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Diffstat (limited to 'absl/numeric/int128.cc')
-rw-r--r-- | absl/numeric/int128.cc | 200 |
1 files changed, 200 insertions, 0 deletions
diff --git a/absl/numeric/int128.cc b/absl/numeric/int128.cc new file mode 100644 index 000000000000..184041fe4a22 --- /dev/null +++ b/absl/numeric/int128.cc @@ -0,0 +1,200 @@ +// 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 <cassert> +#include <cstdlib> +#include <iomanip> +#include <iostream> // NOLINT(readability/streams) +#include <sstream> + +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 Initialize128FromFloat(T v) { + // Rounding behavior is towards zero, same as for built-in types. + + // Undefined behavior if v is NaN or cannot fit into uint128. + assert(!std::isnan(v) && v > -1 && 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(Initialize128FromFloat(v)) {} +uint128::uint128(double v) : uint128(Initialize128FromFloat(v)) {} +uint128::uint128(long double v) : uint128(Initialize128FromFloat(v)) {} + +uint128& uint128::operator/=(const uint128& divisor) { + uint128 quotient = 0; + uint128 remainder = 0; + DivModImpl(*this, divisor, "ient, &remainder); + *this = quotient; + return *this; +} +uint128& uint128::operator%=(const uint128& divisor) { + uint128 quotient = 0; + uint128 remainder = 0; + DivModImpl(*this, divisor, "ient, &remainder); + *this = remainder; + return *this; +} + +std::ostream& operator<<(std::ostream& o, const uint128& b) { + std::ios_base::fmtflags flags = o.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 = b; + 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); + std::string rep = os.str(); + + // Add the requisite padding. + std::streamsize width = o.width(0); + if (static_cast<size_t>(width) > rep.size()) { + if ((flags & std::ios::adjustfield) == std::ios::left) { + rep.append(width - rep.size(), o.fill()); + } else { + rep.insert(0, width - rep.size(), o.fill()); + } + } + + // Stream the final representation in a single "<<" call. + return o << rep; +} + +} // namespace absl |