| /* |
| * Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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| * questions. |
| */ |
| |
| // This file is available under and governed by the GNU General Public |
| // License version 2 only, as published by the Free Software Foundation. |
| // However, the following notice accompanied the original version of this |
| // file: |
| // |
| // Copyright 2010 the V8 project authors. All rights reserved. |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above |
| // copyright notice, this list of conditions and the following |
| // disclaimer in the documentation and/or other materials provided |
| // with the distribution. |
| // * Neither the name of Google Inc. nor the names of its |
| // contributors may be used to endorse or promote products derived |
| // from this software without specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| |
| package jdk.nashorn.internal.runtime.doubleconv; |
| |
| import java.util.Arrays; |
| |
| class Bignum { |
| |
| // 3584 = 128 * 28. We can represent 2^3584 > 10^1000 accurately. |
| // This bignum can encode much bigger numbers, since it contains an |
| // exponent. |
| static final int kMaxSignificantBits = 3584; |
| |
| static final int kChunkSize = 32; // size of int |
| static final int kDoubleChunkSize = 64; // size of long |
| // With bigit size of 28 we loose some bits, but a double still fits easily |
| // into two ints, and more importantly we can use the Comba multiplication. |
| static final int kBigitSize = 28; |
| static final int kBigitMask = (1 << kBigitSize) - 1; |
| // Every instance allocates kbigitLength ints on the stack. Bignums cannot |
| // grow. There are no checks if the stack-allocated space is sufficient. |
| static final int kBigitCapacity = kMaxSignificantBits / kBigitSize; |
| |
| private final int[] bigits_ = new int[kBigitCapacity]; |
| // A vector backed by bigits_buffer_. This way accesses to the array are |
| // checked for out-of-bounds errors. |
| // Vector<int> bigits_; |
| private int used_digits_; |
| // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize). |
| private int exponent_; |
| |
| Bignum() {} |
| |
| void times10() { multiplyByUInt32(10); } |
| |
| static boolean equal(final Bignum a, final Bignum b) { |
| return compare(a, b) == 0; |
| } |
| static boolean lessEqual(final Bignum a, final Bignum b) { |
| return compare(a, b) <= 0; |
| } |
| static boolean less(final Bignum a, final Bignum b) { |
| return compare(a, b) < 0; |
| } |
| |
| // Returns a + b == c |
| static boolean plusEqual(final Bignum a, final Bignum b, final Bignum c) { |
| return plusCompare(a, b, c) == 0; |
| } |
| // Returns a + b <= c |
| static boolean plusLessEqual(final Bignum a, final Bignum b, final Bignum c) { |
| return plusCompare(a, b, c) <= 0; |
| } |
| // Returns a + b < c |
| static boolean plusLess(final Bignum a, final Bignum b, final Bignum c) { |
| return plusCompare(a, b, c) < 0; |
| } |
| |
| private void ensureCapacity(final int size) { |
| if (size > kBigitCapacity) { |
| throw new RuntimeException(); |
| } |
| } |
| |
| // BigitLength includes the "hidden" digits encoded in the exponent. |
| int bigitLength() { return used_digits_ + exponent_; } |
| |
| // Guaranteed to lie in one Bigit. |
| void assignUInt16(final char value) { |
| assert (kBigitSize >= 16); |
| zero(); |
| if (value == 0) return; |
| |
| ensureCapacity(1); |
| bigits_[0] = value; |
| used_digits_ = 1; |
| } |
| |
| |
| void assignUInt64(long value) { |
| final int kUInt64Size = 64; |
| |
| zero(); |
