You are viewing a plain text version of this content. The canonical link for it is here.
Posted to commits@impala.apache.org by ta...@apache.org on 2017/12/14 17:48:40 UTC
[3/8] impala git commit: IMPALA-5754: Improve randomness of
rand()/random()
http://git-wip-us.apache.org/repos/asf/impala/blob/4feb4f3a/be/src/thirdparty/pcg-cpp-0.98/include/pcg_random.hpp
----------------------------------------------------------------------
diff --git a/be/src/thirdparty/pcg-cpp-0.98/include/pcg_random.hpp b/be/src/thirdparty/pcg-cpp-0.98/include/pcg_random.hpp
new file mode 100644
index 0000000..3f04d85
--- /dev/null
+++ b/be/src/thirdparty/pcg-cpp-0.98/include/pcg_random.hpp
@@ -0,0 +1,1751 @@
+/*
+ * PCG Random Number Generation for C++
+ *
+ * Copyright 2014 Melissa O'Neill <on...@pcg-random.org>
+ *
+ * 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.
+ *
+ * For additional information about the PCG random number generation scheme,
+ * including its license and other licensing options, visit
+ *
+ * http://www.pcg-random.org
+ */
+
+/*
+ * This code provides the reference implementation of the PCG family of
+ * random number generators. The code is complex because it implements
+ *
+ * - several members of the PCG family, specifically members corresponding
+ * to the output functions:
+ * - XSH RR (good for 64-bit state, 32-bit output)
+ * - XSH RS (good for 64-bit state, 32-bit output)
+ * - XSL RR (good for 128-bit state, 64-bit output)
+ * - RXS M XS (statistically most powerful generator)
+ * - XSL RR RR (good for 128-bit state, 128-bit output)
+ * - and RXS, RXS M, XSH, XSL (mostly for testing)
+ * - at potentially *arbitrary* bit sizes
+ * - with four different techniques for random streams (MCG, one-stream
+ * LCG, settable-stream LCG, unique-stream LCG)
+ * - and the extended generation schemes allowing arbitrary periods
+ * - with all features of C++11 random number generation (and more),
+ * some of which are somewhat painful, including
+ * - initializing with a SeedSequence which writes 32-bit values
+ * to memory, even though the state of the generator may not
+ * use 32-bit values (it might use smaller or larger integers)
+ * - I/O for RNGs and a prescribed format, which needs to handle
+ * the issue that 8-bit and 128-bit integers don't have working
+ * I/O routines (e.g., normally 8-bit = char, not integer)
+ * - equality and inequality for RNGs
+ * - and a number of convenience typedefs to mask all the complexity
+ *
+ * The code employes a fairly heavy level of abstraction, and has to deal
+ * with various C++ minutia. If you're looking to learn about how the PCG
+ * scheme works, you're probably best of starting with one of the other
+ * codebases (see www.pcg-random.org). But if you're curious about the
+ * constants for the various output functions used in those other, simpler,
+ * codebases, this code shows how they are calculated.
+ *
+ * On the positive side, at least there are convenience typedefs so that you
+ * can say
+ *
+ * pcg32 myRNG;
+ *
+ * rather than:
+ *
+ * pcg_detail::engine<
+ * uint32_t, // Output Type
+ * uint64_t, // State Type
+ * pcg_detail::xsh_rr_mixin<uint32_t, uint64_t>, true, // Output Func
+ * pcg_detail::specific_stream<uint64_t>, // Stream Kind
+ * pcg_detail::default_multiplier<uint64_t> // LCG Mult
+ * > myRNG;
+ *
+ */
+
+#ifndef PCG_RAND_HPP_INCLUDED
+#define PCG_RAND_HPP_INCLUDED 1
+
+#include <cinttypes>
+#include <cstddef>
+#include <cstdlib>
+#include <cstring>
+#include <cassert>
+#include <limits>
+#include <iostream>
+#include <type_traits>
+#include <utility>
+#include <locale>
+#include <new>
+#include <stdexcept>
+
+/*
+ * The pcg_extras namespace contains some support code that is likley to
+ * be useful for a variety of RNGs, including:
+ * - 128-bit int support for platforms where it isn't available natively
+ * - bit twiddling operations
+ * - I/O of 128-bit and 8-bit integers
+ * - Handling the evilness of SeedSeq
+ * - Support for efficiently producing random numbers less than a given
+ * bound
+ */
+
+#include "pcg_extras.hpp"
+
+namespace pcg_detail {
+
+using namespace pcg_extras;
+
+/*
+ * The LCG generators need some constants to function. This code lets you
+ * look up the constant by *type*. For example
+ *
+ * default_multiplier<uint32_t>::multiplier()
+ *
+ * gives you the default multipler for 32-bit integers. We use the name
+ * of the constant and not a generic word like value to allow these classes
+ * to be used as mixins.
+ */
+
+template <typename T>
+struct default_multiplier {
+ // Not defined for an arbitrary type
+};
+
+template <typename T>
+struct default_increment {
+ // Not defined for an arbitrary type
+};
+
+#define PCG_DEFINE_CONSTANT(type, what, kind, constant) \
+ template <> \
+ struct what ## _ ## kind<type> { \
+ static constexpr type kind() { \
+ return constant; \
+ } \
+ };
+
+PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U)
+PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U)
+
+PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U)
+PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U)
+
+PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U)
+PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U)
+
+PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL)
+PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL)
+
+PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier,
+ PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL))
+PCG_DEFINE_CONSTANT(pcg128_t, default, increment,
+ PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL))
+
+
+/*
+ * Each PCG generator is available in four variants, based on how it applies
+ * the additive constant for its underlying LCG; the variations are:
+ *
+ * single stream - all instances use the same fixed constant, thus
+ * the RNG always somewhere in same sequence
+ * mcg - adds zero, resulting in a single stream and reduced
+ * period
+ * specific stream - the constant can be changed at any time, selecting
+ * a different random sequence
+ * unique stream - the constant is based on the memory addresss of the
+ * object, thus every RNG has its own unique sequence
+ *
+ * This variation is provided though mixin classes which define a function
+ * value called increment() that returns the nesessary additive constant.
+ */
+
+
+
+/*
+ * unique stream
+ */
+
+
+template <typename itype>
+class unique_stream {
+protected:
+ static constexpr bool is_mcg = false;
+
+ // Is never called, but is provided for symmetry with specific_stream
+ void set_stream(...)
+ {
+ abort();
+ }
+
+public:
+ typedef itype state_type;
+
+ constexpr itype increment() const {
+ return itype(reinterpret_cast<unsigned long>(this) | 1);
+ }
+
+ constexpr itype stream() const
+ {
+ return increment() >> 1;
+ }
+
+ static constexpr bool can_specify_stream = false;
+
+ static constexpr size_t streams_pow2()
+ {
+ return (sizeof(itype) < sizeof(size_t) ? sizeof(itype)
+ : sizeof(size_t))*8 - 1u;
+ }
+
+protected:
+ constexpr unique_stream() = default;
+};
+
+
+/*
+ * no stream (mcg)
+ */
+
+template <typename itype>
+class no_stream {
+protected:
+ static constexpr bool is_mcg = true;
+
+ // Is never called, but is provided for symmetry with specific_stream
+ void set_stream(...)
+ {
+ abort();
+ }
+
+public:
+ typedef itype state_type;
+
+ static constexpr itype increment() {
+ return 0;
+ }
+
+ static constexpr bool can_specify_stream = false;
+
+ static constexpr size_t streams_pow2()
+ {
+ return 0u;
+ }
+
+protected:
+ constexpr no_stream() = default;
+};
+
+
+/*
+ * single stream/sequence (oneseq)
+ */
+
+template <typename itype>
+class oneseq_stream : public default_increment<itype> {
+protected:
+ static constexpr bool is_mcg = false;
+
+ // Is never called, but is provided for symmetry with specific_stream
+ void set_stream(...)
+ {
+ abort();
+ }
+
+public:
+ typedef itype state_type;
+
+ static constexpr itype stream()
+ {
+ return default_increment<itype>::increment() >> 1;
+ }
+
+ static constexpr bool can_specify_stream = false;
+
+ static constexpr size_t streams_pow2()
+ {
+ return 0u;
+ }
+
+protected:
+ constexpr oneseq_stream() = default;
+};
+
+
+/*
+ * specific stream
+ */
+
+template <typename itype>
+class specific_stream {
+protected:
+ static constexpr bool is_mcg = false;
+
+ itype inc_ = default_increment<itype>::increment();
+
+public:
+ typedef itype state_type;
+ typedef itype stream_state;
+
+ constexpr itype increment() const {
+ return inc_;
+ }
+
+ itype stream()
+ {
+ return inc_ >> 1;
+ }
+
+ void set_stream(itype specific_seq)
+ {
+ inc_ = (specific_seq << 1) | 1;
+ }
+
+ static constexpr bool can_specify_stream = true;
+
+ static constexpr size_t streams_pow2()
+ {
+ return (sizeof(itype)*8) - 1u;
+ }
+
+protected:
+ specific_stream() = default;
+
+ specific_stream(itype specific_seq)
+ : inc_((specific_seq << 1) | itype(1U))
+ {
+ // Nothing (else) to do.
+ }
+};
+
+
+/*
+ * This is where it all comes together. This function joins together three
+ * mixin classes which define
+ * - the LCG additive constant (the stream)
+ * - the LCG multiplier
+ * - the output function
+ * in addition, we specify the type of the LCG state, and the result type,
+ * and whether to use the pre-advance version of the state for the output
+ * (increasing instruction-level parallelism) or the post-advance version
+ * (reducing register pressure).
+ *
+ * Given the high level of parameterization, the code has to use some
+ * template-metaprogramming tricks to handle some of the suble variations
+ * involved.
