Initial work for G-code sender and more intensive usage of Boost

xs/include/boost/polygon/detail/voronoi_robust_fpt.hpp

@@ -0,0 +1,506 @@
+// Boost.Polygon library detail/voronoi_robust_fpt.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_ROBUST_FPT
+#define BOOST_POLYGON_DETAIL_VORONOI_ROBUST_FPT
+
+#include <cmath>
+
+// Geometry predicates with floating-point variables usually require
+// high-precision predicates to retrieve the correct result.
+// Epsilon robust predicates give the result within some epsilon relative
+// error, but are a lot faster than high-precision predicates.
+// To make algorithm robust and efficient epsilon robust predicates are
+// used at the first step. In case of the undefined result high-precision
+// arithmetic is used to produce required robustness. This approach
+// requires exact computation of epsilon intervals within which epsilon
+// robust predicates have undefined value.
+// There are two ways to measure an error of floating-point calculations:
+// relative error and ULPs (units in the last place).
+// Let EPS be machine epsilon, then next inequalities have place:
+// 1 EPS <= 1 ULP <= 2 EPS (1), 0.5 ULP <= 1 EPS <= 1 ULP (2).
+// ULPs are good for measuring rounding errors and comparing values.
+// Relative errors are good for computation of general relative
+// error of formulas or expressions. So to calculate epsilon
+// interval within which epsilon robust predicates have undefined result
+// next schema is used:
+//     1) Compute rounding errors of initial variables using ULPs;
+//     2) Transform ULPs to epsilons using upper bound of the (1);
+//     3) Compute relative error of the formula using epsilon arithmetic;
+//     4) Transform epsilon to ULPs using upper bound of the (2);
+// In case two values are inside undefined ULP range use high-precision
+// arithmetic to produce the correct result, else output the result.
+// Look at almost_equal function to see how two floating-point variables
+// are checked to fit in the ULP range.
+// If A has relative error of r(A) and B has relative error of r(B) then:
+//     1) r(A + B) <= max(r(A), r(B)), for A * B >= 0;
+//     2) r(A - B) <= B*r(A)+A*r(B)/(A-B), for A * B >= 0;
+//     2) r(A * B) <= r(A) + r(B);
+//     3) r(A / B) <= r(A) + r(B);
+// In addition rounding error should be added, that is always equal to
+// 0.5 ULP or at most 1 epsilon. As you might see from the above formulas
+// subtraction relative error may be extremely large, that's why
+// epsilon robust comparator class is used to store floating point values
+// and compute subtraction as the final step of the evaluation.
+// For further information about relative errors and ULPs try this link:
+// http://docs.sun.com/source/806-3568/ncg_goldberg.html
+
+namespace boost {
+namespace polygon {
+namespace detail {
+
+template <typename T>
+T get_sqrt(const T& that) {
+  return (std::sqrt)(that);
+}
+
+template <typename T>
+bool is_pos(const T& that) {
+  return that > 0;
+}
+
+template <typename T>
+bool is_neg(const T& that) {
+  return that < 0;
+}
+
+template <typename T>
+bool is_zero(const T& that) {
+  return that == 0;
+}
+
+template <typename _fpt>
+class robust_fpt {
+ public:
+  typedef _fpt floating_point_type;
+  typedef _fpt relative_error_type;
+
+  // Rounding error is at most 1 EPS.
