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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
//
// https://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 <ostream> // NOLINT(readability/streams)
#include <sstream>
#include <string>
#include <type_traits>
#include "absl/base/optimization.h"
#include "absl/numeric/bits.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
ABSL_DLL 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 uint128. The argument is not 0.
//
// For example:
// Given: 5 (decimal) == 101 (binary)
// Returns: 2
inline ABSL_ATTRIBUTE_ALWAYS_INLINE int Fls128(uint128 n) {
if (uint64_t hi = Uint128High64(n)) {
ABSL_ASSUME(hi != 0);
return 127 - countl_zero(hi);
}
const uint64_t low = Uint128Low64(n);
ABSL_ASSUME(low != 0);
return 63 - countl_zero(low);
}
// Long division/modulo for uint128 implemented using the shift-subtract
// division algorithm adapted from:
// https://stackoverflow.com/questions/5386377/division-without-using
inline 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));
}
#if defined(__clang__) && !defined(__SSE3__)
// Workaround for clang bug: https://bugs.llvm.org/show_bug.cgi?id=38289
// Casting from long double to uint64_t is miscompiled and drops bits.
// It is more work, so only use when we need the workaround.
uint128 MakeUint128FromFloat(long double v) {
// Go 50 bits at a time, that fits in a double
static_assert(std::numeric_limits<double>::digits >= 50, "");
static_assert(std::numeric_limits<long double>::digits <= 150, "");
// Undefined behavior if v is not finite or cannot fit into uint128.
assert(std::isfinite(v) && v > -1 && v < std::ldexp(1.0L, 128));
v = std::ldexp(v, -100);
uint64_t w0 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
v = std::ldexp(v - static_cast<double>(w0), 50);
uint64_t w1 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
v = std::ldexp(v - static_cast<double>(w1), 50);
uint64_t w2 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
return (static_cast<uint128>(w0) << 100) | (static_cast<uint128>(w1) << 50) |
static_cast<uint128>(w2);
}
#endif // __clang__ && !__SSE3__
} // namespace
uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}
#if !defined(ABSL_HAVE_INTRINSIC_INT128)
uint128 operator/(uint128 lhs, uint128 rhs) {
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(lhs, rhs, &quotient, &remainder);
return quotient;
}
uint128 operator%(uint128 lhs, uint128 rhs) {
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(lhs, rhs, &quotient, &remainder);
return remainder;
}
#endif // !defined(ABSL_HAVE_INTRINSIC_INT128)
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()) {
const size_t count = static_cast<size_t>(width) - rep.size();
std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
if (adjustfield == std::ios::left) {
rep.append(count, os.fill());
} else if (adjustfield == std::ios::internal &&
(flags & std::ios::showbase) &&
(flags & std::ios::basefield) == std::ios::hex && v != 0) {
rep.insert(2, count, os.fill());
} else {
rep.insert(0, count, os.fill());
}
}
return os << rep;
}
namespace {
uint128 UnsignedAbsoluteValue(int128 v) {
// Cast to uint128 before possibly negating because -Int128Min() is undefined.
return Int128High64(v) < 0 ? -uint128(v) : uint128(v);
}
} // namespace
#if !defined(ABSL_HAVE_INTRINSIC_INT128)
namespace {
template <typename T>
int128 MakeInt128FromFloat(T v) {
// Conversion when v is NaN or cannot fit into int128 would be undefined
// behavior if using an intrinsic 128-bit integer.
assert(std::isfinite(v) && (std::numeric_limits<T>::max_exponent <= 127 ||
(v >= -std::ldexp(static_cast<T>(1), 127) &&
v < std::ldexp(static_cast<T>(1), 127))));
// We must convert the absolute value and then negate as needed, because
// floating point types are typically sign-magnitude. Otherwise, the
// difference between the high and low 64 bits when interpreted as two's
// complement overwhelms the precision of the mantissa.
uint128 result = v < 0 ? -MakeUint128FromFloat(-v) : MakeUint128FromFloat(v);
return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
Uint128Low64(result));
}
} // namespace
int128::int128(float v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(double v) : int128(MakeInt128FromFloat(v)) {}
int128::int128(long double v) : int128(MakeInt128FromFloat(v)) {}
int128 operator/(int128 lhs, int128 rhs) {
assert(lhs != Int128Min() || rhs != -1); // UB on two's complement.
