In article <bvbnom$2pc6$1@digitaldaemon.com>, Steve Strand says...
>
>After reviewing my erf() code I see that I forgot to initialize q2 in erfc(). Find the corrected code below (one line is
>different).
>

Actually there's far bigger bug in erf: the absolute value (fabs) is not applied to the right term so erf gives wrong results for values between -2.2 and 0...

Here's the corrected code:

#include <iostream.h>
#include <iomanip.h>
#include <strstream.h>
#include <math.h>


static const double rel_error= 1E-12;        //calculate 12 significant figures
//you can adjust rel_error to trade off between accuracy and speed
//but don't ask for > 15 figures (assuming usual 52 bit mantissa in a double)


double erf(double x)
//erf(x) = 2/sqrt(pi)*integral(exp(-t^2),t,0,x)
//       = 2/sqrt(pi)*[x - x^3/3 + x^5/5*2! - x^7/7*3! + ...]
//       = 1-erfc(x)
{
static const double two_sqrtpi=  1.128379167095512574;        // 2/sqrt(pi)
if (fabs(x) > 2.2) {
return 1.0 - erfc(x);        //use continued fraction when fabs(x) > 2.2
}
double sum= x, term= x, xsqr= x*x;
int j= 1;
do {
term*= xsqr/j;
sum-= term/(2*j+1);
++j;
term*= xsqr/j;
sum+= term/(2*j+1);
++j;
} while (fabs(term/sum) > rel_error);   // CORRECTED LINE
return two_sqrtpi*sum;
}


double erfc(double x)
//erfc(x) = 2/sqrt(pi)*integral(exp(-t^2),t,x,inf)
//        = exp(-x^2)/sqrt(pi) * [1/x+ (1/2)/x+ (2/2)/x+ (3/2)/x+ (4/2)/x+ ...]
//        = 1-erf(x)
//expression inside [] is a continued fraction so '+' means add to denominator
only
{
static const double one_sqrtpi=  0.564189583547756287;        // 1/sqrt(pi)
if (fabs(x) < 2.2) {
return 1.0 - erf(x);        //use series when fabs(x) < 2.2
}
if (signbit(x)) {               //continued fraction only valid for x>0
return 2.0 - erfc(-x);
}
double a=1, b=x;                //last two convergent numerators
double c=x, d=x*x+0.5;          //last two convergent denominators
double q1, q2= b/d;             //last two convergents (a/c and b/d)
double n= 1.0, t;
do {
t= a*n+b*x;
a= b;
b= t;
t= c*n+d*x;
c= d;
d= t;
n+= 0.5;
q1= q2;
q2= b/d;
} while (fabs(q1-q2)/q2 > rel_error);
return one_sqrtpi*exp(-x*x)*q2;
}



--
Pierre