1// © 2018 and later: Unicode, Inc. and others.
2// License & terms of use: http://www.unicode.org/copyright.html
3//
4// From the double-conversion library. Original license:
5//
6// Copyright 2012 the V8 project authors. All rights reserved.
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8// modification, are permitted provided that the following conditions are
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10//
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32
33// ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
34#include "unicode/utypes.h"
35#if !UCONFIG_NO_FORMATTING
36
37// ICU PATCH: Customize header file paths for ICU.
38
39#include "double-conversion-fast-dtoa.h"
40
41#include "double-conversion-cached-powers.h"
42#include "double-conversion-diy-fp.h"
43#include "double-conversion-ieee.h"
44
45// ICU PATCH: Wrap in ICU namespace
46U_NAMESPACE_BEGIN
47
48namespace double_conversion {
49
50// The minimal and maximal target exponent define the range of w's binary
51// exponent, where 'w' is the result of multiplying the input by a cached power
52// of ten.
53//
54// A different range might be chosen on a different platform, to optimize digit
55// generation, but a smaller range requires more powers of ten to be cached.
56static const int kMinimalTargetExponent = -60;
57static const int kMaximalTargetExponent = -32;
58
59
60// Adjusts the last digit of the generated number, and screens out generated
61// solutions that may be inaccurate. A solution may be inaccurate if it is
62// outside the safe interval, or if we cannot prove that it is closer to the
63// input than a neighboring representation of the same length.
64//
65// Input: * buffer containing the digits of too_high / 10^kappa
66// * the buffer's length
67// * distance_too_high_w == (too_high - w).f() * unit
68// * unsafe_interval == (too_high - too_low).f() * unit
69// * rest = (too_high - buffer * 10^kappa).f() * unit
70// * ten_kappa = 10^kappa * unit
71// * unit = the common multiplier
72// Output: returns true if the buffer is guaranteed to contain the closest
73// representable number to the input.
74// Modifies the generated digits in the buffer to approach (round towards) w.
75static bool RoundWeed(Vector<char> buffer,
76 int length,
77 uint64_t distance_too_high_w,
78 uint64_t unsafe_interval,
79 uint64_t rest,
80 uint64_t ten_kappa,
81 uint64_t unit) {
82 uint64_t small_distance = distance_too_high_w - unit;
83 uint64_t big_distance = distance_too_high_w + unit;
84 // Let w_low = too_high - big_distance, and
85 // w_high = too_high - small_distance.
86 // Note: w_low < w < w_high
87 //
88 // The real w (* unit) must lie somewhere inside the interval
89 // ]w_low; w_high[ (often written as "(w_low; w_high)")
90
91 // Basically the buffer currently contains a number in the unsafe interval
92 // ]too_low; too_high[ with too_low < w < too_high
93 //
94 // too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95 // ^v 1 unit ^ ^ ^ ^
96 // boundary_high --------------------- . . . .
97 // ^v 1 unit . . . .
98 // - - - - - - - - - - - - - - - - - - - + - - + - - - - - - . .
99 // . . ^ . .
100 // . big_distance . . .
101 // . . . . rest
102 // small_distance . . . .
103 // v . . . .
104 // w_high - - - - - - - - - - - - - - - - - - . . . .
105 // ^v 1 unit . . . .
106 // w ---------------------------------------- . . . .
107 // ^v 1 unit v . . .
108 // w_low - - - - - - - - - - - - - - - - - - - - - . . .
109 // . . v
110 // buffer --------------------------------------------------+-------+--------
111 // . .
112 // safe_interval .
113 // v .
114 // - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .
115 // ^v 1 unit .
116 // boundary_low ------------------------- unsafe_interval
117 // ^v 1 unit v
118 // too_low - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119 //
120 //
121 // Note that the value of buffer could lie anywhere inside the range too_low
122 // to too_high.
