8f2828c4b4
ccdbb5941 Export of internal Abseil changes 01f5f81f9 Export of internal Abseil changes 2c92bdc7c Export of internal Abseil changes e7ebf9803 Export of internal Abseil changes 2eba343b5 Export of internal Abseil changes a8b03d90e Export of internal Abseil changes 1d31b5c36 Export of internal Abseil changes da3a87690 Export of internal Abseil changes 8faf20461 Exclude empty directories (#697) 2069dc796 Export of internal Abseil changes 4832bf6bf Added a BUILD file in root to expose license. (#695) af8f994af Export of internal Abseil changes 33caf1097 Export of internal Abseil changes cf1a02e2d Export of internal Abseil changes git-subtree-dir: third_party/abseil_cpp git-subtree-split: ccdbb5941f992fabda7eae3ce72f55efc17c826a
390 lines
14 KiB
C++
390 lines
14 KiB
C++
// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "absl/numeric/int128.h"
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#include <stddef.h>
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#include <cassert>
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#include <iomanip>
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#include <ostream> // NOLINT(readability/streams)
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#include <sstream>
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#include <string>
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#include <type_traits>
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#include "absl/base/internal/bits.h"
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#include "absl/base/optimization.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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ABSL_DLL const uint128 kuint128max = MakeUint128(
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std::numeric_limits<uint64_t>::max(), std::numeric_limits<uint64_t>::max());
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namespace {
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// Returns the 0-based position of the last set bit (i.e., most significant bit)
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// in the given uint128. The argument is not 0.
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//
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// For example:
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// Given: 5 (decimal) == 101 (binary)
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// Returns: 2
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inline ABSL_ATTRIBUTE_ALWAYS_INLINE int Fls128(uint128 n) {
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if (uint64_t hi = Uint128High64(n)) {
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ABSL_INTERNAL_ASSUME(hi != 0);
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return 127 - base_internal::CountLeadingZeros64(hi);
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}
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const uint64_t low = Uint128Low64(n);
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ABSL_INTERNAL_ASSUME(low != 0);
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return 63 - base_internal::CountLeadingZeros64(low);
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}
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// Long division/modulo for uint128 implemented using the shift-subtract
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// division algorithm adapted from:
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// https://stackoverflow.com/questions/5386377/division-without-using
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inline void DivModImpl(uint128 dividend, uint128 divisor, uint128* quotient_ret,
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uint128* remainder_ret) {
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assert(divisor != 0);
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if (divisor > dividend) {
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*quotient_ret = 0;
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*remainder_ret = dividend;
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return;
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}
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if (divisor == dividend) {
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*quotient_ret = 1;
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*remainder_ret = 0;
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return;
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}
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uint128 denominator = divisor;
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uint128 quotient = 0;
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// Left aligns the MSB of the denominator and the dividend.
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const int shift = Fls128(dividend) - Fls128(denominator);
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denominator <<= shift;
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// Uses shift-subtract algorithm to divide dividend by denominator. The
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// remainder will be left in dividend.
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for (int i = 0; i <= shift; ++i) {
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quotient <<= 1;
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if (dividend >= denominator) {
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dividend -= denominator;
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quotient |= 1;
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}
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denominator >>= 1;
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}
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*quotient_ret = quotient;
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*remainder_ret = dividend;
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}
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template <typename T>
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uint128 MakeUint128FromFloat(T v) {
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static_assert(std::is_floating_point<T>::value, "");
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// Rounding behavior is towards zero, same as for built-in types.
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// Undefined behavior if v is NaN or cannot fit into uint128.
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assert(std::isfinite(v) && v > -1 &&
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(std::numeric_limits<T>::max_exponent <= 128 ||
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v < std::ldexp(static_cast<T>(1), 128)));
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if (v >= std::ldexp(static_cast<T>(1), 64)) {
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uint64_t hi = static_cast<uint64_t>(std::ldexp(v, -64));
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uint64_t lo = static_cast<uint64_t>(v - std::ldexp(static_cast<T>(hi), 64));
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return MakeUint128(hi, lo);
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}
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return MakeUint128(0, static_cast<uint64_t>(v));
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}
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#if defined(__clang__) && !defined(__SSE3__)
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// Workaround for clang bug: https://bugs.llvm.org/show_bug.cgi?id=38289
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// Casting from long double to uint64_t is miscompiled and drops bits.
