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Issue 3870003: Revert "Strtod fast-case that uses DiyFps and cached powers of ten." (Closed)
Patch Set: Created 10 years, 2 months ago
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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
(...skipping 13 matching lines...) Expand all
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 <stdarg.h> 28 #include <stdarg.h>
29 #include <limits.h> 29 #include <limits.h>
30 30
31 #include "v8.h" 31 #include "v8.h"
32 32
33 #include "strtod.h" 33 #include "strtod.h"
34 #include "cached-powers.h" 34 // #include "cached-powers.h"
35 #include "double.h"
36 35
37 namespace v8 { 36 namespace v8 {
38 namespace internal { 37 namespace internal {
39 38
40 // 2^53 = 9007199254740992. 39 // 2^53 = 9007199254740992.
41 // Any integer with at most 15 decimal digits will hence fit into a double 40 // Any integer with at most 15 decimal digits will hence fit into a double
42 // (which has a 53bit significand) without loss of precision. 41 // (which has a 53bit significand) without loss of precision.
43 static const int kMaxExactDoubleIntegerDecimalDigits = 15; 42 static const int kMaxExactDoubleIntegerDecimalDigits = 15;
44 // 2^64 = 18446744073709551616 > 10^19 43 // 2^64 = 18446744073709551616
44 // Any integer with at most 19 digits will hence fit into a 64bit datatype.
45 static const int kMaxUint64DecimalDigits = 19; 45 static const int kMaxUint64DecimalDigits = 19;
46
47 // Max double: 1.7976931348623157 x 10^308 46 // Max double: 1.7976931348623157 x 10^308
48 // Min non-zero double: 4.9406564584124654 x 10^-324 47 // Min non-zero double: 4.9406564584124654 x 10^-324
49 // Any x >= 10^309 is interpreted as +infinity. 48 // Any x >= 10^309 is interpreted as +infinity.
50 // Any x <= 10^-324 is interpreted as 0. 49 // Any x <= 10^-324 is interpreted as 0.
51 // Note that 2.5e-324 (despite being smaller than the min double) will be read 50 // Note that 2.5e-324 (despite being smaller than the min double) will be read
52 // as non-zero (equal to the min non-zero double). 51 // as non-zero (equal to the min non-zero double).
53 static const int kMaxDecimalPower = 309; 52 static const int kMaxDecimalPower = 309;
54 static const int kMinDecimalPower = -324; 53 static const int kMinDecimalPower = -324;
55 54
56 // 2^64 = 18446744073709551616
57 static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF);
58
59
60 static const double exact_powers_of_ten[] = { 55 static const double exact_powers_of_ten[] = {
61 1.0, // 10^0 56 1.0, // 10^0
62 10.0, 57 10.0,
63 100.0, 58 100.0,
64 1000.0, 59 1000.0,
65 10000.0, 60 10000.0,
66 100000.0, 61 100000.0,
67 1000000.0, 62 1000000.0,
68 10000000.0, 63 10000000.0,
69 100000000.0, 64 100000000.0,
(...skipping 65 matching lines...) Expand 10 before | Expand all | Expand 10 after
135 static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { 130 static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
136 for (int i = buffer.length() - 1; i >= 0; --i) { 131 for (int i = buffer.length() - 1; i >= 0; --i) {
137 if (buffer[i] != '0') { 132 if (buffer[i] != '0') {
138 return Vector<const char>(buffer.start(), i + 1); 133 return Vector<const char>(buffer.start(), i + 1);
139 } 134 }
140 } 135 }
141 return Vector<const char>(buffer.start(), 0); 136 return Vector<const char>(buffer.start(), 0);
142 } 137 }
143 138
144 139
145 // Reads digits from the buffer and converts them to a uint64. 140 uint64_t ReadUint64(Vector<const char> buffer) {
146 // Reads in as many digits as fit into a uint64. 141 ASSERT(buffer.length() <= kMaxUint64DecimalDigits);
147 // When the string starts with "1844674407370955161" no further digit is read.
