OLD | NEW |
| (Empty) |
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 "config.h" | |
29 | |
30 #include <math.h> | |
31 | |
32 #include "UnusedParam.h" | |
33 #include "fixed-dtoa.h" | |
34 #include "double.h" | |
35 | |
36 namespace WTF { | |
37 | |
38 namespace double_conversion { | |
39 | |
40 // Represents a 128bit type. This class should be replaced by a native type
on | |
41 // platforms that support 128bit integers. | |
42 class UInt128 { | |
43 public: | |
44 UInt128() : high_bits_(0), low_bits_(0) { } | |
45 UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low)
{ } | |
46 | |
47 void Multiply(uint32_t multiplicand) { | |
48 uint64_t accumulator; | |
49 | |
50 accumulator = (low_bits_ & kMask32) * multiplicand; | |
51 uint32_t part = static_cast<uint32_t>(accumulator & kMask32); | |
52 accumulator >>= 32; | |
53 accumulator = accumulator + (low_bits_ >> 32) * multiplicand; | |
54 low_bits_ = (accumulator << 32) + part; | |
55 accumulator >>= 32; | |
56 accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; | |
57 part = static_cast<uint32_t>(accumulator & kMask32); | |
58 accumulator >>= 32; | |
59 accumulator = accumulator + (high_bits_ >> 32) * multiplicand; | |
60 high_bits_ = (accumulator << 32) + part; | |
61 ASSERT((accumulator >> 32) == 0); | |
62 } | |
63 | |
64 void Shift(int shift_amount) { | |
65 ASSERT(-64 <= shift_amount && shift_amount <= 64); | |
66 if (shift_amount == 0) { | |
67 return; | |
68 } else if (shift_amount == -64) { | |
69 high_bits_ = low_bits_; | |
70 low_bits_ = 0; | |
71 } else if (shift_amount == 64) { | |
72 low_bits_ = high_bits_; | |
73 high_bits_ = 0; | |
74 } else if (shift_amount <= 0) { | |
75 high_bits_ <<= -shift_amount; | |
76 high_bits_ += low_bits_ >> (64 + shift_amount); | |
77 low_bits_ <<= -shift_amount; | |
78 } else { | |
79 low_bits_ >>= shift_amount; | |
80 low_bits_ += high_bits_ << (64 - shift_amount); | |
81 high_bits_ >>= shift_amount; | |
82 } | |
83 } | |
84 | |
85 // Modifies *this to *this MOD (2^power). | |
86 // Returns *this DIV (2^power). | |
87 int DivModPowerOf2(int power) { | |
88 if (power >= 64) { | |
89 int result = static_cast<int>(high_bits_ >> (power - 64)); | |
90 high_bits_ -= static_cast<uint64_t>(result) << (power - 64); | |
91 return result; | |
92 } else { | |
93 uint64_t part_low = low_bits_ >> power; | |
94 uint64_t part_high = high_bits_ << (64 - power); | |
95 int result = static_cast<int>(part_low + part_high); | |
96 high_bits_ = 0; | |
97 low_bits_ -= part_low << power; | |
98 return result; | |
99 } | |
100 } | |
101 | |
102 bool IsZero() const { | |
103 return high_bits_ == 0 && low_bits_ == 0; | |
104 } | |
105 | |
106 int BitAt(int position) { | |
107 if (position >= 64) { | |
108 return static_cast<int>(high_bits_ >> (position - 64)) & 1; | |
109 } else { | |
110 return static_cast<int>(low_bits_ >> position) & 1; | |
111 } | |
112 } | |
113 | |
114 private: | |
115 static const uint64_t kMask32 = 0xFFFFFFFF; | |
116 // Value == (high_bits_ << 64) + low_bits_ | |
117 uint64_t high_bits_; | |
118 uint64_t low_bits_; | |
119 }; | |
120 | |
121 | |
122 static const int kDoubleSignificandSize = 53; // Includes the hidden bit. | |
123 | |
124 | |
125 static void FillDigits32FixedLength(uint32_t number, int requested_length, | |
126 Vector<char> buffer, int* length) { | |
127 for (int i = requested_length - 1; i >= 0; --i) { | |
128 buffer[(*length) + i] = '0' + number % 10; | |
129 number /= 10; | |
130 } | |
131 *length += requested_length; | |
132 } | |
133 | |
134 | |
135 static void FillDigits32(uint32_t number, Vector<char> buffer, int* length)
