boost/polygon/detail/voronoi_ctypes.hpp
// Boost.Polygon library detail/voronoi_ctypes.hpp header file
// Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_POLYGON_DETAIL_VORONOI_CTYPES
#define BOOST_POLYGON_DETAIL_VORONOI_CTYPES
#include <boost/cstdint.hpp>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <utility>
#include <vector>
namespace boost {
namespace polygon {
namespace detail {
typedef boost::int32_t int32;
typedef boost::int64_t int64;
typedef boost::uint32_t uint32;
typedef boost::uint64_t uint64;
typedef double fpt64;
// If two floating-point numbers in the same format are ordered (x < y),
// then they are ordered the same way when their bits are reinterpreted as
// sign-magnitude integers. Values are considered to be almost equal if
// their integer bits reinterpretations differ in not more than maxUlps units.
template <typename _fpt>
struct ulp_comparison;
template <>
struct ulp_comparison<fpt64> {
enum Result {
LESS = -1,
EQUAL = 0,
MORE = 1
};
Result operator()(fpt64 a, fpt64 b, unsigned int maxUlps) const {
uint64 ll_a, ll_b;
// Reinterpret double bits as 64-bit signed integer.
std::memcpy(&ll_a, &a, sizeof(fpt64));
std::memcpy(&ll_b, &b, sizeof(fpt64));
// Positive 0.0 is integer zero. Negative 0.0 is 0x8000000000000000.
// Map negative zero to an integer zero representation - making it
// identical to positive zero - the smallest negative number is
// represented by negative one, and downwards from there.
if (ll_a < 0x8000000000000000ULL)
ll_a = 0x8000000000000000ULL - ll_a;
if (ll_b < 0x8000000000000000ULL)
ll_b = 0x8000000000000000ULL - ll_b;
// Compare 64-bit signed integer representations of input values.
// Difference in 1 Ulp is equivalent to a relative error of between
// 1/4,000,000,000,000,000 and 1/8,000,000,000,000,000.
if (ll_a > ll_b)
return (ll_a - ll_b <= maxUlps) ? EQUAL : LESS;
return (ll_b - ll_a <= maxUlps) ? EQUAL : MORE;
}
};
template <typename _fpt>
struct extened_exponent_fpt_traits;
template <>
struct extened_exponent_fpt_traits<fpt64> {
public:
typedef int exp_type;
enum {
MAX_SIGNIFICANT_EXP_DIF = 54
};
};
// Floating point type wrapper. Allows to extend exponent boundaries to the
// integer type range. This class does not handle division by zero, subnormal
// numbers or NaNs.
template <typename _fpt, typename _traits = extened_exponent_fpt_traits<_fpt> >
class extended_exponent_fpt {
public:
typedef _fpt fpt_type;
typedef typename _traits::exp_type exp_type;
explicit extended_exponent_fpt(fpt_type val) {
val_ = std::frexp(val, &exp_);
}
extended_exponent_fpt(fpt_type val, exp_type exp) {
val_ = std::frexp(val, &exp_);
exp_ += exp;
}
bool is_pos() const {
return val_ > 0;
}
bool is_neg() const {
return val_ < 0;
}
bool is_zero() const {
return val_ == 0;
}
extended_exponent_fpt operator-() const {
return extended_exponent_fpt(-val_, exp_);
}
extended_exponent_fpt operator+(const extended_exponent_fpt& that) const {
if (this->val_ == 0.0 ||
that.exp_ > this->exp_ + _traits::MAX_SIGNIFICANT_EXP_DIF) {
return that;
}
if (that.val_ == 0.0 ||
this->exp_ > that.exp_ + _traits::MAX_SIGNIFICANT_EXP_DIF) {
return *this;
}
if (this->exp_ >= that.exp_) {
exp_type exp_dif = this->exp_ - that.exp_;
fpt_type val = std::ldexp(this->val_, exp_dif) + that.val_;
return extended_exponent_fpt(val, that.exp_);
} else {
exp_type exp_dif = that.exp_ - this->exp_;
fpt_type val = std::ldexp(that.val_, exp_dif) + this->val_;
return extended_exponent_fpt(val, this->exp_);
}
}
extended_exponent_fpt operator-(const extended_exponent_fpt& that) const {
if (this->val_ == 0.0 ||
that.exp_ > this->exp_ + _traits::MAX_SIGNIFICANT_EXP_DIF) {
return extended_exponent_fpt(-that.val_, that.exp_);
}
if (that.val_ == 0.0 ||
