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exponent.cxx
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exponent.cxx
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// THE EXPONENT FUNCTION (CHAPTER 1.22)
// ---------------------------------
// This program computes the exponent function
// using Taylor series and diagonal Pade series
// (Chapter 1.22).
// The complete explanation is in the book.
#include<stdio.h>
#include<math.h>
double expTaylor(double arg){
const int K=10;
double x=arg;
int m=0;
while(fabs(x)>0.5){
x /= 2.;
m++;
}
double sum=1.;
for(int n=K; n>00; n--){
sum *= x/n;
sum += 1.;
}
for(int i=0; i<m; i++)
sum *= sum;
return sum;
} // calculate exp(arg) using Taylor series of length 10
double expPade(double arg){
const int K=5;
double x=arg;
int m=0;
while(fabs(x)>0.5){
x /= 2.;
m++;
}
double nom=1.;
for(int n=K; n>00; n--){
nom *= x*(K-n+1)/(n*(2*K-n+1));
nom += 1.;
}
double denom=1.;
for(int n=K; n>00; n--){
denom *= -x*(K-n+1)/(n*(2*K-n+1));
denom += 1.;
}
double sum = nom/denom;
for(int i=0; i<m; i++)
sum *= sum;
return sum;
} // calculate exp(arg) using Pade series of length 10
main(){
printf("%f=%f=%f\n",exp(-2.),expTaylor(-2.),expPade(-2.));
}