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25
26 // This file is available under and governed by the GNU General Public
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28 // However, the following notice accompanied the original version of this
29 // file:
30 //
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57
58 package jdk.nashorn.internal.runtime.doubleconv;
59
60 import java.util.Arrays;
61
62 class Bignum {
63
64 // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately.
65 // This bignum can encode much bigger numbers, since it contains an
66 // exponent.
67 static final int kMaxSignificantBits = 3584;
68
69 static final int kChunkSize = 32; // size of int
70 static final int kDoubleChunkSize = 64; // size of long
71 // With bigit size of 28 we loose some bits, but a double still fits easily
72 // into two ints, and more importantly we can use the Comba multiplication.
73 static final int kBigitSize = 28;
74 static final int kBigitMask = (1 << kBigitSize) - 1;
75 // Every instance allocates kbigitLength ints on the stack. Bignums cannot
76 // grow. There are no checks if the stack-allocated space is sufficient.
77 static final int kBigitCapacity = kMaxSignificantBits / kBigitSize;
78
79 private int[] bigits_ = new int[kBigitCapacity];
80 // A vector backed by bigits_buffer_. This way accesses to the array are
81 // checked for out-of-bounds errors.
82 // Vector<int> bigits_;
83 private int used_digits_;
84 // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize).
85 private int exponent_;
86
87 Bignum() {}
88
89 void times10() { multiplyByUInt32(10); }
90
91 static boolean equal(final Bignum a, final Bignum b) {
92 return compare(a, b) == 0;
93 }
94 static boolean lessEqual(final Bignum a, final Bignum b) {
95 return compare(a, b) <= 0;
96 }
97 static boolean less(final Bignum a, final Bignum b) {
98 return compare(a, b) < 0;
99 }
100
101 // Returns a + b == c
102 static boolean plusEqual(final Bignum a, final Bignum b, final Bignum c) {
103 return plusCompare(a, b, c) == 0;
104 }
105 // Returns a + b <= c
106 static boolean plusLessEqual(final Bignum a, final Bignum b, final Bignum c) {
107 return plusCompare(a, b, c) <= 0;
108 }
109 // Returns a + b < c
110 static boolean plusLess(final Bignum a, final Bignum b, final Bignum c) {
111 return plusCompare(a, b, c) < 0;
112 }
113
114 private void ensureCapacity(final int size) {
115 if (size > kBigitCapacity) {
116 throw new RuntimeException();
117 }
118 }
119
120 // BigitLength includes the "hidden" digits encoded in the exponent.
121 int bigitLength() { return used_digits_ + exponent_; }
122
123 // Guaranteed to lie in one Bigit.
124 void assignUInt16(final char value) {
125 assert (kBigitSize >= 16);
126 zero();
127 if (value == 0) return;
128
129 ensureCapacity(1);
130 bigits_[0] = value;
131 used_digits_ = 1;
132 }
133
134
135 void assignUInt64(long value) {
136 final int kUInt64Size = 64;
137
138 zero();
139 if (value == 0) return;
140
141 final int needed_bigits = kUInt64Size / kBigitSize + 1;
142 ensureCapacity(needed_bigits);
143 for (int i = 0; i < needed_bigits; ++i) {
144 bigits_[i] = (int) (value & kBigitMask);
145 value = value >>> kBigitSize;
146 }
147 used_digits_ = needed_bigits;
148 clamp();
149 }
150
151
152 void assignBignum(final Bignum other) {
153 exponent_ = other.exponent_;
154 for (int i = 0; i < other.used_digits_; ++i) {
155 bigits_[i] = other.bigits_[i];
156 }
157 // Clear the excess digits (if there were any).