+  enum {
+    ROUNDING_ERROR = 1
+  };
+
+  robust_fpt() : fpv_(0.0), re_(0.0) {}
+  explicit robust_fpt(floating_point_type fpv) :
+      fpv_(fpv), re_(0.0) {}
+  robust_fpt(floating_point_type fpv, relative_error_type error) :
+      fpv_(fpv), re_(error) {}
+
+  floating_point_type fpv() const { return fpv_; }
+  relative_error_type re() const { return re_; }
+  relative_error_type ulp() const { return re_; }
+
+  robust_fpt& operator=(const robust_fpt& that) {
+    this->fpv_ = that.fpv_;
+    this->re_ = that.re_;
+    return *this;
+  }
+
+  bool has_pos_value() const {
+    return is_pos(fpv_);
+  }
+
+  bool has_neg_value() const {
+    return is_neg(fpv_);
+  }
+
+  bool has_zero_value() const {
+    return is_zero(fpv_);
+  }
+
+  robust_fpt operator-() const {
+    return robust_fpt(-fpv_, re_);
+  }
+
+  robust_fpt& operator+=(const robust_fpt& that) {
+    floating_point_type fpv = this->fpv_ + that.fpv_;
+    if ((!is_neg(this->fpv_) && !is_neg(that.fpv_)) ||
+        (!is_pos(this->fpv_) && !is_pos(that.fpv_))) {
+      this->re_ = (std::max)(this->re_, that.re_) + ROUNDING_ERROR;
+    } else {
+      floating_point_type temp =
+        (this->fpv_ * this->re_ - that.fpv_ * that.re_) / fpv;
+      if (is_neg(temp))
+        temp = -temp;
+      this->re_ = temp + ROUNDING_ERROR;
+    }
+    this->fpv_ = fpv;
+    return *this;
+  }
+
+  robust_fpt& operator-=(const robust_fpt& that) {
+    floating_point_type fpv = this->fpv_ - that.fpv_;
+    if ((!is_neg(this->fpv_) && !is_pos(that.fpv_)) ||
+        (!is_pos(this->fpv_) && !is_neg(that.fpv_))) {
+       this->re_ = (std::max)(this->re_, that.re_) + ROUNDING_ERROR;
+    } else {
+      floating_point_type temp =
+        (this->fpv_ * this->re_ + that.fpv_ * that.re_) / fpv;
+      if (is_neg(temp))
+         temp = -temp;
+      this->re_ = temp + ROUNDING_ERROR;
+    }
+    this->fpv_ = fpv;
+    return *this;
+  }
+
+  robust_fpt& operator*=(const robust_fpt& that) {
+    this->re_ += that.re_ + ROUNDING_ERROR;
+    this->fpv_ *= that.fpv_;
+    return *this;
+  }
+
+  robust_fpt& operator/=(const robust_fpt& that) {
+    this->re_ += that.re_ + ROUNDING_ERROR;
+    this->fpv_ /= that.fpv_;
+    return *this;
+  }
+
+  robust_fpt operator+(const robust_fpt& that) const {
+    floating_point_type fpv = this->fpv_ + that.fpv_;
+    relative_error_type re;
+    if ((!is_neg(this->fpv_) && !is_neg(that.fpv_)) ||
+        (!is_pos(this->fpv_) && !is_pos(that.fpv_))) {
+      re = (std::max)(this->re_, that.re_) + ROUNDING_ERROR;
+    } else {
+      floating_point_type temp =
+        (this->fpv_ * this->re_ - that.fpv_ * that.re_) / fpv;
+      if (is_neg(temp))
+        temp = -temp;
+      re = temp + ROUNDING_ERROR;
+    }
+    return robust_fpt(fpv, re);
+  }
+
+  robust_fpt operator-(const robust_fpt& that) const {
+    floating_point_type fpv = this->fpv_ - that.fpv_;
+    relative_error_type re;
+    if ((!is_neg(this->fpv_) && !is_pos(that.fpv_)) ||
+        (!is_pos(this->fpv_) && !is_neg(that.fpv_))) {
+      re = (std::max)(this->re_, that.re_) + ROUNDING_ERROR;
+    } else {
+      floating_point_type temp =
+        (this->fpv_ * this->re_ + that.fpv_ * that.re_) / fpv;
+      if (is_neg(temp))
+        temp = -temp;