this->exp_ > that.exp_ + _traits::MAX_SIGNIFICANT_EXP_DIF) {
return *this;
}
if (this->exp_ >= that.exp_) {
exp_type exp_dif = this->exp_ - that.exp_;
fpt_type val = std::ldexp(this->val_, exp_dif) - that.val_;
return extended_exponent_fpt(val, that.exp_);
} else {
exp_type exp_dif = that.exp_ - this->exp_;
fpt_type val = std::ldexp(-that.val_, exp_dif) + this->val_;
return extended_exponent_fpt(val, this->exp_);
}
}
extended_exponent_fpt operator*(const extended_exponent_fpt& that) const {
fpt_type val = this->val_ * that.val_;
exp_type exp = this->exp_ + that.exp_;
return extended_exponent_fpt(val, exp);
}
extended_exponent_fpt operator/(const extended_exponent_fpt& that) const {
fpt_type val = this->val_ / that.val_;
exp_type exp = this->exp_ - that.exp_;
return extended_exponent_fpt(val, exp);
}
extended_exponent_fpt& operator+=(const extended_exponent_fpt& that) {
return *this = *this + that;
}
extended_exponent_fpt& operator-=(const extended_exponent_fpt& that) {
return *this = *this - that;
}
extended_exponent_fpt& operator*=(const extended_exponent_fpt& that) {
return *this = *this * that;
}
extended_exponent_fpt& operator/=(const extended_exponent_fpt& that) {
return *this = *this / that;
}
extended_exponent_fpt sqrt() const {
fpt_type val = val_;
exp_type exp = exp_;
if (exp & 1) {
val *= 2.0;
--exp;
}
return extended_exponent_fpt(std::sqrt(val), exp >> 1);
}
fpt_type d() const {
return std::ldexp(val_, exp_);
}
private:
fpt_type val_;
exp_type exp_;
};
typedef extended_exponent_fpt<double> efpt64;
template <typename _fpt>
extended_exponent_fpt<_fpt> get_sqrt(const extended_exponent_fpt<_fpt>& that) {
return that.sqrt();
}
template <typename _fpt>
bool is_pos(const extended_exponent_fpt<_fpt>& that) {
return that.is_pos();
}
template <typename _fpt>
bool is_neg(const extended_exponent_fpt<_fpt>& that) {
return that.is_neg();
}
template <typename _fpt>
bool is_zero(const extended_exponent_fpt<_fpt>& that) {
return that.is_zero();
}
// Very efficient stack allocated big integer class.
// Supports next set of arithmetic operations: +, -, *.
template<std::size_t N>
class extended_int {
public:
extended_int() {}
extended_int(int32 that) {
if (that > 0) {
this->chunks_[0] = that;
this->count_ = 1;
} else if (that < 0) {
this->chunks_[0] = -that;
this->count_ = -1;
} else {
this->count_ = 0;
}
}
extended_int(int64 that) {
if (that > 0) {
this->chunks_[0] = static_cast<uint32>(that);
this->chunks_[1] = that >> 32;
this->count_ = this->chunks_[1] ? 2 : 1;
} else if (that < 0) {
that = -that;
this->chunks_[0] = static_cast<uint32>(that);
this->chunks_[1] = that >> 32;
this->count_ = this->chunks_[1] ? -2 : -1;
} else {
this->count_ = 0;
}
}
extended_int(const std::vector<uint32>& chunks, bool plus = true) {
this->count_ = static_cast<int32>((std::min)(N, chunks.size()));
for (int i = 0; i < this->count_; ++i)
this->chunks_[i] = chunks[chunks.size() - i - 1];
if (!plus)
this->count_ = -this->count_;
}
template<std::size_t M>
extended_int(const extended_int<M>& that) {
this->count_ = that.count();
std::memcpy(this->chunks_, that.chunks(), that.size() * sizeof(uint32));
}
extended_int& operator=(int32 that) {
if (that > 0) {
this->chunks_[0] = that;
this->count_ = 1;
} else if (that < 0) {
this->chunks_[0] = -that;
this->count_ = -1;
} else {
this->count_ = 0;
}
return *this;
}
extended_int& operator=(int64 that) {
if (that > 0) {
this->chunks_[0] = static_cast<uint32>(that);
this->chunks_[1] = that >> 32;
this->count_ = this->chunks_[1] ? 2 : 1;
} else if (that < 0) {
that = -that;
this->chunks_[0] = static_cast<uint32>(that);
this->chunks_[1] = that >> 32;
this->count_ = this->chunks_[1] ? -2 : -1;
} else {
this->count_ = 0;
}
return *this;
}
template<std::size_t M>
