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815 lines
25 KiB
815 lines
25 KiB
// © 2018 and later: Unicode, Inc. and others.
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// License & terms of use: http://www.unicode.org/copyright.html
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//
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// From the double-conversion library. Original license:
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//
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// Copyright 2010 the V8 project authors. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following
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// disclaimer in the documentation and/or other materials provided
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// with the distribution.
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// * Neither the name of Google Inc. nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// ICU PATCH: ifdef around UCONFIG_NO_FORMATTING
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#include "unicode/utypes.h"
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#if !UCONFIG_NO_FORMATTING
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#include <algorithm>
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#include <cstring>
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// ICU PATCH: Customize header file paths for ICU.
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#include "double-conversion-bignum.h"
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#include "double-conversion-utils.h"
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// ICU PATCH: Wrap in ICU namespace
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U_NAMESPACE_BEGIN
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namespace double_conversion {
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Bignum::Chunk& Bignum::RawBigit(const int index) {
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DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
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return bigits_buffer_[index];
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}
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const Bignum::Chunk& Bignum::RawBigit(const int index) const {
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DOUBLE_CONVERSION_ASSERT(static_cast<unsigned>(index) < kBigitCapacity);
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return bigits_buffer_[index];
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}
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template<typename S>
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static int BitSize(const S value) {
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(void) value; // Mark variable as used.
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return 8 * sizeof(value);
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}
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// Guaranteed to lie in one Bigit.
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void Bignum::AssignUInt16(const uint16_t value) {
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DOUBLE_CONVERSION_ASSERT(kBigitSize >= BitSize(value));
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Zero();
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if (value > 0) {
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RawBigit(0) = value;
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used_bigits_ = 1;
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}
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}
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void Bignum::AssignUInt64(uint64_t value) {
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Zero();
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for(int i = 0; value > 0; ++i) {
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RawBigit(i) = value & kBigitMask;
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value >>= kBigitSize;
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++used_bigits_;
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}
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}
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void Bignum::AssignBignum(const Bignum& other) {
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exponent_ = other.exponent_;
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for (int i = 0; i < other.used_bigits_; ++i) {
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RawBigit(i) = other.RawBigit(i);
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}
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used_bigits_ = other.used_bigits_;
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}
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static uint64_t ReadUInt64(const Vector<const char> buffer,
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const int from,
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const int digits_to_read) {
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uint64_t result = 0;
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for (int i = from; i < from + digits_to_read; ++i) {
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const int digit = buffer[i] - '0';
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DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9);
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result = result * 10 + digit;
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}
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return result;
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}
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void Bignum::AssignDecimalString(const Vector<const char> value) {
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// 2^64 = 18446744073709551616 > 10^19
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static const int kMaxUint64DecimalDigits = 19;
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Zero();
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int length = value.length();
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unsigned pos = 0;
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// Let's just say that each digit needs 4 bits.
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while (length >= kMaxUint64DecimalDigits) {
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const uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits);
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pos += kMaxUint64DecimalDigits;
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length -= kMaxUint64DecimalDigits;
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MultiplyByPowerOfTen(kMaxUint64DecimalDigits);
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AddUInt64(digits);
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}
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const uint64_t digits = ReadUInt64(value, pos, length);
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MultiplyByPowerOfTen(length);
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AddUInt64(digits);
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Clamp();
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}
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static uint64_t HexCharValue(const int c) {
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if ('0' <= c && c <= '9') {
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return c - '0';
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}
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if ('a' <= c && c <= 'f') {
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return 10 + c - 'a';
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}
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DOUBLE_CONVERSION_ASSERT('A' <= c && c <= 'F');
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return 10 + c - 'A';
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}
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// Unlike AssignDecimalString(), this function is "only" used
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// for unit-tests and therefore not performance critical.
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void Bignum::AssignHexString(Vector<const char> value) {
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Zero();
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// Required capacity could be reduced by ignoring leading zeros.
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EnsureCapacity(((value.length() * 4) + kBigitSize - 1) / kBigitSize);
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DOUBLE_CONVERSION_ASSERT(sizeof(uint64_t) * 8 >= kBigitSize + 4); // TODO: static_assert
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// Accumulates converted hex digits until at least kBigitSize bits.
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// Works with non-factor-of-four kBigitSizes.