+      re = temp + ROUNDING_ERROR;
+    }
+    return robust_fpt(fpv, re);
+  }
+
+  robust_fpt operator*(const robust_fpt& that) const {
+    floating_point_type fpv = this->fpv_ * that.fpv_;
+    relative_error_type re = this->re_ + that.re_ + ROUNDING_ERROR;
+    return robust_fpt(fpv, re);
+  }
+
+  robust_fpt operator/(const robust_fpt& that) const {
+    floating_point_type fpv = this->fpv_ / that.fpv_;
+    relative_error_type re = this->re_ + that.re_ + ROUNDING_ERROR;
+    return robust_fpt(fpv, re);
+  }
+
+  robust_fpt sqrt() const {
+    return robust_fpt(get_sqrt(fpv_),
+                      re_ * static_cast<relative_error_type>(0.5) +
+                      ROUNDING_ERROR);
+  }
+
+ private:
+  floating_point_type fpv_;
+  relative_error_type re_;
+};
+
+template <typename T>
+robust_fpt<T> get_sqrt(const robust_fpt<T>& that) {
+  return that.sqrt();
+}
+
+template <typename T>
+bool is_pos(const robust_fpt<T>& that) {
+  return that.has_pos_value();
+}
+
+template <typename T>
+bool is_neg(const robust_fpt<T>& that) {
+  return that.has_neg_value();
+}
+
+template <typename T>
+bool is_zero(const robust_fpt<T>& that) {
+  return that.has_zero_value();
+}
+
+// robust_dif consists of two not negative values: value1 and value2.
+// The resulting expression is equal to the value1 - value2.
+// Subtraction of a positive value is equivalent to the addition to value2
+// and subtraction of a negative value is equivalent to the addition to
+// value1. The structure implicitly avoids difference computation.
+template <typename T>
+class robust_dif {
+ public:
+  robust_dif() :
+      positive_sum_(0),
+      negative_sum_(0) {}
+
+  explicit robust_dif(const T& value) :
+      positive_sum_((value > 0)?value:0),
+      negative_sum_((value < 0)?-value:0) {}
+
+  robust_dif(const T& pos, const T& neg) :
+      positive_sum_(pos),
+      negative_sum_(neg) {}
+
+  T dif() const {
+    return positive_sum_ - negative_sum_;
+  }
+
+  T pos() const {
+    return positive_sum_;
+  }
+
+  T neg() const {
+    return negative_sum_;
+  }
+
+  robust_dif<T> operator-() const {
+    return robust_dif(negative_sum_, positive_sum_);
+  }
+
+  robust_dif<T>& operator+=(const T& val) {
+    if (!is_neg(val))
+      positive_sum_ += val;
+    else
+      negative_sum_ -= val;
+    return *this;
+  }
+
+  robust_dif<T>& operator+=(const robust_dif<T>& that) {
+    positive_sum_ += that.positive_sum_;
+    negative_sum_ += that.negative_sum_;
+    return *this;
+  }
+
+  robust_dif<T>& operator-=(const T& val) {
+    if (!is_neg(val))
+      negative_sum_ += val;
+    else
+      positive_sum_ -= val;
+    return *this;
+  }
+
+  robust_dif<T>& operator-=(const robust_dif<T>& that) {
+    positive_sum_ += that.negative_sum_;
+    negative_sum_ += that.positive_sum_;
+    return *this;
+  }
+
+  robust_dif<T>& operator*=(const T& val) {
+    if (!is_neg(val)) {
+      positive_sum_ *= val;
+      negative_sum_ *= val;
+    } else {
+      positive_sum_ *= -val;
+      negative_sum_ *= -val;
+      swap();
+    }
+    return *this;
+  }
+
+  robust_dif<T>& operator*=(const robust_dif<T>& that) {
+    T positive_sum = this->positive_sum_ * that.positive_sum_ +
+                     this->negative_sum_ * that.negative_sum_;
