atanh

atanh

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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( )