bm_fpm.cpp

#include <iomanip>
#include <iostream>
#include <functional>
#include <limits>

typedef std::function<double(double)> func_t;

double bisection_method(func_t f, double min, double max) {
  double mid;
  double minval, midval, maxval;

  while ((max - min) > std::numeric_limits<double>::epsilon()) {
    minval = f(min); maxval = f(max);
    mid = (max + min) / 2; midval = f(mid);

    min = (minval * midval > 0) ? mid : min;
    max = (midval * maxval > 0) ? mid : max;
  }

  return (max + min) / 2;
}

double false_position_method(func_t f, double min, double max) {
  double mid;
  double minval, midval, maxval;

  while ((max - min) > std::numeric_limits<double>::epsilon()) {
    minval = f(min); maxval = f(max);
    mid = (max * minval - min * maxval) / (minval - maxval); midval = f(mid);

    min = (minval * midval >= 0) ? mid : min;
    max = (midval * maxval >= 0) ? mid : max;
  }

  return (max + min) / 2;
}

int main() {
  double ans;
  func_t f = [](double x) { return x * x - 2; };
  std::cout << std::setprecision(100);

  ans = bisection_method(f, 0, 2);
  std::cout << "bisection method: ";
  std::cout << ans << std::endl;

  ans = false_position_method(f, 0, 2);
  std::cout << "false position method: ";
  std::cout << ans << std::endl;
}