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27
28#include <math.h>
29
30#include "bignum-dtoa.h"
31
32#include "bignum.h"
33#include "ieee.h"
34
35namespace double_conversion {
36
37static int NormalizedExponent(uint64_t significand, int exponent) {
38 ASSERT(significand != 0);
39 while ((significand & Double::kHiddenBit) == 0) {
40 significand = significand << 1;
41 exponent = exponent - 1;
42 }
43 return exponent;
44}
45
46
47// Forward declarations:
48// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
49static int EstimatePower(int exponent);
50// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
51// and denominator.
52static void InitialScaledStartValues(uint64_t significand,
53 int exponent,
54 bool lower_boundary_is_closer,
55 int estimated_power,
56 bool need_boundary_deltas,
57 Bignum* numerator,
58 Bignum* denominator,
59 Bignum* delta_minus,
60 Bignum* delta_plus);
61// Multiplies numerator/denominator so that its values lies in the range 1-10.
62// Returns decimal_point s.t.
63// v = numerator'/denominator' * 10^(decimal_point-1)
64// where numerator' and denominator' are the values of numerator and
65// denominator after the call to this function.
66static void FixupMultiply10(int estimated_power, bool is_even,
67 int* decimal_point,
68 Bignum* numerator, Bignum* denominator,
69 Bignum* delta_minus, Bignum* delta_plus);
70// Generates digits from the left to the right and stops when the generated
71// digits yield the shortest decimal representation of v.
72static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
73 Bignum* delta_minus, Bignum* delta_plus,
74 bool is_even,
75 Vector<char> buffer, int* length);
76// Generates 'requested_digits' after the decimal point.
77static void BignumToFixed(int requested_digits, int* decimal_point,
78 Bignum* numerator, Bignum* denominator,
79 Vector<char>(buffer), int* length);
80// Generates 'count' digits of numerator/denominator.
81// Once 'count' digits have been produced rounds the result depending on the
82// remainder (remainders of exactly .5 round upwards). Might update the
83// decimal_point when rounding up (for example for 0.9999).
84static void GenerateCountedDigits(int count, int* decimal_point,
85 Bignum* numerator, Bignum* denominator,
86 Vector<char>(buffer), int* length);
87
88
89void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
90 Vector<char> buffer, int* length, int* decimal_point) {
91 ASSERT(v > 0);
92 ASSERT(!Double(v).IsSpecial());
93 uint64_t significand;
94 int exponent;
95 bool lower_boundary_is_closer;
96 if (mode == BIGNUM_DTOA_SHORTEST_SINGLE) {
97 float f = static_cast<float>(v);
98 ASSERT(f == v);
99 significand = Single(f).Significand();
100 exponent = Single(f).Exponent();
101 lower_boundary_is_closer = Single(f).LowerBoundaryIsCloser();
102 } else {
103 significand = Double(v).Significand();
104 exponent = Double(v).Exponent();
105 lower_boundary_is_closer = Double(v).LowerBoundaryIsCloser();
106 }
107 bool need_boundary_deltas =
108 (mode == BIGNUM_DTOA_SHORTEST || mode == BIGNUM_DTOA_SHORTEST_SINGLE);
109
110 bool is_even = (significand & 1) == 0;
111 int normalized_exponent = NormalizedExponent(significand, exponent);
112 // estimated_power might be too low by 1.
113 int estimated_power = EstimatePower(normalized_exponent);
114
115 // Shortcut for Fixed.
116 // The requested digits correspond to the digits after the point. If the
117 // number is much too small, then there is no need in trying to get any
118 // digits.
119 if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
120 buffer[0] = '\0';
121 *length = 0;
122 // Set decimal-point to -requested_digits. This is what Gay does.
123 // Note that it should not have any effect anyways since the string is
124 // empty.
125 *decimal_point = -requested_digits;
126 return;
127 }
128
129 Bignum numerator;
130 Bignum denominator;
131 Bignum delta_minus;
132 Bignum delta_plus;
133 // Make sure the bignum can grow large enough. The smallest double equals
134 // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
135 // The maximum double is 1.7976931348623157e308 which needs fewer than
136 // 308*4 binary digits.
