Calculates the inverse hyperbolic tangent of a number

include <math.h>
double atanh ( double x  );
float atanhf ( float x  );
long double atanhl ( long double x  );

The atanh( ) functions return the number whose hyperbolic tangent is equal to their argument x. Because the hyperbolic tangent of any number is between -1 and +1, atanh( ) incurs a domain error if the absolute value of the argument is greater than 1. Furthermore, a range error may result if the absolute value of the argument is equal to 1.

Example

double x[ ] = { -1.0, -0.5, 0.0, 0.5, 0.99, 1.0, 1.01 };

puts("            x              atanh(x) \n"
     "  ---------------------------------------");
for ( int i = 0; i < sizeof(x) / sizeof(x[0]); ++i )
{
  errno = 0;
  printf("%+15.2f %+20.10f\n", x[i], atanh(x[i]) );
  if ( errno)
    perror("atanh");
}

This code produces the following output:

            x              atanh(x)
  ---------------------------------------
          -1.00                 -inf
atanh: Numerical argument out of domain
          -0.50        -0.5493061443
          +0.00        +0.0000000000
          +0.50        +0.5493061443
          +0.99        +2.6466524124
          +1.00                 +inf
atanh: Numerical argument out of domain
          +1.01                 +nan
atanh: Numerical argument out of domain

See Also

Other hyperbolic trigonometry functions for real numbers: asinh( ), acosh( ), sinh( ), cosh( ), and tanh( ); the hyperbolic tangent and inverse hyperbolic tangent functions for complex numbers: ctanh( ) and catanh( )