158 for (int i = other.used_digits_; i < used_digits_; ++i) {
159 bigits_[i] = 0;
160 }
161 used_digits_ = other.used_digits_;
162 }
163
164
165 static long readUInt64(final String str,
166 final int from,
167 final int digits_to_read) {
168 long result = 0;
169 for (int i = from; i < from + digits_to_read; ++i) {
170 final int digit = str.charAt(i) - '0';
171 assert (0 <= digit && digit <= 9);
172 result = result * 10 + digit;
173 }
174 return result;
175 }
176
177
178 void assignDecimalString(final String str) {
179 // 2^64 = 18446744073709551616 > 10^19
180 final int kMaxUint64DecimalDigits = 19;
181 zero();
182 int length = str.length();
183 int pos = 0;
184 // Let's just say that each digit needs 4 bits.
185 while (length >= kMaxUint64DecimalDigits) {
186 final long digits = readUInt64(str, pos, kMaxUint64DecimalDigits);
187 pos += kMaxUint64DecimalDigits;
188 length -= kMaxUint64DecimalDigits;
189 multiplyByPowerOfTen(kMaxUint64DecimalDigits);
190 addUInt64(digits);
191 }
192 final long digits = readUInt64(str, pos, length);
193 multiplyByPowerOfTen(length);
194 addUInt64(digits);
195 clamp();
196 }
197
198
199 static int hexCharValue(final char c) {
200 if ('0' <= c && c <= '9') return c - '0';
201 if ('a' <= c && c <= 'f') return 10 + c - 'a';
202 assert ('A' <= c && c <= 'F');
203 return 10 + c - 'A';
204 }
205
206
207 void assignHexString(final String str) {
208 zero();
209 final int length = str.length();
210
211 final int needed_bigits = length * 4 / kBigitSize + 1;
212 ensureCapacity(needed_bigits);
213 int string_index = length - 1;
214 for (int i = 0; i < needed_bigits - 1; ++i) {
215 // These bigits are guaranteed to be "full".
216 int current_bigit = 0;
217 for (int j = 0; j < kBigitSize / 4; j++) {
218 current_bigit += hexCharValue(str.charAt(string_index--)) << (j * 4);
219 }
220 bigits_[i] = current_bigit;
221 }
222 used_digits_ = needed_bigits - 1;
223
224 int most_significant_bigit = 0; // Could be = 0;
225 for (int j = 0; j <= string_index; ++j) {
226 most_significant_bigit <<= 4;
227 most_significant_bigit += hexCharValue(str.charAt(j));
228 }
229 if (most_significant_bigit != 0) {
230 bigits_[used_digits_] = most_significant_bigit;
231 used_digits_++;
232 }
233 clamp();
234 }
235
236
237 void addUInt64(final long operand) {
238 if (operand == 0) return;
239 final Bignum other = new Bignum();
240 other.assignUInt64(operand);
241 addBignum(other);
242 }
243
244
245 void addBignum(final Bignum other) {
246 assert (isClamped());
247 assert (other.isClamped());
248
249 // If this has a greater exponent than other append zero-bigits to this.
250 // After this call exponent_ <= other.exponent_.
251 align(other);
252
253 // There are two possibilities:
254 // aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
255 // bbbbb 00000000
256 // ----------------
257 // ccccccccccc 0000
258 // or
259 // aaaaaaaaaa 0000
260 // bbbbbbbbb 0000000
261 // -----------------
262 // cccccccccccc 0000
263 // In both cases we might need a carry bigit.
264
265 ensureCapacity(1 + Math.max(bigitLength(), other.bigitLength()) - exponent_);
266 int carry = 0;
267 int bigit_pos = other.exponent_ - exponent_;
268 assert (bigit_pos >= 0);
269 for (int i = 0; i < other.used_digits_; ++i) {
270 final int sum = bigits_[bigit_pos] + other.bigits_[i] + carry;
271 bigits_[bigit_pos] = sum & kBigitMask;
272 carry = sum >>> kBigitSize;
273 bigit_pos++;
274 }
275
276 while (carry != 0) {
277 final int sum = bigits_[bigit_pos] + carry;
278 bigits_[bigit_pos] = sum & kBigitMask;
279 carry = sum >>> kBigitSize;
280 bigit_pos++;
281 }
282 used_digits_ = Math.max(bigit_pos, used_digits_);
283 assert (isClamped());
284 }
285
286
287 void subtractBignum(final Bignum other) {
288 assert (isClamped());
289 assert (other.isClamped());
290 // We require this to be bigger than other.