+ */
+
+template <typename xtype, typename itype,
+ typename output_mixin,
+ bool output_previous = true,
+ typename stream_mixin = oneseq_stream<itype>,
+ typename multiplier_mixin = default_multiplier<itype> >
+class engine : protected output_mixin,
+ public stream_mixin,
+ protected multiplier_mixin {
+protected:
+ itype state_;
+
+ struct can_specify_stream_tag {};
+ struct no_specifiable_stream_tag {};
+
+ using stream_mixin::increment;
+ using multiplier_mixin::multiplier;
+
+public:
+ typedef xtype result_type;
+ typedef itype state_type;
+
+ static constexpr size_t period_pow2()
+ {
+ return sizeof(state_type)*8 - 2*stream_mixin::is_mcg;
+ }
+
+ // It would be nice to use std::numeric_limits for these, but
+ // we can't be sure that it'd be defined for the 128-bit types.
+
+ static constexpr result_type min()
+ {
+ return result_type(0UL);
+ }
+
+ static constexpr result_type max()
+ {
+ return ~result_type(0UL);
+ }
+
+protected:
+ itype bump(itype state)
+ {
+ return state * multiplier() + increment();
+ }
+
+ itype base_generate()
+ {
+ return state_ = bump(state_);
+ }
+
+ itype base_generate0()
+ {
+ itype old_state = state_;
+ state_ = bump(state_);
+ return old_state;
+ }
+
+public:
+ result_type operator()()
+ {
+ if (output_previous)
+ return this->output(base_generate0());
+ else
+ return this->output(base_generate());
+ }
+
+ result_type operator()(result_type upper_bound)
+ {
+ return bounded_rand(*this, upper_bound);
+ }
+
+protected:
+ static itype advance(itype state, itype delta,
+ itype cur_mult, itype cur_plus);
+
+ static itype distance(itype cur_state, itype newstate, itype cur_mult,
+ itype cur_plus, itype mask = ~itype(0U));
+
+ itype distance(itype newstate, itype mask = ~itype(0U)) const
+ {
+ return distance(state_, newstate, multiplier(), increment(), mask);
+ }
+
+public:
+ void advance(itype delta)
+ {
+ state_ = advance(state_, delta, this->multiplier(), this->increment());
+ }
+
+ void backstep(itype delta)
+ {
+ advance(-delta);
+ }
+
+ void discard(itype delta)
+ {
+ advance(delta);
+ }
+
+ bool wrapped()
+ {
+ if (stream_mixin::is_mcg) {
+ // For MCGs, the low order two bits never change. In this
+ // implementation, we keep them fixed at 3 to make this test
+ // easier.
+ return state_ == 3;
+ } else {
+ return state_ == 0;
+ }
+ }
+
+ engine(itype state = itype(0xcafef00dd15ea5e5ULL))
+ : state_(this->is_mcg ? state|state_type(3U)
+ : bump(state + this->increment()))
+ {
+ // Nothing else to do.
+ }
+
+ // This function may or may not exist. It thus has to be a template
+ // to use SFINAE; users don't have to worry about its template-ness.
+
+ template <typename sm = stream_mixin>
+ engine(itype state, typename sm::stream_state stream_seed)
+ : stream_mixin(stream_seed),
+ state_(this->is_mcg ? state|state_type(3U)
+ : bump(state + this->increment()))
+ {
+ // Nothing else to do.
+ }
+
+ template<typename SeedSeq>
+ engine(SeedSeq&& seedSeq, typename std::enable_if<
+ !stream_mixin::can_specify_stream
+ && !std::is_convertible<SeedSeq, itype>::value
+ && !std::is_convertible<SeedSeq, engine>::value,
+ no_specifiable_stream_tag>::type = {})
+ : engine(generate_one<itype>(std::forward<SeedSeq>(seedSeq)))
+ {
+ // Nothing else to do.
+ }
+
+ template<typename SeedSeq>
+ engine(SeedSeq&& seedSeq, typename std::enable_if<
+ stream_mixin::can_specify_stream
+ && !std::is_convertible<SeedSeq, itype>::value
+ && !std::is_convertible<SeedSeq, engine>::value,
+ can_specify_stream_tag>::type = {})
+ : engine(generate_one<itype,1,2>(seedSeq),
+ generate_one<itype,0,2>(seedSeq))
+ {
+ // Nothing else to do.
+ }
+
+
+ template<typename... Args>
+ void seed(Args&&... args)
+ {
+ new (this) engine(std::forward<Args>(args)...);
+ }
+
+ template <typename xtype1, typename itype1,
+ typename output_mixin1, bool output_previous1,
+ typename stream_mixin_lhs, typename multiplier_mixin_lhs,
+ typename stream_mixin_rhs, typename multiplier_mixin_rhs>
+ friend bool operator==(const engine<xtype1,itype1,
+ output_mixin1,output_previous1,
+ stream_mixin_lhs, multiplier_mixin_lhs>&,
+ const engine<xtype1,itype1,
+ output_mixin1,output_previous1,
+ stream_mixin_rhs, multiplier_mixin_rhs>&);
+
+ template <typename xtype1, typename itype1,
+ typename output_mixin1, bool output_previous1,
+ typename stream_mixin_lhs, typename multiplier_mixin_lhs,
+ typename stream_mixin_rhs, typename multiplier_mixin_rhs>
+ friend itype1 operator-(const engine<xtype1,itype1,
+ output_mixin1,output_previous1,
+ stream_mixin_lhs, multiplier_mixin_lhs>&,
+ const engine<xtype1,itype1,
+ output_mixin1,output_previous1,
+ stream_mixin_rhs, multiplier_mixin_rhs>&);
+
+ template <typename CharT, typename Traits,
+ typename xtype1, typename itype1,
+ typename output_mixin1, bool output_previous1,
+ typename stream_mixin1, typename multiplier_mixin1>
+ friend std::basic_ostream<CharT,Traits>&
+ operator<<(std::basic_ostream<CharT,Traits>& out,
+ const engine<xtype1,itype1,
+ output_mixin1,output_previous1,
+ stream_mixin1, multiplier_mixin1>&);
+
+ template <typename CharT, typename Traits,
+ typename xtype1, typename itype1,
+ typename output_mixin1, bool output_previous1,
+ typename stream_mixin1, typename multiplier_mixin1>
+ friend std::basic_istream<CharT,Traits>&
+ operator>>(std::basic_istream<CharT,Traits>& in,
+ engine<xtype1, itype1,
+ output_mixin1, output_previous1,
+ stream_mixin1, multiplier_mixin1>& rng);
+};
+
+template <typename CharT, typename Traits,
+ typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin, typename multiplier_mixin>
+std::basic_ostream<CharT,Traits>&
+operator<<(std::basic_ostream<CharT,Traits>& out,
+ const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin, multiplier_mixin>& rng)
+{
+ auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left);
+ auto space = out.widen(' ');
+ auto orig_fill = out.fill();
+
+ out << rng.multiplier() << space
+ << rng.increment() << space
+ << rng.state_;
+
+ out.flags(orig_flags);
+ out.fill(orig_fill);
+ return out;
+}
+
+
+template <typename CharT, typename Traits,
+ typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin, typename multiplier_mixin>
+std::basic_istream<CharT,Traits>&
+operator>>(std::basic_istream<CharT,Traits>& in,
+ engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin, multiplier_mixin>& rng)
+{
+ auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws);
+
+ itype multiplier, increment, state;
+ in >> multiplier >> increment >> state;
+
+ if (!in.fail()) {
+ bool good = true;
+ if (multiplier != rng.multiplier()) {
+ good = false;
+ } else if (rng.can_specify_stream) {
+ rng.set_stream(increment >> 1);
+ } else if (increment != rng.increment()) {
+ good = false;
+ }
+ if (good) {
+ rng.state_ = state;
+ } else {
+ in.clear(std::ios::failbit);
+ }
+ }
+
+ in.flags(orig_flags);
+ return in;
+}
+
+
+template <typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin, typename multiplier_mixin>
+itype engine<xtype,itype,output_mixin,output_previous,stream_mixin,
+ multiplier_mixin>::advance(
+ itype state, itype delta, itype cur_mult, itype cur_plus)
+{
+ // The method used here is based on Brown, "Random Number Generation
+ // with Arbitrary Stride,", Transactions of the American Nuclear
+ // Society (Nov. 1994). The algorithm is very similar to fast
+ // exponentiation.
+ //
+ // Even though delta is an unsigned integer, we can pass a
+ // signed integer to go backwards, it just goes "the long way round".
+
+ constexpr itype ZERO = 0u; // itype may be a non-trivial types, so
+ constexpr itype ONE = 1u; // we define some ugly constants.