| if (value == 0) return; |
| |
| final int needed_bigits = kUInt64Size / kBigitSize + 1; |
| ensureCapacity(needed_bigits); |
| for (int i = 0; i < needed_bigits; ++i) { |
| bigits_[i] = (int) (value & kBigitMask); |
| value = value >>> kBigitSize; |
| } |
| used_digits_ = needed_bigits; |
| clamp(); |
| } |
| |
| |
| void assignBignum(final Bignum other) { |
| exponent_ = other.exponent_; |
| for (int i = 0; i < other.used_digits_; ++i) { |
| bigits_[i] = other.bigits_[i]; |
| } |
| // Clear the excess digits (if there were any). |
| for (int i = other.used_digits_; i < used_digits_; ++i) { |
| bigits_[i] = 0; |
| } |
| used_digits_ = other.used_digits_; |
| } |
| |
| |
| static long readUInt64(final String str, |
| final int from, |
| final int digits_to_read) { |
| long result = 0; |
| for (int i = from; i < from + digits_to_read; ++i) { |
| final int digit = str.charAt(i) - '0'; |
| assert (0 <= digit && digit <= 9); |
| result = result * 10 + digit; |
| } |
| return result; |
| } |
| |
| |
| void assignDecimalString(final String str) { |
| // 2^64 = 18446744073709551616 > 10^19 |
| final int kMaxUint64DecimalDigits = 19; |
| zero(); |
| int length = str.length(); |
| int pos = 0; |
| // Let's just say that each digit needs 4 bits. |
| while (length >= kMaxUint64DecimalDigits) { |
| final long digits = readUInt64(str, pos, kMaxUint64DecimalDigits); |
| pos += kMaxUint64DecimalDigits; |
| length -= kMaxUint64DecimalDigits; |
| multiplyByPowerOfTen(kMaxUint64DecimalDigits); |
| addUInt64(digits); |
| } |
| final long digits = readUInt64(str, pos, length); |
| multiplyByPowerOfTen(length); |
| addUInt64(digits); |
| clamp(); |
| } |
| |
| |
| static int hexCharValue(final char c) { |
| if ('0' <= c && c <= '9') return c - '0'; |
| if ('a' <= c && c <= 'f') return 10 + c - 'a'; |
| assert ('A' <= c && c <= 'F'); |
| return 10 + c - 'A'; |
| } |
| |
| |
| void assignHexString(final String str) { |
| zero(); |
| final int length = str.length(); |
| |
| final int needed_bigits = length * 4 / kBigitSize + 1; |
| ensureCapacity(needed_bigits); |
| int string_index = length - 1; |
| for (int i = 0; i < needed_bigits - 1; ++i) { |
| // These bigits are guaranteed to be "full". |
| int current_bigit = 0; |
| for (int j = 0; j < kBigitSize / 4; j++) { |
| current_bigit += hexCharValue(str.charAt(string_index--)) << (j * 4); |
| } |
| bigits_[i] = current_bigit; |
| } |
| used_digits_ = needed_bigits - 1; |
| |
| int most_significant_bigit = 0; // Could be = 0; |
| for (int j = 0; j <= string_index; ++j) { |
| most_significant_bigit <<= 4; |
| most_significant_bigit += hexCharValue(str.charAt(j)); |
| } |
| if (most_significant_bigit != 0) { |
| bigits_[used_digits_] = most_significant_bigit; |
| used_digits_++; |
| } |
| clamp(); |
| } |
| |
| |
| void addUInt64(final long operand) { |
| if (operand == 0) return; |
| final Bignum other = new Bignum(); |
| other.assignUInt64(operand); |
| addBignum(other); |
| } |
| |
| |
| void addBignum(final Bignum other) { |
| assert (isClamped()); |
| assert (other.isClamped()); |
| |
| // If this has a greater exponent than other append zero-bigits to this. |
| // After this call exponent_ <= other.exponent_. |
| align(other); |
| |
| // There are two possibilities: |
| // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
| // bbbbb 00000000 |
| // ---------------- |
| // ccccccccccc 0000 |
| // or |
| // aaaaaaaaaa 0000 |
| // bbbbbbbbb 0000000 |
| // ----------------- |
| // cccccccccccc 0000 |
| // In both cases we might need a carry bigit. |
| |
| ensureCapacity(1 + Math.max(bigitLength(), other.bigitLength()) - exponent_); |