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uint64_t tmp = 0; // Accumulates converted hex digits until at least
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for (int cnt = 0; !value.is_empty(); value.pop_back()) {
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tmp |= (HexCharValue(value.last()) << cnt);
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if ((cnt += 4) >= kBigitSize) {
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RawBigit(used_bigits_++) = (tmp & kBigitMask);
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cnt -= kBigitSize;
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tmp >>= kBigitSize;
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}
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}
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if (tmp > 0) {
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RawBigit(used_bigits_++) = tmp;
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}
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Clamp();
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}
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void Bignum::AddUInt64(const uint64_t operand) {
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if (operand == 0) {
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return;
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}
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Bignum other;
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other.AssignUInt64(operand);
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AddBignum(other);
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}
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void Bignum::AddBignum(const Bignum& other) {
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DOUBLE_CONVERSION_ASSERT(IsClamped());
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DOUBLE_CONVERSION_ASSERT(other.IsClamped());
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// If this has a greater exponent than other append zero-bigits to this.
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// After this call exponent_ <= other.exponent_.
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Align(other);
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// There are two possibilities:
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// aaaaaaaaaaa 0000 (where the 0s represent a's exponent)
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// bbbbb 00000000
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// ----------------
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// ccccccccccc 0000
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// or
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// aaaaaaaaaa 0000
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// bbbbbbbbb 0000000
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// -----------------
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// cccccccccccc 0000
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// In both cases we might need a carry bigit.
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EnsureCapacity(1 + (std::max)(BigitLength(), other.BigitLength()) - exponent_);
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Chunk carry = 0;
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int bigit_pos = other.exponent_ - exponent_;
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DOUBLE_CONVERSION_ASSERT(bigit_pos >= 0);
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for (int i = used_bigits_; i < bigit_pos; ++i) {
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RawBigit(i) = 0;
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}
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for (int i = 0; i < other.used_bigits_; ++i) {
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const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
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const Chunk sum = my + other.RawBigit(i) + carry;
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RawBigit(bigit_pos) = sum & kBigitMask;
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carry = sum >> kBigitSize;
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++bigit_pos;
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}
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while (carry != 0) {
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const Chunk my = (bigit_pos < used_bigits_) ? RawBigit(bigit_pos) : 0;
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const Chunk sum = my + carry;
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RawBigit(bigit_pos) = sum & kBigitMask;
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carry = sum >> kBigitSize;
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++bigit_pos;
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}
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used_bigits_ = (std::max)(bigit_pos, static_cast<int>(used_bigits_));
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DOUBLE_CONVERSION_ASSERT(IsClamped());
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}
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void Bignum::SubtractBignum(const Bignum& other) {
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DOUBLE_CONVERSION_ASSERT(IsClamped());
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DOUBLE_CONVERSION_ASSERT(other.IsClamped());
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// We require this to be bigger than other.
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DOUBLE_CONVERSION_ASSERT(LessEqual(other, *this));
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Align(other);
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const int offset = other.exponent_ - exponent_;
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Chunk borrow = 0;
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int i;
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for (i = 0; i < other.used_bigits_; ++i) {
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DOUBLE_CONVERSION_ASSERT((borrow == 0) || (borrow == 1));
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const Chunk difference = RawBigit(i + offset) - other.RawBigit(i) - borrow;
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RawBigit(i + offset) = difference & kBigitMask;
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borrow = difference >> (kChunkSize - 1);
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}
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while (borrow != 0) {
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const Chunk difference = RawBigit(i + offset) - borrow;
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RawBigit(i + offset) = difference & kBigitMask;
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borrow = difference >> (kChunkSize - 1);
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++i;
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}
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Clamp();
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}
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void Bignum::ShiftLeft(const int shift_amount) {
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if (used_bigits_ == 0) {
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return;
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}
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exponent_ += (shift_amount / kBigitSize);
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const int local_shift = shift_amount % kBigitSize;
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EnsureCapacity(used_bigits_ + 1);
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BigitsShiftLeft(local_shift);
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}
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void Bignum::MultiplyByUInt32(const uint32_t factor) {
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if (factor == 1) {
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return;
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}
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if (factor == 0) {
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Zero();
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return;
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}
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if (used_bigits_ == 0) {
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return;
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}
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// The product of a bigit with the factor is of size kBigitSize + 32.
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// Assert that this number + 1 (for the carry) fits into double chunk.