+ itype acc_mult = 1;
+ itype acc_plus = 0;
+ while (delta > ZERO) {
+ if (delta & ONE) {
+ acc_mult *= cur_mult;
+ acc_plus = acc_plus*cur_mult + cur_plus;
+ }
+ cur_plus = (cur_mult+ONE)*cur_plus;
+ cur_mult *= cur_mult;
+ delta >>= 1;
+ }
+ return acc_mult * state + acc_plus;
+}
+
+template <typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin, typename multiplier_mixin>
+itype engine<xtype,itype,output_mixin,output_previous,stream_mixin,
+ multiplier_mixin>::distance(
+ itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask)
+{
+ constexpr itype ONE = 1u; // itype could be weird, so use constant
+ itype the_bit = stream_mixin::is_mcg ? itype(4u) : itype(1u);
+ itype distance = 0u;
+ while ((cur_state & mask) != (newstate & mask)) {
+ if ((cur_state & the_bit) != (newstate & the_bit)) {
+ cur_state = cur_state * cur_mult + cur_plus;
+ distance |= the_bit;
+ }
+ assert((cur_state & the_bit) == (newstate & the_bit));
+ the_bit <<= 1;
+ cur_plus = (cur_mult+ONE)*cur_plus;
+ cur_mult *= cur_mult;
+ }
+ return stream_mixin::is_mcg ? distance >> 2 : distance;
+}
+
+template <typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin_lhs, typename multiplier_mixin_lhs,
+ typename stream_mixin_rhs, typename multiplier_mixin_rhs>
+itype operator-(const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
+ const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
+{
+ if (lhs.multiplier() != rhs.multiplier()
+ || lhs.increment() != rhs.increment())
+ throw std::logic_error("incomparable generators");
+ return rhs.distance(lhs.state_);
+}
+
+
+template <typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin_lhs, typename multiplier_mixin_lhs,
+ typename stream_mixin_rhs, typename multiplier_mixin_rhs>
+bool operator==(const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
+ const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
+{
+ return (lhs.multiplier() == rhs.multiplier())
+ && (lhs.increment() == rhs.increment())
+ && (lhs.state_ == rhs.state_);
+}
+
+template <typename xtype, typename itype,
+ typename output_mixin, bool output_previous,
+ typename stream_mixin_lhs, typename multiplier_mixin_lhs,
+ typename stream_mixin_rhs, typename multiplier_mixin_rhs>
+inline bool operator!=(const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
+ const engine<xtype,itype,
+ output_mixin,output_previous,
+ stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
+{
+ return !operator==(lhs,rhs);
+}
+
+
+template <typename xtype, typename itype,
+ template<typename XT,typename IT> class output_mixin,
+ bool output_previous = (sizeof(itype) <= 8)>
+using oneseq_base = engine<xtype, itype,
+ output_mixin<xtype, itype>, output_previous,
+ oneseq_stream<itype> >;
+
+template <typename xtype, typename itype,
+ template<typename XT,typename IT> class output_mixin,
+ bool output_previous = (sizeof(itype) <= 8)>
+using unique_base = engine<xtype, itype,
+ output_mixin<xtype, itype>, output_previous,
+ unique_stream<itype> >;
+
+template <typename xtype, typename itype,
+ template<typename XT,typename IT> class output_mixin,
+ bool output_previous = (sizeof(itype) <= 8)>
+using setseq_base = engine<xtype, itype,
+ output_mixin<xtype, itype>, output_previous,
+ specific_stream<itype> >;
+
+template <typename xtype, typename itype,
+ template<typename XT,typename IT> class output_mixin,
+ bool output_previous = (sizeof(itype) <= 8)>
+using mcg_base = engine<xtype, itype,
+ output_mixin<xtype, itype>, output_previous,
+ no_stream<itype> >;
+
+/*
+ * OUTPUT FUNCTIONS.
+ *
+ * These are the core of the PCG generation scheme. They specify how to
+ * turn the base LCG's internal state into the output value of the final
+ * generator.
+ *
+ * They're implemented as mixin classes.
+ *
+ * All of the classes have code that is written to allow it to be applied
+ * at *arbitrary* bit sizes, although in practice they'll only be used at
+ * standard sizes supported by C++.
+ */
+
+/*
+ * XSH RS -- high xorshift, followed by a random shift
+ *
+ * Fast. A good performer.
+ */
+
+template <typename xtype, typename itype>
+struct xsh_rs_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t sparebits = bits - xtypebits;
+ constexpr bitcount_t opbits =
+ sparebits-5 >= 64 ? 5
+ : sparebits-4 >= 32 ? 4
+ : sparebits-3 >= 16 ? 3
+ : sparebits-2 >= 4 ? 2
+ : sparebits-1 >= 1 ? 1
+ : 0;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ constexpr bitcount_t maxrandshift = mask;
+ constexpr bitcount_t topspare = opbits;
+ constexpr bitcount_t bottomspare = sparebits - topspare;
+ constexpr bitcount_t xshift = topspare + (xtypebits+maxrandshift)/2;
+ bitcount_t rshift =
+ opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
+ internal ^= internal >> xshift;
+ xtype result = xtype(internal >> (bottomspare - maxrandshift + rshift));
+ return result;
+ }
+};
+
+/*
+ * XSH RR -- high xorshift, followed by a random rotate
+ *
+ * Fast. A good performer. Slightly better statistically than XSH RS.
+ */
+
+template <typename xtype, typename itype>
+struct xsh_rr_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype)*8);
+ constexpr bitcount_t sparebits = bits - xtypebits;
+ constexpr bitcount_t wantedopbits =
+ xtypebits >= 128 ? 7
+ : xtypebits >= 64 ? 6
+ : xtypebits >= 32 ? 5
+ : xtypebits >= 16 ? 4
+ : 3;
+ constexpr bitcount_t opbits =
+ sparebits >= wantedopbits ? wantedopbits
+ : sparebits;
+ constexpr bitcount_t amplifier = wantedopbits - opbits;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ constexpr bitcount_t topspare = opbits;
+ constexpr bitcount_t bottomspare = sparebits - topspare;
+ constexpr bitcount_t xshift = (topspare + xtypebits)/2;
+ bitcount_t rot = opbits ? bitcount_t(internal >> (bits - opbits)) & mask
+ : 0;
+ bitcount_t amprot = (rot << amplifier) & mask;
+ internal ^= internal >> xshift;
+ xtype result = xtype(internal >> bottomspare);
+ result = rotr(result, amprot);
+ return result;
+ }
+};
+
+/*
+ * RXS -- random xorshift
+ */
+
+template <typename xtype, typename itype>
+struct rxs_mixin {
+static xtype output_rxs(itype internal)
+ {
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype)*8);
+ constexpr bitcount_t shift = bits - xtypebits;
+ constexpr bitcount_t extrashift = (xtypebits - shift)/2;
+ bitcount_t rshift = shift > 64+8 ? (internal >> (bits - 6)) & 63
+ : shift > 32+4 ? (internal >> (bits - 5)) & 31
+ : shift > 16+2 ? (internal >> (bits - 4)) & 15
+ : shift > 8+1 ? (internal >> (bits - 3)) & 7
+ : shift > 4+1 ? (internal >> (bits - 2)) & 3
+ : shift > 2+1 ? (internal >> (bits - 1)) & 1
+ : 0;
+ internal ^= internal >> (shift + extrashift - rshift);
+ xtype result = internal >> rshift;
+ return result;
+ }
+};
+
+/*
+ * RXS M XS -- random xorshift, mcg multiply, fixed xorshift
+ *
+ * The most statistically powerful generator, but all those steps
+ * make it slower than some of the others. We give it the rottenest jobs.
+ *
+ * Because it's usually used in contexts where the state type and the
+ * result type are the same, it is a permutation and is thus invertable.
+ * We thus provide a function to invert it. This function is used to
+ * for the "inside out" generator used by the extended generator.
+ */
+
+/* Defined type-based concepts for the multiplication step. They're actually
+ * all derived by truncating the 128-bit, which was computed to be a good
+ * "universal" constant.
+ */
+
+template <typename T>
+struct mcg_multiplier {
+ // Not defined for an arbitrary type
+};
+
+template <typename T>
+struct mcg_unmultiplier {
+ // Not defined for an arbitrary type
+};
+
+PCG_DEFINE_CONSTANT(uint8_t, mcg, multiplier, 217U)
+PCG_DEFINE_CONSTANT(uint8_t, mcg, unmultiplier, 105U)
+
+PCG_DEFINE_CONSTANT(uint16_t, mcg, multiplier, 62169U)
+PCG_DEFINE_CONSTANT(uint16_t, mcg, unmultiplier, 28009U)
+
+PCG_DEFINE_CONSTANT(uint32_t, mcg, multiplier, 277803737U)
+PCG_DEFINE_CONSTANT(uint32_t, mcg, unmultiplier, 2897767785U)
+
+PCG_DEFINE_CONSTANT(uint64_t, mcg, multiplier, 12605985483714917081ULL)
+PCG_DEFINE_CONSTANT(uint64_t, mcg, unmultiplier, 15009553638781119849ULL)
+
+PCG_DEFINE_CONSTANT(pcg128_t, mcg, multiplier,
+ PCG_128BIT_CONSTANT(17766728186571221404ULL, 12605985483714917081ULL))
+PCG_DEFINE_CONSTANT(pcg128_t, mcg, unmultiplier,
+ PCG_128BIT_CONSTANT(14422606686972528997ULL, 15009553638781119849ULL))
+
+
+template <typename xtype, typename itype>
+struct rxs_m_xs_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t opbits = xtypebits >= 128 ? 6
+ : xtypebits >= 64 ? 5
+ : xtypebits >= 32 ? 4
+ : xtypebits >= 16 ? 3
+ : 2;
+ constexpr bitcount_t shift = bits - xtypebits;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ bitcount_t rshift =
+ opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
+ internal ^= internal >> (opbits + rshift);
+ internal *= mcg_multiplier<itype>::multiplier();
+ xtype result = internal >> shift;
+ result ^= result >> ((2U*xtypebits+2U)/3U);
+ return result;
+ }
+
+ static itype unoutput(itype internal)
+ {
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t opbits = bits >= 128 ? 6
+ : bits >= 64 ? 5
+ : bits >= 32 ? 4
+ : bits >= 16 ? 3
+ : 2;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+
+ internal = unxorshift(internal, bits, (2U*bits+2U)/3U);
+
+ internal *= mcg_unmultiplier<itype>::unmultiplier();
+
+ bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
+ internal = unxorshift(internal, bits, opbits + rshift);
+
+ return internal;
+ }
+};
+
+
+/*
+ * RXS M -- random xorshift, mcg multiply
+ */
+
+template <typename xtype, typename itype>
+struct rxs_m_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t opbits = xtypebits >= 128 ? 6
+ : xtypebits >= 64 ? 5
+ : xtypebits >= 32 ? 4
+ : xtypebits >= 16 ? 3
+ : 2;
+ constexpr bitcount_t shift = bits - xtypebits;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
+ internal ^= internal >> (opbits + rshift);
+ internal *= mcg_multiplier<itype>::multiplier();
+ xtype result = internal >> shift;
+ return result;
+ }
+};
+
+/*
+ * XSL RR -- fixed xorshift (to low bits), random rotate
+ *
+ * Useful for 128-bit types that are split across two CPU registers.