| int carry = 0; |
| int bigit_pos = other.exponent_ - exponent_; |
| assert (bigit_pos >= 0); |
| for (int i = 0; i < other.used_digits_; ++i) { |
| final int sum = bigits_[bigit_pos] + other.bigits_[i] + carry; |
| bigits_[bigit_pos] = sum & kBigitMask; |
| carry = sum >>> kBigitSize; |
| bigit_pos++; |
| } |
| |
| while (carry != 0) { |
| final int sum = bigits_[bigit_pos] + carry; |
| bigits_[bigit_pos] = sum & kBigitMask; |
| carry = sum >>> kBigitSize; |
| bigit_pos++; |
| } |
| used_digits_ = Math.max(bigit_pos, used_digits_); |
| assert (isClamped()); |
| } |
| |
| |
| void subtractBignum(final Bignum other) { |
| assert (isClamped()); |
| assert (other.isClamped()); |
| // We require this to be bigger than other. |
| assert (lessEqual(other, this)); |
| |
| align(other); |
| |
| final int offset = other.exponent_ - exponent_; |
| int borrow = 0; |
| int i; |
| for (i = 0; i < other.used_digits_; ++i) { |
| assert ((borrow == 0) || (borrow == 1)); |
| final int difference = bigits_[i + offset] - other.bigits_[i] - borrow; |
| bigits_[i + offset] = difference & kBigitMask; |
| borrow = difference >>> (kChunkSize - 1); |
| } |
| while (borrow != 0) { |
| final int difference = bigits_[i + offset] - borrow; |
| bigits_[i + offset] = difference & kBigitMask; |
| borrow = difference >>> (kChunkSize - 1); |
| ++i; |
| } |
| clamp(); |
| } |
| |
| |
| void shiftLeft(final int shift_amount) { |
| if (used_digits_ == 0) return; |
| exponent_ += shift_amount / kBigitSize; |
| final int local_shift = shift_amount % kBigitSize; |
| ensureCapacity(used_digits_ + 1); |
| bigitsShiftLeft(local_shift); |
| } |
| |
| |
| void multiplyByUInt32(final int factor) { |
| if (factor == 1) return; |
| if (factor == 0) { |
| zero(); |
| return; |
| } |
| if (used_digits_ == 0) return; |
| |
| // The product of a bigit with the factor is of size kBigitSize + 32. |
| // Assert that this number + 1 (for the carry) fits into double int. |
| assert (kDoubleChunkSize >= kBigitSize + 32 + 1); |
| long carry = 0; |
| for (int i = 0; i < used_digits_; ++i) { |
| final long product = (factor & 0xFFFFFFFFL) * bigits_[i] + carry; |
| bigits_[i] = (int) (product & kBigitMask); |
| carry = product >>> kBigitSize; |
| } |
| while (carry != 0) { |
| ensureCapacity(used_digits_ + 1); |
| bigits_[used_digits_] = (int) (carry & kBigitMask); |
| used_digits_++; |
| carry >>>= kBigitSize; |
| } |
| } |
| |
| |
| void multiplyByUInt64(final long factor) { |
| if (factor == 1) return; |
| if (factor == 0) { |
| zero(); |
| return; |
| } |
| assert (kBigitSize < 32); |
| long carry = 0; |
| final long low = factor & 0xFFFFFFFFL; |
| final long high = factor >>> 32; |
| for (int i = 0; i < used_digits_; ++i) { |
| final long product_low = low * bigits_[i]; |
| final long product_high = high * bigits_[i]; |
| final long tmp = (carry & kBigitMask) + product_low; |
| bigits_[i] = (int) (tmp & kBigitMask); |
| carry = (carry >>> kBigitSize) + (tmp >>> kBigitSize) + |
| (product_high << (32 - kBigitSize)); |
| } |
| while (carry != 0) { |
| ensureCapacity(used_digits_ + 1); |
| bigits_[used_digits_] = (int) (carry & kBigitMask); |
| used_digits_++; |
| carry >>>= kBigitSize; |
| } |
| } |
| |
| |
| void multiplyByPowerOfTen(final int exponent) { |
| final long kFive27 = 0x6765c793fa10079dL; |
| final int kFive1 = 5; |
| final int kFive2 = kFive1 * 5; |
| final int kFive3 = kFive2 * 5; |
| final int kFive4 = kFive3 * 5; |
| final int kFive5 = kFive4 * 5; |
| final int kFive6 = kFive5 * 5; |
| final int kFive7 = kFive6 * 5; |