137 ASSERT(Bignum::kMaxSignificantBits >= 324*4);
138 InitialScaledStartValues(significand, exponent, lower_boundary_is_closer,
139 estimated_power, need_boundary_deltas,
140 &numerator, &denominator,
141 &delta_minus, &delta_plus);
142 // We now have v = (numerator / denominator) * 10^estimated_power.
143 FixupMultiply10(estimated_power, is_even, decimal_point,
144 &numerator, &denominator,
145 &delta_minus, &delta_plus);
146 // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
147 // 1 <= (numerator + delta_plus) / denominator < 10
148 switch (mode) {
149 case BIGNUM_DTOA_SHORTEST:
150 case BIGNUM_DTOA_SHORTEST_SINGLE:
151 GenerateShortestDigits(&numerator, &denominator,
152 &delta_minus, &delta_plus,
153 is_even, buffer, length);
154 break;
155 case BIGNUM_DTOA_FIXED:
156 BignumToFixed(requested_digits, decimal_point,
157 &numerator, &denominator,
158 buffer, length);
159 break;
160 case BIGNUM_DTOA_PRECISION:
161 GenerateCountedDigits(requested_digits, decimal_point,
162 &numerator, &denominator,
163 buffer, length);
164 break;
165 default:
166 UNREACHABLE();
167 }
168 buffer[*length] = '\0';
169}
170
171
172// The procedure starts generating digits from the left to the right and stops
173// when the generated digits yield the shortest decimal representation of v. A
174// decimal representation of v is a number lying closer to v than to any other
175// double, so it converts to v when read.
176//
177// This is true if d, the decimal representation, is between m- and m+, the
178// upper and lower boundaries. d must be strictly between them if !is_even.
179// m- := (numerator - delta_minus) / denominator
180// m+ := (numerator + delta_plus) / denominator
181//
182// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
183// If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
184// will be produced. This should be the standard precondition.
185static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
186 Bignum* delta_minus, Bignum* delta_plus,
187 bool is_even,
188 Vector<char> buffer, int* length) {
189 // Small optimization: if delta_minus and delta_plus are the same just reuse
190 // one of the two bignums.
191 if (Bignum::Equal(*delta_minus, *delta_plus)) {
192 delta_plus = delta_minus;
193 }
194 *length = 0;
195 for (;;) {
196 uint16_t digit;
197 digit = numerator->DivideModuloIntBignum(*denominator);
198 ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
199 // digit = numerator / denominator (integer division).
200 // numerator = numerator % denominator.
201 buffer[(*length)++] = static_cast<char>(digit + '0');
202
203 // Can we stop already?
204 // If the remainder of the division is less than the distance to the lower
205 // boundary we can stop. In this case we simply round down (discarding the
206 // remainder).
207 // Similarly we test if we can round up (using the upper boundary).
208 bool in_delta_room_minus;
209 bool in_delta_room_plus;
210 if (is_even) {
211 in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
212 } else {
213 in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
214 }
215 if (is_even) {
216 in_delta_room_plus =
217 Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
218 } else {
219 in_delta_room_plus =
220 Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
221 }
222 if (!in_delta_room_minus && !in_delta_room_plus) {
223 // Prepare for next iteration.
224 numerator->Times10();
225 delta_minus->Times10();
226 // We optimized delta_plus to be equal to delta_minus (if they share the
227 // same value). So don't multiply delta_plus if they point to the same
228 // object.
229 if (delta_minus != delta_plus) {
230 delta_plus->Times10();
231 }
232 } else if (in_delta_room_minus && in_delta_room_plus) {
233 // Let's see if 2*numerator < denominator.
234 // If yes, then the next digit would be < 5 and we can round down.
235 int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
236 if (compare < 0) {
237 // Remaining digits are less than .5. -> Round down (== do nothing).