{ | |
136 int number_length = 0; | |
137 // We fill the digits in reverse order and exchange them afterwards. | |
138 while (number != 0) { | |
139 int digit = number % 10; | |
140 number /= 10; | |
141 buffer[(*length) + number_length] = '0' + digit; | |
142 number_length++; | |
143 } | |
144 // Exchange the digits. | |
145 int i = *length; | |
146 int j = *length + number_length - 1; | |
147 while (i < j) { | |
148 char tmp = buffer[i]; | |
149 buffer[i] = buffer[j]; | |
150 buffer[j] = tmp; | |
151 i++; | |
152 j--; | |
153 } | |
154 *length += number_length; | |
155 } | |
156 | |
157 | |
158 static void FillDigits64FixedLength(uint64_t number, int requested_length, | |
159 Vector<char> buffer, int* length) { | |
160 UNUSED_PARAM(requested_length); | |
161 const uint32_t kTen7 = 10000000; | |
162 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
163 uint32_t part2 = static_cast<uint32_t>(number % kTen7); | |
164 number /= kTen7; | |
165 uint32_t part1 = static_cast<uint32_t>(number % kTen7); | |
166 uint32_t part0 = static_cast<uint32_t>(number / kTen7); | |
167 | |
168 FillDigits32FixedLength(part0, 3, buffer, length); | |
169 FillDigits32FixedLength(part1, 7, buffer, length); | |
170 FillDigits32FixedLength(part2, 7, buffer, length); | |
171 } | |
172 | |
173 | |
174 static void FillDigits64(uint64_t number, Vector<char> buffer, int* length)
{ | |
175 const uint32_t kTen7 = 10000000; | |
176 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
177 uint32_t part2 = static_cast<uint32_t>(number % kTen7); | |
178 number /= kTen7; | |
179 uint32_t part1 = static_cast<uint32_t>(number % kTen7); | |
180 uint32_t part0 = static_cast<uint32_t>(number / kTen7); | |
181 | |
182 if (part0 != 0) { | |
183 FillDigits32(part0, buffer, length); | |
184 FillDigits32FixedLength(part1, 7, buffer, length); | |
185 FillDigits32FixedLength(part2, 7, buffer, length); | |
186 } else if (part1 != 0) { | |
187 FillDigits32(part1, buffer, length); | |
188 FillDigits32FixedLength(part2, 7, buffer, length); | |
189 } else { | |
190 FillDigits32(part2, buffer, length); | |
191 } | |
192 } | |
193 | |
194 | |
195 static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { | |
196 // An empty buffer represents 0. | |
197 if (*length == 0) { | |
198 buffer[0] = '1'; | |
199 *decimal_point = 1; | |
200 *length = 1; | |
201 return; | |
202 } | |
203 // Round the last digit until we either have a digit that was not '9' or
until | |
204 // we reached the first digit. | |
205 buffer[(*length) - 1]++; | |
206 for (int i = (*length) - 1; i > 0; --i) { | |
207 if (buffer[i] != '0' + 10) { | |
208 return; | |
209 } | |
210 buffer[i] = '0'; | |
211 buffer[i - 1]++; | |
212 } | |
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 | |
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 | |
217 // (indicating that the point is now one digit to the right). | |
218 if (buffer[0] == '0' + 10) { | |
219 buffer[0] = '1'; | |
220 (*decimal_point)++; | |
221 } | |
222 } | |
223 | |
224 | |
225 // The given fractionals number represents a fixed-point number with binary | |
226 // point at bit (-exponent). | |
227 // Preconditions: | |
228 // -128 <= exponent <= 0. | |
229 // 0 <= fractionals * 2^exponent < 1 | |
230 // The buffer holds the result. | |
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 | |
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 | |
235 // rounding-up will change the contents of the buffer to "20000". | |
236 static void FillFractionals(uint64_t fractionals, int exponent, | |
237 int fractional_count, Vector<char> buffer, | |