123 //
124 // boundary_low, boundary_high and w are approximations of the real boundaries
125 // and v (the input number). They are guaranteed to be precise up to one unit.
126 // In fact the error is guaranteed to be strictly less than one unit.
127 //
128 // Anything that lies outside the unsafe interval is guaranteed not to round
129 // to v when read again.
130 // Anything that lies inside the safe interval is guaranteed to round to v
131 // when read again.
132 // If the number inside the buffer lies inside the unsafe interval but not
133 // inside the safe interval then we simply do not know and bail out (returning
134 // false).
135 //
136 // Similarly we have to take into account the imprecision of 'w' when finding
137 // the closest representation of 'w'. If we have two potential
138 // representations, and one is closer to both w_low and w_high, then we know
139 // it is closer to the actual value v.
140 //
141 // By generating the digits of too_high we got the largest (closest to
142 // too_high) buffer that is still in the unsafe interval. In the case where
143 // w_high < buffer < too_high we try to decrement the buffer.
144 // This way the buffer approaches (rounds towards) w.
145 // There are 3 conditions that stop the decrementation process:
146 // 1) the buffer is already below w_high
147 // 2) decrementing the buffer would make it leave the unsafe interval
148 // 3) decrementing the buffer would yield a number below w_high and farther
149 // away than the current number. In other words:
150 // (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
151 // Instead of using the buffer directly we use its distance to too_high.
152 // Conceptually rest ~= too_high - buffer
153 // We need to do the following tests in this order to avoid over- and
154 // underflows.
155 DOUBLE_CONVERSION_ASSERT(rest <= unsafe_interval);
156 while (rest < small_distance && // Negated condition 1
157 unsafe_interval - rest >= ten_kappa && // Negated condition 2
158 (rest + ten_kappa < small_distance || // buffer{-1} > w_high
159 small_distance - rest >= rest + ten_kappa - small_distance)) {
160 buffer[length - 1]--;
161 rest += ten_kappa;
162 }
163
164 // We have approached w+ as much as possible. We now test if approaching w-
165 // would require changing the buffer. If yes, then we have two possible
166 // representations close to w, but we cannot decide which one is closer.
167 if (rest < big_distance &&
168 unsafe_interval - rest >= ten_kappa &&
169 (rest + ten_kappa < big_distance ||
170 big_distance - rest > rest + ten_kappa - big_distance)) {
171 return false;
172 }
173
174 // Weeding test.
175 // The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
176 // Since too_low = too_high - unsafe_interval this is equivalent to
177 // [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
178 // Conceptually we have: rest ~= too_high - buffer
179 return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
180}
181
182
183// Rounds the buffer upwards if the result is closer to v by possibly adding
184// 1 to the buffer. If the precision of the calculation is not sufficient to
185// round correctly, return false.
186// The rounding might shift the whole buffer in which case the kappa is
187// adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
188//
189// If 2*rest > ten_kappa then the buffer needs to be round up.
190// rest can have an error of +/- 1 unit. This function accounts for the
191// imprecision and returns false, if the rounding direction cannot be
192// unambiguously determined.
193//
194// Precondition: rest < ten_kappa.
195static bool RoundWeedCounted(Vector<char> buffer,
196 int length,
197 uint64_t rest,
198 uint64_t ten_kappa,
199 uint64_t unit,
200 int* kappa) {
201 DOUBLE_CONVERSION_ASSERT(rest < ten_kappa);
202 // The following tests are done in a specific order to avoid overflows. They
203 // will work correctly with any uint64 values of rest < ten_kappa and unit.
204 //
205 // If the unit is too big, then we don't know which way to round. For example
206 // a unit of 50 means that the real number lies within rest +/- 50. If
207 // 10^kappa == 40 then there is no way to tell which way to round.
208 if (unit >= ten_kappa) return false;
209 // Even if unit is just half the size of 10^kappa we are already completely
210 // lost. (And after the previous test we know that the expression will not
211 // over/underflow.)
