384 lines
14 KiB
C++
384 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/optimization.h"
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#include "absl/numeric/bits.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 - countl_zero(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 - countl_zero(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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#if !defined(ABSL_HAVE_INTRINSIC_INT128)
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uint128 operator/(uint128 lhs, uint128 rhs) {
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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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}
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uint128 operator%(uint128 lhs, uint128 rhs) {
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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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}
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#endif // !defined(ABSL_HAVE_INTRINSIC_INT128)
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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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