| final int kFive8 = kFive7 * 5; |
| final int kFive9 = kFive8 * 5; |
| final int kFive10 = kFive9 * 5; |
| final int kFive11 = kFive10 * 5; |
| final int kFive12 = kFive11 * 5; |
| final int kFive13 = kFive12 * 5; |
| final int kFive1_to_12[] = |
| { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
| kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
| |
| assert (exponent >= 0); |
| if (exponent == 0) return; |
| if (used_digits_ == 0) return; |
| |
| // We shift by exponent at the end just before returning. |
| int remaining_exponent = exponent; |
| while (remaining_exponent >= 27) { |
| multiplyByUInt64(kFive27); |
| remaining_exponent -= 27; |
| } |
| while (remaining_exponent >= 13) { |
| multiplyByUInt32(kFive13); |
| remaining_exponent -= 13; |
| } |
| if (remaining_exponent > 0) { |
| multiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
| } |
| shiftLeft(exponent); |
| } |
| |
| |
| void square() { |
| assert (isClamped()); |
| final int product_length = 2 * used_digits_; |
| ensureCapacity(product_length); |
| |
| // Comba multiplication: compute each column separately. |
| // Example: r = a2a1a0 * b2b1b0. |
| // r = 1 * a0b0 + |
| // 10 * (a1b0 + a0b1) + |
| // 100 * (a2b0 + a1b1 + a0b2) + |
| // 1000 * (a2b1 + a1b2) + |
| // 10000 * a2b2 |
| // |
| // In the worst case we have to accumulate nb-digits products of digit*digit. |
| // |
| // Assert that the additional number of bits in a DoubleChunk are enough to |
| // sum up used_digits of Bigit*Bigit. |
| if ((1L << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { |
| throw new RuntimeException("unimplemented"); |
| } |
| long accumulator = 0; |
| // First shift the digits so we don't overwrite them. |
| final int copy_offset = used_digits_; |
| for (int i = 0; i < used_digits_; ++i) { |
| bigits_[copy_offset + i] = bigits_[i]; |
| } |
| // We have two loops to avoid some 'if's in the loop. |
| for (int i = 0; i < used_digits_; ++i) { |
| // Process temporary digit i with power i. |
| // The sum of the two indices must be equal to i. |
| int bigit_index1 = i; |
| int bigit_index2 = 0; |
| // Sum all of the sub-products. |
| while (bigit_index1 >= 0) { |
| final int int1 = bigits_[copy_offset + bigit_index1]; |
| final int int2 = bigits_[copy_offset + bigit_index2]; |
| accumulator += ((long) int1) * int2; |
| bigit_index1--; |
| bigit_index2++; |
| } |
| bigits_[i] = (int) (accumulator & kBigitMask); |
| accumulator >>>= kBigitSize; |
| } |
| for (int i = used_digits_; i < product_length; ++i) { |
| int bigit_index1 = used_digits_ - 1; |
| int bigit_index2 = i - bigit_index1; |
| // Invariant: sum of both indices is again equal to i. |
| // Inner loop runs 0 times on last iteration, emptying accumulator. |
| while (bigit_index2 < used_digits_) { |
| final int int1 = bigits_[copy_offset + bigit_index1]; |
| final int int2 = bigits_[copy_offset + bigit_index2]; |
| accumulator += ((long) int1) * int2; |
| bigit_index1--; |
| bigit_index2++; |
| } |
| // The overwritten bigits_[i] will never be read in further loop iterations, |
| // because bigit_index1 and bigit_index2 are always greater |
| // than i - used_digits_. |
| bigits_[i] = (int) (accumulator & kBigitMask); |
| accumulator >>>= kBigitSize; |
| } |
| // Since the result was guaranteed to lie inside the number the |
| // accumulator must be 0 now. |
| assert (accumulator == 0); |
| |
| // Don't forget to update the used_digits and the exponent. |
| used_digits_ = product_length; |
| exponent_ *= 2; |
| clamp(); |
| } |
| |
| |
| void assignPowerUInt16(int base, final int power_exponent) { |