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DOUBLE_CONVERSION_ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1);
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DoubleChunk carry = 0;
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for (int i = 0; i < used_bigits_; ++i) {
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const DoubleChunk product = static_cast<DoubleChunk>(factor) * RawBigit(i) + carry;
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RawBigit(i) = static_cast<Chunk>(product & kBigitMask);
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carry = (product >> kBigitSize);
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}
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while (carry != 0) {
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EnsureCapacity(used_bigits_ + 1);
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RawBigit(used_bigits_) = carry & kBigitMask;
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used_bigits_++;
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carry >>= kBigitSize;
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}
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}
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void Bignum::MultiplyByUInt64(const uint64_t factor) {
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if (factor == 1) {
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return;
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}
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if (factor == 0) {
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Zero();
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return;
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}
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if (used_bigits_ == 0) {
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return;
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}
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DOUBLE_CONVERSION_ASSERT(kBigitSize < 32);
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uint64_t carry = 0;
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const uint64_t low = factor & 0xFFFFFFFF;
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const uint64_t high = factor >> 32;
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for (int i = 0; i < used_bigits_; ++i) {
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const uint64_t product_low = low * RawBigit(i);
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const uint64_t product_high = high * RawBigit(i);
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const uint64_t tmp = (carry & kBigitMask) + product_low;
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RawBigit(i) = tmp & kBigitMask;
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carry = (carry >> kBigitSize) + (tmp >> kBigitSize) +
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(product_high << (32 - kBigitSize));
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}
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while (carry != 0) {
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EnsureCapacity(used_bigits_ + 1);
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RawBigit(used_bigits_) = carry & kBigitMask;
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used_bigits_++;
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carry >>= kBigitSize;
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}
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}
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void Bignum::MultiplyByPowerOfTen(const int exponent) {
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static const uint64_t kFive27 = DOUBLE_CONVERSION_UINT64_2PART_C(0x6765c793, fa10079d);
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static const uint16_t kFive1 = 5;
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static const uint16_t kFive2 = kFive1 * 5;
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static const uint16_t kFive3 = kFive2 * 5;
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static const uint16_t kFive4 = kFive3 * 5;
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static const uint16_t kFive5 = kFive4 * 5;
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static const uint16_t kFive6 = kFive5 * 5;
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static const uint32_t kFive7 = kFive6 * 5;
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static const uint32_t kFive8 = kFive7 * 5;
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static const uint32_t kFive9 = kFive8 * 5;
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static const uint32_t kFive10 = kFive9 * 5;
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static const uint32_t kFive11 = kFive10 * 5;
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static const uint32_t kFive12 = kFive11 * 5;
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static const uint32_t kFive13 = kFive12 * 5;
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static const uint32_t kFive1_to_12[] =
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{ kFive1, kFive2, kFive3, kFive4, kFive5, kFive6,
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kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 };
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DOUBLE_CONVERSION_ASSERT(exponent >= 0);
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if (exponent == 0) {
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return;
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}
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if (used_bigits_ == 0) {
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return;
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}
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// We shift by exponent at the end just before returning.
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int remaining_exponent = exponent;
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while (remaining_exponent >= 27) {
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MultiplyByUInt64(kFive27);
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remaining_exponent -= 27;
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}
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while (remaining_exponent >= 13) {
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MultiplyByUInt32(kFive13);
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remaining_exponent -= 13;
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}
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if (remaining_exponent > 0) {
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MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]);
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}
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ShiftLeft(exponent);
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}
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void Bignum::Square() {
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DOUBLE_CONVERSION_ASSERT(IsClamped());
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const int product_length = 2 * used_bigits_;
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EnsureCapacity(product_length);
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// Comba multiplication: compute each column separately.
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// Example: r = a2a1a0 * b2b1b0.
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// r = 1 * a0b0 +
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// 10 * (a1b0 + a0b1) +
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// 100 * (a2b0 + a1b1 + a0b2) +
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// 1000 * (a2b1 + a1b2) +
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// 10000 * a2b2
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//
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// In the worst case we have to accumulate nb-digits products of digit*digit.
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//
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// Assert that the additional number of bits in a DoubleChunk are enough to
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// sum up used_digits of Bigit*Bigit.
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if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_bigits_) {
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DOUBLE_CONVERSION_UNIMPLEMENTED();
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}
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DoubleChunk accumulator = 0;
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// First shift the digits so we don't overwrite them.
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const int copy_offset = used_bigits_;
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for (int i = 0; i < used_bigits_; ++i) {
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RawBigit(copy_offset + i) = RawBigit(i);
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}
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// We have two loops to avoid some 'if's in the loop.
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for (int i = 0; i < used_bigits_; ++i) {
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// Process temporary digit i with power i.