238 int* length, int* decimal_point) { | |
239 ASSERT(-128 <= exponent && exponent <= 0); | |
240 // 'fractionals' is a fixed-point number, with binary point at bit | |
241 // (-exponent). Inside the function the non-converted remainder of fract
ionals | |
242 // is a fixed-point number, with binary point at bit 'point'. | |
243 if (-exponent <= 64) { | |
244 // One 64 bit number is sufficient. | |
245 ASSERT(fractionals >> 56 == 0); | |
246 int point = -exponent; | |
247 for (int i = 0; i < fractional_count; ++i) { | |
248 if (fractionals == 0) break; | |
249 // Instead of multiplying by 10 we multiply by 5 and adjust the
point | |
250 // location. This way the fractionals variable will not overflow
. | |
251 // Invariant at the beginning of the loop: fractionals < 2^point
. | |
252 // Initially we have: point <= 64 and fractionals < 2^56 | |
253 // After each iteration the point is decremented by one. | |
254 // Note that 5^3 = 125 < 128 = 2^7. | |
255 // Therefore three iterations of this loop will not overflow fra
ctionals | |
256 // (even without the subtraction at the end of the loop body). A
t this | |
257 // time point will satisfy point <= 61 and therefore fractionals
< 2^point | |
258 // and any further multiplication of fractionals by 5 will not o
verflow. | |
259 fractionals *= 5; | |
260 point--; | |
261 int digit = static_cast<int>(fractionals >> point); | |
262 buffer[*length] = '0' + digit; | |
263 (*length)++; | |
264 fractionals -= static_cast<uint64_t>(digit) << point; | |
265 } | |
266 // If the first bit after the point is set we have to round up. | |
267 if (((fractionals >> (point - 1)) & 1) == 1) { | |
268 RoundUp(buffer, length, decimal_point); | |
269 } | |
270 } else { // We need 128 bits. | |
271 ASSERT(64 < -exponent && -exponent <= 128); | |
272 UInt128 fractionals128 = UInt128(fractionals, 0); | |
273 fractionals128.Shift(-exponent - 64); | |
274 int point = 128; | |
275 for (int i = 0; i < fractional_count; ++i) { | |
276 if (fractionals128.IsZero()) break; | |
277 // As before: instead of multiplying by 10 we multiply by 5 and
adjust the | |
278 // point location. | |
279 // This multiplication will not overflow for the same reasons as
before. | |
280 fractionals128.Multiply(5); | |
281 point--; | |
282 int digit = fractionals128.DivModPowerOf2(point); | |
283 buffer[*length] = '0' + digit; | |
284 (*length)++; | |
285 } | |
286 if (fractionals128.BitAt(point - 1) == 1) { | |
287 RoundUp(buffer, length, decimal_point); | |
288 } | |
289 } | |
290 } | |
291 | |
292 | |
293 // Removes leading and trailing zeros. | |
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)
{ | |
296 while (*length > 0 && buffer[(*length) - 1] == '0') { | |
297 (*length)--; | |
298 } | |
299 int first_non_zero = 0; | |
300 while (first_non_zero < *length && buffer[first_non_zero] == '0') { | |
301 first_non_zero++; | |
302 } | |
303 if (first_non_zero != 0) { | |
304 for (int i = first_non_zero; i < *length; ++i) { | |
305 buffer[i - first_non_zero] = buffer[i]; | |
306 } | |
307 *length -= first_non_zero; | |
308 *decimal_point -= first_non_zero; | |
309 } | |
310 } | |
311 | |
312 | |
313 bool FastFixedDtoa(double v, | |
314 int fractional_count, | |
315 Vector<char> buffer, | |
316 int* length, | |
317 int* decimal_point) { | |
318 const uint32_t kMaxUInt32 = 0xFFFFFFFF; | |
319 uint64_t significand = Double(v).Significand(); | |
320 int exponent = Double(v).Exponent(); | |
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 | |
323 // don't know how to compute the representation. 2^73 ~= 9.5*10^21. | |