212 if (ten_kappa - unit <= unit) return false;
213 // If 2 * (rest + unit) <= 10^kappa we can safely round down.
214 if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
215 return true;
216 }
217 // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
218 if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
219 // Increment the last digit recursively until we find a non '9' digit.
220 buffer[length - 1]++;
221 for (int i = length - 1; i > 0; --i) {
222 if (buffer[i] != '0' + 10) break;
223 buffer[i] = '0';
224 buffer[i - 1]++;
225 }
226 // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
227 // exception of the first digit all digits are now '0'. Simply switch the
228 // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
229 // the power (the kappa) is increased.
230 if (buffer[0] == '0' + 10) {
231 buffer[0] = '1';
232 (*kappa) += 1;
233 }
234 return true;
235 }
236 return false;
237}
238
239// Returns the biggest power of ten that is less than or equal to the given
240// number. We furthermore receive the maximum number of bits 'number' has.
241//
242// Returns power == 10^(exponent_plus_one-1) such that
243// power <= number < power * 10.
244// If number_bits == 0 then 0^(0-1) is returned.
245// The number of bits must be <= 32.
246// Precondition: number < (1 << (number_bits + 1)).
247
248// Inspired by the method for finding an integer log base 10 from here:
249// http://graphics.stanford.edu/~seander/bithacks.html#IntegerLog10
250static unsigned int const kSmallPowersOfTen[] =
251 {0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
252 1000000000};
253
254static void BiggestPowerTen(uint32_t number,
255 int number_bits,
256 uint32_t* power,
257 int* exponent_plus_one) {
258 DOUBLE_CONVERSION_ASSERT(number < (1u << (number_bits + 1)));
259 // 1233/4096 is approximately 1/lg(10).
260 int exponent_plus_one_guess = ((number_bits + 1) * 1233 >> 12);
261 // We increment to skip over the first entry in the kPowersOf10 table.
262 // Note: kPowersOf10[i] == 10^(i-1).
263 exponent_plus_one_guess++;
264 // We don't have any guarantees that 2^number_bits <= number.
265 if (number < kSmallPowersOfTen[exponent_plus_one_guess]) {
266 exponent_plus_one_guess--;
267 }
268 *power = kSmallPowersOfTen[exponent_plus_one_guess];
269 *exponent_plus_one = exponent_plus_one_guess;
270}
271
272// Generates the digits of input number w.
273// w is a floating-point number (DiyFp), consisting of a significand and an
274// exponent. Its exponent is bounded by kMinimalTargetExponent and
275// kMaximalTargetExponent.
276// Hence -60 <= w.e() <= -32.
277//
278// Returns false if it fails, in which case the generated digits in the buffer
279// should not be used.
280// Preconditions:
281// * low, w and high are correct up to 1 ulp (unit in the last place). That
282// is, their error must be less than a unit of their last digits.
283// * low.e() == w.e() == high.e()
284// * low < w < high, and taking into account their error: low~ <= high~
285// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
286// Postconditions: returns false if procedure fails.
287// otherwise:
288// * buffer is not null-terminated, but len contains the number of digits.
289// * buffer contains the shortest possible decimal digit-sequence
290// such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
291// correct values of low and high (without their error).
292// * if more than one decimal representation gives the minimal number of
293// decimal digits then the one closest to W (where W is the correct value
294// of w) is chosen.
295// Remark: this procedure takes into account the imprecision of its input
296// numbers. If the precision is not enough to guarantee all the postconditions
297// then false is returned. This usually happens rarely (~0.5%).
298//
299// Say, for the sake of example, that
300// w.e() == -48, and w.f() == 0x1234567890abcdef
301// w's value can be computed by w.f() * 2^w.e()
302// We can obtain w's integral digits by simply shifting w.f() by -w.e().
303// -> w's integral part is 0x1234
304// w's fractional part is therefore 0x567890abcdef.
305// Printing w's integral part is easy (simply print 0x1234 in decimal).