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// The sum of the two indices must be equal to i.
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int bigit_index1 = i;
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int bigit_index2 = 0;
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// Sum all of the sub-products.
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while (bigit_index1 >= 0) {
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const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
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const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
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accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
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bigit_index1--;
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bigit_index2++;
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}
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RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
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accumulator >>= kBigitSize;
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}
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for (int i = used_bigits_; i < product_length; ++i) {
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int bigit_index1 = used_bigits_ - 1;
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int bigit_index2 = i - bigit_index1;
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// Invariant: sum of both indices is again equal to i.
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// Inner loop runs 0 times on last iteration, emptying accumulator.
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while (bigit_index2 < used_bigits_) {
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const Chunk chunk1 = RawBigit(copy_offset + bigit_index1);
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const Chunk chunk2 = RawBigit(copy_offset + bigit_index2);
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accumulator += static_cast<DoubleChunk>(chunk1) * chunk2;
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bigit_index1--;
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bigit_index2++;
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}
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// The overwritten RawBigit(i) will never be read in further loop iterations,
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// because bigit_index1 and bigit_index2 are always greater
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// than i - used_bigits_.
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RawBigit(i) = static_cast<Chunk>(accumulator) & kBigitMask;
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accumulator >>= kBigitSize;
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}
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// Since the result was guaranteed to lie inside the number the
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// accumulator must be 0 now.
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DOUBLE_CONVERSION_ASSERT(accumulator == 0);
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// Don't forget to update the used_digits and the exponent.
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used_bigits_ = product_length;
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exponent_ *= 2;
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Clamp();
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}
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void Bignum::AssignPowerUInt16(uint16_t base, const int power_exponent) {
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DOUBLE_CONVERSION_ASSERT(base != 0);
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DOUBLE_CONVERSION_ASSERT(power_exponent >= 0);
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if (power_exponent == 0) {
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AssignUInt16(1);
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return;
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}
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Zero();
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int shifts = 0;
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// We expect base to be in range 2-32, and most often to be 10.
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// It does not make much sense to implement different algorithms for counting
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// the bits.
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while ((base & 1) == 0) {
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base >>= 1;
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shifts++;
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}
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int bit_size = 0;
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int tmp_base = base;
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while (tmp_base != 0) {
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tmp_base >>= 1;
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bit_size++;
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}
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const int final_size = bit_size * power_exponent;
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// 1 extra bigit for the shifting, and one for rounded final_size.
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EnsureCapacity(final_size / kBigitSize + 2);
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// Left to Right exponentiation.
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int mask = 1;
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while (power_exponent >= mask) mask <<= 1;
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// The mask is now pointing to the bit above the most significant 1-bit of
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// power_exponent.
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// Get rid of first 1-bit;
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mask >>= 2;
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uint64_t this_value = base;
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bool delayed_multiplication = false;
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const uint64_t max_32bits = 0xFFFFFFFF;
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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) {
|
|
DOUBLE_CONVERSION_ASSERT(bit_size > 0);
|
|
const uint64_t base_bits_mask =
|
|
~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1);
|
|
const bool 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.
|
|
uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) {
|
|
DOUBLE_CONVERSION_ASSERT(IsClamped());
|
|
DOUBLE_CONVERSION_ASSERT(other.IsClamped());
|
|
DOUBLE_CONVERSION_ASSERT(other.used_bigits_ > 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);
|
|
|
|
uint16_t 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).
|
|
DOUBLE_CONVERSION_ASSERT(other.RawBigit(other.used_bigits_ - 1) >= ((1 << kBigitSize) / 16));
|
|
DOUBLE_CONVERSION_ASSERT(RawBigit(used_bigits_ - 1) < 0x10000);
|
|
// Remove the multiples of the first digit.
|
|
// Example this = 23 and other equals 9. -> Remove 2 multiples.
|
|
result += static_cast<uint16_t>(RawBigit(used_bigits_ - 1));
|
|
SubtractTimes(other, RawBigit(used_bigits_ - 1));
|
|
}
|
|
|
|
DOUBLE_CONVERSION_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
|
|
// RawBigit(used_bigits_ - 1) is safe.
|
|
const Chunk this_bigit = RawBigit(used_bigits_ - 1);
|
|
const Chunk other_bigit = other.RawBigit(other.used_bigits_ - 1);
|
|
|
|
if (other.used_bigits_ == 1) {
|
|
// Shortcut for easy (and common) case.