238 } else if (compare > 0) {
239 // Remaining digits are more than .5 of denominator. -> Round up.
240 // Note that the last digit could not be a '9' as otherwise the whole
241 // loop would have stopped earlier.
242 // We still have an assert here in case the preconditions were not
243 // satisfied.
244 ASSERT(buffer[(*length) - 1] != '9');
245 buffer[(*length) - 1]++;
246 } else {
247 // Halfway case.
248 // TODO(floitsch): need a way to solve half-way cases.
249 // For now let's round towards even (since this is what Gay seems to
250 // do).
251
252 if ((buffer[(*length) - 1] - '0') % 2 == 0) {
253 // Round down => Do nothing.
254 } else {
255 ASSERT(buffer[(*length) - 1] != '9');
256 buffer[(*length) - 1]++;
257 }
258 }
259 return;
260 } else if (in_delta_room_minus) {
261 // Round down (== do nothing).
262 return;
263 } else { // in_delta_room_plus
264 // Round up.
265 // Note again that the last digit could not be '9' since this would have
266 // stopped the loop earlier.
267 // We still have an ASSERT here, in case the preconditions were not
268 // satisfied.
269 ASSERT(buffer[(*length) -1] != '9');
270 buffer[(*length) - 1]++;
271 return;
272 }
273 }
274}
275
276
277// Let v = numerator / denominator < 10.
278// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
279// from left to right. Once 'count' digits have been produced we decide wether
280// to round up or down. Remainders of exactly .5 round upwards. Numbers such
281// as 9.999999 propagate a carry all the way, and change the
282// exponent (decimal_point), when rounding upwards.
283static void GenerateCountedDigits(int count, int* decimal_point,
284 Bignum* numerator, Bignum* denominator,
285 Vector<char> buffer, int* length) {
286 ASSERT(count >= 0);
287 for (int i = 0; i < count - 1; ++i) {
288 uint16_t digit;
289 digit = numerator->DivideModuloIntBignum(*denominator);
290 ASSERT(digit <= 9); // digit is a uint16_t and therefore always positive.
291 // digit = numerator / denominator (integer division).
292 // numerator = numerator % denominator.
293 buffer[i] = static_cast<char>(digit + '0');
294 // Prepare for next iteration.
295 numerator->Times10();
296 }
297 // Generate the last digit.
298 uint16_t digit;
299 digit = numerator->DivideModuloIntBignum(*denominator);
300 if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
301 digit++;
302 }
303 ASSERT(digit <= 10);
304 buffer[count - 1] = static_cast<char>(digit + '0');
305 // Correct bad digits (in case we had a sequence of '9's). Propagate the
306 // carry until we hat a non-'9' or til we reach the first digit.
307 for (int i = count - 1; i > 0; --i) {
308 if (buffer[i] != '0' + 10) break;
309 buffer[i] = '0';
310 buffer[i - 1]++;
311 }
312 if (buffer[0] == '0' + 10) {
313 // Propagate a carry past the top place.
314 buffer[0] = '1';
315 (*decimal_point)++;
316 }
317 *length = count;
318}
319
320
321// Generates 'requested_digits' after the decimal point. It might omit
322// trailing '0's. If the input number is too small then no digits at all are
323// generated (ex.: 2 fixed digits for 0.00001).
324//
325// Input verifies: 1 <= (numerator + delta) / denominator < 10.
326static void BignumToFixed(int requested_digits, int* decimal_point,
327 Bignum* numerator, Bignum* denominator,
328 Vector<char>(buffer), int* length) {
329 // Note that we have to look at more than just the requested_digits, since
330 // a number could be rounded up. Example: v=0.5 with requested_digits=0.
331 // Even though the power of v equals 0 we can't just stop here.
332 if (-(*decimal_point) > requested_digits) {
333 // The number is definitively too small.
334 // Ex: 0.001 with requested_digits == 1.
335 // Set decimal-point to -requested_digits. This is what Gay does.
336 // Note that it should not have any effect anyways since the string is
337 // empty.
