[ round-off error eps ] 浮點數誤差模板

有些計算幾何的過程中會產生捨位誤差，這時候就需要決定一個很小的數，去避開這個捨位誤差問題，我們稱那個很小的數為EPS

• A < B ....... A - B < - EPS
• A > B ....... A - B > EPS
• A == B ....... abs(A - B) <= EPS
• A <= B ....... A - B <= EPS
• A >= B ....... A - B >= - EPS

因為我的計算幾何模板在實作時是用template實作的，所以如果需要處理浮點數誤差時，需要傳入一個新的資料結構，所以寫了這份模板

	#ifndef SUNMOON_DOUBLE
	#define SUNMOON_DOUBLE
	#include <cmath>
	#include <iostream>
	const double EPS = 1e-9;
	struct Double {
	double d;
	Double(double d = 0) : d(d) {}
	Double operator-() const { return -d; }
	Double operator+(const Double &b) const { return d + b.d; }
	Double operator-(const Double &b) const { return d - b.d; }
	Double operator*(const Double &b) const { return d * b.d; }
	Double operator/(const Double &b) const { return d / b.d; }
	Double operator+=(const Double &b) { return d += b.d; }
	Double operator-=(const Double &b) { return d -= b.d; }
	Double operator*=(const Double &b) { return d *= b.d; }
	Double operator/=(const Double &b) { return d /= b.d; }
	bool operator<(const Double &b) const { return d - b.d < -EPS; }
	bool operator>(const Double &b) const { return d - b.d > EPS; }
	bool operator==(const Double &b) const { return fabs(d - b.d) <= EPS; }
	bool operator!=(const Double &b) const { return fabs(d - b.d) > EPS; }
	bool operator<=(const Double &b) const { return d - b.d <= EPS; }
	bool operator>=(const Double &b) const { return d - b.d >= -EPS; }
	friend std::ostream &operator<<(std::ostream &os, const Double &db) {
	return os << db.d;
	}
	friend std::istream &operator>>(std::istream &is, Double &db) {
	return is >> db.d;
	}
	};
	#endif

view raw eps.cpp hosted with ❤ by GitHub