|
|
int quotient = this_bigit / other_bigit;
|
|
RawBigit(used_bigits_ - 1) = this_bigit - other_bigit * quotient;
|
|
DOUBLE_CONVERSION_ASSERT(quotient < 0x10000);
|
|
result += static_cast<uint16_t>(quotient);
|
|
Clamp();
|
|
return result;
|
|
}
|
|
|
|
const int division_estimate = this_bigit / (other_bigit + 1);
|
|
DOUBLE_CONVERSION_ASSERT(division_estimate < 0x10000);
|
|
result += static_cast<uint16_t>(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;
|
|
}
|
|
|
|
|
|
template<typename S>
|
|
static int SizeInHexChars(S number) {
|
|
DOUBLE_CONVERSION_ASSERT(number > 0);
|
|
int result = 0;
|
|
while (number != 0) {
|
|
number >>= 4;
|
|
result++;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
|
|
static char HexCharOfValue(const int value) {
|
|
DOUBLE_CONVERSION_ASSERT(0 <= value && value <= 16);
|
|
if (value < 10) {
|
|
return static_cast<char>(value + '0');
|
|
}
|
|
return static_cast<char>(value - 10 + 'A');
|
|
}
|
|
|
|
|
|
bool Bignum::ToHexString(char* buffer, const int buffer_size) const {
|
|
DOUBLE_CONVERSION_ASSERT(IsClamped());
|
|
// Each bigit must be printable as separate hex-character.
|
|
DOUBLE_CONVERSION_ASSERT(kBigitSize % 4 == 0);
|
|
static const int kHexCharsPerBigit = kBigitSize / 4;
|
|
|
|
if (used_bigits_ == 0) {
|
|
if (buffer_size < 2) {
|
|
return false;
|
|
}
|
|
buffer[0] = '0';
|
|
buffer[1] = '\0';
|
|
return true;
|
|
}
|
|
// We add 1 for the terminating '\0' character.
|
|
const int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit +
|
|
SizeInHexChars(RawBigit(used_bigits_ - 1)) + 1;
|
|
if (needed_chars > buffer_size) {
|
|
return false;
|
|
}
|
|
int string_index = needed_chars - 1;
|
|
buffer[string_index--] = '\0';
|
|
for (int i = 0; i < exponent_; ++i) {
|
|
for (int j = 0; j < kHexCharsPerBigit; ++j) {
|
|
buffer[string_index--] = '0';
|
|
}
|
|
}
|
|
for (int i = 0; i < used_bigits_ - 1; ++i) {
|
|
Chunk current_bigit = RawBigit(i);
|
|
for (int j = 0; j < kHexCharsPerBigit; ++j) {
|
|
buffer[string_index--] = HexCharOfValue(current_bigit & 0xF);
|
|
current_bigit >>= 4;
|
|
}
|
|
}
|
|
// And finally the last bigit.
|
|
Chunk most_significant_bigit = RawBigit(used_bigits_ - 1);
|
|
while (most_significant_bigit != 0) {
|
|
buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF);
|
|
most_significant_bigit >>= 4;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
Bignum::Chunk Bignum::BigitOrZero(const int index) const {
|
|
if (index >= BigitLength()) {
|
|
return 0;
|
|
}
|
|
if (index < exponent_) {
|
|
return 0;
|
|
}
|
|
return RawBigit(index - exponent_);
|
|
}
|
|
|
|
|
|
int Bignum::Compare(const Bignum& a, const Bignum& b) {
|
|
DOUBLE_CONVERSION_ASSERT(a.IsClamped());
|
|
DOUBLE_CONVERSION_ASSERT(b.IsClamped());
|
|
const int bigit_length_a = a.BigitLength();
|
|
const 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 >= (std::min)(a.exponent_, b.exponent_); --i) {
|
|
const Chunk bigit_a = a.BigitOrZero(i);
|
|
const Chunk 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;
|
|
}
|
|
|
|
|
|
int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) {
|
|
DOUBLE_CONVERSION_ASSERT(a.IsClamped());
|
|
DOUBLE_CONVERSION_ASSERT(b.IsClamped());
|
|
DOUBLE_CONVERSION_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;
|
|
}
|
|
|
|
Chunk borrow = 0;
|
|
// Starting at min_exponent all digits are == 0. So no need to compare them.