+ */
+
+template <typename xtype, typename itype>
+struct xsl_rr_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t sparebits = bits - xtypebits;
+ constexpr bitcount_t wantedopbits = xtypebits >= 128 ? 7
+ : xtypebits >= 64 ? 6
+ : xtypebits >= 32 ? 5
+ : xtypebits >= 16 ? 4
+ : 3;
+ constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
+ : sparebits;
+ constexpr bitcount_t amplifier = wantedopbits - opbits;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ constexpr bitcount_t topspare = sparebits;
+ constexpr bitcount_t bottomspare = sparebits - topspare;
+ constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
+
+ bitcount_t rot =
+ opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
+ bitcount_t amprot = (rot << amplifier) & mask;
+ internal ^= internal >> xshift;
+ xtype result = xtype(internal >> bottomspare);
+ result = rotr(result, amprot);
+ return result;
+ }
+};
+
+
+/*
+ * XSL RR RR -- fixed xorshift (to low bits), random rotate (both parts)
+ *
+ * Useful for 128-bit types that are split across two CPU registers.
+ * If you really want an invertable 128-bit RNG, I guess this is the one.
+ */
+
+template <typename T> struct halfsize_trait {};
+template <> struct halfsize_trait<pcg128_t> { typedef uint64_t type; };
+template <> struct halfsize_trait<uint64_t> { typedef uint32_t type; };
+template <> struct halfsize_trait<uint32_t> { typedef uint16_t type; };
+template <> struct halfsize_trait<uint16_t> { typedef uint8_t type; };
+
+template <typename xtype, typename itype>
+struct xsl_rr_rr_mixin {
+ typedef typename halfsize_trait<itype>::type htype;
+
+ static itype output(itype internal)
+ {
+ constexpr bitcount_t htypebits = bitcount_t(sizeof(htype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t sparebits = bits - htypebits;
+ constexpr bitcount_t wantedopbits = htypebits >= 128 ? 7
+ : htypebits >= 64 ? 6
+ : htypebits >= 32 ? 5
+ : htypebits >= 16 ? 4
+ : 3;
+ constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
+ : sparebits;
+ constexpr bitcount_t amplifier = wantedopbits - opbits;
+ constexpr bitcount_t mask = (1 << opbits) - 1;
+ constexpr bitcount_t topspare = sparebits;
+ constexpr bitcount_t xshift = (topspare + htypebits) / 2;
+
+ bitcount_t rot =
+ opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
+ bitcount_t amprot = (rot << amplifier) & mask;
+ internal ^= internal >> xshift;
+ htype lowbits = htype(internal);
+ lowbits = rotr(lowbits, amprot);
+ htype highbits = htype(internal >> topspare);
+ bitcount_t rot2 = lowbits & mask;
+ bitcount_t amprot2 = (rot2 << amplifier) & mask;
+ highbits = rotr(highbits, amprot2);
+ return (itype(highbits) << topspare) ^ itype(lowbits);
+ }
+};
+
+
+/*
+ * XSH -- fixed xorshift (to high bits)
+ *
+ * You shouldn't use this at 64-bits or less.
+ */
+
+template <typename xtype, typename itype>
+struct xsh_mixin {
+ static xtype output(itype internal)
+ {
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t sparebits = bits - xtypebits;
+ constexpr bitcount_t topspare = 0;
+ constexpr bitcount_t bottomspare = sparebits - topspare;
+ constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
+
+ internal ^= internal >> xshift;
+ xtype result = internal >> bottomspare;
+ return result;
+ }
+};
+
+/*
+ * XSL -- fixed xorshift (to low bits)
+ *
+ * You shouldn't use this at 64-bits or less.
+ */
+
+template <typename xtype, typename itype>
+struct xsl_mixin {
+ inline xtype output(itype internal)
+ {
+ constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
+ constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
+ constexpr bitcount_t sparebits = bits - xtypebits;
+ constexpr bitcount_t topspare = sparebits;
+ constexpr bitcount_t bottomspare = sparebits - topspare;
+ constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
+
+ internal ^= internal >> xshift;
+ xtype result = internal >> bottomspare;
+ return result;
+ }
+};
+
+/* ---- End of Output Functions ---- */
+
+
+template <typename baseclass>
+struct inside_out : private baseclass {
+ inside_out() = delete;
+
+ typedef typename baseclass::result_type result_type;
+ typedef typename baseclass::state_type state_type;
+ static_assert(sizeof(result_type) == sizeof(state_type),
+ "Require a RNG whose output function is a permutation");
+
+ static bool external_step(result_type& randval, size_t i)
+ {
+ state_type state = baseclass::unoutput(randval);
+ state = state * baseclass::multiplier() + baseclass::increment()
+ + state_type(i*2);
+ result_type result = baseclass::output(state);
+ randval = result;
+ state_type zero =
+ baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
+ return result == zero;
+ }
+
+ static bool external_advance(result_type& randval, size_t i,
+ result_type delta, bool forwards = true)
+ {
+ state_type state = baseclass::unoutput(randval);
+ state_type mult = baseclass::multiplier();
+ state_type inc = baseclass::increment() + state_type(i*2);
+ state_type zero =
+ baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
+ state_type dist_to_zero = baseclass::distance(state, zero, mult, inc);
+ bool crosses_zero =
+ forwards ? dist_to_zero <= delta
+ : (-dist_to_zero) <= delta;
+ if (!forwards)
+ delta = -delta;
+ state = baseclass::advance(state, delta, mult, inc);
+ randval = baseclass::output(state);
+ return crosses_zero;
+ }
+};
+
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd = true>
+class extended : public baseclass {
+public:
+ typedef typename baseclass::state_type state_type;
+ typedef typename baseclass::result_type result_type;
+ typedef inside_out<extvalclass> insideout;
+
+private:
+ static constexpr bitcount_t rtypebits = sizeof(result_type)*8;
+ static constexpr bitcount_t stypebits = sizeof(state_type)*8;
+
+ static constexpr bitcount_t tick_limit_pow2 = 64U;
+
+ static constexpr size_t table_size = 1UL << table_pow2;
+ static constexpr size_t table_shift = stypebits - table_pow2;
+ static constexpr state_type table_mask =
+ (state_type(1U) << table_pow2) - state_type(1U);
+
+ static constexpr bool may_tick =
+ (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2);
+ static constexpr size_t tick_shift = stypebits - advance_pow2;
+ static constexpr state_type tick_mask =
+ may_tick ? state_type(
+ (uint64_t(1) << (advance_pow2*may_tick)) - 1)
+ // ^-- stupidity to appease GCC warnings
+ : ~state_type(0U);
+
+ static constexpr bool may_tock = stypebits < tick_limit_pow2;
+
+ result_type data_[table_size];
+
+ PCG_NOINLINE void advance_table();
+
+ PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true);
+
+ result_type& get_extended_value()
+ {
+ state_type state = this->state_;
+ if (kdd && baseclass::is_mcg) {
+ // The low order bits of an MCG are constant, so drop them.
+ state >>= 2;
+ }
+ size_t index = kdd ? state & table_mask
+ : state >> table_shift;
+
+ if (may_tick) {
+ bool tick = kdd ? (state & tick_mask) == state_type(0u)
+ : (state >> tick_shift) == state_type(0u);
+ if (tick)
+ advance_table();
+ }
+ if (may_tock) {
+ bool tock = state == state_type(0u);
+ if (tock)
+ advance_table();
+ }
+ return data_[index];
+ }
+
+public:
+ static constexpr size_t period_pow2()
+ {
+ return baseclass::period_pow2() + table_size*extvalclass::period_pow2();
+ }
+
+ __attribute__((always_inline)) result_type operator()()
+ {
+ result_type rhs = get_extended_value();
+ result_type lhs = this->baseclass::operator()();
+ return lhs ^ rhs;
+ }
+
+ result_type operator()(result_type upper_bound)
+ {
+ return bounded_rand(*this, upper_bound);
+ }
+
+ void set(result_type wanted)
+ {
+ result_type& rhs = get_extended_value();
+ result_type lhs = this->baseclass::operator()();
+ rhs = lhs ^ wanted;
+ }
+
+ void advance(state_type distance, bool forwards = true);
+
+ void backstep(state_type distance)
+ {
+ advance(distance, false);
+ }
+
+ extended(const result_type* data)
+ : baseclass()
+ {
+ datainit(data);
+ }
+
+ extended(const result_type* data, state_type seed)
+ : baseclass(seed)
+ {
+ datainit(data);
+ }
+
+ // This function may or may not exist. It thus has to be a template
+ // to use SFINAE; users don't have to worry about its template-ness.
+
+ template <typename bc = baseclass>
+ extended(const result_type* data, state_type seed,
+ typename bc::stream_state stream_seed)
+ : baseclass(seed, stream_seed)
+ {
+ datainit(data);
+ }
+
+ extended()
+ : baseclass()
+ {
+ selfinit();
+ }
+
+ extended(state_type seed)
+ : baseclass(seed)
+ {
+ selfinit();
+ }
+
+ // This function may or may not exist. It thus has to be a template
+ // to use SFINAE; users don't have to worry about its template-ness.
