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// Copyright 2017 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/numeric/int128.h"
#include <stddef.h>
#include <cassert>
#include <iomanip>
#include <iostream> // NOLINT(readability/streams)
#include <sstream>
#include <string>
#include <type_traits>
namespace absl {
const uint128 kuint128max = MakeUint128(std::numeric_limits<uint64_t>::max(),
std::numeric_limits<uint64_t>::max());
namespace {
// Returns the 0-based position of the last set bit (i.e., most significant bit)
// in the given uint64_t. The argument may not be 0.
//
// For example:
// Given: 5 (decimal) == 101 (binary)
// Returns: 2
#define STEP(T, n, pos, sh) \
do { \
if ((n) >= (static_cast<T>(1) << (sh))) { \
(n) = (n) >> (sh); \
(pos) |= (sh); \
} \
} while (0)
static inline int Fls64(uint64_t n) {
assert(n != 0);
int pos = 0;
STEP(uint64_t, n, pos, 0x20);
uint32_t n32 = static_cast<uint32_t>(n);
STEP(uint32_t, n32, pos, 0x10);
STEP(uint32_t, n32, pos, 0x08);
STEP(uint32_t, n32, pos, 0x04);
return pos + ((uint64_t{0x3333333322221100} >> (n32 << 2)) & 0x3);
}
#undef STEP
// Like Fls64() above, but returns the 0-based position of the last set bit
// (i.e., most significant bit) in the given uint128. The argument may not be 0.
static inline int Fls128(uint128 n) {
if (uint64_t hi = Uint128High64(n)) {
return Fls64(hi) + 64;
}
return Fls64(Uint128Low64(n));
}
// Long division/modulo for uint128 implemented using the shift-subtract
// division algorithm adapted from:
// http://stackoverflow.com/questions/5386377/division-without-using
void DivModImpl(uint128 dividend, uint128 divisor, uint128* quotient_ret,
uint128* remainder_ret) {
assert(divisor != 0);
if (divisor > dividend) {
*quotient_ret = 0;
*remainder_ret = dividend;
return;
}
if (divisor == dividend) {
*quotient_ret = 1;
*remainder_ret = 0;
return;
}
uint128 denominator = divisor;
uint128 quotient = 0;
// Left aligns the MSB of the denominator and the dividend.
const int shift = Fls128(dividend) - Fls128(denominator);
denominator <<= shift;
// Uses shift-subtract algorithm to divide dividend by denominator. The
// remainder will be left in dividend.
for (int i = 0; i <= shift; ++i) {
quotient <<= 1;
if (dividend >= denominator) {
dividend -= denominator;
quotient |= 1;
}
denominator >>= 1;
}
*quotient_ret = quotient;
*remainder_ret = dividend;
}
template <typename T>
uint128 MakeUint128FromFloat(T v) {
static_assert(std::is_floating_point<T>::value, "");
// Rounding behavior is towards zero, same as for built-in types.
// Undefined behavior if v is NaN or cannot fit into uint128.
assert(std::isfinite(v) && v > -1 &&
(std::numeric_limits<T>::max_exponent <= 128 ||
v < std::ldexp(static_cast<T>(1), 128)));
if (v >= std::ldexp(static_cast<T>(1), 64)) {
uint64_t hi = static_cast<uint64_t>(std::ldexp(v, -64));
uint64_t lo = static_cast<uint64_t>(v - std::ldexp(static_cast<T>(hi), 64));
return MakeUint128(hi, lo);
}
return MakeUint128(0, static_cast<uint64_t>(v));
}
} // namespace
uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}
uint128 operator/(uint128 lhs, uint128 rhs) {
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(lhs, rhs, "ient, &remainder);
return quotient;
}
uint128 operator%(uint128 lhs, uint128 rhs) {
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(lhs, rhs, "ient, &remainder);
return remainder;
}
namespace {
std::string Uint128ToFormattedString(uint128 v, std::ios_base::fmtflags flags) {
// Select a divisor which is the largest power of the base < 2^64.
uint128 div;
int div_base_log;
switch (flags & std::ios::basefield) {
case std::ios::hex:
div = 0x1000000000000000; // 16^15
div_base_log = 15;
break;
case std::ios::oct:
div = 01000000000000000000000; // 8^21
div_base_log = 21;
break;
default: // std::ios::dec
div = 10000000000000000000u; // 10^19
div_base_log = 19;
break;
}
// Now piece together the uint128 representation from three chunks of the
// original value, each less than "div" and therefore representable as a
// uint64_t.
std::ostringstream os;
std::ios_base::fmtflags copy_mask =
std::ios::basefield | std::ios::showbase | std::ios::uppercase;
os.setf(flags & copy_mask, copy_mask);
uint128 high = v;
uint128 low;
DivModImpl(high, div, &high, &low);
uint128 mid;
DivModImpl(high, div, &high, &mid);
if (Uint128Low64(high) != 0) {
os << Uint128Low64(high);
os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
os << Uint128Low64(mid);
os << std::setw(div_base_log);
} else if (Uint128Low64(mid) != 0) {
os << Uint128Low64(mid);
os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
}
os << Uint128Low64(low);
return os.str();
}
} // namespace
std::ostream& operator<<(std::ostream& os, uint128 v) {
std::ios_base::fmtflags flags = os.flags();
std::string rep = Uint128ToFormattedString(v, flags);
// Add the requisite padding.
std::streamsize width = os.width(0);
if (static_cast<size_t>(width) > rep.size()) {
std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
if (adjustfield == std::ios::left) {
rep.append(width - rep.size(), os.fill());
} else if (adjustfield == std::ios::internal &&
(flags & std::ios::showbase) &&
(flags & std::ios::basefield) == std::ios::hex && v != 0) {
rep.insert(2, width - rep.size(), os.fill());
} else {
rep.insert(0, width - rep.size(), os.fill());
}
}
return os << rep;
}
} // namespace absl
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