148 // Since 2^64 = 18446744073709551616 it would still be possible read another
149 // digit if it was less or equal than 6, but this would complicate the code.
150 static uint64_t ReadUint64(Vector<const char> buffer,
151 int* number_of_read_digits) {
152 uint64_t result = 0; 142 uint64_t result = 0;
153 int i = 0; 143 for (int i = 0; i < buffer.length(); ++i) {
154 while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { 144 int digit = buffer[i] - '0';
155 int digit = buffer[i++] - '0';
156 ASSERT(0 <= digit && digit <= 9); 145 ASSERT(0 <= digit && digit <= 9);
157 result = 10 * result + digit; 146 result = 10 * result + digit;
158 } 147 }
159 *number_of_read_digits = i;
160 return result; 148 return result;
161 } 149 }
162 150
163 151
164 // Reads a DiyFp from the buffer.
165 // The returned DiyFp is not necessarily normalized.
166 // If remaining_decimals is zero then the returned DiyFp is accurate.
167 // Otherwise it has been rounded and has error of at most 1/2 ulp.
168 static void ReadDiyFp(Vector<const char> buffer,
169 DiyFp* result,
170 int* remaining_decimals) {
171 int read_digits;
172 uint64_t significand = ReadUint64(buffer, &read_digits);
173 if (buffer.length() == read_digits) {
174 *result = DiyFp(significand, 0);
175 *remaining_decimals = 0;
176 } else {
177 // Round the significand.
178 if (buffer[read_digits] >= '5') {
179 significand++;
180 }
181 // Compute the binary exponent.
182 int exponent = 0;
183 *result = DiyFp(significand, exponent);
184 *remaining_decimals = buffer.length() - read_digits;
185 }
186 }
187
188
189 static bool DoubleStrtod(Vector<const char> trimmed, 152 static bool DoubleStrtod(Vector<const char> trimmed,
190 int exponent, 153 int exponent,
191 double* result) { 154 double* result) {
192 #if (defined(V8_TARGET_ARCH_IA32) || defined(USE_SIMULATOR)) && !defined(WIN32) 155 #if (defined(V8_TARGET_ARCH_IA32) || defined(USE_SIMULATOR)) && !defined(WIN32)
193 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is 156 // On x86 the floating-point stack can be 64 or 80 bits wide. If it is
194 // 80 bits wide (as is the case on Linux) then double-rounding occurs and the 157 // 80 bits wide (as is the case on Linux) then double-rounding occurs and the
195 // result is not accurate. 158 // result is not accurate.
196 // We know that Windows32 uses 64 bits and is therefore accurate. 159 // We know that Windows32 uses 64 bits and is therefore accurate.
197 // Note that the ARM simulator is compiled for 32bits. It therefore exhibits 160 // Note that the ARM simulator is compiled for 32bits. It therefore exhibits
198 // the same problem. 161 // the same problem.
199 return false; 162 return false;
200 #endif 163 #endif
201 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { 164 if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) {
202 int read_digits;
203 // The trimmed input fits into a double. 165 // The trimmed input fits into a double.
204 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we 166 // If the 10^exponent (resp. 10^-exponent) fits into a double too then we
205 // can compute the result-double simply by multiplying (resp. dividing) the 167 // can compute the result-double simply by multiplying (resp. dividing) the
206 // two numbers. 168 // two numbers.
207 // This is possible because IEEE guarantees that floating-point operations 169 // This is possible because IEEE guarantees that floating-point operations
208 // return the best possible approximation. 170 // return the best possible approximation.
209 if (exponent < 0 && -exponent < kExactPowersOfTenSize) { 171 if (exponent < 0 && -exponent < kExactPowersOfTenSize) {
210 // 10^-exponent fits into a double. 172 // 10^-exponent fits into a double.