+
+ template <typename bc = baseclass>
+ extended(state_type seed, typename bc::stream_state stream_seed)
+ : baseclass(seed, stream_seed)
+ {
+ selfinit();
+ }
+
+private:
+ void selfinit();
+ void datainit(const result_type* data);
+
+public:
+
+ template<typename SeedSeq, typename = typename std::enable_if<
+ !std::is_convertible<SeedSeq, result_type>::value
+ && !std::is_convertible<SeedSeq, extended>::value>::type>
+ extended(SeedSeq&& seedSeq)
+ : baseclass(seedSeq)
+ {
+ generate_to<table_size>(seedSeq, data_);
+ }
+
+ template<typename... Args>
+ void seed(Args&&... args)
+ {
+ new (this) extended(std::forward<Args>(args)...);
+ }
+
+ template <bitcount_t table_pow2_, bitcount_t advance_pow2_,
+ typename baseclass_, typename extvalclass_, bool kdd_>
+ friend bool operator==(const extended<table_pow2_, advance_pow2_,
+ baseclass_, extvalclass_, kdd_>&,
+ const extended<table_pow2_, advance_pow2_,
+ baseclass_, extvalclass_, kdd_>&);
+
+ template <typename CharT, typename Traits,
+ bitcount_t table_pow2_, bitcount_t advance_pow2_,
+ typename baseclass_, typename extvalclass_, bool kdd_>
+ friend std::basic_ostream<CharT,Traits>&
+ operator<<(std::basic_ostream<CharT,Traits>& out,
+ const extended<table_pow2_, advance_pow2_,
+ baseclass_, extvalclass_, kdd_>&);
+
+ template <typename CharT, typename Traits,
+ bitcount_t table_pow2_, bitcount_t advance_pow2_,
+ typename baseclass_, typename extvalclass_, bool kdd_>
+ friend std::basic_istream<CharT,Traits>&
+ operator>>(std::basic_istream<CharT,Traits>& in,
+ extended<table_pow2_, advance_pow2_,
+ baseclass_, extvalclass_, kdd_>&);
+
+};
+
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::datainit(
+ const result_type* data)
+{
+ for (size_t i = 0; i < table_size; ++i)
+ data_[i] = data[i];
+}
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::selfinit()
+{
+ // We need to fill the extended table with something, and we have
+ // very little provided data, so we use the base generator to
+ // produce values. Although not ideal (use a seed sequence, folks!),
+ // unexpected correlations are mitigated by
+ // - using XOR differences rather than the number directly
+ // - the way the table is accessed, its values *won't* be accessed
+ // in the same order the were written.
+ // - any strange correlations would only be apparent if we
+ // were to backstep the generator so that the base generator
+ // was generating the same values again
+ result_type xdiff = baseclass::operator()() - baseclass::operator()();
+ for (size_t i = 0; i < table_size; ++i) {
+ data_[i] = baseclass::operator()() ^ xdiff;
+ }
+}
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+bool operator==(const extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& lhs,
+ const extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& rhs)
+{
+ auto& base_lhs = static_cast<const baseclass&>(lhs);
+ auto& base_rhs = static_cast<const baseclass&>(rhs);
+ return base_lhs == base_rhs
+ && !memcmp((void*) lhs.data_, (void*) rhs.data_, sizeof(lhs.data_));
+}
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+inline bool operator!=(const extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& lhs,
+ const extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& rhs)
+{
+ return lhs != rhs;
+}
+
+template <typename CharT, typename Traits,
+ bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+std::basic_ostream<CharT,Traits>&
+operator<<(std::basic_ostream<CharT,Traits>& out,
+ const extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& rng)
+{
+ auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left);
+ auto space = out.widen(' ');
+ auto orig_fill = out.fill();
+
+ out << rng.multiplier() << space
+ << rng.increment() << space
+ << rng.state_;
+
+ for (const auto& datum : rng.data_)
+ out << space << datum;
+
+ out.flags(orig_flags);
+ out.fill(orig_fill);
+ return out;
+}
+
+template <typename CharT, typename Traits,
+ bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+std::basic_istream<CharT,Traits>&
+operator>>(std::basic_istream<CharT,Traits>& in,
+ extended<table_pow2, advance_pow2,
+ baseclass, extvalclass, kdd>& rng)
+{
+ extended<table_pow2, advance_pow2, baseclass, extvalclass> new_rng;
+ auto& base_rng = static_cast<baseclass&>(new_rng);
+ in >> base_rng;
+
+ if (in.fail())
+ return in;
+
+ auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws);
+
+ for (auto& datum : new_rng.data_) {
+ in >> datum;
+ if (in.fail())
+ goto bail;
+ }
+
+ rng = new_rng;
+
+bail:
+ in.flags(orig_flags);
+ return in;
+}
+
+
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+void
+extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table()
+{
+ bool carry = false;
+ for (size_t i = 0; i < table_size; ++i) {
+ if (carry) {
+ carry = insideout::external_step(data_[i],i+1);
+ }
+ bool carry2 = insideout::external_step(data_[i],i+1);
+ carry = carry || carry2;
+ }
+}
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+void
+extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table(
+ state_type delta, bool isForwards)
+{
+ typedef typename baseclass::state_type base_state_t;
+ typedef typename extvalclass::state_type ext_state_t;
+ constexpr bitcount_t basebits = sizeof(base_state_t)*8;
+ constexpr bitcount_t extbits = sizeof(ext_state_t)*8;
+ static_assert(basebits <= extbits || advance_pow2 > 0,
+ "Current implementation might overflow its carry");
+
+ base_state_t carry = 0;
+ for (size_t i = 0; i < table_size; ++i) {
+ base_state_t total_delta = carry + delta;
+ ext_state_t trunc_delta = ext_state_t(total_delta);
+ if (basebits > extbits) {
+ carry = total_delta >> extbits;
+ } else {
+ carry = 0;
+ }
+ carry +=
+ insideout::external_advance(data_[i],i+1, trunc_delta, isForwards);
+ }
+}
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename baseclass, typename extvalclass, bool kdd>
+void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance(
+ state_type distance, bool forwards)
+{
+ static_assert(kdd,
+ "Efficient advance is too hard for non-kdd extension. "
+ "For a weak advance, cast to base class");
+ state_type zero =
+ baseclass::is_mcg ? this->state_ & state_type(3U) : state_type(0U);
+ if (may_tick) {
+ state_type ticks = distance >> (advance_pow2*may_tick);
+ // ^-- stupidity to appease GCC
+ // warnings
+ state_type adv_mask =
+ baseclass::is_mcg ? tick_mask << 2 : tick_mask;
+ state_type next_advance_distance = this->distance(zero, adv_mask);
+ if (!forwards)
+ next_advance_distance = (-next_advance_distance) & tick_mask;
+ if (next_advance_distance < (distance & tick_mask)) {
+ ++ticks;
+ }
+ if (ticks)
+ advance_table(ticks, forwards);
+ }
+ if (forwards) {
+ if (may_tock && this->distance(zero) <= distance)
+ advance_table();
+ baseclass::advance(distance);
+ } else {
+ if (may_tock && -(this->distance(zero)) <= distance)
+ advance_table(state_type(1U), false);
+ baseclass::advance(-distance);
+ }
+}
+
+} // namespace pcg_detail
+
+namespace pcg_engines {
+
+using namespace pcg_detail;
+
+/* Predefined types for XSH RS */
+
+typedef oneseq_base<uint8_t, uint16_t, xsh_rs_mixin> oneseq_xsh_rs_16_8;
+typedef oneseq_base<uint16_t, uint32_t, xsh_rs_mixin> oneseq_xsh_rs_32_16;
+typedef oneseq_base<uint32_t, uint64_t, xsh_rs_mixin> oneseq_xsh_rs_64_32;
+typedef oneseq_base<uint64_t, pcg128_t, xsh_rs_mixin> oneseq_xsh_rs_128_64;
+
+typedef unique_base<uint8_t, uint16_t, xsh_rs_mixin> unique_xsh_rs_16_8;
+typedef unique_base<uint16_t, uint32_t, xsh_rs_mixin> unique_xsh_rs_32_16;
+typedef unique_base<uint32_t, uint64_t, xsh_rs_mixin> unique_xsh_rs_64_32;
+typedef unique_base<uint64_t, pcg128_t, xsh_rs_mixin> unique_xsh_rs_128_64;
+
+typedef setseq_base<uint8_t, uint16_t, xsh_rs_mixin> setseq_xsh_rs_16_8;
+typedef setseq_base<uint16_t, uint32_t, xsh_rs_mixin> setseq_xsh_rs_32_16;
+typedef setseq_base<uint32_t, uint64_t, xsh_rs_mixin> setseq_xsh_rs_64_32;
+typedef setseq_base<uint64_t, pcg128_t, xsh_rs_mixin> setseq_xsh_rs_128_64;
+
+typedef mcg_base<uint8_t, uint16_t, xsh_rs_mixin> mcg_xsh_rs_16_8;
+typedef mcg_base<uint16_t, uint32_t, xsh_rs_mixin> mcg_xsh_rs_32_16;
+typedef mcg_base<uint32_t, uint64_t, xsh_rs_mixin> mcg_xsh_rs_64_32;
+typedef mcg_base<uint64_t, pcg128_t, xsh_rs_mixin> mcg_xsh_rs_128_64;
+
+/* Predefined types for XSH RR */
+
+typedef oneseq_base<uint8_t, uint16_t, xsh_rr_mixin> oneseq_xsh_rr_16_8;
+typedef oneseq_base<uint16_t, uint32_t, xsh_rr_mixin> oneseq_xsh_rr_32_16;
+typedef oneseq_base<uint32_t, uint64_t, xsh_rr_mixin> oneseq_xsh_rr_64_32;
+typedef oneseq_base<uint64_t, pcg128_t, xsh_rr_mixin> oneseq_xsh_rr_128_64;
+
+typedef unique_base<uint8_t, uint16_t, xsh_rr_mixin> unique_xsh_rr_16_8;
+typedef unique_base<uint16_t, uint32_t, xsh_rr_mixin> unique_xsh_rr_32_16;
+typedef unique_base<uint32_t, uint64_t, xsh_rr_mixin> unique_xsh_rr_64_32;
+typedef unique_base<uint64_t, pcg128_t, xsh_rr_mixin> unique_xsh_rr_128_64;
+
+typedef setseq_base<uint8_t, uint16_t, xsh_rr_mixin> setseq_xsh_rr_16_8;
+typedef setseq_base<uint16_t, uint32_t, xsh_rr_mixin> setseq_xsh_rr_32_16;
+typedef setseq_base<uint32_t, uint64_t, xsh_rr_mixin> setseq_xsh_rr_64_32;
+typedef setseq_base<uint64_t, pcg128_t, xsh_rr_mixin> setseq_xsh_rr_128_64;
+
+typedef mcg_base<uint8_t, uint16_t, xsh_rr_mixin> mcg_xsh_rr_16_8;
+typedef mcg_base<uint16_t, uint32_t, xsh_rr_mixin> mcg_xsh_rr_32_16;
+typedef mcg_base<uint32_t, uint64_t, xsh_rr_mixin> mcg_xsh_rr_64_32;
+typedef mcg_base<uint64_t, pcg128_t, xsh_rr_mixin> mcg_xsh_rr_128_64;
+
+
+/* Predefined types for RXS M XS */
+
+typedef oneseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_8_8;
+typedef oneseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_16_16;
+typedef oneseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_32_32;
+typedef oneseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_64_64;
+typedef oneseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_128_128;
+
+typedef unique_base<uint8_t, uint8_t, rxs_m_xs_mixin> unique_rxs_m_xs_8_8;
+typedef unique_base<uint16_t, uint16_t, rxs_m_xs_mixin> unique_rxs_m_xs_16_16;
+typedef unique_base<uint32_t, uint32_t, rxs_m_xs_mixin> unique_rxs_m_xs_32_32;
+typedef unique_base<uint64_t, uint64_t, rxs_m_xs_mixin> unique_rxs_m_xs_64_64;
+typedef unique_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> unique_rxs_m_xs_128_128;
+
+typedef setseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> setseq_rxs_m_xs_8_8;
+typedef setseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> setseq_rxs_m_xs_16_16;
+typedef setseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> setseq_rxs_m_xs_32_32;
+typedef setseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> setseq_rxs_m_xs_64_64;
+typedef setseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> setseq_rxs_m_xs_128_128;
+
+ // MCG versions don't make sense here, so aren't defined.