+    T negative_sum = this->positive_sum_ * that.negative_sum_ +
+                     this->negative_sum_ * that.positive_sum_;
+    positive_sum_ = positive_sum;
+    negative_sum_ = negative_sum;
+    return *this;
+  }
+
+  robust_dif<T>& operator/=(const T& val) {
+    if (!is_neg(val)) {
+      positive_sum_ /= val;
+      negative_sum_ /= val;
+    } else {
+      positive_sum_ /= -val;
+      negative_sum_ /= -val;
+      swap();
+    }
+    return *this;
+  }
+
+ private:
+  void swap() {
+    (std::swap)(positive_sum_, negative_sum_);
+  }
+
+  T positive_sum_;
+  T negative_sum_;
+};
+
+template<typename T>
+robust_dif<T> operator+(const robust_dif<T>& lhs,
+                        const robust_dif<T>& rhs) {
+  return robust_dif<T>(lhs.pos() + rhs.pos(), lhs.neg() + rhs.neg());
+}
+
+template<typename T>
+robust_dif<T> operator+(const robust_dif<T>& lhs, const T& rhs) {
+  if (!is_neg(rhs)) {
+    return robust_dif<T>(lhs.pos() + rhs, lhs.neg());
+  } else {
+    return robust_dif<T>(lhs.pos(), lhs.neg() - rhs);
+  }
+}
+
+template<typename T>
+robust_dif<T> operator+(const T& lhs, const robust_dif<T>& rhs) {
+  if (!is_neg(lhs)) {
+    return robust_dif<T>(lhs + rhs.pos(), rhs.neg());
+  } else {
+    return robust_dif<T>(rhs.pos(), rhs.neg() - lhs);
+  }
+}
+
+template<typename T>
+robust_dif<T> operator-(const robust_dif<T>& lhs,
+                        const robust_dif<T>& rhs) {
+  return robust_dif<T>(lhs.pos() + rhs.neg(), lhs.neg() + rhs.pos());
+}
+
+template<typename T>
+robust_dif<T> operator-(const robust_dif<T>& lhs, const T& rhs) {
+  if (!is_neg(rhs)) {
+    return robust_dif<T>(lhs.pos(), lhs.neg() + rhs);
+  } else {
+    return robust_dif<T>(lhs.pos() - rhs, lhs.neg());
+  }
+}
+
+template<typename T>
+robust_dif<T> operator-(const T& lhs, const robust_dif<T>& rhs) {
+  if (!is_neg(lhs)) {
+    return robust_dif<T>(lhs + rhs.neg(), rhs.pos());
+  } else {
+    return robust_dif<T>(rhs.neg(), rhs.pos() - lhs);
+  }
+}
+
+template<typename T>
+robust_dif<T> operator*(const robust_dif<T>& lhs,
+                        const robust_dif<T>& rhs) {
+  T res_pos = lhs.pos() * rhs.pos() + lhs.neg() * rhs.neg();
+  T res_neg = lhs.pos() * rhs.neg() + lhs.neg() * rhs.pos();
+  return robust_dif<T>(res_pos, res_neg);
+}
+
+template<typename T>
+robust_dif<T> operator*(const robust_dif<T>& lhs, const T& val) {
+  if (!is_neg(val)) {
+    return robust_dif<T>(lhs.pos() * val, lhs.neg() * val);
+  } else {
+    return robust_dif<T>(-lhs.neg() * val, -lhs.pos() * val);
+  }
+}
+
+template<typename T>
+robust_dif<T> operator*(const T& val, const robust_dif<T>& rhs) {
+  if (!is_neg(val)) {
+    return robust_dif<T>(val * rhs.pos(), val * rhs.neg());
+  } else {
+    return robust_dif<T>(-val * rhs.neg(), -val * rhs.pos());
+  }
+}
+
+template<typename T>
+robust_dif<T> operator/(const robust_dif<T>& lhs, const T& val) {
+  if (!is_neg(val)) {
+    return robust_dif<T>(lhs.pos() / val, lhs.neg() / val);
+  } else {
+    return robust_dif<T>(-lhs.neg() / val, -lhs.pos() / val);
+  }
+}
+
+// Used to compute expressions that operate with sqrts with predefined
+// relative error. Evaluates expressions of the next type:
+// sum(i = 1 .. n)(A[i] * sqrt(B[i])), 1 <= n <= 4.