324 // If necessary this limit could probably be increased, but we don't nee
d | |
325 // more. | |
326 if (exponent > 20) return false; | |
327 if (fractional_count > 20) return false; | |
328 *length = 0; | |
329 // At most kDoubleSignificandSize bits of the significand are non-zero. | |
330 // Given a 64 bit integer we have 11 0s followed by 53 potentially non-z
ero | |
331 // bits: 0..11*..0xxx..53*..xx | |
332 if (exponent + kDoubleSignificandSize > 64) { | |
333 // The exponent must be > 11. | |
334 // | |
335 // We know that v = significand * 2^exponent. | |
336 // And the exponent > 11. | |
337 // We simplify the task by dividing v by 10^17. | |
338 // The quotient delivers the first digits, and the remainder fits in
to a 64 | |
339 // bit number. | |
340 // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. | |
341 const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5); // 5^17 | |
342 uint64_t divisor = kFive17; | |
343 int divisor_power = 17; | |
344 uint64_t dividend = significand; | |
345 uint32_t quotient; | |
346 uint64_t remainder; | |
347 // Let v = f * 2^e with f == significand and e == exponent. | |
348 // Then need q (quotient) and r (remainder) as follows: | |
349 // v = q * 10^17 + r | |
350 // f * 2^e = q * 10^17 + r | |
351 // f * 2^e = q * 5^17 * 2^17 + r | |
352 // If e > 17 then | |
353 // f * 2^(e-17) = q * 5^17 + r/2^17 | |
354 // else | |
355 // f = q * 5^17 * 2^(17-e) + r/2^e | |
356 if (exponent > divisor_power) { | |
357 // We only allow exponents of up to 20 and therefore (17 - e) <=
3 | |
358 dividend <<= exponent - divisor_power; | |
359 quotient = static_cast<uint32_t>(dividend / divisor); | |
360 remainder = (dividend % divisor) << divisor_power; | |
361 } else { | |
362 divisor <<= divisor_power - exponent; | |
363 quotient = static_cast<uint32_t>(dividend / divisor); | |
364 remainder = (dividend % divisor) << exponent; | |
365 } | |
366 FillDigits32(quotient, buffer, length); | |
367 FillDigits64FixedLength(remainder, divisor_power, buffer, length); | |
368 *decimal_point = *length; | |
369 } else if (exponent >= 0) { | |
370 // 0 <= exponent <= 11 | |
371 significand <<= exponent; | |
372 FillDigits64(significand, buffer, length); | |
373 *decimal_point = *length; | |
374 } else if (exponent > -kDoubleSignificandSize) { | |
375 // We have to cut the number. | |
376 uint64_t integrals = significand >> -exponent; | |
377 uint64_t fractionals = significand - (integrals << -exponent); | |
378 if (integrals > kMaxUInt32) { | |
379 FillDigits64(integrals, buffer, length); | |
380 } else { | |
381 FillDigits32(static_cast<uint32_t>(integrals), buffer, length); | |
382 } | |
383 *decimal_point = *length; | |
384 FillFractionals(fractionals, exponent, fractional_count, | |
385 buffer, length, decimal_point); | |
386 } else if (exponent < -128) { | |
387 // This configuration (with at most 20 digits) means that all digits
must be | |
388 // 0. | |
389 ASSERT(fractional_count <= 20); | |
390 buffer[0] = '\0'; | |
391 *length = 0; | |
392 *decimal_point = -fractional_count; | |
393 } else { | |
394 *decimal_point = 0; | |
395 FillFractionals(significand, exponent, fractional_count, | |
396 buffer, length, decimal_point); | |
397 } | |
398 TrimZeros(buffer, length, decimal_point); | |
399 buffer[*length] = '\0'; | |
400 if ((*length) == 0) { | |
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. | |
403 *decimal_point = -fractional_count; | |
404 } | |
405 return true; | |
406 } | |
407 | |
408 } // namespace double_conversion | |
409 | |
410 } // namespace WTF | |
OLD | NEW |