291 assert (lessEqual(other, this));
292
293 align(other);
294
295 final int offset = other.exponent_ - exponent_;
296 int borrow = 0;
297 int i;
298 for (i = 0; i < other.used_digits_; ++i) {
299 assert ((borrow == 0) || (borrow == 1));
300 final int difference = bigits_[i + offset] - other.bigits_[i] - borrow;
301 bigits_[i + offset] = difference & kBigitMask;
302 borrow = difference >>> (kChunkSize - 1);
303 }
304 while (borrow != 0) {
305 final int difference = bigits_[i + offset] - borrow;
306 bigits_[i + offset] = difference & kBigitMask;
307 borrow = difference >>> (kChunkSize - 1);
308 ++i;
309 }
310 clamp();
311 }
312
313
314 void shiftLeft(final int shift_amount) {
315 if (used_digits_ == 0) return;
316 exponent_ += shift_amount / kBigitSize;
317 final int local_shift = shift_amount % kBigitSize;
318 ensureCapacity(used_digits_ + 1);
319 bigitsShiftLeft(local_shift);
320 }
321
322
323 void multiplyByUInt32(final int factor) {
324 if (factor == 1) return;
325 if (factor == 0) {
326 zero();
327 return;
328 }
329 if (used_digits_ == 0) return;
330
331 // The product of a bigit with the factor is of size kBigitSize + 32.
332 // Assert that this number + 1 (for the carry) fits into double int.
333 assert (kDoubleChunkSize >= kBigitSize + 32 + 1);
334 long carry = 0;
335 for (int i = 0; i < used_digits_; ++i) {
336 final long product = (factor & 0xFFFFFFFFL) * bigits_[i] + carry;
337 bigits_[i] = (int) (product & kBigitMask);
338 carry = product >>> kBigitSize;
339 }
340 while (carry != 0) {
341 ensureCapacity(used_digits_ + 1);
342 bigits_[used_digits_] = (int) (carry & kBigitMask);
343 used_digits_++;
344 carry >>>= kBigitSize;
345 }
346 }
347
348
349 void multiplyByUInt64(final long factor) {
350 if (factor == 1) return;
351 if (factor == 0) {
352 zero();
353 return;
354 }
355 assert (kBigitSize < 32);
356 long carry = 0;
357 final long low = factor & 0xFFFFFFFFL;
358 final long high = factor >>> 32;
359 for (int i = 0; i < used_digits_; ++i) {
360 final long product_low = low * bigits_[i];
361 final long product_high = high * bigits_[i];
362 final long tmp = (carry & kBigitMask) + product_low;
363 bigits_[i] = (int) (tmp & kBigitMask);
364 carry = (carry >>> kBigitSize) + (tmp >>> kBigitSize) +
365 (product_high << (32 - kBigitSize));
366 }
367 while (carry != 0) {
368 ensureCapacity(used_digits_ + 1);
369 bigits_[used_digits_] = (int) (carry & kBigitMask);
370 used_digits_++;
371 carry >>>= kBigitSize;
372 }
373 }
374
375
376 void multiplyByPowerOfTen(final int exponent) {
377 final long kFive27 = 0x6765c793fa10079dL;
378 final int kFive1 = 5;
379 final int kFive2 = kFive1 * 5;
380 final int kFive3 = kFive2 * 5;
381 final int kFive4 = kFive3 * 5;
382 final int kFive5 = kFive4 * 5;
383 final int kFive6 = kFive5 * 5;
384 final int kFive7 = kFive6 * 5;
385 final int kFive8 = kFive7 * 5;
386 final int kFive9 = kFive8 * 5;
387 final int kFive10 = kFive9 * 5;
388 final int kFive11 = kFive10 * 5;
389 final int kFive12 = kFive11 * 5;
390 final int kFive13 = kFive12 * 5;
391 final int kFive1_to_12[] =
392 { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
393 kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
394
395 assert (exponent >= 0);
396 if (exponent == 0) return;
397 if (used_digits_ == 0) return;
398
399 // We shift by exponent at the end just before returning.
