |
177 | |
178 if (part0 != 0) { | |
179 FillDigits32(part0, buffer, length); | |
180 FillDigits32FixedLength(part1, 7, buffer, length); | |
181 FillDigits32FixedLength(part2, 7, buffer, length); | |
182 } else if (part1 != 0) { | |
183 FillDigits32(part1, buffer, length); | |
184 FillDigits32FixedLength(part2, 7, buffer, length); | |
185 } else { | |
186 FillDigits32(part2, buffer, length); | |
187 } | |
188 } | |
189 | |
190 | |
191 static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { | |
192 // An empty buffer represents 0. | |
193 if (*length == 0) { | |
194 buffer[0] = '1'; | |
195 *decimal_point = 1; | |
196 *length = 1; | |
197 return; | |
198 } | |
199 // Round the last digit until we either have a digit that was not '9' or until | |
200 // we reached the first digit. | |
201 buffer[(*length) - 1]++; | |
202 for (int i = (*length) - 1; i > 0; --i) { | |
203 if (buffer[i] != '0' + 10) { | |
204 return; | |
205 } | |
206 buffer[i] = '0'; | |
207 buffer[i - 1]++; | |
208 } | |
209 // If the first digit is now '0' + 10, we would need to set it to '0' and add | |
210 // a '1' in front. However we reach the first digit only if all following | |
211 // digits had been '9' before rounding up. Now all trailing digits are '0' and | |
212 // we simply switch the first digit to '1' and update the decimal-point | |
213 // (indicating that the point is now one digit to the right). | |
214 if (buffer[0] == '0' + 10) { | |
215 buffer[0] = '1'; | |
216 (*decimal_point)++; | |
217 } | |
218 } | |
219 | |
220 | |
221 // The given fractionals number represents a fixed-point number with binary | |
222 // point at bit (-exponent). | |
223 // Preconditions: | |
224 // -128 <= exponent <= 0. | |
225 // 0 <= fractionals * 2^exponent < 1 | |
226 // The buffer holds the result. | |
227 // The function will round its result. During the rounding-process digits not | |
228 // generated by this function might be updated, and the decimal-point variable | |
229 // might be updated. If this function generates the digits 99 and the buffer | |
230 // already contained "199" (thus yielding a buffer of "19999") then a | |
231 // rounding-up will change the contents of the buffer to "20000". | |
232 static void FillFractionals(uint64_t fractionals, int exponent, | |
233 int fractional_count, Vector<char> buffer, | |
234 int* length, int* decimal_point) { | |
235 ASSERT(-128 <= exponent && exponent <= 0); | |
236 // 'fractionals' is a fixed-point number, with binary point at bit | |
237 // (-exponent). Inside the function the non-converted remainder of fractionals | |
238 // is a fixed-point number, with binary point at bit 'point'. | |
239 if (-exponent <= 64) { | |
240 // One 64 bit number is sufficient. | |
241 ASSERT(fractionals >> 56 == 0); | |
242 int point = -exponent; | |
243 for (int i = 0; i < fractional_count; ++i) { | |
244 if (fractionals == 0) break; | |
245 // Instead of multiplying by 10 we multiply by 5 and adjust the point | |
246 // location. This way the fractionals variable will not overflow. | |
247 // Invariant at the beginning of the loop: fractionals < 2^point. | |
248 // Initially we have: point <= 64 and fractionals < 2^56 | |
249 // After each iteration the point is decremented by one. | |
250 // Note that 5^3 = 125 < 128 = 2^7. | |
251 // Therefore three iterations of this loop will not overflow fractionals | |
252 // (even without the subtraction at the end of the loop body). At this tim
e | |
253 // point will satisfy point <= 61 and therefore fractionals < 2^point and | |
254 // any further multiplication of fractionals by 5 will not overflow. | |
255 fractionals *= 5; | |
256 point--; | |
257 int digit = static_cast<int>(fractionals >> point); | |
258 buffer[*length] = '0' + digit; | |
259 (*length)++; | |
260 fractionals -= static_cast<uint64_t>(digit) << point; | |
261 } | |
262 // If the first bit after the point is set we have to round up. | |
263 if (((fractionals >> (point - 1)) & 1) == 1) { | |
264 RoundUp(buffer, length, decimal_point); | |
265 } | |
266 } else { // We need 128 bits. | |
267 ASSERT(64 < -exponent && -exponent <= 128); | |
268 UInt128 fractionals128 = UInt128(fractionals, 0); | |
269 fractionals128.Shift(-exponent - 64); | |
270 int point = 128; | |
271 for (int i = 0; i < fractional_count; ++i) { | |
272 if (fractionals128.IsZero()) break; | |
273 // As before: instead of multiplying by 10 we multiply by 5 and adjust the | |
274 // point location. | |
275 // This multiplication will not overflow for the same reasons as before. | |
276 fractionals128.Multiply(5); | |
277 point--; | |
278 int digit = fractionals128.DivModPowerOf2(point); | |
279 buffer[*length] = '0' + digit; | |
280 (*length)++; | |
281 } | |
282 if (fractionals128.BitAt(point - 1) == 1) { | |