extended_int& operator=(const extended_int<M>& that) {
this->count_ = that.count();
std::memcpy(this->chunks_, that.chunks(), that.size() * sizeof(uint32));
return *this;
}
bool is_pos() const {
return this->count_ > 0;
}
bool is_neg() const {
return this->count_ < 0;
}
bool is_zero() const {
return this->count_ == 0;
}
bool operator==(const extended_int& that) const {
if (this->count_ != that.count())
return false;
for (std::size_t i = 0; i < this->size(); ++i)
if (this->chunks_[i] != that.chunks()[i])
return false;
return true;
}
bool operator!=(const extended_int& that) const {
return !(*this == that);
}
bool operator<(const extended_int& that) const {
if (this->count_ != that.count())
return this->count_ < that.count();
std::size_t i = this->size();
if (!i)
return false;
do {
--i;
if (this->chunks_[i] != that.chunks()[i])
return (this->chunks_[i] < that.chunks()[i]) ^ (this->count_ < 0);
} while (i);
return false;
}
bool operator>(const extended_int& that) const {
return that < *this;
}
bool operator<=(const extended_int& that) const {
return !(that < *this);
}
bool operator>=(const extended_int& that) const {
return !(*this < that);
}
extended_int operator-() const {
extended_int ret_val = *this;
ret_val.neg();
return ret_val;
}
void neg() {
this->count_ = -this->count_;
}
extended_int operator+(const extended_int& that) const {
extended_int ret_val;
ret_val.add(*this, that);
return ret_val;
}
void add(const extended_int& e1, const extended_int& e2) {
if (!e1.count()) {
*this = e2;
return;
}
if (!e2.count()) {
*this = e1;
return;
}
if ((e1.count() > 0) ^ (e2.count() > 0)) {
dif(e1.chunks(), e1.size(), e2.chunks(), e2.size());
} else {
add(e1.chunks(), e1.size(), e2.chunks(), e2.size());
}
if (e1.count() < 0)
this->count_ = -this->count_;
}
extended_int operator-(const extended_int& that) const {
extended_int ret_val;
ret_val.dif(*this, that);
return ret_val;
}
void dif(const extended_int& e1, const extended_int& e2) {
if (!e1.count()) {
*this = e2;
this->count_ = -this->count_;
return;
}
if (!e2.count()) {
*this = e1;
return;
}
if ((e1.count() > 0) ^ (e2.count() > 0)) {
add(e1.chunks(), e1.size(), e2.chunks(), e2.size());
} else {
dif(e1.chunks(), e1.size(), e2.chunks(), e2.size());
}
if (e1.count() < 0)
this->count_ = -this->count_;
}
extended_int operator*(int32 that) const {
extended_int temp(that);
return (*this) * temp;
}
extended_int operator*(int64 that) const {
extended_int temp(that);
return (*this) * temp;
}
extended_int operator*(const extended_int& that) const {
extended_int ret_val;
ret_val.mul(*this, that);
return ret_val;
}
void mul(const extended_int& e1, const extended_int& e2) {
if (!e1.count() || !e2.count()) {
this->count_ = 0;
return;
}
mul(e1.chunks(), e1.size(), e2.chunks(), e2.size());
if ((e1.count() > 0) ^ (e2.count() > 0))
this->count_ = -this->count_;
}
const uint32* chunks() const {
return chunks_;
}
int32 count() const {
return count_;
}
std::size_t size() const {
return (std::abs)(count_);
}
std::pair<fpt64, int> p() const {
std::pair<fpt64, int> ret_val(0, 0);
std::size_t sz = this->size();
if (!sz) {
return ret_val;
} else {
if (sz == 1) {
ret_val.first = static_cast<fpt64>(this->chunks_[0]);
} else if (sz == 2) {
ret_val.first = static_cast<fpt64>(this->chunks_[1]) *
static_cast<fpt64>(0x100000000LL) +
static_cast<fpt64>(this->chunks_[0]);
} else {
for (std::size_t i = 1; i <= 3; ++i) {
ret_val.first *= static_cast<fpt64>(0x100000000LL);
ret_val.first += static_cast<fpt64>(this->chunks_[sz - i]);
}
ret_val.second = static_cast<int>((sz - 3) << 5);
}
}
if (this->count_ < 0)
ret_val.first = -ret_val.first;
return ret_val;
}
fpt64 d() const {
std::pair<fpt64, int> p = this->p();
return std::ldexp(p.first, p.second);
}
private:
void add(const uint32* c1, std::size_t sz1,
const uint32* c2, std::size_t sz2) {
if (sz1 < sz2) {
add(c2, sz2, c1, sz1);
return;
}
this->count_ = static_cast<int32>(sz1);
uint64 temp = 0;
for (std::size_t i = 0; i < sz2; ++i) {
temp += static_cast<uint64>(c1[i]) + static_cast<uint64>(c2[i]);
this->chunks_[i] = static_cast<uint32>(temp);
temp >>= 32;
}
for (std::size_t i = sz2; i < sz1; ++i) {
temp += static_cast<uint64>(c1[i]);
this->chunks_[i] = static_cast<uint32>(temp);
temp >>= 32;
}
if (temp && (this->count_ != N)) {
this->chunks_[this->count_] = static_cast<uint32>(temp);
++this->count_;
}
}
void dif(const uint32* c1, std::size_t sz1,
const uint32* c2, std::size_t sz2,
bool rec = false) {
if (sz1 < sz2) {
dif(c2, sz2, c1, sz1, true);
this->count_ = -this->count_;
return;
} else if ((sz1 == sz2) && !rec) {
do {
--sz1;
if (c1[sz1] < c2[sz1]) {
++sz1;
dif(c2, sz1, c1, sz1, true);
this->count_ = -this->count_;
return;
} else if (c1[sz1] > c2[sz1]) {
++sz1;
break;
}
} while (sz1);
if (!sz1) {
this->count_ = 0;
return;
}
sz2 = sz1;
}
this->count_ = static_cast<int32>(sz1-1);
bool flag = false;
for (std::size_t i = 0; i < sz2; ++i) {
this->chunks_[i] = c1[i] - c2[i] - (flag?1:0);
flag = (c1[i] < c2[i]) || ((c1[i] == c2[i]) && flag);
}
for (std::size_t i = sz2; i < sz1; ++i) {
this->chunks_[i] = c1[i] - (flag?1:0);
flag = !c1[i] && flag;
}
if (this->chunks_[this->count_])
++this->count_;
}
void mul(const uint32* c1, std::size_t sz1,
const uint32* c2, std::size_t sz2) {
uint64 cur = 0, nxt, tmp;
this->count_ = static_cast<int32>((std::min)(N, sz1 + sz2 - 1));
for (std::size_t shift = 0; shift < static_cast<std::size_t>(this->count_);
++shift) {
nxt = 0;
for (std::size_t first = 0; first <= shift; ++first) {
if (first >= sz1)
break;
std::size_t second = shift - first;
if (second >= sz2)
continue;
tmp = static_cast<uint64>(c1[first]) * static_cast<uint64>(c2[second]);
cur += static_cast<uint32>(tmp);
nxt += tmp >> 32;
}
this->chunks_[shift] = static_cast<uint32>(cur);
cur = nxt + (cur >> 32);
}
if (cur && (this->count_ != N)) {
this->chunks_[this->count_] = static_cast<uint32>(cur);
++this->count_;
}
}
uint32 chunks_[N];
int32 count_;
};
template <std::size_t N>
bool is_pos(const extended_int<N>& that) {
return that.count() > 0;
}
template <std::size_t N>
bool is_neg(const extended_int<N>& that) {
return that.count() < 0;
}
template <std::size_t N>
bool is_zero(const extended_int<N>& that) {
return !that.count();
}
struct type_converter_fpt {
template <typename T>
fpt64 operator()(const T& that) const {
return static_cast<fpt64>(that);
}
template <std::size_t N>
fpt64 operator()(const extended_int<N>& that) const {
return that.d();
}
fpt64 operator()(const extended_exponent_fpt<fpt64>& that) const {
return that.d();
}
};
struct type_converter_efpt {
template <std::size_t N>
extended_exponent_fpt<fpt64> operator()(const extended_int<N>& that) const {
std::pair<fpt64, int> p = that.p();
return extended_exponent_fpt<fpt64>(p.first, p.second);
}
};
// Voronoi coordinate type traits make it possible to extend algorithm
// input coordinate range to any user provided integer type and algorithm
// output coordinate range to any ieee-754 like floating point type.
template <typename T>
struct voronoi_ctype_traits;
template <>
struct voronoi_ctype_traits<int32> {
typedef int32 int_type;
typedef int64 int_x2_type;
typedef uint64 uint_x2_type;
typedef extended_int<64> big_int_type;
typedef fpt64 fpt_type;
typedef extended_exponent_fpt<fpt_type> efpt_type;
typedef ulp_comparison<fpt_type> ulp_cmp_type;
typedef type_converter_fpt to_fpt_converter_type;
typedef type_converter_efpt to_efpt_converter_type;
};
} // detail
} // polygon
} // boost
#endif // BOOST_POLYGON_DETAIL_VORONOI_CTYPES