#include <stdio.h>

#include <stdlib.h>

#include<conio.h>

#include<math.h>

#include<string.h>

double f(double x)

{

return (4*x*x/(1+x*x));

}

double Romberg(double top,double bottom,double precision)

{

int k=1;

double S,x,T1,T2,S1,S2,C1,C2,R1,R2,h=bottom-top;

/*

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*/

//S梯形公式，T梯型变步长，S梯形加速，C幸普森加速，R龙贝格求积

T1=h*(f(top)+f(bottom))/2;//梯形公式

while(1)

{

S=0;

x=top+h/2;

do

{

S+=f(x);

x+=h;

}while(x<bottom);

T2=(T1+h*S)/2.0;

if(fabs(T2-T1)<precision)

{

return T2;

}

S2=T2+(T2-T1)/3;//梯形加速

if(k==1)

{

T1=T2;

S1=S2;//几下原来的S2

h/=2;

k+=1;

continue;

}

C2=S2+(S2-S1)/15;//新的S2减原来的S2，即使S1,幸普森加速

if(k==2)

{

C1=C2;

T1=T2;

S1=S2;

h/=2;

k+=1;

continue;

}

R2=C2+(C2-C1)/63.0;

if(k==3)

{

R1=R2;

C1=C2;

T1=T2;

S1=S2;

h/=2;

k+=1;

continue;

}

if(fabs(S2-S1)<precision)

{

return S2;

}

C1=C2;

T1=T2;

S1=S2;

h/=2;

k+=1;

if(fabs(R2-R1)<precision);

{

return R2;

}

}

}

int main()

{

double top,bottom,precision,S;

printf("Pletopse input the begin: ");

scanf("%lf",&top);

printf("Pletopse input the end: ");

scanf("%lf",&bottom);

printf("Pletopse input the precision:");

scanf("%lf",&precision);

S=Romberg(top,bottom,precision);

printf("The result is:%lf",S);

getch();

return 0;

}