log的c实现

#include <stdio.h> 
const int N=100; 

double coef(int n) 
{ 
if(n==0) return 0; 
double t=1.0/n; 
if(n%2==0) t=-t; 
return t; 
}//x^n的系数 
double horner(double x) 
{ 
double u=coef(N); 
for(int i=N-1;i>=0;i--) 
u=u*x+coef(i); 
return u; 
} 
double sqrt(double b) 
{ 
double x=1;int step=0; 
while((x*x-b<-0.000000000000001||x*x-b>0.000000000000001)&&step<50) 
{x=(b/x+x)/2.0;step++;} 
return x; 
}//开平方 

double ln(double x)//ln(1+x)=x-x^2/2+x^3/3-x^4/4…… 
{ 
if(x>1.5) 
{ 
for(int i=0;x>1.25;i++) 
x=sqrt(x); 
return (1<<i)*horner(x-1); 
} 
else if(x<0.7&&x>0) 
{ 
for(int i=0;x<0.7;i++) 
x=sqrt(x); 
return (1<<i)*horner(x-1); 
} 
else if(x>0) 
return horner(x-1); 
} 
double log(double m,double base=10) 
{ 
return ln(m)/ln(base);//换底公式 
} 
double exp(double x) 
{ 
double sum=1; 
for(int i=N;i>0;i--) 
{ 
sum/=i; 
sum*=x; 
sum+=1; 
} 
return sum; 

}//e^x≈1+x+x^2/2!+x^3/3!+……+x^n/n! 

double pow(double m,double n) 
{ 
return exp(n*ln(m)); 
} 

main() 
{ 
printf("100^2.5=");printf("%f\n",pow(100,2.5)); 
printf("lg(1000)=");printf("%f\n",log(1000)); 
}