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3// modification, are permitted provided that the following conditions are
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26// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
27
28#include "config.h"
29
30#include <cmath>
31
32#include <wtf/dtoa/fixed-dtoa.h>
33#include <wtf/dtoa/ieee.h>
34
35namespace WTF {
36namespace double_conversion {
37
38// Represents a 128bit type. This class should be replaced by a native type on
39// platforms that support 128bit integers.
40class 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) const {
105 if (position >= 64) {
106 return static_cast<int>(high_bits_ >> (position - 64)) & 1;
107 } else {
108 return static_cast<int>(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
120static const int kDoubleSignificandSize = 53; // Includes the hidden bit.
121
122
123static void FillDigits32FixedLength(uint32_t number, int requested_length,
124 BufferReference<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
133static void FillDigits32(uint32_t number, BufferReference<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] = static_cast<char>('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++;
150 j--;
151 }
152 *length += number_length;
153}
154
155
156static void FillDigits64FixedLength(uint64_t number,
157 BufferReference<char> buffer, int* length) {
158 const uint32_t kTen7 = 10000000;
159 // For efficiency cut the number into 3 uint32_t parts, and print those.
160 uint32_t part2 = static_cast<uint32_t>(number % kTen7);
161 number /= kTen7;
162 uint32_t part1 = static_cast<uint32_t>(number % kTen7);
163 uint32_t part0 = static_cast<uint32_t>(number / kTen7);
164
165 FillDigits32FixedLength(part0, 3, buffer, length);
166 FillDigits32FixedLength(part1, 7, buffer, length);
167 FillDigits32FixedLength(part2, 7, buffer, length);
168}
169
170
171static void FillDigits64(uint64_t number, BufferReference<char> buffer, int* length) {
172 const uint32_t kTen7 = 10000000;
173 // For efficiency cut the number into 3 uint32_t parts, and print those.
174 uint32_t part2 = static_cast<uint32_t>(number % kTen7);
175 number /= kTen7;
176 uint32_t part1 = static_cast<uint32_t>(number % kTen7);
177 uint32_t part0 = static_cast<uint32_t>(number / kTen7);
178
179 if (part0 != 0) {
180 FillDigits32(part0, buffer, length);
181 FillDigits32FixedLength(part1, 7, buffer, length);
182 FillDigits32FixedLength(part2, 7, buffer, length);
183 } else if (part1 != 0) {
184 FillDigits32(part1, buffer, length);
185 FillDigits32FixedLength(part2, 7, buffer, length);
186 } else {
187 FillDigits32(part2, buffer, length);
188 }
189}
190
191
192static void RoundUp(BufferReference<char> buffer, int* length, int* decimal_point) {
193 // An empty buffer represents 0.
194 if (*length == 0) {
195 buffer[0] = '1';
196 *decimal_point = 1;
197 *length = 1;
198 return;
199 }
200 // Round the last digit until we either have a digit that was not '9' or until
201 // we reached the first digit.
202 buffer[(*length) - 1]++;
203 for (int i = (*length) - 1; i > 0; --i) {
204 if (buffer[i] != '0' + 10) {
205 return;
206 }
207 buffer[i] = '0';
208 buffer[i - 1]++;
209 }
210 // If the first digit is now '0' + 10, we would need to set it to '0' and add
211 // a '1' in front. However we reach the first digit only if all following
212 // digits had been '9' before rounding up. Now all trailing digits are '0' and
213 // we simply switch the first digit to '1' and update the decimal-point
214 // (indicating that the point is now one digit to the right).
215 if (buffer[0] == '0' + 10) {
216 buffer[0] = '1';
217 (*decimal_point)++;
218 }
219}
220
221
222// The given fractionals number represents a fixed-point number with binary
223// point at bit (-exponent).
224// Preconditions:
225// -128 <= exponent <= 0.
226// 0 <= fractionals * 2^exponent < 1
227// The buffer holds the result.
228// The function will round its result. During the rounding-process digits not
229// generated by this function might be updated, and the decimal-point variable
230// might be updated. If this function generates the digits 99 and the buffer
231// already contained "199" (thus yielding a buffer of "19999") then a
232// rounding-up will change the contents of the buffer to "20000".
233static void FillFractionals(uint64_t fractionals, int exponent,
234 int fractional_count, BufferReference<char> buffer,
235 int* length, int* decimal_point) {
236 ASSERT(-128 <= exponent && exponent <= 0);
237 // 'fractionals' is a fixed-point number, with binary point at bit
238 // (-exponent). Inside the function the non-converted remainder of fractionals
239 // is a fixed-point number, with binary point at bit 'point'.
240 if (-exponent <= 64) {
241 // One 64 bit number is sufficient.
242 ASSERT(fractionals >> 56 == 0);
243 int point = -exponent;
244 for (int i = 0; i < fractional_count; ++i) {
245 if (fractionals == 0) break;
246 // Instead of multiplying by 10 we multiply by 5 and adjust the point
247 // location. This way the fractionals variable will not overflow.
248 // Invariant at the beginning of the loop: fractionals < 2^point.
249 // Initially we have: point <= 64 and fractionals < 2^56
250 // After each iteration the point is decremented by one.
251 // Note that 5^3 = 125 < 128 = 2^7.
252 // Therefore three iterations of this loop will not overflow fractionals
253 // (even without the subtraction at the end of the loop body). At this
254 // time point will satisfy point <= 61 and therefore fractionals < 2^point
255 // and any further multiplication of fractionals by 5 will not overflow.
256 fractionals *= 5;
257 point--;
258 int digit = static_cast<int>(fractionals >> point);
259 ASSERT(digit <= 9);
260 buffer[*length] = static_cast<char>('0' + digit);
261 (*length)++;
262 fractionals -= static_cast<uint64_t>(digit) << point;
263 }
264 // If the first bit after the point is set we have to round up.
265 ASSERT(fractionals == 0 || point - 1 >= 0);
266 if ((fractionals != 0) && ((fractionals >> (point - 1)) & 1) == 1) {
267 RoundUp(buffer, length, decimal_point);
268 }
269 } else { // We need 128 bits.
270 ASSERT(64 < -exponent && -exponent <= 128);
271 UInt128 fractionals128 = UInt128(fractionals, 0);
272 fractionals128.Shift(-exponent - 64);
273 int point = 128;
274 for (int i = 0; i < fractional_count; ++i) {
275 if (fractionals128.IsZero()) break;
276 // As before: instead of multiplying by 10 we multiply by 5 and adjust the
277 // point location.
278 // This multiplication will not overflow for the same reasons as before.
279 fractionals128.Multiply(5);
280 point--;
281 int digit = fractionals128.DivModPowerOf2(point);
282 ASSERT(digit <= 9);
283 buffer[*length] = static_cast<char>('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.
295static void TrimZeros(BufferReference<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
313bool FastFixedDtoa(double v,
314 int fractional_count,
315 BufferReference<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) then 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 need
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-zero
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 into 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, 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} // namespace WTF
410