+template <typename _int, typename _fpt, typename _converter>
+class robust_sqrt_expr {
+ public:
+  enum MAX_RELATIVE_ERROR {
+    MAX_RELATIVE_ERROR_EVAL1 = 4,
+    MAX_RELATIVE_ERROR_EVAL2 = 7,
+    MAX_RELATIVE_ERROR_EVAL3 = 16,
+    MAX_RELATIVE_ERROR_EVAL4 = 25
+  };
+
+  // Evaluates expression (re = 4 EPS):
+  // A[0] * sqrt(B[0]).
+  _fpt eval1(_int* A, _int* B) {
+    _fpt a = convert(A[0]);
+    _fpt b = convert(B[0]);
+    return a * get_sqrt(b);
+  }
+
+  // Evaluates expression (re = 7 EPS):
+  // A[0] * sqrt(B[0]) + A[1] * sqrt(B[1]).
+  _fpt eval2(_int* A, _int* B) {
+    _fpt a = eval1(A, B);
+    _fpt b = eval1(A + 1, B + 1);
+    if ((!is_neg(a) && !is_neg(b)) ||
+        (!is_pos(a) && !is_pos(b)))
+      return a + b;
+    return convert(A[0] * A[0] * B[0] - A[1] * A[1] * B[1]) / (a - b);
+  }
+
+  // Evaluates expression (re = 16 EPS):
+  // A[0] * sqrt(B[0]) + A[1] * sqrt(B[1]) + A[2] * sqrt(B[2]).
+  _fpt eval3(_int* A, _int* B) {
+    _fpt a = eval2(A, B);
+    _fpt b = eval1(A + 2, B + 2);
+    if ((!is_neg(a) && !is_neg(b)) ||
+        (!is_pos(a) && !is_pos(b)))
+      return a + b;
+    tA[3] = A[0] * A[0] * B[0] + A[1] * A[1] * B[1] - A[2] * A[2] * B[2];
+    tB[3] = 1;
+    tA[4] = A[0] * A[1] * 2;
+    tB[4] = B[0] * B[1];
+    return eval2(tA + 3, tB + 3) / (a - b);
+  }
+
+
+  // Evaluates expression (re = 25 EPS):
+  // A[0] * sqrt(B[0]) + A[1] * sqrt(B[1]) +
+  // A[2] * sqrt(B[2]) + A[3] * sqrt(B[3]).
+  _fpt eval4(_int* A, _int* B) {
+    _fpt a = eval2(A, B);
+    _fpt b = eval2(A + 2, B + 2);
+    if ((!is_neg(a) && !is_neg(b)) ||
+        (!is_pos(a) && !is_pos(b)))
+      return a + b;
+    tA[0] = A[0] * A[0] * B[0] + A[1] * A[1] * B[1] -
+            A[2] * A[2] * B[2] - A[3] * A[3] * B[3];
+    tB[0] = 1;
+    tA[1] = A[0] * A[1] * 2;
+    tB[1] = B[0] * B[1];
+    tA[2] = A[2] * A[3] * -2;
+    tB[2] = B[2] * B[3];
+    return eval3(tA, tB) / (a - b);
+  }
+
+ private:
+  _int tA[5];
+  _int tB[5];
+  _converter convert;
+};
+}  // detail
+}  // polygon
+}  // boost
+
+#endif  // BOOST_POLYGON_DETAIL_VORONOI_ROBUST_FPT