| assert (base != 0); |
| assert (power_exponent >= 0); |
| if (power_exponent == 0) { |
| assignUInt16((char) 1); |
| return; |
| } |
| zero(); |
| int shifts = 0; |
| // We expect base to be in range 2-32, and most often to be 10. |
| // It does not make much sense to implement different algorithms for counting |
| // the bits. |
| while ((base & 1) == 0) { |
| base >>>= 1; |
| shifts++; |
| } |
| int bit_size = 0; |
| int tmp_base = base; |
| while (tmp_base != 0) { |
| tmp_base >>>= 1; |
| bit_size++; |
| } |
| final int final_size = bit_size * power_exponent; |
| // 1 extra bigit for the shifting, and one for rounded final_size. |
| ensureCapacity(final_size / kBigitSize + 2); |
| |
| // Left to Right exponentiation. |
| int mask = 1; |
| while (power_exponent >= mask) mask <<= 1; |
| |
| // The mask is now pointing to the bit above the most significant 1-bit of |
| // power_exponent. |
| // Get rid of first 1-bit; |
| mask >>>= 2; |
| long this_value = base; |
| |
| boolean delayed_multipliciation = false; |
| final long max_32bits = 0xFFFFFFFFL; |
| while (mask != 0 && this_value <= max_32bits) { |
| this_value = this_value * this_value; |
| // Verify that there is enough space in this_value to perform the |
| // multiplication. The first bit_size bits must be 0. |
| if ((power_exponent & mask) != 0) { |
| final long base_bits_mask = |
| ~((1L << (64 - bit_size)) - 1); |
| final boolean high_bits_zero = (this_value & base_bits_mask) == 0; |
| if (high_bits_zero) { |
| this_value *= base; |
| } else { |
| delayed_multipliciation = true; |
| } |
| } |
| mask >>>= 1; |
| } |
| assignUInt64(this_value); |
| if (delayed_multipliciation) { |
| multiplyByUInt32(base); |
| } |
| |
| // Now do the same thing as a bignum. |
| while (mask != 0) { |
| square(); |
| if ((power_exponent & mask) != 0) { |
| multiplyByUInt32(base); |
| } |
| mask >>>= 1; |
| } |
| |
| // And finally add the saved shifts. |
| shiftLeft(shifts * power_exponent); |
| } |
| |
| |
| // Precondition: this/other < 16bit. |
| char divideModuloIntBignum(final Bignum other) { |
| assert (isClamped()); |
| assert (other.isClamped()); |
| assert (other.used_digits_ > 0); |
| |
| // Easy case: if we have less digits than the divisor than the result is 0. |
| // Note: this handles the case where this == 0, too. |
| if (bigitLength() < other.bigitLength()) { |
| return 0; |
| } |
| |
| align(other); |
| |
| char result = 0; |
| |
| // Start by removing multiples of 'other' until both numbers have the same |
| // number of digits. |
| while (bigitLength() > other.bigitLength()) { |
| // This naive approach is extremely inefficient if `this` divided by other |
| // is big. This function is implemented for doubleToString where |
| // the result should be small (less than 10). |
| assert (other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); |
| assert (bigits_[used_digits_ - 1] < 0x10000); |
| // Remove the multiples of the first digit. |
| // Example this = 23 and other equals 9. -> Remove 2 multiples. |
| result += (bigits_[used_digits_ - 1]); |
| subtractTimes(other, bigits_[used_digits_ - 1]); |
| } |
| |
| assert (bigitLength() == other.bigitLength()); |
| |
| // Both bignums are at the same length now. |
| // Since other has more than 0 digits we know that the access to |
| // bigits_[used_digits_ - 1] is safe. |
| final int this_bigit = bigits_[used_digits_ - 1]; |
| final int other_bigit = other.bigits_[other.used_digits_ - 1]; |
| |
| if (other.used_digits_ == 1) { |
| // Shortcut for easy (and common) case. |