211 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 173 *result = static_cast<double>(ReadUint64(trimmed));
212 ASSERT(read_digits == trimmed.length());
213 *result /= exact_powers_of_ten[-exponent]; 174 *result /= exact_powers_of_ten[-exponent];
214 return true; 175 return true;
215 } 176 }
216 if (0 <= exponent && exponent < kExactPowersOfTenSize) { 177 if (0 <= exponent && exponent < kExactPowersOfTenSize) {
217 // 10^exponent fits into a double. 178 // 10^exponent fits into a double.
218 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 179 *result = static_cast<double>(ReadUint64(trimmed));
219 ASSERT(read_digits == trimmed.length());
220 *result *= exact_powers_of_ten[exponent]; 180 *result *= exact_powers_of_ten[exponent];
221 return true; 181 return true;
222 } 182 }
223 int remaining_digits = 183 int remaining_digits =
224 kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); 184 kMaxExactDoubleIntegerDecimalDigits - trimmed.length();
225 if ((0 <= exponent) && 185 if ((0 <= exponent) &&
226 (exponent - remaining_digits < kExactPowersOfTenSize)) { 186 (exponent - remaining_digits < kExactPowersOfTenSize)) {
227 // The trimmed string was short and we can multiply it with 187 // The trimmed string was short and we can multiply it with
228 // 10^remaining_digits. As a result the remaining exponent now fits 188 // 10^remaining_digits. As a result the remaining exponent now fits
229 // into a double too. 189 // into a double too.
230 *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); 190 *result = static_cast<double>(ReadUint64(trimmed));
231 ASSERT(read_digits == trimmed.length());
232 *result *= exact_powers_of_ten[remaining_digits]; 191 *result *= exact_powers_of_ten[remaining_digits];
233 *result *= exact_powers_of_ten[exponent - remaining_digits]; 192 *result *= exact_powers_of_ten[exponent - remaining_digits];
234 return true; 193 return true;
235 } 194 }
236 } 195 }
237 return false; 196 return false;
238 } 197 }
239 198
240 199
241 // Returns 10^exponent as an exact DiyFp.
242 // The given exponent must be in the range [1; kDecimalExponentDistance[.
243 static DiyFp AdjustmentPowerOfTen(int exponent) {
244 ASSERT(0 < exponent);
245 ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
246 // Simply hardcode the remaining powers for the given decimal exponent
247 // distance.
248 ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
249 switch (exponent) {
250 case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60);
251 case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57);
252 case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54);
253 case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50);
254 case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47);
255 case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44);
256 case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40);
257 default:
258 UNREACHABLE();
259 return DiyFp(0, 0);
260 }
261 }
262
263
264 // If the function returns true then the result is the correct double.
265 // Otherwise it is either the correct double or the double that is just below
266 // the correct double.
267 static bool DiyFpStrtod(Vector<const char> buffer,
268 int exponent,
269 double* result) {
270 DiyFp input;
271 int remaining_decimals;
272 ReadDiyFp(buffer, &input, &remaining_decimals);
273 // Since we may have dropped some digits the input is not accurate.
274 // If remaining_decimals is different than 0 than the error is at most
275 // .5 ulp (unit in the last place).
276 // We don't want to deal with fractions and therefore keep a common
277 // denominator.
278 const int kDenominatorLog = 3;
279 const int kDenominator = 1 << kDenominatorLog;
280 // Move the remaining decimals into the exponent.
281 exponent += remaining_decimals;
282 int error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
283
284 int old_e = input.e();
285 input.Normalize();
286 error <<= old_e - input.e();
287
288 ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent);
289 if (exponent < PowersOfTenCache::kMinDecimalExponent) {
290 *result = 0.0;
291 return true;
292 }
293 DiyFp cached_power;
294 int cached_decimal_exponent;
295 PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent,
296 &cached_power,
297 &cached_decimal_exponent);
298
299 if (cached_decimal_exponent != exponent) {
300 int adjustment_exponent = exponent - cached_decimal_exponent;
301 DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent);
302 input.Multiply(adjustment_power);
303 if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) {
304 // The product of input with the adjustment power fits into a 64 bit
305 // integer.