400 int remaining_exponent = exponent;
401 while (remaining_exponent >= 27) {
402 multiplyByUInt64(kFive27);
403 remaining_exponent -= 27;
404 }
405 while (remaining_exponent >= 13) {
406 multiplyByUInt32(kFive13);
407 remaining_exponent -= 13;
408 }
409 if (remaining_exponent > 0) {
410 multiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
411 }
412 shiftLeft(exponent);
413 }
414
415
416 void square() {
417 assert (isClamped());
418 final int product_length = 2 * used_digits_;
419 ensureCapacity(product_length);
420
421 // Comba multiplication: compute each column separately.
422 // Example: r = a2a1a0 * b2b1b0.
423 // r = 1 * a0b0 +
424 // 10 * (a1b0 + a0b1) +
425 // 100 * (a2b0 + a1b1 + a0b2) +
426 // 1000 * (a2b1 + a1b2) +
427 // 10000 * a2b2
428 //
429 // In the worst case we have to accumulate nb-digits products of digit*digit.
430 //
431 // Assert that the additional number of bits in a DoubleChunk are enough to
432 // sum up used_digits of Bigit*Bigit.
433 if ((1L << (2 * (kChunkSize - kBigitSize))) <= used_digits_) {
434 throw new RuntimeException("unimplemented");
435 }
436 long accumulator = 0;
437 // First shift the digits so we don't overwrite them.
438 final int copy_offset = used_digits_;
439 for (int i = 0; i < used_digits_; ++i) {
440 bigits_[copy_offset + i] = bigits_[i];
441 }
442 // We have two loops to avoid some 'if's in the loop.
443 for (int i = 0; i < used_digits_; ++i) {
444 // Process temporary digit i with power i.
445 // The sum of the two indices must be equal to i.
446 int bigit_index1 = i;
447 int bigit_index2 = 0;
448 // Sum all of the sub-products.
449 while (bigit_index1 >= 0) {
450 final int int1 = bigits_[copy_offset + bigit_index1];
451 final int int2 = bigits_[copy_offset + bigit_index2];
452 accumulator += ((long) int1) * int2;
453 bigit_index1--;
454 bigit_index2++;
455 }
456 bigits_[i] = (int) (accumulator & kBigitMask);
457 accumulator >>>= kBigitSize;
458 }
459 for (int i = used_digits_; i < product_length; ++i) {
460 int bigit_index1 = used_digits_ - 1;
461 int bigit_index2 = i - bigit_index1;
462 // Invariant: sum of both indices is again equal to i.
463 // Inner loop runs 0 times on last iteration, emptying accumulator.
464 while (bigit_index2 < used_digits_) {
465 final int int1 = bigits_[copy_offset + bigit_index1];
466 final int int2 = bigits_[copy_offset + bigit_index2];
467 accumulator += ((long) int1) * int2;
468 bigit_index1--;
469 bigit_index2++;
470 }
471 // The overwritten bigits_[i] will never be read in further loop iterations,
472 // because bigit_index1 and bigit_index2 are always greater
473 // than i - used_digits_.
474 bigits_[i] = (int) (accumulator & kBigitMask);
475 accumulator >>>= kBigitSize;
476 }
477 // Since the result was guaranteed to lie inside the number the
478 // accumulator must be 0 now.
479 assert (accumulator == 0);
480
481 // Don't forget to update the used_digits and the exponent.
482 used_digits_ = product_length;
483 exponent_ *= 2;
484 clamp();
485 }
486
487
488 void assignPowerUInt16(int base, final int power_exponent) {
489 assert (base != 0);
490 assert (power_exponent >= 0);
491 if (power_exponent == 0) {
492 assignUInt16((char) 1);
493 return;
494 }
495 zero();
496 int shifts = 0;
497 // We expect base to be in range 2-32, and most often to be 10.