338 *decimal_point = -requested_digits;
339 *length = 0;
340 return;
341 } else if (-(*decimal_point) == requested_digits) {
342 // We only need to verify if the number rounds down or up.
343 // Ex: 0.04 and 0.06 with requested_digits == 1.
344 ASSERT(*decimal_point == -requested_digits);
345 // Initially the fraction lies in range (1, 10]. Multiply the denominator
346 // by 10 so that we can compare more easily.
347 denominator->Times10();
348 if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
349 // If the fraction is >= 0.5 then we have to include the rounded
350 // digit.
351 buffer[0] = '1';
352 *length = 1;
353 (*decimal_point)++;
354 } else {
355 // Note that we caught most of similar cases earlier.
356 *length = 0;
357 }
358 return;
359 } else {
360 // The requested digits correspond to the digits after the point.
361 // The variable 'needed_digits' includes the digits before the point.
362 int needed_digits = (*decimal_point) + requested_digits;
363 GenerateCountedDigits(needed_digits, decimal_point,
364 numerator, denominator,
365 buffer, length);
366 }
367}
368
369
370// Returns an estimation of k such that 10^(k-1) <= v < 10^k where
371// v = f * 2^exponent and 2^52 <= f < 2^53.
372// v is hence a normalized double with the given exponent. The output is an
373// approximation for the exponent of the decimal approimation .digits * 10^k.
374//
375// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
376// Note: this property holds for v's upper boundary m+ too.
377// 10^k <= m+ < 10^k+1.
378// (see explanation below).
379//
380// Examples:
381// EstimatePower(0) => 16
382// EstimatePower(-52) => 0
383//
384// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
385static int EstimatePower(int exponent) {
386 // This function estimates log10 of v where v = f*2^e (with e == exponent).
387 // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
388 // Note that f is bounded by its container size. Let p = 53 (the double's
389 // significand size). Then 2^(p-1) <= f < 2^p.
390 //
391 // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
392 // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
393 // The computed number undershoots by less than 0.631 (when we compute log3
394 // and not log10).
395 //
396 // Optimization: since we only need an approximated result this computation
397 // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
398 // not really measurable, though.
399 //
400 // Since we want to avoid overshooting we decrement by 1e10 so that
401 // floating-point imprecisions don't affect us.
402 //
403 // Explanation for v's boundary m+: the computation takes advantage of
404 // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
405 // (even for denormals where the delta can be much more important).
406
407 const double k1Log10 = 0.30102999566398114; // 1/lg(10)
408
409 // For doubles len(f) == 53 (don't forget the hidden bit).
410 const int kSignificandSize = Double::kSignificandSize;
411 double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
412 return static_cast<int>(estimate);
413}
414
415
416// See comments for InitialScaledStartValues.
417static void InitialScaledStartValuesPositiveExponent(
418 uint64_t significand, int exponent,
419 int estimated_power, bool need_boundary_deltas,
420 Bignum* numerator, Bignum* denominator,
421 Bignum* delta_minus, Bignum* delta_plus) {
422 // A positive exponent implies a positive power.
423 ASSERT(estimated_power >= 0);
424 // Since the estimated_power is positive we simply multiply the denominator
425 // by 10^estimated_power.
426
427 // numerator = v.
428 numerator->AssignUInt64(significand);
429 numerator->ShiftLeft(exponent);
430 // denominator = 10^estimated_power.
431 denominator->AssignPowerUInt16(10, estimated_power);
432
433 if (need_boundary_deltas) {
434 // Introduce a common denominator so that the deltas to the boundaries are
435 // integers.
436 denominator->ShiftLeft(1);
437 numerator->ShiftLeft(1);
438 // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
439 // denominator (of 2) delta_plus equals 2^e.
440 delta_plus->AssignUInt16(1);
441 delta_plus->ShiftLeft(exponent);
442 // Same for delta_minus. The adjustments if f == 2^p-1 are done later.