| final int quotient = Integer.divideUnsigned(this_bigit, other_bigit); |
| bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; |
| assert (Integer.compareUnsigned(quotient, 0x10000) < 0); |
| result += quotient; |
| clamp(); |
| return result; |
| } |
| |
| final int division_estimate = Integer.divideUnsigned(this_bigit, (other_bigit + 1)); |
| assert (Integer.compareUnsigned(division_estimate, 0x10000) < 0); |
| result += division_estimate; |
| subtractTimes(other, division_estimate); |
| |
| if (other_bigit * (division_estimate + 1) > this_bigit) { |
| // No need to even try to subtract. Even if other's remaining digits were 0 |
| // another subtraction would be too much. |
| return result; |
| } |
| |
| while (lessEqual(other, this)) { |
| subtractBignum(other); |
| result++; |
| } |
| return result; |
| } |
| |
| |
| static int sizeInHexChars(int number) { |
| assert (number > 0); |
| int result = 0; |
| while (number != 0) { |
| number >>>= 4; |
| result++; |
| } |
| return result; |
| } |
| |
| |
| static char hexCharOfValue(final int value) { |
| assert (0 <= value && value <= 16); |
| if (value < 10) return (char) (value + '0'); |
| return (char) (value - 10 + 'A'); |
| } |
| |
| |
| String toHexString() { |
| assert (isClamped()); |
| // Each bigit must be printable as separate hex-character. |
| assert (kBigitSize % 4 == 0); |
| final int kHexCharsPerBigit = kBigitSize / 4; |
| |
| if (used_digits_ == 0) { |
| return "0"; |
| } |
| |
| final int needed_chars = (bigitLength() - 1) * kHexCharsPerBigit + |
| sizeInHexChars(bigits_[used_digits_ - 1]); |
| final StringBuilder buffer = new StringBuilder(needed_chars); |
| buffer.setLength(needed_chars); |
| |
| int string_index = needed_chars - 1; |
| for (int i = 0; i < exponent_; ++i) { |
| for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| buffer.setCharAt(string_index--, '0'); |
| } |
| } |
| for (int i = 0; i < used_digits_ - 1; ++i) { |
| int current_bigit = bigits_[i]; |
| for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| buffer.setCharAt(string_index--, hexCharOfValue(current_bigit & 0xF)); |
| current_bigit >>>= 4; |
| } |
| } |
| // And finally the last bigit. |
| int most_significant_bigit = bigits_[used_digits_ - 1]; |
| while (most_significant_bigit != 0) { |
| buffer.setCharAt(string_index--, hexCharOfValue(most_significant_bigit & 0xF)); |
| most_significant_bigit >>>= 4; |
| } |
| return buffer.toString(); |
| } |
| |
| |
| int bigitAt(final int index) { |
| if (index >= bigitLength()) return 0; |
| if (index < exponent_) return 0; |
| return bigits_[index - exponent_]; |
| } |
| |
| |
| static int compare(final Bignum a, final Bignum b) { |
| assert (a.isClamped()); |
| assert (b.isClamped()); |
| final int bigit_length_a = a.bigitLength(); |
| final int bigit_length_b = b.bigitLength(); |
| if (bigit_length_a < bigit_length_b) return -1; |
| if (bigit_length_a > bigit_length_b) return +1; |
| for (int i = bigit_length_a - 1; i >= Math.min(a.exponent_, b.exponent_); --i) { |
| final int bigit_a = a.bigitAt(i); |
| final int bigit_b = b.bigitAt(i); |
| if (bigit_a < bigit_b) return -1; |
| if (bigit_a > bigit_b) return +1; |
| // Otherwise they are equal up to this digit. Try the next digit. |
| } |
| return 0; |
| } |
| |
| |
| static int plusCompare(final Bignum a, final Bignum b, final Bignum c) { |
| assert (a.isClamped()); |
| assert (b.isClamped()); |
| assert (c.isClamped()); |
| if (a.bigitLength() < b.bigitLength()) { |
| return plusCompare(b, a, c); |
| } |
| if (a.bigitLength() + 1 < c.bigitLength()) return -1; |
| if (a.bigitLength() > c.bigitLength()) return +1; |
| // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
| // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
| // of 'a'. |
| if (a.exponent_ >= b.bigitLength() && a.bigitLength() < c.bigitLength()) { |
| return -1; |
| } |
| |
| int borrow = 0; |
| // Starting at min_exponent all digits are == 0. So no need to compare them. |
| final int min_exponent = Math.min(Math.min(a.exponent_, b.exponent_), c.exponent_); |
| for (int i = c.bigitLength() - 1; i >= min_exponent; --i) { |
| final int int_a = a.bigitAt(i); |
| final int int_b = b.bigitAt(i); |
| final int int_c = c.bigitAt(i); |
| final int sum = int_a + int_b; |
| if (sum > int_c + borrow) { |
| return +1; |
| } else { |
| borrow = int_c + borrow - sum; |
| if (borrow > 1) return -1; |
| borrow <<= kBigitSize; |
| } |
| } |
| if (borrow == 0) return 0; |
| return -1; |
| } |
| |
| |
| void clamp() { |
| while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { |
| used_digits_--; |
| } |
| if (used_digits_ == 0) { |
| // Zero. |
| exponent_ = 0; |
| } |
| } |
| |
| |
| boolean isClamped() { |
| return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; |
| } |
| |
| |
| void zero() { |
| for (int i = 0; i < used_digits_; ++i) { |
| bigits_[i] = 0; |
| } |
| used_digits_ = 0; |
| exponent_ = 0; |
| } |
| |
| |
| void align(final Bignum other) { |
| if (exponent_ > other.exponent_) { |
| // If "X" represents a "hidden" digit (by the exponent) then we are in the |
| // following case (a == this, b == other): |
| // a: aaaaaaXXXX or a: aaaaaXXX |
| // b: bbbbbbX b: bbbbbbbbXX |
| // We replace some of the hidden digits (X) of a with 0 digits. |
| // a: aaaaaa000X or a: aaaaa0XX |
| final int zero_digits = exponent_ - other.exponent_; |
| ensureCapacity(used_digits_ + zero_digits); |
| for (int i = used_digits_ - 1; i >= 0; --i) { |
| bigits_[i + zero_digits] = bigits_[i]; |
| } |
| for (int i = 0; i < zero_digits; ++i) { |
| bigits_[i] = 0; |
| } |
| used_digits_ += zero_digits; |
| exponent_ -= zero_digits; |
| assert (used_digits_ >= 0); |
| assert (exponent_ >= 0); |
| } |
| } |
| |
| |
| void bigitsShiftLeft(final int shift_amount) { |
| assert (shift_amount < kBigitSize); |
| assert (shift_amount >= 0); |
| int carry = 0; |
| for (int i = 0; i < used_digits_; ++i) { |
| final int new_carry = bigits_[i] >>> (kBigitSize - shift_amount); |
| bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; |
| carry = new_carry; |
| } |
| if (carry != 0) { |
| bigits_[used_digits_] = carry; |
| used_digits_++; |
| } |
| } |
| |
| |
| void subtractTimes(final Bignum other, final int factor) { |
| assert (exponent_ <= other.exponent_); |
| if (factor < 3) { |
| for (int i = 0; i < factor; ++i) { |
| subtractBignum(other); |
| } |
| return; |
| } |
| int borrow = 0; |
| final int exponent_diff = other.exponent_ - exponent_; |
| for (int i = 0; i < other.used_digits_; ++i) { |
| final long product = ((long) factor) * other.bigits_[i]; |
| final long remove = borrow + product; |
| final int difference = bigits_[i + exponent_diff] - (int) (remove & kBigitMask); |
| bigits_[i + exponent_diff] = difference & kBigitMask; |
| borrow = (int) ((difference >>> (kChunkSize - 1)) + |
| (remove >>> kBigitSize)); |
| } |
| for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { |
| if (borrow == 0) return; |
| final int difference = bigits_[i] - borrow; |
| bigits_[i] = difference & kBigitMask; |
| borrow = difference >>> (kChunkSize - 1); |
| } |
| clamp(); |
| } |
| |
| @Override |
| public String toString() { |
| return "Bignum" + Arrays.toString(bigits_); |
| } |
| } |