498 // It does not make much sense to implement different algorithms for counting
499 // the bits.
500 while ((base & 1) == 0) {
501 base >>>= 1;
502 shifts++;
503 }
504 int bit_size = 0;
505 int tmp_base = base;
506 while (tmp_base != 0) {
507 tmp_base >>>= 1;
508 bit_size++;
509 }
510 final int final_size = bit_size * power_exponent;
511 // 1 extra bigit for the shifting, and one for rounded final_size.
512 ensureCapacity(final_size / kBigitSize + 2);
513
514 // Left to Right exponentiation.
515 int mask = 1;
516 while (power_exponent >= mask) mask <<= 1;
517
518 // The mask is now pointing to the bit above the most significant 1-bit of
519 // power_exponent.
520 // Get rid of first 1-bit;
521 mask >>>= 2;
522 long this_value = base;
523
524 boolean delayed_multipliciation = false;
525 final long max_32bits = 0xFFFFFFFFL;
526 while (mask != 0 && this_value <= max_32bits) {
527 this_value = this_value * this_value;
528 // Verify that there is enough space in this_value to perform the
529 // multiplication. The first bit_size bits must be 0.
530 if ((power_exponent & mask) != 0) {
531 final long base_bits_mask =
532 ~((1L << (64 - bit_size)) - 1);
533 final boolean high_bits_zero = (this_value & base_bits_mask) == 0;
534 if (high_bits_zero) {
535 this_value *= base;
536 } else {
537 delayed_multipliciation = true;
538 }
539 }
540 mask >>>= 1;
541 }
542 assignUInt64(this_value);
543 if (delayed_multipliciation) {
544 multiplyByUInt32(base);
545 }
546
547 // Now do the same thing as a bignum.
548 while (mask != 0) {
549 square();
550 if ((power_exponent & mask) != 0) {
551 multiplyByUInt32(base);
552 }
553 mask >>>= 1;
554 }
555
556 // And finally add the saved shifts.
557 shiftLeft(shifts * power_exponent);
558 }
559
560
561 // Precondition: this/other < 16bit.
562 char divideModuloIntBignum(final Bignum other) {
563 assert (isClamped());
564 assert (other.isClamped());
565 assert (other.used_digits_ > 0);
566
567 // Easy case: if we have less digits than the divisor than the result is 0.
568 // Note: this handles the case where this == 0, too.
569 if (bigitLength() < other.bigitLength()) {
570 return 0;
571 }
572
573 align(other);
574
575 char result = 0;
576
577 // Start by removing multiples of 'other' until both numbers have the same
578 // number of digits.
579 while (bigitLength() > other.bigitLength()) {
580 // This naive approach is extremely inefficient if `this` divided by other
581 // is big. This function is implemented for doubleToString where
582 // the result should be small (less than 10).
583 assert (other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16));
584 assert (bigits_[used_digits_ - 1] < 0x10000);
585 // Remove the multiples of the first digit.
586 // Example this = 23 and other equals 9. -> Remove 2 multiples.
587 result += (bigits_[used_digits_ - 1]);
588 subtractTimes(other, bigits_[used_digits_ - 1]);
589 }
590
591 assert (bigitLength() == other.bigitLength());
592
593 // Both bignums are at the same length now.
594 // Since other has more than 0 digits we know that the access to
595 // bigits_[used_digits_ - 1] is safe.
596 final int this_bigit = bigits_[used_digits_ - 1];
597 final int other_bigit = other.bigits_[other.used_digits_ - 1];
598
599 if (other.used_digits_ == 1) {
600 // Shortcut for easy (and common) case.
601 final int quotient = Integer.divideUnsigned(this_bigit, other_bigit);
602 bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient;
603 assert (Integer.compareUnsigned(quotient, 0x10000) < 0);
604 result += quotient;
605 clamp();
606 return result;
607 }
608
609 final int division_estimate = Integer.divideUnsigned(this_bigit, (other_bigit + 1));
610 assert (Integer.compareUnsigned(division_estimate, 0x10000) < 0);
611 result += division_estimate;
612 subtractTimes(other, division_estimate);
613
614 if (other_bigit * (division_estimate + 1) > this_bigit) {
615 // No need to even try to subtract. Even if other's remaining digits were 0
616 // another subtraction would be too much.