+
+/* Predefined types for XSL RR (only defined for "large" types) */
+
+typedef oneseq_base<uint32_t, uint64_t, xsl_rr_mixin> oneseq_xsl_rr_64_32;
+typedef oneseq_base<uint64_t, pcg128_t, xsl_rr_mixin> oneseq_xsl_rr_128_64;
+
+typedef unique_base<uint32_t, uint64_t, xsl_rr_mixin> unique_xsl_rr_64_32;
+typedef unique_base<uint64_t, pcg128_t, xsl_rr_mixin> unique_xsl_rr_128_64;
+
+typedef setseq_base<uint32_t, uint64_t, xsl_rr_mixin> setseq_xsl_rr_64_32;
+typedef setseq_base<uint64_t, pcg128_t, xsl_rr_mixin> setseq_xsl_rr_128_64;
+
+typedef mcg_base<uint32_t, uint64_t, xsl_rr_mixin> mcg_xsl_rr_64_32;
+typedef mcg_base<uint64_t, pcg128_t, xsl_rr_mixin> mcg_xsl_rr_128_64;
+
+
+/* Predefined types for XSL RR RR (only defined for "large" types) */
+
+typedef oneseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
+ oneseq_xsl_rr_rr_64_64;
+typedef oneseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
+ oneseq_xsl_rr_rr_128_128;
+
+typedef unique_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
+ unique_xsl_rr_rr_64_64;
+typedef unique_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
+ unique_xsl_rr_rr_128_128;
+
+typedef setseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
+ setseq_xsl_rr_rr_64_64;
+typedef setseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
+ setseq_xsl_rr_rr_128_128;
+
+ // MCG versions don't make sense here, so aren't defined.
+
+/* Extended generators */
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename BaseRNG, bool kdd = true>
+using ext_std8 = extended<table_pow2, advance_pow2, BaseRNG,
+ oneseq_rxs_m_xs_8_8, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename BaseRNG, bool kdd = true>
+using ext_std16 = extended<table_pow2, advance_pow2, BaseRNG,
+ oneseq_rxs_m_xs_16_16, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename BaseRNG, bool kdd = true>
+using ext_std32 = extended<table_pow2, advance_pow2, BaseRNG,
+ oneseq_rxs_m_xs_32_32, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2,
+ typename BaseRNG, bool kdd = true>
+using ext_std64 = extended<table_pow2, advance_pow2, BaseRNG,
+ oneseq_rxs_m_xs_64_64, kdd>;
+
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_oneseq_rxs_m_xs_32_32 =
+ ext_std32<table_pow2, advance_pow2, oneseq_rxs_m_xs_32_32, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_mcg_xsh_rs_64_32 =
+ ext_std32<table_pow2, advance_pow2, mcg_xsh_rs_64_32, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_oneseq_xsh_rs_64_32 =
+ ext_std32<table_pow2, advance_pow2, oneseq_xsh_rs_64_32, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_setseq_xsh_rr_64_32 =
+ ext_std32<table_pow2, advance_pow2, setseq_xsh_rr_64_32, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_mcg_xsl_rr_128_64 =
+ ext_std64<table_pow2, advance_pow2, mcg_xsl_rr_128_64, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_oneseq_xsl_rr_128_64 =
+ ext_std64<table_pow2, advance_pow2, oneseq_xsl_rr_128_64, kdd>;
+
+template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
+using ext_setseq_xsl_rr_128_64 =
+ ext_std64<table_pow2, advance_pow2, setseq_xsl_rr_128_64, kdd>;
+
+} // namespace pcg_engines
+
+typedef pcg_engines::setseq_xsh_rr_64_32 pcg32;
+typedef pcg_engines::oneseq_xsh_rr_64_32 pcg32_oneseq;
+typedef pcg_engines::unique_xsh_rr_64_32 pcg32_unique;
+typedef pcg_engines::mcg_xsh_rs_64_32 pcg32_fast;
+
+typedef pcg_engines::setseq_xsl_rr_128_64 pcg64;
+typedef pcg_engines::oneseq_xsl_rr_128_64 pcg64_oneseq;
+typedef pcg_engines::unique_xsl_rr_128_64 pcg64_unique;
+typedef pcg_engines::mcg_xsl_rr_128_64 pcg64_fast;
+
+typedef pcg_engines::setseq_rxs_m_xs_8_8 pcg8_once_insecure;
+typedef pcg_engines::setseq_rxs_m_xs_16_16 pcg16_once_insecure;
+typedef pcg_engines::setseq_rxs_m_xs_32_32 pcg32_once_insecure;
+typedef pcg_engines::setseq_rxs_m_xs_64_64 pcg64_once_insecure;
+typedef pcg_engines::setseq_xsl_rr_rr_128_128 pcg128_once_insecure;
+
+typedef pcg_engines::oneseq_rxs_m_xs_8_8 pcg8_oneseq_once_insecure;
+typedef pcg_engines::oneseq_rxs_m_xs_16_16 pcg16_oneseq_once_insecure;
+typedef pcg_engines::oneseq_rxs_m_xs_32_32 pcg32_oneseq_once_insecure;
+typedef pcg_engines::oneseq_rxs_m_xs_64_64 pcg64_oneseq_once_insecure;
+typedef pcg_engines::oneseq_xsl_rr_rr_128_128 pcg128_oneseq_once_insecure;
+
+
+// These two extended RNGs provide two-dimensionally equidistributed
+// 32-bit generators. pcg32_k2_fast occupies the same space as pcg64,
+// and can be called twice to generate 64 bits, but does not required
+// 128-bit math; on 32-bit systems, it's faster than pcg64 as well.
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true> pcg32_k2;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true> pcg32_k2_fast;
+
+// These eight extended RNGs have about as much state as arc4random
+//
+// - the k variants are k-dimensionally equidistributed
+// - the c variants offer better crypographic security
+//
+// (just how good the cryptographic security is is an open question)
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true> pcg32_k64;
+typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,true> pcg32_k64_oneseq;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true> pcg32_k64_fast;
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,false> pcg32_c64;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,false> pcg32_c64_oneseq;
+typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,false> pcg32_c64_fast;
+
+typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,true> pcg64_k32;
+typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,true> pcg64_k32_oneseq;
+typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,true> pcg64_k32_fast;
+
+typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,false> pcg64_c32;
+typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,false> pcg64_c32_oneseq;
+typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,false> pcg64_c32_fast;
+
+// These eight extended RNGs have more state than the Mersenne twister
+//
+// - the k variants are k-dimensionally equidistributed
+// - the c variants offer better crypographic security
+//
+// (just how good the cryptographic security is is an open question)
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,true> pcg32_k1024;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,true> pcg32_k1024_fast;
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,false> pcg32_c1024;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,false> pcg32_c1024_fast;
+
+typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,true> pcg64_k1024;
+typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,true> pcg64_k1024_fast;
+
+typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,false> pcg64_c1024;
+typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,false> pcg64_c1024_fast;
+
+// These generators have an insanely huge period (2^524352), and is suitable
+// for silly party tricks, such as dumping out 64 KB ZIP files at an arbitrary
+// point in the future. [Actually, over the full period of the generator, it
+// will produce every 64 KB ZIP file 2^64 times!]
+
+typedef pcg_engines::ext_setseq_xsh_rr_64_32<14,16,true> pcg32_k16384;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<14,32,true> pcg32_k16384_fast;
+
+#endif // PCG_RAND_HPP_INCLUDED
http://git-wip-us.apache.org/repos/asf/impala/blob/4feb4f3a/be/src/thirdparty/pcg-cpp-0.98/include/pcg_uint128.hpp
----------------------------------------------------------------------
diff --git a/be/src/thirdparty/pcg-cpp-0.98/include/pcg_uint128.hpp b/be/src/thirdparty/pcg-cpp-0.98/include/pcg_uint128.hpp
new file mode 100644
index 0000000..99b20e7
--- /dev/null
+++ b/be/src/thirdparty/pcg-cpp-0.98/include/pcg_uint128.hpp
@@ -0,0 +1,750 @@
+/*
+ * PCG Random Number Generation for C++
+ *
+ * Copyright 2014 Melissa O'Neill <on...@pcg-random.org>
+ *
+ * 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.
