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