443 delta_minus->AssignUInt16(1);
444 delta_minus->ShiftLeft(exponent);
445 }
446}
447
448
449// See comments for InitialScaledStartValues
450static void InitialScaledStartValuesNegativeExponentPositivePower(
451 uint64_t significand, int exponent,
452 int estimated_power, bool need_boundary_deltas,
453 Bignum* numerator, Bignum* denominator,
454 Bignum* delta_minus, Bignum* delta_plus) {
455 // v = f * 2^e with e < 0, and with estimated_power >= 0.
456 // This means that e is close to 0 (have a look at how estimated_power is
457 // computed).
458
459 // numerator = significand
460 // since v = significand * 2^exponent this is equivalent to
461 // numerator = v * / 2^-exponent
462 numerator->AssignUInt64(significand);
463 // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
464 denominator->AssignPowerUInt16(10, estimated_power);
465 denominator->ShiftLeft(-exponent);
466
467 if (need_boundary_deltas) {
468 // Introduce a common denominator so that the deltas to the boundaries are
469 // integers.
470 denominator->ShiftLeft(1);
471 numerator->ShiftLeft(1);
472 // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
473 // denominator (of 2) delta_plus equals 2^e.
474 // Given that the denominator already includes v's exponent the distance
475 // to the boundaries is simply 1.
476 delta_plus->AssignUInt16(1);
477 // Same for delta_minus. The adjustments if f == 2^p-1 are done later.
478 delta_minus->AssignUInt16(1);
479 }
480}
481
482
483// See comments for InitialScaledStartValues
484static void InitialScaledStartValuesNegativeExponentNegativePower(
485 uint64_t significand, int exponent,
486 int estimated_power, bool need_boundary_deltas,
487 Bignum* numerator, Bignum* denominator,
488 Bignum* delta_minus, Bignum* delta_plus) {
489 // Instead of multiplying the denominator with 10^estimated_power we
490 // multiply all values (numerator and deltas) by 10^-estimated_power.
491
492 // Use numerator as temporary container for power_ten.
493 Bignum* power_ten = numerator;
494 power_ten->AssignPowerUInt16(10, -estimated_power);
495
496 if (need_boundary_deltas) {
497 // Since power_ten == numerator we must make a copy of 10^estimated_power
498 // before we complete the computation of the numerator.
499 // delta_plus = delta_minus = 10^estimated_power
500 delta_plus->AssignBignum(*power_ten);
501 delta_minus->AssignBignum(*power_ten);
502 }
503
504 // numerator = significand * 2 * 10^-estimated_power
505 // since v = significand * 2^exponent this is equivalent to
506 // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
507 // Remember: numerator has been abused as power_ten. So no need to assign it
508 // to itself.
509 ASSERT(numerator == power_ten);
510 numerator->MultiplyByUInt64(significand);
511
512 // denominator = 2 * 2^-exponent with exponent < 0.
513 denominator->AssignUInt16(1);
514 denominator->ShiftLeft(-exponent);
515
516 if (need_boundary_deltas) {
517 // Introduce a common denominator so that the deltas to the boundaries are
518 // integers.
519 numerator->ShiftLeft(1);
520 denominator->ShiftLeft(1);
521 // With this shift the boundaries have their correct value, since
522 // delta_plus = 10^-estimated_power, and
523 // delta_minus = 10^-estimated_power.
524 // These assignments have been done earlier.
525 // The adjustments if f == 2^p-1 (lower boundary is closer) are done later.
526 }
527}
528
529
530// Let v = significand * 2^exponent.
531// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
532// and denominator. The functions GenerateShortestDigits and
533// GenerateCountedDigits will then convert this ratio to its decimal
534// representation d, with the required accuracy.
535// Then d * 10^estimated_power is the representation of v.
536// (Note: the fraction and the estimated_power might get adjusted before
537// generating the decimal representation.)
538//
539// The initial start values consist of:
540// - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
541// - a scaled (common) denominator.
542// optionally (used by GenerateShortestDigits to decide if it has the shortest
543// decimal converting back to v):
544// - v - m-: the distance to the lower boundary.