306// In order to print its fraction we repeatedly multiply the fraction by 10 and
307// get each digit. Example the first digit after the point would be computed by
308// (0x567890abcdef * 10) >> 48. -> 3
309// The whole thing becomes slightly more complicated because we want to stop
310// once we have enough digits. That is, once the digits inside the buffer
311// represent 'w' we can stop. Everything inside the interval low - high
312// represents w. However we have to pay attention to low, high and w's
313// imprecision.
314static bool DigitGen(DiyFp low,
315 DiyFp w,
316 DiyFp high,
317 Vector<char> buffer,
318 int* length,
319 int* kappa) {
320 DOUBLE_CONVERSION_ASSERT(low.e() == w.e() && w.e() == high.e());
321 DOUBLE_CONVERSION_ASSERT(low.f() + 1 <= high.f() - 1);
322 DOUBLE_CONVERSION_ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
323 // low, w and high are imprecise, but by less than one ulp (unit in the last
324 // place).
325 // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
326 // the new numbers are outside of the interval we want the final
327 // representation to lie in.
328 // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
329 // numbers that are certain to lie in the interval. We will use this fact
330 // later on.
331 // We will now start by generating the digits within the uncertain
332 // interval. Later we will weed out representations that lie outside the safe
333 // interval and thus _might_ lie outside the correct interval.
334 uint64_t unit = 1;
335 DiyFp too_low = DiyFp(low.f() - unit, low.e());
336 DiyFp too_high = DiyFp(high.f() + unit, high.e());
337 // too_low and too_high are guaranteed to lie outside the interval we want the
338 // generated number in.
339 DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
340 // We now cut the input number into two parts: the integral digits and the
341 // fractionals. We will not write any decimal separator though, but adapt
342 // kappa instead.
343 // Reminder: we are currently computing the digits (stored inside the buffer)
344 // such that: too_low < buffer * 10^kappa < too_high
345 // We use too_high for the digit_generation and stop as soon as possible.
346 // If we stop early we effectively round down.
347 DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
348 // Division by one is a shift.
349 uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
350 // Modulo by one is an and.
351 uint64_t fractionals = too_high.f() & (one.f() - 1);
352 uint32_t divisor;
353 int divisor_exponent_plus_one;
354 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
355 &divisor, &divisor_exponent_plus_one);
356 *kappa = divisor_exponent_plus_one;
357 *length = 0;
358 // Loop invariant: buffer = too_high / 10^kappa (integer division)
359 // The invariant holds for the first iteration: kappa has been initialized
360 // with the divisor exponent + 1. And the divisor is the biggest power of ten
361 // that is smaller than integrals.
362 while (*kappa > 0) {
363 int digit = integrals / divisor;
364 DOUBLE_CONVERSION_ASSERT(digit <= 9);
365 buffer[*length] = static_cast<char>('0' + digit);
366 (*length)++;
367 integrals %= divisor;
368 (*kappa)--;
369 // Note that kappa now equals the exponent of the divisor and that the
370 // invariant thus holds again.
371 uint64_t rest =
372 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
373 // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
374 // Reminder: unsafe_interval.e() == one.e()
375 if (rest < unsafe_interval.f()) {
376 // Rounding down (by not emitting the remaining digits) yields a number
377 // that lies within the unsafe interval.
378 return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
379 unsafe_interval.f(), rest,
380 static_cast<uint64_t>(divisor) << -one.e(), unit);
381 }
382 divisor /= 10;
383 }
384
385 // The integrals have been generated. We are at the point of the decimal
386 // separator. In the following loop we simply multiply the remaining digits by
387 // 10 and divide by one. We just need to pay attention to multiply associated
388 // data (like the interval or 'unit'), too.
389 // Note that the multiplication by 10 does not overflow, because w.e >= -60
390 // and thus one.e >= -60.