283 RoundUp(buffer, length, decimal_point); | |
284 } | |
285 } | |
286 } | |
287 | |
288 | |
289 // Removes leading and trailing zeros. | |
290 // If leading zeros are removed then the decimal point position is adjusted. | |
291 static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) { | |
292 while (*length > 0 && buffer[(*length) - 1] == '0') { | |
293 (*length)--; | |
294 } | |
295 int first_non_zero = 0; | |
296 while (first_non_zero < *length && buffer[first_non_zero] == '0') { | |
297 first_non_zero++; | |
298 } | |
299 if (first_non_zero != 0) { | |
300 for (int i = first_non_zero; i < *length; ++i) { | |
301 buffer[i - first_non_zero] = buffer[i]; | |
302 } | |
303 *length -= first_non_zero; | |
304 *decimal_point -= first_non_zero; | |
305 } | |
306 } | |
307 | |
308 | |
309 bool FastFixedDtoa(double v, | |
310 int fractional_count, | |
311 Vector<char> buffer, | |
312 int* length, | |
313 int* decimal_point) { | |
314 const uint32_t kMaxUInt32 = 0xFFFFFFFF; | |
315 uint64_t significand = Double(v).Significand(); | |
316 int exponent = Double(v).Exponent(); | |
317 // v = significand * 2^exponent (with significand a 53bit integer). | |
318 // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we | |
319 // don't know how to compute the representation. 2^73 ~= 9.5*10^21. | |
320 // If necessary this limit could probably be increased, but we don't need | |
321 // more. | |
322 if (exponent > 20) return false; | |
323 if (fractional_count > 20) return false; | |
324 *length = 0; | |
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-zero | |
327 // bits: 0..11*..0xxx..53*..xx | |
328 if (exponent + kDoubleSignificandSize > 64) { | |
329 // The exponent must be > 11. | |
330 // | |
331 // We know that v = significand * 2^exponent. | |
332 // And the exponent > 11. | |
333 // We simplify the task by dividing v by 10^17. | |
334 // The quotient delivers the first digits, and the remainder fits into a 64 | |
335 // bit number. | |
336 // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. | |
337 const uint64_t kFive17 = V8_2PART_UINT64_C(0xB1, A2BC2EC5); // 5^17 | |
338 uint64_t divisor = kFive17; | |
339 int divisor_power = 17; | |
340 uint64_t dividend = significand; | |
341 uint64_t quotient; | |
342 uint64_t remainder; | |
343 // Let v = f * 2^e with f == significand and e == exponent. | |
344 // Then need q (quotient) and r (remainder) as follows: | |
345 // v = q * 10^17 + r | |
346 // f * 2^e = q * 10^17 + r | |
347 // f * 2^e = q * 5^17 * 2^17 + r | |
348 // If e > 17 then | |
349 // f * 2^(e-17) = q * 5^17 + r/2^17 | |
350 // else | |
351 // f = q * 5^17 * 2^(17-e) + r/2^e | |
352 if (exponent > divisor_power) { | |
353 // We only allow exponents of up to 20 and therefore (17 - e) <= 3 | |
354 dividend <<= exponent - divisor_power; | |
355 quotient = dividend / divisor; | |
356 remainder = (dividend % divisor) << divisor_power; | |
357 } else { | |
358 divisor <<= divisor_power - exponent; | |
359 quotient = dividend / divisor; | |
360 remainder = (dividend % divisor) << exponent; | |
361 } | |
362 FillDigits32(quotient, buffer, length); | |
363 FillDigits64FixedLength(remainder, divisor_power, buffer, length); | |
364 *decimal_point = *length; | |
365 } else if (exponent >= 0) { | |
366 // 0 <= exponent <= 11 | |
367 significand <<= exponent; | |
368 FillDigits64(significand, buffer, length); | |
369 *decimal_point = *length; | |
370 } else if (exponent > -kDoubleSignificandSize) { | |
371 // We have to cut the number. | |
372 uint64_t integrals = significand >> -exponent; | |
373 uint64_t fractionals = significand - (integrals << -exponent); | |
374 if (integrals > kMaxUInt32) { | |
375 FillDigits64(integrals, buffer, length); | |
376 } else { | |
377 FillDigits32(static_cast<uint32_t>(integrals), buffer, length); | |
378 } | |
379 *decimal_point = *length; | |
380 FillFractionals(fractionals, exponent, fractional_count, | |
381 buffer, length, decimal_point); | |
382 } else if (exponent < -128) { | |
383 // This configuration (with at most 20 digits) means that all digits must be | |
384 // 0. | |
385 ASSERT(fractional_count <= 20); | |
386 buffer[0] = '\0'; | |
387 *length = 0; | |
388 *decimal_point = -fractional_count; | |
389 } else { | |
390 *decimal_point = 0; | |
391 FillFractionals(significand, exponent, fractional_count, | |
392 buffer, length, decimal_point); | |
393 } | |
394 TrimZeros(buffer, length, decimal_point); | |
395 buffer[*length] = '\0'; | |
396 if ((*length) == 0) { | |
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. | |
399 *decimal_point = -fractional_count; | |
400 } | |
401 return true; | |
402 } | |
403 | |
404 } } // namespace v8::internal | |
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