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
&quotient, &remainder);
if ((Int128High64(lhs) < 0) != (Int128High64(rhs) < 0)) quotient = -quotient;
return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(quotient)),
Uint128Low64(quotient));
}
int128 operator%(int128 lhs, int128 rhs) {
assert(lhs != Int128Min() || rhs != -1); // UB on two's complement.
uint128 quotient = 0;
uint128 remainder = 0;
DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
&quotient, &remainder);
if (Int128High64(lhs) < 0) remainder = -remainder;
return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(remainder)),
Uint128Low64(remainder));
}
#endif // ABSL_HAVE_INTRINSIC_INT128
std::ostream& operator<<(std::ostream& os, int128 v) {
std::ios_base::fmtflags flags = os.flags();
std::string rep;
// Add the sign if needed.
bool print_as_decimal =
(flags & std::ios::basefield) == std::ios::dec ||
(flags & std::ios::basefield) == std::ios_base::fmtflags();
if (print_as_decimal) {
if (Int128High64(v) < 0) {
rep = "-";
} else if (flags & std::ios::showpos) {
rep = "+";
}
}
rep.append(Uint128ToFormattedString(
print_as_decimal ? UnsignedAbsoluteValue(v) : uint128(v), os.flags()));
// Add the requisite padding.
std::streamsize width = os.width(0);
if (static_cast<size_t>(width) > rep.size()) {
const size_t count = static_cast<size_t>(width) - rep.size();
switch (flags & std::ios::adjustfield) {
case std::ios::left:
rep.append(count, os.fill());
break;
case std::ios::internal:
if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) {
rep.insert(1, count, os.fill());
} else if ((flags & std::ios::basefield) == std::ios::hex &&
(flags & std::ios::showbase) && v != 0) {
rep.insert(2, count, os.fill());
} else {
rep.insert(0, count, os.fill());
}
break;
default: // std::ios::right
rep.insert(0, count, os.fill());
break;
}
}
return os << rep;
}
ABSL_NAMESPACE_END
} // namespace absl
#ifdef ABSL_INTERNAL_NEED_REDUNDANT_CONSTEXPR_DECL
namespace std {
constexpr bool numeric_limits<absl::uint128>::is_specialized;
constexpr bool numeric_limits<absl::uint128>::is_signed;
constexpr bool numeric_limits<absl::uint128>::is_integer;
constexpr bool numeric_limits<absl::uint128>::is_exact;
constexpr bool numeric_limits<absl::uint128>::has_infinity;
constexpr bool numeric_limits<absl::uint128>::has_quiet_NaN;
constexpr bool numeric_limits<absl::uint128>::has_signaling_NaN;
constexpr float_denorm_style numeric_limits<absl::uint128>::has_denorm;
constexpr bool numeric_limits<absl::uint128>::has_denorm_loss;
constexpr float_round_style numeric_limits<absl::uint128>::round_style;
constexpr bool numeric_limits<absl::uint128>::is_iec559;
constexpr bool numeric_limits<absl::uint128>::is_bounded;
constexpr bool numeric_limits<absl::uint128>::is_modulo;
constexpr int numeric_limits<absl::uint128>::digits;
constexpr int numeric_limits<absl::uint128>::digits10;
constexpr int numeric_limits<absl::uint128>::max_digits10;
constexpr int numeric_limits<absl::uint128>::radix;
constexpr int numeric_limits<absl::uint128>::min_exponent;
constexpr int numeric_limits<absl::uint128>::min_exponent10;
constexpr int numeric_limits<absl::uint128>::max_exponent;
constexpr int numeric_limits<absl::uint128>::max_exponent10;
constexpr bool numeric_limits<absl::uint128>::traps;
constexpr bool numeric_limits<absl::uint128>::tinyness_before;
constexpr bool numeric_limits<absl::int128>::is_specialized;
constexpr bool numeric_limits<absl::int128>::is_signed;
constexpr bool numeric_limits<absl::int128>::is_integer;
constexpr bool numeric_limits<absl::int128>::is_exact;
constexpr bool numeric_limits<absl::int128>::has_infinity;
constexpr bool numeric_limits<absl::int128>::has_quiet_NaN;
constexpr bool numeric_limits<absl::int128>::has_signaling_NaN;
constexpr float_denorm_style numeric_limits<absl::int128>::has_denorm;
constexpr bool numeric_limits<absl::int128>::has_denorm_loss;
constexpr float_round_style numeric_limits<absl::int128>::round_style;
constexpr bool numeric_limits<absl::int128>::is_iec559;
constexpr bool numeric_limits<absl::int128>::is_bounded;
constexpr bool numeric_limits<absl::int128>::is_modulo;
constexpr int numeric_limits<absl::int128>::digits;
constexpr int numeric_limits<absl::int128>::digits10;
constexpr int numeric_limits<absl::int128>::max_digits10;
constexpr int numeric_limits<absl::int128>::radix;
constexpr int numeric_limits<absl::int128>::min_exponent;
constexpr int numeric_limits<absl::int128>::min_exponent10;
constexpr int numeric_limits<absl::int128>::max_exponent;
constexpr int numeric_limits<absl::int128>::max_exponent10;
constexpr bool numeric_limits<absl::int128>::traps;
constexpr bool numeric_limits<absl::int128>::tinyness_before;
} // namespace std
#endif