391 DOUBLE_CONVERSION_ASSERT(one.e() >= -60);
392 DOUBLE_CONVERSION_ASSERT(fractionals < one.f());
393 DOUBLE_CONVERSION_ASSERT(DOUBLE_CONVERSION_UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
394 for (;;) {
395 fractionals *= 10;
396 unit *= 10;
397 unsafe_interval.set_f(unsafe_interval.f() * 10);
398 // Integer division by one.
399 int digit = static_cast<int>(fractionals >> -one.e());
400 DOUBLE_CONVERSION_ASSERT(digit <= 9);
401 buffer[*length] = static_cast<char>('0' + digit);
402 (*length)++;
403 fractionals &= one.f() - 1; // Modulo by one.
404 (*kappa)--;
405 if (fractionals < unsafe_interval.f()) {
406 return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
407 unsafe_interval.f(), fractionals, one.f(), unit);
408 }
409 }
410}
411
412
413
414// Generates (at most) requested_digits digits of input number w.
415// w is a floating-point number (DiyFp), consisting of a significand and an
416// exponent. Its exponent is bounded by kMinimalTargetExponent and
417// kMaximalTargetExponent.
418// Hence -60 <= w.e() <= -32.
419//
420// Returns false if it fails, in which case the generated digits in the buffer
421// should not be used.
422// Preconditions:
423// * w is correct up to 1 ulp (unit in the last place). That
424// is, its error must be strictly less than a unit of its last digit.
425// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
426//
427// Postconditions: returns false if procedure fails.
428// otherwise:
429// * buffer is not null-terminated, but length contains the number of
430// digits.
431// * the representation in buffer is the most precise representation of
432// requested_digits digits.
433// * buffer contains at most requested_digits digits of w. If there are less
434// than requested_digits digits then some trailing '0's have been removed.
435// * kappa is such that
436// w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
437//
438// Remark: This procedure takes into account the imprecision of its input
439// numbers. If the precision is not enough to guarantee all the postconditions
440// then false is returned. This usually happens rarely, but the failure-rate
441// increases with higher requested_digits.
442static bool DigitGenCounted(DiyFp w,
443 int requested_digits,
444 Vector<char> buffer,
445 int* length,
446 int* kappa) {
447 DOUBLE_CONVERSION_ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
448 DOUBLE_CONVERSION_ASSERT(kMinimalTargetExponent >= -60);
449 DOUBLE_CONVERSION_ASSERT(kMaximalTargetExponent <= -32);
450 // w is assumed to have an error less than 1 unit. Whenever w is scaled we
451 // also scale its error.
452 uint64_t w_error = 1;
453 // We cut the input number into two parts: the integral digits and the
454 // fractional digits. We don't emit any decimal separator, but adapt kappa
455 // instead. Example: instead of writing "1.2" we put "12" into the buffer and
456 // increase kappa by 1.
457 DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
458 // Division by one is a shift.
459 uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
460 // Modulo by one is an and.
461 uint64_t fractionals = w.f() & (one.f() - 1);
462 uint32_t divisor;
463 int divisor_exponent_plus_one;
464 BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
465 &divisor, &divisor_exponent_plus_one);
466 *kappa = divisor_exponent_plus_one;
467 *length = 0;
468
469 // Loop invariant: buffer = w / 10^kappa (integer division)
470 // The invariant holds for the first iteration: kappa has been initialized
471 // with the divisor exponent + 1. And the divisor is the biggest power of ten
472 // that is smaller than 'integrals'.
473 while (*kappa > 0) {
474 int digit = integrals / divisor;
475 DOUBLE_CONVERSION_ASSERT(digit <= 9);
476 buffer[*length] = static_cast<char>('0' + digit);
477 (*length)++;
478 requested_digits--;
479 integrals %= divisor;
480 (*kappa)--;
481 // Note that kappa now equals the exponent of the divisor and that the
482 // invariant thus holds again.