|
|
const int min_exponent = (std::min)((std::min)(a.exponent_, b.exponent_), c.exponent_);
|
|
for (int i = c.BigitLength() - 1; i >= min_exponent; --i) {
|
|
const Chunk chunk_a = a.BigitOrZero(i);
|
|
const Chunk chunk_b = b.BigitOrZero(i);
|
|
const Chunk chunk_c = c.BigitOrZero(i);
|
|
const Chunk sum = chunk_a + chunk_b;
|
|
if (sum > chunk_c + borrow) {
|
|
return +1;
|
|
} else {
|
|
borrow = chunk_c + borrow - sum;
|
|
if (borrow > 1) {
|
|
return -1;
|
|
}
|
|
borrow <<= kBigitSize;
|
|
}
|
|
}
|
|
if (borrow == 0) {
|
|
return 0;
|
|
}
|
|
return -1;
|
|
}
|
|
|
|
|
|
void Bignum::Clamp() {
|
|
while (used_bigits_ > 0 && RawBigit(used_bigits_ - 1) == 0) {
|
|
used_bigits_--;
|
|
}
|
|
if (used_bigits_ == 0) {
|
|
// Zero.
|
|
exponent_ = 0;
|
|
}
|
|
}
|
|
|
|
|
|
void Bignum::Align(const Bignum& other) {
|
|
if (exponent_ > other.exponent_) {
|
|
// If "X" represents a "hidden" bigit (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
|
|
const int zero_bigits = exponent_ - other.exponent_;
|
|
EnsureCapacity(used_bigits_ + zero_bigits);
|
|
for (int i = used_bigits_ - 1; i >= 0; --i) {
|
|
RawBigit(i + zero_bigits) = RawBigit(i);
|
|
}
|
|
for (int i = 0; i < zero_bigits; ++i) {
|
|
RawBigit(i) = 0;
|
|
}
|
|
used_bigits_ += zero_bigits;
|
|
exponent_ -= zero_bigits;
|
|
|
|
DOUBLE_CONVERSION_ASSERT(used_bigits_ >= 0);
|
|
DOUBLE_CONVERSION_ASSERT(exponent_ >= 0);
|
|
}
|
|
}
|
|
|
|
|
|
void Bignum::BigitsShiftLeft(const int shift_amount) {
|
|
DOUBLE_CONVERSION_ASSERT(shift_amount < kBigitSize);
|
|
DOUBLE_CONVERSION_ASSERT(shift_amount >= 0);
|
|
Chunk carry = 0;
|
|
for (int i = 0; i < used_bigits_; ++i) {
|
|
const Chunk new_carry = RawBigit(i) >> (kBigitSize - shift_amount);
|
|
RawBigit(i) = ((RawBigit(i) << shift_amount) + carry) & kBigitMask;
|
|
carry = new_carry;
|
|
}
|
|
if (carry != 0) {
|
|
RawBigit(used_bigits_) = carry;
|
|
used_bigits_++;
|
|
}
|
|
}
|
|
|
|
|
|
void Bignum::SubtractTimes(const Bignum& other, const int factor) {
|
|
DOUBLE_CONVERSION_ASSERT(exponent_ <= other.exponent_);
|
|
if (factor < 3) {
|
|
for (int i = 0; i < factor; ++i) {
|
|
SubtractBignum(other);
|
|
}
|
|
return;
|
|
}
|
|
Chunk borrow = 0;
|
|
const int exponent_diff = other.exponent_ - exponent_;
|
|
for (int i = 0; i < other.used_bigits_; ++i) {
|
|
const DoubleChunk product = static_cast<DoubleChunk>(factor) * other.RawBigit(i);
|
|
const DoubleChunk remove = borrow + product;
|
|
const Chunk difference = RawBigit(i + exponent_diff) - (remove & kBigitMask);
|
|
RawBigit(i + exponent_diff) = difference & kBigitMask;
|
|
borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) +
|
|
(remove >> kBigitSize));
|
|
}
|
|
for (int i = other.used_bigits_ + exponent_diff; i < used_bigits_; ++i) {
|
|
if (borrow == 0) {
|
|
return;
|
|
}
|
|
const Chunk difference = RawBigit(i) - borrow;
|
|
RawBigit(i) = difference & kBigitMask;
|
|
borrow = difference >> (kChunkSize - 1);
|
|
}
|
|
Clamp();
|
|
}
|
|
|
|
|
|
} // namespace double_conversion
|
|
|
|
// ICU PATCH: Close ICU namespace
|
|
U_NAMESPACE_END
|
|
#endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING
|