f0611.cpp

钱能C++程序设计教程(第二版)的源码和课件

//==================================
// f0611.cpp
// 辛普生积分
//==================================
#include<iostream>
#include<fstream>
#include<cmath>
using namespace std;
//----------------------------------
double g(double x){
  return 1/x;
}//---------------------------------
double simpson(double a, double b, double(*f)(double)){
  double I2n=0,h=b-a,T2n=h*(f(a)+f(b))/2,In=T2n,Tn;
  for(int n=1; abs(I2n-In)>1e-3; n+=n,h/=2.0){
    In=I2n; Tn=T2n;       // In老积分值
    double sigma=0;
    for(int k=0; k<n; k++)
      sigma += f(a+(k+0.5)*h);
    T2n=(Tn+h*sigma)/2;
    I2n=(4*T2n-Tn)/3;     // I2n新积分值
  }
  return I2n;
}//---------------------------------
int main(){
  ifstream in("integral.txt");
  cout<<fixed; cout.precision(3);
  for(double b; in>>b; )
    cout<<simpson(1,b,g)<<"\n";
}//=================================