483 if (requested_digits == 0) break;
484 divisor /= 10;
485 }
486
487 if (requested_digits == 0) {
488 uint64_t rest =
489 (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
490 return RoundWeedCounted(buffer, *length, rest,
491 static_cast<uint64_t>(divisor) << -one.e(), w_error,
492 kappa);
493 }
494
495 // The integrals have been generated. We are at the point of the decimal
496 // separator. In the following loop we simply multiply the remaining digits by
497 // 10 and divide by one. We just need to pay attention to multiply associated
498 // data (the 'unit'), too.
499 // Note that the multiplication by 10 does not overflow, because w.e >= -60
500 // and thus one.e >= -60.
501 DOUBLE_CONVERSION_ASSERT(one.e() >= -60);
502 DOUBLE_CONVERSION_ASSERT(fractionals < one.f());
503 DOUBLE_CONVERSION_ASSERT(DOUBLE_CONVERSION_UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
504 while (requested_digits > 0 && fractionals > w_error) {
505 fractionals *= 10;
506 w_error *= 10;
507 // Integer division by one.
508 int digit = static_cast<int>(fractionals >> -one.e());
509 DOUBLE_CONVERSION_ASSERT(digit <= 9);
510 buffer[*length] = static_cast<char>('0' + digit);
511 (*length)++;
512 requested_digits--;
513 fractionals &= one.f() - 1; // Modulo by one.
514 (*kappa)--;
515 }
516 if (requested_digits != 0) return false;
517 return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
518 kappa);
519}
520
521
522// Provides a decimal representation of v.
523// Returns true if it succeeds, otherwise the result cannot be trusted.
524// There will be *length digits inside the buffer (not null-terminated).
525// If the function returns true then
526// v == (double) (buffer * 10^decimal_exponent).
527// The digits in the buffer are the shortest representation possible: no
528// 0.09999999999999999 instead of 0.1. The shorter representation will even be
529// chosen even if the longer one would be closer to v.
530// The last digit will be closest to the actual v. That is, even if several
531// digits might correctly yield 'v' when read again, the closest will be
532// computed.
533static bool Grisu3(double v,
534 FastDtoaMode mode,
535 Vector<char> buffer,
536 int* length,
537 int* decimal_exponent) {
538 DiyFp w = Double(v).AsNormalizedDiyFp();
539 // boundary_minus and boundary_plus are the boundaries between v and its
540 // closest floating-point neighbors. Any number strictly between
541 // boundary_minus and boundary_plus will round to v when convert to a double.
542 // Grisu3 will never output representations that lie exactly on a boundary.
543 DiyFp boundary_minus, boundary_plus;
544 if (mode == FAST_DTOA_SHORTEST) {
545 Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
546 } else {
547 DOUBLE_CONVERSION_ASSERT(mode == FAST_DTOA_SHORTEST_SINGLE);
548 float single_v = static_cast<float>(v);
549 Single(single_v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
550 }
551 DOUBLE_CONVERSION_ASSERT(boundary_plus.e() == w.e());
552 DiyFp ten_mk; // Cached power of ten: 10^-k
553 int mk; // -k
554 int ten_mk_minimal_binary_exponent =
555 kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
556 int ten_mk_maximal_binary_exponent =
557 kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
558 PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
559 ten_mk_minimal_binary_exponent,
560 ten_mk_maximal_binary_exponent,
561 &ten_mk, &mk);
562 DOUBLE_CONVERSION_ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
563 DiyFp::kSignificandSize) &&
564 (kMaximalTargetExponent >= w.e() + ten_mk.e() +
565 DiyFp::kSignificandSize));
566 // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
567 // 64 bit significand and ten_mk is thus only precise up to 64 bits.
568
569 // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
570 // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
571 // off by a small amount.
