absl/numeric/int128.cc - third_party/abseil-cpp - Git at Google

 // 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 {
 inline namespace lts_2019_08_08 {

 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, &quotient, &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, &quotient, &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;
 }

 }  // inline namespace lts_2019_08_08
 }  // 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;
 }  // namespace std
	// 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 {
	inline namespace lts_2019_08_08 {

	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, &quotient, &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, &quotient, &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;
	}

	} // inline namespace lts_2019_08_08
	} // 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;
	} // namespace std