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// It is more work, so only use when we need the workaround.
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uint128 MakeUint128FromFloat(long double v) {
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// Go 50 bits at a time, that fits in a double
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static_assert(std::numeric_limits<double>::digits >= 50, "");
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static_assert(std::numeric_limits<long double>::digits <= 150, "");
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// Undefined behavior if v is not finite or cannot fit into uint128.
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assert(std::isfinite(v) && v > -1 && v < std::ldexp(1.0L, 128));
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v = std::ldexp(v, -100);
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uint64_t w0 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
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v = std::ldexp(v - static_cast<double>(w0), 50);
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uint64_t w1 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
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v = std::ldexp(v - static_cast<double>(w1), 50);
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uint64_t w2 = static_cast<uint64_t>(static_cast<double>(std::trunc(v)));
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return (static_cast<uint128>(w0) << 100) | (static_cast<uint128>(w1) << 50) |
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static_cast<uint128>(w2);
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}
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#endif // __clang__ && !__SSE3__
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} // namespace
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uint128::uint128(float v) : uint128(MakeUint128FromFloat(v)) {}
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uint128::uint128(double v) : uint128(MakeUint128FromFloat(v)) {}
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uint128::uint128(long double v) : uint128(MakeUint128FromFloat(v)) {}
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uint128 operator/(uint128 lhs, uint128 rhs) {
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#if defined(ABSL_HAVE_INTRINSIC_INT128)
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return static_cast<unsigned __int128>(lhs) /
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static_cast<unsigned __int128>(rhs);
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#else // ABSL_HAVE_INTRINSIC_INT128
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uint128 quotient = 0;
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uint128 remainder = 0;
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DivModImpl(lhs, rhs, "ient, &remainder);
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return quotient;
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#endif // ABSL_HAVE_INTRINSIC_INT128
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}
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uint128 operator%(uint128 lhs, uint128 rhs) {
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#if defined(ABSL_HAVE_INTRINSIC_INT128)
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return static_cast<unsigned __int128>(lhs) %
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static_cast<unsigned __int128>(rhs);
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#else // ABSL_HAVE_INTRINSIC_INT128
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uint128 quotient = 0;
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uint128 remainder = 0;
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DivModImpl(lhs, rhs, "ient, &remainder);
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return remainder;
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#endif // ABSL_HAVE_INTRINSIC_INT128
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}
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namespace {
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std::string Uint128ToFormattedString(uint128 v, std::ios_base::fmtflags flags) {
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// Select a divisor which is the largest power of the base < 2^64.
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uint128 div;
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int div_base_log;
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switch (flags & std::ios::basefield) {
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case std::ios::hex:
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div = 0x1000000000000000; // 16^15
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div_base_log = 15;
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break;
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case std::ios::oct:
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div = 01000000000000000000000; // 8^21
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div_base_log = 21;
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break;
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default: // std::ios::dec
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div = 10000000000000000000u; // 10^19
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div_base_log = 19;
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break;
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}
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// Now piece together the uint128 representation from three chunks of the
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// original value, each less than "div" and therefore representable as a
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// uint64_t.
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std::ostringstream os;
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std::ios_base::fmtflags copy_mask =
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std::ios::basefield | std::ios::showbase | std::ios::uppercase;
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os.setf(flags & copy_mask, copy_mask);
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uint128 high = v;
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uint128 low;
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DivModImpl(high, div, &high, &low);
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uint128 mid;
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DivModImpl(high, div, &high, &mid);
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if (Uint128Low64(high) != 0) {
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os << Uint128Low64(high);
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os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
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os << Uint128Low64(mid);
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os << std::setw(div_base_log);
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} else if (Uint128Low64(mid) != 0) {
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os << Uint128Low64(mid);
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os << std::noshowbase << std::setfill('0') << std::setw(div_base_log);
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}
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os << Uint128Low64(low);
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return os.str();
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}
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} // namespace
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std::ostream& operator<<(std::ostream& os, uint128 v) {
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std::ios_base::fmtflags flags = os.flags();
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std::string rep = Uint128ToFormattedString(v, flags);
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// Add the requisite padding.