617 return result;
618 }
619
620 while (lessEqual(other, this)) {
621 subtractBignum(other);
622 result++;
623 }
624 return result;
625 }
626
627
628 static int sizeInHexChars(int number) {
629 assert (number > 0);
630 int result = 0;
631 while (number != 0) {
632 number >>>= 4;
633 result++;
634 }
635 return result;
636 }
637
638
639 static char hexCharOfValue(final int value) {
640 assert (0 <= value && value <= 16);
641 if (value < 10) return (char) (value + '0');
642 return (char) (value - 10 + 'A');
643 }
644
645
646 String toHexString() {
647 assert (isClamped());
648 // Each bigit must be printable as separate hex-character.
649 assert (kBigitSize % 4 == 0);
650 final int kHexCharsPerBigit = kBigitSize / 4;
651
652 if (used_digits_ == 0) {
653 return "0";
654 }
655
656 final int needed_chars = (bigitLength() - 1) * kHexCharsPerBigit +
657 sizeInHexChars(bigits_[used_digits_ - 1]);
658 final StringBuilder buffer = new StringBuilder(needed_chars);
659 buffer.setLength(needed_chars);
660
661 int string_index = needed_chars - 1;
662 for (int i = 0; i < exponent_; ++i) {
663 for (int j = 0; j < kHexCharsPerBigit; ++j) {
664 buffer.setCharAt(string_index--, '0');
665 }
666 }
667 for (int i = 0; i < used_digits_ - 1; ++i) {
668 int current_bigit = bigits_[i];
669 for (int j = 0; j < kHexCharsPerBigit; ++j) {
670 buffer.setCharAt(string_index--, hexCharOfValue(current_bigit & 0xF));
671 current_bigit >>>= 4;
672 }
673 }
674 // And finally the last bigit.
675 int most_significant_bigit = bigits_[used_digits_ - 1];
676 while (most_significant_bigit != 0) {
677 buffer.setCharAt(string_index--, hexCharOfValue(most_significant_bigit & 0xF));
678 most_significant_bigit >>>= 4;
679 }
680 return buffer.toString();
681 }
682
683
684 int bigitAt(final int index) {
685 if (index >= bigitLength()) return 0;
686 if (index < exponent_) return 0;
687 return bigits_[index - exponent_];
688 }
689
690
691 static int compare(final Bignum a, final Bignum b) {
692 assert (a.isClamped());
693 assert (b.isClamped());
694 final int bigit_length_a = a.bigitLength();
695 final int bigit_length_b = b.bigitLength();
696 if (bigit_length_a < bigit_length_b) return -1;
697 if (bigit_length_a > bigit_length_b) return +1;
698 for (int i = bigit_length_a - 1; i >= Math.min(a.exponent_, b.exponent_); --i) {
699 final int bigit_a = a.bigitAt(i);
700 final int bigit_b = b.bigitAt(i);
701 if (bigit_a < bigit_b) return -1;
702 if (bigit_a > bigit_b) return +1;
703 // Otherwise they are equal up to this digit. Try the next digit.
704 }
705 return 0;
706 }
707
708
709 static int plusCompare(final Bignum a, final Bignum b, final Bignum c) {
710 assert (a.isClamped());
711 assert (b.isClamped());
712 assert (c.isClamped());
713 if (a.bigitLength() < b.bigitLength()) {
714 return plusCompare(b, a, c);
715 }
716 if (a.bigitLength() + 1 < c.bigitLength()) return -1;
717 if (a.bigitLength() > c.bigitLength()) return +1;
718 // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than
719 // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one
720 // of 'a'.