545// - m+ - v: the distance to the upper boundary.
546//
547// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
548//
549// Let ep == estimated_power, then the returned values will satisfy:
550// v / 10^ep = numerator / denominator.
551// v's boundarys m- and m+:
552// m- / 10^ep == v / 10^ep - delta_minus / denominator
553// m+ / 10^ep == v / 10^ep + delta_plus / denominator
554// Or in other words:
555// m- == v - delta_minus * 10^ep / denominator;
556// m+ == v + delta_plus * 10^ep / denominator;
557//
558// Since 10^(k-1) <= v < 10^k (with k == estimated_power)
559// or 10^k <= v < 10^(k+1)
560// we then have 0.1 <= numerator/denominator < 1
561// or 1 <= numerator/denominator < 10
562//
563// It is then easy to kickstart the digit-generation routine.
564//
565// The boundary-deltas are only filled if the mode equals BIGNUM_DTOA_SHORTEST
566// or BIGNUM_DTOA_SHORTEST_SINGLE.
567
568static void InitialScaledStartValues(uint64_t significand,
569 int exponent,
570 bool lower_boundary_is_closer,
571 int estimated_power,
572 bool need_boundary_deltas,
573 Bignum* numerator,
574 Bignum* denominator,
575 Bignum* delta_minus,
576 Bignum* delta_plus) {
577 if (exponent >= 0) {
578 InitialScaledStartValuesPositiveExponent(
579 significand, exponent, estimated_power, need_boundary_deltas,
580 numerator, denominator, delta_minus, delta_plus);
581 } else if (estimated_power >= 0) {
582 InitialScaledStartValuesNegativeExponentPositivePower(
583 significand, exponent, estimated_power, need_boundary_deltas,
584 numerator, denominator, delta_minus, delta_plus);
585 } else {
586 InitialScaledStartValuesNegativeExponentNegativePower(
587 significand, exponent, estimated_power, need_boundary_deltas,
588 numerator, denominator, delta_minus, delta_plus);
589 }
590
591 if (need_boundary_deltas && lower_boundary_is_closer) {
592 // The lower boundary is closer at half the distance of "normal" numbers.
593 // Increase the common denominator and adapt all but the delta_minus.
594 denominator->ShiftLeft(1); // *2
595 numerator->ShiftLeft(1); // *2
596 delta_plus->ShiftLeft(1); // *2
597 }
598}
599
600
601// This routine multiplies numerator/denominator so that its values lies in the
602// range 1-10. That is after a call to this function we have:
603// 1 <= (numerator + delta_plus) /denominator < 10.
604// Let numerator the input before modification and numerator' the argument
605// after modification, then the output-parameter decimal_point is such that
606// numerator / denominator * 10^estimated_power ==
607// numerator' / denominator' * 10^(decimal_point - 1)
608// In some cases estimated_power was too low, and this is already the case. We
609// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
610// estimated_power) but do not touch the numerator or denominator.
611// Otherwise the routine multiplies the numerator and the deltas by 10.
612static void FixupMultiply10(int estimated_power, bool is_even,
613 int* decimal_point,
614 Bignum* numerator, Bignum* denominator,
615 Bignum* delta_minus, Bignum* delta_plus) {
616 bool in_range;
617 if (is_even) {
618 // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
619 // are rounded to the closest floating-point number with even significand.
620 in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
621 } else {
622 in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
623 }
624 if (in_range) {
625 // Since numerator + delta_plus >= denominator we already have
626 // 1 <= numerator/denominator < 10. Simply update the estimated_power.
627 *decimal_point = estimated_power + 1;
628 } else {
629 *decimal_point = estimated_power;
630 numerator->Times10();
631 if (Bignum::Equal(*delta_minus, *delta_plus)) {
632 delta_minus->Times10();
633 delta_plus->AssignBignum(*delta_minus);
634 } else {
635 delta_minus->Times10();
636 delta_plus->Times10();
637 }
638 }
639}
640
641} // namespace double_conversion
642