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Diffstat (limited to 'third_party/abseil_cpp/absl/numeric/int128.cc')
| -rw-r--r-- | third_party/abseil_cpp/absl/numeric/int128.cc | 404 |
1 files changed, 404 insertions, 0 deletions
diff --git a/third_party/abseil_cpp/absl/numeric/int128.cc b/third_party/abseil_cpp/absl/numeric/int128.cc new file mode 100644 index 000000000000..b605a87042c1 --- /dev/null +++ b/third_party/abseil_cpp/absl/numeric/int128.cc @@ -0,0 +1,404 @@ +// 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> + +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 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: +// https://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)); +} + +#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)) {} + +uint128 operator/(uint128 lhs, uint128 rhs) { +#if defined(ABSL_HAVE_INTRINSIC_INT128) + return static_cast<unsigned __int128>(lhs) / + static_cast<unsigned __int128>(rhs); +#else // ABSL_HAVE_INTRINSIC_INT128 + uint128 quotient = 0; + uint128 remainder = 0; + DivModImpl(lhs, rhs, "ient, &remainder); + return quotient; +#endif // ABSL_HAVE_INTRINSIC_INT128 +} +uint128 operator%(uint128 lhs, uint128 rhs) { +#if defined(ABSL_HAVE_INTRINSIC_INT128) + return static_cast<unsigned __int128>(lhs) % + static_cast<unsigned __int128>(rhs); +#else // ABSL_HAVE_INTRINSIC_INT128 + uint128 quotient = 0; + uint128 remainder = 0; + DivModImpl(lhs, rhs, "ient, &remainder); + return remainder; +#endif // 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()) { + 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 { + +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), + "ient, &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), + "ient, &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()) { + switch (flags & std::ios::adjustfield) { + case std::ios::left: + rep.append(width - rep.size(), os.fill()); + break; + case std::ios::internal: + if (print_as_decimal && (rep[0] == '+' || rep[0] == '-')) { + rep.insert(1, width - rep.size(), os.fill()); + } else if ((flags & std::ios::basefield) == std::ios::hex && + (flags & std::ios::showbase) && v != 0) { + rep.insert(2, width - rep.size(), os.fill()); + } else { + rep.insert(0, width - rep.size(), os.fill()); + } + break; + default: // std::ios::right + rep.insert(0, width - rep.size(), os.fill()); + break; + } + } + + return os << rep; +} + +ABSL_NAMESPACE_END +} // namespace absl + +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 |