atanh function

Synopsis

$atanh(number)

Technical

atanh() calls the C library's atanh() function to return the inverse hyperbolic tangent of number. A finite result requires a number strictly between -1 and 1. tanh() performs the corresponding hyperbolic tangent operation.

The normal rules about number arguments apply. The first argument word is converted with atof(), accepting decimal fractions and scientific notation; additional words are ignored. Missing input returns the empty string. Nonnumeric input converts to zero, and a numeric prefix can be accepted even when followed by nonnumeric text.

Returns

The calculation uses a C double, and the result string is formatted with %.50g, rather than being limited to six decimal places. The floating_point_math and floating_point_precision settings do not change this calculation or formatting. Additional displayed rounding digits do not imply 50 digits of accuracy.

The library reports a domain error for values below -1 or above 1, including infinities. Exactly -1 or 1 causes a pole error instead. EPIC returns DOM for a reported EDOM error and RANGE for a reported ERANGE error, including a pole error. A platform that reports errors only through floating-point exception flags can instead produce a NaN string for an out-of-domain input or a signed infinity string at a pole. Validate the range rather than relying on one particular error string.

Very small subnormal inputs can also cause a platform-dependent range error. The shared wrapper returns the empty string for any other reported error. It checks only errno, not floating-point exception flags, and resets errno after argument conversion, so conversion errors are not validated by this wrapper.

Examples

The approximate examples describe the numeric value; the returned string may contain more digits.

Source

source/functions.c registers atanh and implements function_atanh through the shared math-function and error-return macros. include/functions.h defines argument conversion and formatting. The C/POSIX inverse hyperbolic tangent specification defines the domain, poles, and library error reporting.