306 ASSERT(DiyFp::kSignificandSize == 64);
307 } else {
308 // The adjustment power is exact. There is hence only an error of 0.5.
309 error += kDenominator / 2;
310 }
311 }
312
313 input.Multiply(cached_power);
314 // The error introduced by a multiplication of a*b equals
315 // error_a + error_b + error_a*error_b/2^64 + 0.5
316 // Substituting a with 'input' and b with 'cached_power' we have
317 // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp),
318 // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64
319 int error_b = kDenominator / 2;
320 int error_ab = (error == 0 ? 0 : 1); // We round up to 1.
321 int fixed_error = kDenominator / 2;
322 error += error_b + error_ab + fixed_error;
323
324 old_e = input.e();
325 input.Normalize();
326 error <<= old_e - input.e();
327
328 // See if the double's significand changes if we add/subtract the error.
329 int order_of_magnitude = DiyFp::kSignificandSize + input.e();
330 int effective_significand_size =
331 Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude);
332 int precision_digits_count =
333 DiyFp::kSignificandSize - effective_significand_size;
334 if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) {
335 // This can only happen for very small denormals. In this case the
336 // half-way multiplied by the denominator exceeds the range of an uint64.
337 // Simply shift everything to the right.
338 int shift_amount = (precision_digits_count + kDenominatorLog) -
339 DiyFp::kSignificandSize + 1;
340 input.set_f(input.f() >> shift_amount);
341 input.set_e(input.e() + shift_amount);
342 // We add 1 for the lost precision of error, and kDenominator for
343 // the lost precision of input.f().
344 error = (error >> shift_amount) + 1 + kDenominator;
345 precision_digits_count -= shift_amount;
346 }
347 // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too.
348 ASSERT(DiyFp::kSignificandSize == 64);
349 ASSERT(precision_digits_count < 64);
350 uint64_t one64 = 1;
351 uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1;
352 uint64_t precision_bits = input.f() & precision_bits_mask;
353 uint64_t half_way = one64 << (precision_digits_count - 1);
354 precision_bits *= kDenominator;
355 half_way *= kDenominator;
356 // If the last_bits are too close to the half-way case than we are too
357 // inaccurate and round down. In this case we return false so that we can
358 // fall back to a more precise algorithm.
359 uint64_t significand = input.f();
360 if (precision_bits >= half_way + error) {
361 significand = (significand >> precision_digits_count) + 1;
362 exponent = input.e() + precision_digits_count;
363 } else {
364 significand = (significand >> precision_digits_count);
365 exponent = input.e() + precision_digits_count;
366 }
367 Double d = Double(significand, exponent);
368 *result = d.value();
369 if (half_way - error < precision_bits && precision_bits < half_way + error) {
370 // Too imprecise. The caller will have to fall back to a slower version.
371 // However the returned number is guaranteed to be either the correct
372 // double, or the next-lower double.
373 return false;
374 } else {
375 return true;
376 }
377 }
378
379
380 double Strtod(Vector<const char> buffer, int exponent) { 200 double Strtod(Vector<const char> buffer, int exponent) {
381 Vector<const char> left_trimmed = TrimLeadingZeros(buffer); 201 Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
382 Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); 202 Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
383 exponent += left_trimmed.length() - trimmed.length(); 203 exponent += left_trimmed.length() - trimmed.length();
384 if (trimmed.length() == 0) return 0.0; 204 if (trimmed.length() == 0) return 0.0;
385 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; 205 if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY;
386 if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; 206 if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0;
387
388 double result; 207 double result;
389 if (DoubleStrtod(trimmed, exponent, &result) || 208 if (DoubleStrtod(trimmed, exponent, &result)) {
390 DiyFpStrtod(trimmed, exponent, &result)) {
391 return result; 209 return result;
392 } 210 }
393 return old_strtod(trimmed, exponent); 211 return old_strtod(trimmed, exponent);
394 } 212 }
395 213
396 } } // namespace v8::internal 214 } } // namespace v8::internal
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