+ *
+ * For additional information about the PCG random number generation scheme,
+ * including its license and other licensing options, visit
+ *
+ * http://www.pcg-random.org
+ */
+
+/*
+ * This code provides a a C++ class that can provide 128-bit (or higher)
+ * integers. To produce 2K-bit integers, it uses two K-bit integers,
+ * placed in a union that allowes the code to also see them as four K/2 bit
+ * integers (and access them either directly name, or by index).
+ *
+ * It may seem like we're reinventing the wheel here, because several
+ * libraries already exist that support large integers, but most existing
+ * libraries provide a very generic multiprecision code, but here we're
+ * operating at a fixed size. Also, most other libraries are fairly
+ * heavyweight. So we use a direct implementation. Sadly, it's much slower
+ * than hand-coded assembly or direct CPU support.
+ */
+
+#ifndef PCG_UINT128_HPP_INCLUDED
+#define PCG_UINT128_HPP_INCLUDED 1
+
+#include <cstdint>
+#include <cstdio>
+#include <cassert>
+#include <climits>
+#include <utility>
+#include <initializer_list>
+#include <type_traits>
+
+/*
+ * We want to lay the type out the same way that a native type would be laid
+ * out, which means we must know the machine's endian, at compile time.
+ * This ugliness attempts to do so.
+ */
+
+#ifndef PCG_LITTLE_ENDIAN
+ #if defined(__BYTE_ORDER__)
+ #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
+ #define PCG_LITTLE_ENDIAN 1
+ #elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
+ #define PCG_LITTLE_ENDIAN 0
+ #else
+ #error __BYTE_ORDER__ does not match a standard endian, pick a side
+ #endif
+ #elif __LITTLE_ENDIAN__ || _LITTLE_ENDIAN
+ #define PCG_LITTLE_ENDIAN 1
+ #elif __BIG_ENDIAN__ || _BIG_ENDIAN
+ #define PCG_LITTLE_ENDIAN 0
+ #elif __x86_64 || __x86_64__ || __i386 || __i386__
+ #define PCG_LITTLE_ENDIAN 1
+ #elif __powerpc__ || __POWERPC__ || __ppc__ || __PPC__ \
+ || __m68k__ || __mc68000__
+ #define PCG_LITTLE_ENDIAN 0
+ #else
+ #error Unable to determine target endianness
+ #endif
+#endif
+
+namespace pcg_extras {
+
+// Recent versions of GCC have intrinsics we can use to quickly calculate
+// the number of leading and trailing zeros in a number. If possible, we
+// use them, otherwise we fall back to old-fashioned bit twiddling to figure
+// them out.
+
+#ifndef PCG_BITCOUNT_T
+ typedef uint8_t bitcount_t;
+#else
+ typedef PCG_BITCOUNT_T bitcount_t;
+#endif
+
+/*
+ * Provide some useful helper functions
+ * * flog2 floor(log2(x))
+ * * trailingzeros number of trailing zero bits
+ */
+
+#ifdef __GNUC__ // Any GNU-compatible compiler supporting C++11 has
+ // some useful intrinsics we can use.
+
+inline bitcount_t flog2(uint32_t v)
+{
+ return 31 - __builtin_clz(v);
+}
+
+inline bitcount_t trailingzeros(uint32_t v)
+{
+ return __builtin_ctz(v);
+}
+
+inline bitcount_t flog2(uint64_t v)
+{
+#if UINT64_MAX == ULONG_MAX
+ return 63 - __builtin_clzl(v);
+#elif UINT64_MAX == ULLONG_MAX
+ return 63 - __builtin_clzll(v);
+#else
+ #error Cannot find a function for uint64_t
+#endif
+}
+
+inline bitcount_t trailingzeros(uint64_t v)
+{
+#if UINT64_MAX == ULONG_MAX
+ return __builtin_ctzl(v);
+#elif UINT64_MAX == ULLONG_MAX
+ return __builtin_ctzll(v);
+#else
+ #error Cannot find a function for uint64_t
+#endif
+}
+
+#else // Otherwise, we fall back to bit twiddling
+ // implementations
+
+inline bitcount_t flog2(uint32_t v)
+{
+ // Based on code by Eric Cole and Mark Dickinson, which appears at
+ // https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogDeBruijn
+
+ static const uint8_t multiplyDeBruijnBitPos[32] = {
+ 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30,
+ 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31
+ };
+
+ v |= v >> 1; // first round down to one less than a power of 2
+ v |= v >> 2;
+ v |= v >> 4;
+ v |= v >> 8;
+ v |= v >> 16;
+
+ return multiplyDeBruijnBitPos[(uint32_t)(v * 0x07C4ACDDU) >> 27];
+}
+
+inline bitcount_t trailingzeros(uint32_t v)
+{
+ static const uint8_t multiplyDeBruijnBitPos[32] = {
+ 0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
+ 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
+ };
+
+ return multiplyDeBruijnBitPos[((uint32_t)((v & -v) * 0x077CB531U)) >> 27];
+}
+
+inline bitcount_t flog2(uint64_t v)
+{
+ uint32_t high = v >> 32;
+ uint32_t low = uint32_t(v);
+
+ return high ? 32+flog2(high) : flog2(low);
+}
+
+inline bitcount_t trailingzeros(uint64_t v)
+{
+ uint32_t high = v >> 32;
+ uint32_t low = uint32_t(v);
+
+ return low ? trailingzeros(low) : trailingzeros(high)+32;
+}
+
+#endif
+
+template <typename UInt>
+inline bitcount_t clog2(UInt v)
+{
+ return flog2(v) + ((v & (-v)) != v);
+}
+
+template <typename UInt>
+inline UInt addwithcarry(UInt x, UInt y, bool carryin, bool* carryout)
+{
+ UInt half_result = y + carryin;
+ UInt result = x + half_result;
+ *carryout = (half_result < y) || (result < x);
+ return result;
+}
+
+template <typename UInt>
+inline UInt subwithcarry(UInt x, UInt y, bool carryin, bool* carryout)
+{
+ UInt half_result = y + carryin;
+ UInt result = x - half_result;
+ *carryout = (half_result < y) || (result > x);
+ return result;
+}
+
+
+template <typename UInt, typename UIntX2>
+class uint_x4 {
+// private:
+public:
+ union {
+#if PCG_LITTLE_ENDIAN
+ struct {
+ UInt v0, v1, v2, v3;
+ } w;
+ struct {
+ UIntX2 v01, v23;
+ } d;
+#else
+ struct {
+ UInt v3, v2, v1, v0;
+ } w;
+ struct {
+ UIntX2 v23, v01;
+ } d;
+#endif
+ // For the array access versions, the code that uses the array
+ // must handle endian itself. Yuck.
+ UInt wa[4];
+ UIntX2 da[2];
+ };
+
+public:
+ uint_x4() = default;
+
+ constexpr uint_x4(UInt v3, UInt v2, UInt v1, UInt v0)
+#if PCG_LITTLE_ENDIAN
+ : w{v0, v1, v2, v3}
+#else
+ : w{v3, v2, v1, v0}
+#endif
+ {
+ // Nothing (else) to do
+ }
+
+ constexpr uint_x4(UIntX2 v23, UIntX2 v01)
+#if PCG_LITTLE_ENDIAN
+ : d{v01,v23}
+#else
+ : d{v23,v01}
+#endif
+ {
+ // Nothing (else) to do
+ }
+
+ template<class Integral,
+ typename std::enable_if<(std::is_integral<Integral>::value
+ && sizeof(Integral) <= sizeof(UIntX2))
+ >::type* = nullptr>
+ constexpr uint_x4(Integral v01)
+#if PCG_LITTLE_ENDIAN
+ : d{UIntX2(v01),0UL}
+#else
+ : d{0UL,UIntX2(v01)}
+#endif
+ {
+ // Nothing (else) to do
+ }
+
+ explicit constexpr operator uint64_t() const
+ {
+ return d.v01;
+ }
+
+ explicit constexpr operator uint32_t() const
+ {
+ return w.v0;
+ }
+
+ explicit constexpr operator int() const
+ {
+ return w.v0;
+ }
+
+ explicit constexpr operator uint16_t() const
+ {
+ return w.v0;
+ }
+
+ explicit constexpr operator uint8_t() const
+ {
+ return w.v0;
+ }
+
+ typedef typename std::conditional<std::is_same<uint64_t,
+ unsigned long>::value,
+ unsigned long long,
+ unsigned long>::type
+ uint_missing_t;
+
+ explicit constexpr operator uint_missing_t() const
+ {
+ return d.v01;
+ }
+
+ explicit constexpr operator bool() const
+ {
+ return d.v01 || d.v23;
+ }
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator*(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend std::pair< uint_x4<U,V>,uint_x4<U,V> >
+ divmod(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator+(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator-(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator<<(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator>>(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator&(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator|(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator^(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator==(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator!=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator<(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator<=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator>(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bool operator>=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator~(const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend uint_x4<U,V> operator-(const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bitcount_t flog2(const uint_x4<U,V>&);
+
+ template<typename U, typename V>
+ friend bitcount_t trailingzeros(const uint_x4<U,V>&);
+
+ uint_x4& operator*=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this * rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator/=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this / rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator%=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this % rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator+=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this + rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator-=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this - rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator&=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this & rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator|=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this | rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator^=(const uint_x4& rhs)
+ {
+ uint_x4 result = *this ^ rhs;
+ return *this = result;
+ }
+
+ uint_x4& operator>>=(bitcount_t shift)
+ {
+ uint_x4 result = *this >> shift;
+ return *this = result;
+ }
+
+ uint_x4& operator<<=(bitcount_t shift)
+ {
+ uint_x4 result = *this << shift;
+ return *this = result;
+ }
+
+};
+
+template<typename U, typename V>
+bitcount_t flog2(const uint_x4<U,V>& v)
+{
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t i = 4; i !=0; /* dec in loop */) {
+ --i;
+#else
+ for (uint8_t i = 0; i < 4; ++i) {
+#endif
+ if (v.wa[i] == 0)
+ continue;
+ return flog2(v.wa[i]) + (sizeof(U)*CHAR_BIT)*i;
+ }
+ abort();
+}
+
+template<typename U, typename V>
+bitcount_t trailingzeros(const uint_x4<U,V>& v)
+{
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t i = 0; i < 4; ++i) {
+#else
+ for (uint8_t i = 4; i !=0; /* dec in loop */) {
+ --i;
+#endif
+ if (v.wa[i] != 0)
+ return trailingzeros(v.wa[i]) + (sizeof(U)*CHAR_BIT)*i;
+ }
+ return (sizeof(U)*CHAR_BIT)*4;
+}
+
+template <typename UInt, typename UIntX2>
+std::pair< uint_x4<UInt,UIntX2>, uint_x4<UInt,UIntX2> >
+ divmod(const uint_x4<UInt,UIntX2>& orig_dividend,
+ const uint_x4<UInt,UIntX2>& divisor)
+{
+ // If the dividend is less than the divisor, the answer is always zero.
