--- old/src/jdk.scripting.nashorn/share/classes/jdk/nashorn/internal/runtime/doubleconv/Bignum.java 2020-04-15 18:50:45.000000000 +0530 +++ /dev/null 2020-04-15 18:50:45.000000000 +0530 @@ -1,844 +0,0 @@ -/* - * 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 - * or visit www.oracle.com if you need additional information or have any - * 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 int used_digits_; - // The Bignum's value equals value(bigits_) * 2^(exponent_ * kBigitSize). - private int exponent_; - private final int[] bigits_ = new int[kBigitCapacity]; - - 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_multiplication = 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) { - assert bit_size > 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_multiplication = true; - } - } - mask >>>= 1; - } - assignUInt64(this_value); - if (delayed_multiplication) { - 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 bigitOrZero(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.bigitOrZero(i); - final int bigit_b = b.bigitOrZero(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.bigitOrZero(i); - final int int_b = b.bigitOrZero(i); - final int int_c = c.bigitOrZero(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_); - } -}