721 if (a.exponent_ >= b.bigitLength() && a.bigitLength() < c.bigitLength()) {
722 return -1;
723 }
724
725 int borrow = 0;
726 // Starting at min_exponent all digits are == 0. So no need to compare them.
727 final int min_exponent = Math.min(Math.min(a.exponent_, b.exponent_), c.exponent_);
728 for (int i = c.bigitLength() - 1; i >= min_exponent; --i) {
729 final int int_a = a.bigitAt(i);
730 final int int_b = b.bigitAt(i);
731 final int int_c = c.bigitAt(i);
732 final int sum = int_a + int_b;
733 if (sum > int_c + borrow) {
734 return +1;
735 } else {
736 borrow = int_c + borrow - sum;
737 if (borrow > 1) return -1;
738 borrow <<= kBigitSize;
739 }
740 }
741 if (borrow == 0) return 0;
742 return -1;
743 }
744
745
746 void clamp() {
747 while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) {
748 used_digits_--;
749 }
750 if (used_digits_ == 0) {
751 // Zero.
752 exponent_ = 0;
753 }
754 }
755
756
757 boolean isClamped() {
758 return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0;
759 }
760
761
762 void zero() {
763 for (int i = 0; i < used_digits_; ++i) {
764 bigits_[i] = 0;
765 }
766 used_digits_ = 0;
767 exponent_ = 0;
768 }
769
770
771 void align(final Bignum other) {
772 if (exponent_ > other.exponent_) {
773 // If "X" represents a "hidden" digit (by the exponent) then we are in the
774 // following case (a == this, b == other):
775 // a: aaaaaaXXXX or a: aaaaaXXX
776 // b: bbbbbbX b: bbbbbbbbXX
777 // We replace some of the hidden digits (X) of a with 0 digits.
778 // a: aaaaaa000X or a: aaaaa0XX
779 final int zero_digits = exponent_ - other.exponent_;
780 ensureCapacity(used_digits_ + zero_digits);
781 for (int i = used_digits_ - 1; i >= 0; --i) {
782 bigits_[i + zero_digits] = bigits_[i];
783 }
784 for (int i = 0; i < zero_digits; ++i) {
785 bigits_[i] = 0;
786 }
787 used_digits_ += zero_digits;
788 exponent_ -= zero_digits;
789 assert (used_digits_ >= 0);
790 assert (exponent_ >= 0);
791 }
792 }
793
794
795 void bigitsShiftLeft(final int shift_amount) {
796 assert (shift_amount < kBigitSize);
797 assert (shift_amount >= 0);
798 int carry = 0;
799 for (int i = 0; i < used_digits_; ++i) {
800 final int new_carry = bigits_[i] >>> (kBigitSize - shift_amount);
801 bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask;
802 carry = new_carry;
803 }
804 if (carry != 0) {
805 bigits_[used_digits_] = carry;
806 used_digits_++;
807 }
808 }
809
810
811 void subtractTimes(final Bignum other, final int factor) {
812 assert (exponent_ <= other.exponent_);
813 if (factor < 3) {
814 for (int i = 0; i < factor; ++i) {
815 subtractBignum(other);
816 }
817 return;
818 }
819 int borrow = 0;
820 final int exponent_diff = other.exponent_ - exponent_;
821 for (int i = 0; i < other.used_digits_; ++i) {
822 final long product = ((long) factor) * other.bigits_[i];
823 final long remove = borrow + product;
824 final int difference = bigits_[i + exponent_diff] - (int) (remove & kBigitMask);
825 bigits_[i + exponent_diff] = difference & kBigitMask;
826 borrow = (int) ((difference >>> (kChunkSize - 1)) +
827 (remove >>> kBigitSize));
828 }
829 for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) {
830 if (borrow == 0) return;
831 final int difference = bigits_[i] - borrow;
832 bigits_[i] = difference & kBigitMask;
833 borrow = difference >>> (kChunkSize - 1);
834 }
835 clamp();
836 }
837
838 @Override
839 public String toString() {
840 return "Bignum" + Arrays.toString(bigits_);
841 }
842 }