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ClickHouse/base/pcg-random/pcg_uint128.hpp
Antonio Andelic e64436fef3 Fix typos with new codespell
2022-09-02 08:54:48 +00:00

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/*
* PCG Random Number Generation for C++
*
* Copyright 2014-2017 Melissa O'Neill <oneill@pcg-random.org>,
* and the PCG Project contributors.
*
* SPDX-License-Identifier: (Apache-2.0 OR MIT)
*
* Licensed under the Apache License, Version 2.0 (provided in
* LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0)
* or under the MIT license (provided in LICENSE-MIT.txt and at
* http://opensource.org/licenses/MIT), at your option. This file may not
* be copied, modified, or distributed except according to those terms.
*
* Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either
* express or implied. See your chosen license for details.
*
* For additional information about the PCG random number generation scheme,
* 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 allows 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__ || _M_X64 || __i386 || __i386__ || _M_IX86
#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
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