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std::streamsize width = os.width(0);
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if (static_cast<size_t>(width) > rep.size()) {
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std::ios::fmtflags adjustfield = flags & std::ios::adjustfield;
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if (adjustfield == std::ios::left) {
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rep.append(width - rep.size(), os.fill());
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} else if (adjustfield == std::ios::internal &&
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(flags & std::ios::showbase) &&
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(flags & std::ios::basefield) == std::ios::hex && v != 0) {
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rep.insert(2, width - rep.size(), os.fill());
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} else {
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rep.insert(0, width - rep.size(), os.fill());
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}
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}
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return os << rep;
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}
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namespace {
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uint128 UnsignedAbsoluteValue(int128 v) {
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// Cast to uint128 before possibly negating because -Int128Min() is undefined.
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return Int128High64(v) < 0 ? -uint128(v) : uint128(v);
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}
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} // namespace
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#if !defined(ABSL_HAVE_INTRINSIC_INT128)
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namespace {
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template <typename T>
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int128 MakeInt128FromFloat(T v) {
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// Conversion when v is NaN or cannot fit into int128 would be undefined
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// behavior if using an intrinsic 128-bit integer.
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assert(std::isfinite(v) && (std::numeric_limits<T>::max_exponent <= 127 ||
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(v >= -std::ldexp(static_cast<T>(1), 127) &&
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v < std::ldexp(static_cast<T>(1), 127))));
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// We must convert the absolute value and then negate as needed, because
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// floating point types are typically sign-magnitude. Otherwise, the
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// difference between the high and low 64 bits when interpreted as two's
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// complement overwhelms the precision of the mantissa.
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uint128 result = v < 0 ? -MakeUint128FromFloat(-v) : MakeUint128FromFloat(v);
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return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(result)),
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Uint128Low64(result));
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}
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} // namespace
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int128::int128(float v) : int128(MakeInt128FromFloat(v)) {}
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int128::int128(double v) : int128(MakeInt128FromFloat(v)) {}
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int128::int128(long double v) : int128(MakeInt128FromFloat(v)) {}
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int128 operator/(int128 lhs, int128 rhs) {
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assert(lhs != Int128Min() || rhs != -1); // UB on two's complement.
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uint128 quotient = 0;
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uint128 remainder = 0;
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DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
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"ient, &remainder);
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if ((Int128High64(lhs) < 0) != (Int128High64(rhs) < 0)) quotient = -quotient;
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return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(quotient)),
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Uint128Low64(quotient));
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}
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int128 operator%(int128 lhs, int128 rhs) {
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assert(lhs != Int128Min() || rhs != -1); // UB on two's complement.
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uint128 quotient = 0;
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uint128 remainder = 0;
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DivModImpl(UnsignedAbsoluteValue(lhs), UnsignedAbsoluteValue(rhs),
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"ient, &remainder);
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if (Int128High64(lhs) < 0) remainder = -remainder;
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return MakeInt128(int128_internal::BitCastToSigned(Uint128High64(remainder)),
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Uint128Low64(remainder));
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}
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#endif // ABSL_HAVE_INTRINSIC_INT128
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std::ostream& operator<<(std::ostream& os, int128 v) {
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std::ios_base::fmtflags flags = os.flags();
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std::string rep;
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// Add the sign if needed.
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bool print_as_decimal =
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(flags & std::ios::basefield) == std::ios::dec ||
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(flags & std::ios::basefield) == std::ios_base::fmtflags();
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if (print_as_decimal) {
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if (Int128High64(v) < 0) {
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rep = "-";
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} else if (flags & std::ios::showpos) {
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rep = "+";
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}
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}
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rep.append(Uint128ToFormattedString(
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print_as_decimal ? UnsignedAbsoluteValue(v) : uint128(v), os.flags()));
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// Add the requisite padding.