572 // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
573 // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
574 // (f-1) * 2^e < w*10^k < (f+1) * 2^e
575 DiyFp scaled_w = DiyFp::Times(w, ten_mk);
576 DOUBLE_CONVERSION_ASSERT(scaled_w.e() ==
577 boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
578 // In theory it would be possible to avoid some recomputations by computing
579 // the difference between w and boundary_minus/plus (a power of 2) and to
580 // compute scaled_boundary_minus/plus by subtracting/adding from
581 // scaled_w. However the code becomes much less readable and the speed
582 // enhancements are not terriffic.
583 DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
584 DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
585
586 // DigitGen will generate the digits of scaled_w. Therefore we have
587 // v == (double) (scaled_w * 10^-mk).
588 // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
589 // integer than it will be updated. For instance if scaled_w == 1.23 then
590 // the buffer will be filled with "123" und the decimal_exponent will be
591 // decreased by 2.
592 int kappa;
593 bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
594 buffer, length, &kappa);
595 *decimal_exponent = -mk + kappa;
596 return result;
597}
598
599
600// The "counted" version of grisu3 (see above) only generates requested_digits
601// number of digits. This version does not generate the shortest representation,
602// and with enough requested digits 0.1 will at some point print as 0.9999999...
603// Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
604// therefore the rounding strategy for halfway cases is irrelevant.
605static bool Grisu3Counted(double v,
606 int requested_digits,
607 Vector<char> buffer,
608 int* length,
609 int* decimal_exponent) {
610 DiyFp w = Double(v).AsNormalizedDiyFp();
611 DiyFp ten_mk; // Cached power of ten: 10^-k
612 int mk; // -k
613 int ten_mk_minimal_binary_exponent =
614 kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
615 int ten_mk_maximal_binary_exponent =
616 kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
617 PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
618 ten_mk_minimal_binary_exponent,
619 ten_mk_maximal_binary_exponent,
620 &ten_mk, &mk);
621 DOUBLE_CONVERSION_ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
622 DiyFp::kSignificandSize) &&
623 (kMaximalTargetExponent >= w.e() + ten_mk.e() +
624 DiyFp::kSignificandSize));
625 // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
626 // 64 bit significand and ten_mk is thus only precise up to 64 bits.
627
628 // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
629 // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
630 // off by a small amount.
631 // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
632 // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
633 // (f-1) * 2^e < w*10^k < (f+1) * 2^e
634 DiyFp scaled_w = DiyFp::Times(w, ten_mk);
635
636 // We now have (double) (scaled_w * 10^-mk).
637 // DigitGen will generate the first requested_digits digits of scaled_w and
638 // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
639 // will not always be exactly the same since DigitGenCounted only produces a
640 // limited number of digits.)
641 int kappa;
642 bool result = DigitGenCounted(scaled_w, requested_digits,
643 buffer, length, &kappa);
644 *decimal_exponent = -mk + kappa;
645 return result;
646}
647
648
649bool FastDtoa(double v,
650 FastDtoaMode mode,
651 int requested_digits,
652 Vector<char> buffer,
653 int* length,
654 int* decimal_point) {
655 DOUBLE_CONVERSION_ASSERT(v > 0);
656 DOUBLE_CONVERSION_ASSERT(!Double(v).IsSpecial());
657
658 bool result = false;
659 int decimal_exponent = 0;
660 switch (mode) {
661 case FAST_DTOA_SHORTEST:
662 case FAST_DTOA_SHORTEST_SINGLE:
663 result = Grisu3(v, mode, buffer, length, &decimal_exponent);
664 break;
665 case FAST_DTOA_PRECISION:
666 result = Grisu3Counted(v, requested_digits,
667 buffer, length, &decimal_exponent);
668 break;
669 default:
670 DOUBLE_CONVERSION_UNREACHABLE();
671 }
672 if (result) {
673 *decimal_point = *length + decimal_exponent;
674 buffer[*length] = '\0';
675 }
676 return result;
677}
678
679} // namespace double_conversion
680
681// ICU PATCH: Close ICU namespace
682U_NAMESPACE_END
683#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
684