+ // This takes care of boundary cases like 0/x (which would otherwise be
+ // problematic because we can't take the log of zero. (The boundary case
+ // of division by zero is undefined.)
+ if (orig_dividend < divisor)
+ return { uint_x4<UInt,UIntX2>(0UL), orig_dividend };
+
+ auto dividend = orig_dividend;
+
+ auto log2_divisor = flog2(divisor);
+ auto log2_dividend = flog2(dividend);
+ // assert(log2_dividend >= log2_divisor);
+ bitcount_t logdiff = log2_dividend - log2_divisor;
+
+ constexpr uint_x4<UInt,UIntX2> ONE(1UL);
+ if (logdiff == 0)
+ return { ONE, dividend - divisor };
+
+ // Now we change the log difference to
+ // floor(log2(divisor)) - ceil(log2(dividend))
+ // to ensure that we *underestimate* the result.
+ logdiff -= 1;
+
+ uint_x4<UInt,UIntX2> quotient(0UL);
+
+ auto qfactor = ONE << logdiff;
+ auto factor = divisor << logdiff;
+
+ do {
+ dividend -= factor;
+ quotient += qfactor;
+ while (dividend < factor) {
+ factor >>= 1;
+ qfactor >>= 1;
+ }
+ } while (dividend >= divisor);
+
+ return { quotient, dividend };
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator/(const uint_x4<UInt,UIntX2>& dividend,
+ const uint_x4<UInt,UIntX2>& divisor)
+{
+ return divmod(dividend, divisor).first;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator%(const uint_x4<UInt,UIntX2>& dividend,
+ const uint_x4<UInt,UIntX2>& divisor)
+{
+ return divmod(dividend, divisor).second;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator*(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+ bool carryin = false;
+ bool carryout;
+ UIntX2 a0b0 = UIntX2(a.w.v0) * UIntX2(b.w.v0);
+ r.w.v0 = UInt(a0b0);
+ r.w.v1 = UInt(a0b0 >> 32);
+
+ UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(b.w.v0);
+ r.w.v2 = UInt(a1b0 >> 32);
+ r.w.v1 = addwithcarry(r.w.v1, UInt(a1b0), carryin, &carryout);
+ carryin = carryout;
+ r.w.v2 = addwithcarry(r.w.v2, UInt(0U), carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+ UIntX2 a0b1 = UIntX2(a.w.v0) * UIntX2(b.w.v1);
+ carryin = false;
+ r.w.v2 = addwithcarry(r.w.v2, UInt(a0b1 >> 32), carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+ carryin = false;
+ r.w.v1 = addwithcarry(r.w.v1, UInt(a0b1), carryin, &carryout);
+ carryin = carryout;
+ r.w.v2 = addwithcarry(r.w.v2, UInt(0U), carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+ UIntX2 a1b1 = UIntX2(a.w.v1) * UIntX2(b.w.v1);
+ carryin = false;
+ r.w.v2 = addwithcarry(r.w.v2, UInt(a1b1), carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = addwithcarry(r.w.v3, UInt(a1b1 >> 32), carryin, &carryout);
+
+ r.d.v23 += a.d.v01 * b.d.v23 + a.d.v23 * b.d.v01;
+
+ return r;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator+(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+
+ bool carryin = false;
+ bool carryout;
+ r.w.v0 = addwithcarry(a.w.v0, b.w.v0, carryin, &carryout);
+ carryin = carryout;
+ r.w.v1 = addwithcarry(a.w.v1, b.w.v1, carryin, &carryout);
+ carryin = carryout;
+ r.w.v2 = addwithcarry(a.w.v2, b.w.v2, carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = addwithcarry(a.w.v3, b.w.v3, carryin, &carryout);
+
+ return r;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator-(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+
+ bool carryin = false;
+ bool carryout;
+ r.w.v0 = subwithcarry(a.w.v0, b.w.v0, carryin, &carryout);
+ carryin = carryout;
+ r.w.v1 = subwithcarry(a.w.v1, b.w.v1, carryin, &carryout);
+ carryin = carryout;
+ r.w.v2 = subwithcarry(a.w.v2, b.w.v2, carryin, &carryout);
+ carryin = carryout;
+ r.w.v3 = subwithcarry(a.w.v3, b.w.v3, carryin, &carryout);
+
+ return r;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator&(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ return uint_x4<UInt,UIntX2>(a.d.v23 & b.d.v23, a.d.v01 & b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator|(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ return uint_x4<UInt,UIntX2>(a.d.v23 | b.d.v23, a.d.v01 | b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator^(const uint_x4<UInt,UIntX2>& a,
+ const uint_x4<UInt,UIntX2>& b)
+{
+ return uint_x4<UInt,UIntX2>(a.d.v23 ^ b.d.v23, a.d.v01 ^ b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator~(const uint_x4<UInt,UIntX2>& v)
+{
+ return uint_x4<UInt,UIntX2>(~v.d.v23, ~v.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator-(const uint_x4<UInt,UIntX2>& v)
+{
+ return uint_x4<UInt,UIntX2>(0UL,0UL) - v;
+}
+
+template <typename UInt, typename UIntX2>
+bool operator==(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return (a.d.v01 == b.d.v01) && (a.d.v23 == b.d.v23);
+}
+
+template <typename UInt, typename UIntX2>
+bool operator!=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return !operator==(a,b);
+}
+
+
+template <typename UInt, typename UIntX2>
+bool operator<(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return (a.d.v23 < b.d.v23)
+ || ((a.d.v23 == b.d.v23) && (a.d.v01 < b.d.v01));
+}
+
+template <typename UInt, typename UIntX2>
+bool operator>(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return operator<(b,a);
+}
+
+template <typename UInt, typename UIntX2>
+bool operator<=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return !(operator<(b,a));
+}
+
+template <typename UInt, typename UIntX2>
+bool operator>=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+ return !(operator<(a,b));
+}
+
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator<<(const uint_x4<UInt,UIntX2>& v,
+ const bitcount_t shift)
+{
+ uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+ const bitcount_t bits = sizeof(UInt) * CHAR_BIT;
+ const bitcount_t bitmask = bits - 1;
+ const bitcount_t shiftdiv = shift / bits;
+ const bitcount_t shiftmod = shift & bitmask;
+
+ if (shiftmod) {
+ UInt carryover = 0;
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#else
+ for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+ --out, --in;
+#endif
+ r.wa[out] = (v.wa[in] << shiftmod) | carryover;
+ carryover = (v.wa[in] >> (bits - shiftmod));
+ }
+ } else {
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#else
+ for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+ --out, --in;
+#endif
+ r.wa[out] = v.wa[in];
+ }
+ }
+
+ return r;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator>>(const uint_x4<UInt,UIntX2>& v,
+ const bitcount_t shift)
+{
+ uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+ const bitcount_t bits = sizeof(UInt) * CHAR_BIT;
+ const bitcount_t bitmask = bits - 1;
+ const bitcount_t shiftdiv = shift / bits;
+ const bitcount_t shiftmod = shift & bitmask;
+
+ if (shiftmod) {
+ UInt carryover = 0;
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+ --out, --in;
+#else
+ for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#endif
+ r.wa[out] = (v.wa[in] >> shiftmod) | carryover;
+ carryover = (v.wa[in] << (bits - shiftmod));
+ }
+ } else {
+#if PCG_LITTLE_ENDIAN
+ for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+ --out, --in;
+#else
+ for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#endif
+ r.wa[out] = v.wa[in];
+ }
+ }
+
+ return r;
+}
+
+} // namespace pcg_extras
+
+#endif // PCG_UINT128_HPP_INCLUDED
http://git-wip-us.apache.org/repos/asf/impala/blob/4feb4f3a/bin/rat_exclude_files.txt
----------------------------------------------------------------------
diff --git a/bin/rat_exclude_files.txt b/bin/rat_exclude_files.txt
index fdb1926..30ebc26 100644
--- a/bin/rat_exclude_files.txt
+++ b/bin/rat_exclude_files.txt
@@ -79,6 +79,7 @@ tests/comparison/ORACLE.txt
bin/distcc/README.md
tests/comparison/POSTGRES.txt
docs/README.md
+be/src/thirdparty/pcg-cpp-0.98/README.md
# http://www.apache.org/legal/src-headers.html: "Test data for which the addition of a
# source header would cause the tests to fail."
@@ -139,6 +140,7 @@ NOTICE.txt
# Notices in thirdparty sources included in the Impala repo and called out in /LICENSE.txt
be/src/thirdparty/squeasel/LICENSE
+be/src/thirdparty/pcg-cpp-0.98/LICENSE.txt
# http://www.apache.org/legal/src-headers.html: 'Snippet' files that are combined as form
# a larger file where the larger file would have duplicate licensing headers.