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std::streamsize width = os.width(0);
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if (static_cast<size_t>(width) > rep.size()) {
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switch (flags & std::ios::adjustfield) {
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case std::ios::left:
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rep.append(width - rep.size(), os.fill());
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break;
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case std::ios::internal:
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if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) {
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rep.insert(1, width - rep.size(), os.fill());
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} else if ((flags & std::ios::basefield) == std::ios::hex &&
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(flags & std::ios::showbase) && v != 0) {
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rep.insert(2, width - rep.size(), os.fill());
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} else {
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rep.insert(0, width - rep.size(), os.fill());
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}
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break;
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default: // std::ios::right
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rep.insert(0, width - rep.size(), os.fill());
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break;
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}
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}
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return os << rep;
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}
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ABSL_NAMESPACE_END
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} // namespace absl
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namespace std {
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constexpr bool numeric_limits<absl::uint128>::is_specialized;
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constexpr bool numeric_limits<absl::uint128>::is_signed;
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constexpr bool numeric_limits<absl::uint128>::is_integer;
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constexpr bool numeric_limits<absl::uint128>::is_exact;
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constexpr bool numeric_limits<absl::uint128>::has_infinity;
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constexpr bool numeric_limits<absl::uint128>::has_quiet_NaN;
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constexpr bool numeric_limits<absl::uint128>::has_signaling_NaN;
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constexpr float_denorm_style numeric_limits<absl::uint128>::has_denorm;
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constexpr bool numeric_limits<absl::uint128>::has_denorm_loss;
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constexpr float_round_style numeric_limits<absl::uint128>::round_style;
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constexpr bool numeric_limits<absl::uint128>::is_iec559;
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constexpr bool numeric_limits<absl::uint128>::is_bounded;
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constexpr bool numeric_limits<absl::uint128>::is_modulo;
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constexpr int numeric_limits<absl::uint128>::digits;
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constexpr int numeric_limits<absl::uint128>::digits10;
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constexpr int numeric_limits<absl::uint128>::max_digits10;
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constexpr int numeric_limits<absl::uint128>::radix;
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constexpr int numeric_limits<absl::uint128>::min_exponent;
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constexpr int numeric_limits<absl::uint128>::min_exponent10;
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constexpr int numeric_limits<absl::uint128>::max_exponent;
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constexpr int numeric_limits<absl::uint128>::max_exponent10;
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constexpr bool numeric_limits<absl::uint128>::traps;
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constexpr bool numeric_limits<absl::uint128>::tinyness_before;
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constexpr bool numeric_limits<absl::int128>::is_specialized;
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constexpr bool numeric_limits<absl::int128>::is_signed;
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constexpr bool numeric_limits<absl::int128>::is_integer;
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constexpr bool numeric_limits<absl::int128>::is_exact;
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constexpr bool numeric_limits<absl::int128>::has_infinity;
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constexpr bool numeric_limits<absl::int128>::has_quiet_NaN;
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constexpr bool numeric_limits<absl::int128>::has_signaling_NaN;
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constexpr float_denorm_style numeric_limits<absl::int128>::has_denorm;
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constexpr bool numeric_limits<absl::int128>::has_denorm_loss;
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constexpr float_round_style numeric_limits<absl::int128>::round_style;
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constexpr bool numeric_limits<absl::int128>::is_iec559;
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constexpr bool numeric_limits<absl::int128>::is_bounded;
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constexpr bool numeric_limits<absl::int128>::is_modulo;
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constexpr int numeric_limits<absl::int128>::digits;
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constexpr int numeric_limits<absl::int128>::digits10;
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constexpr int numeric_limits<absl::int128>::max_digits10;
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constexpr int numeric_limits<absl::int128>::radix;
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constexpr int numeric_limits<absl::int128>::min_exponent;
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constexpr int numeric_limits<absl::int128>::min_exponent10;
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constexpr int numeric_limits<absl::int128>::max_exponent;
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constexpr int numeric_limits<absl::int128>::max_exponent10;
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constexpr bool numeric_limits<absl::int128>::traps;
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constexpr bool numeric_limits<absl::int128>::tinyness_before;
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} // namespace std
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