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Defined in header <math.h> | ||
|---|---|---|
float atanhf( float arg ); | (1) | (since C99) |
double atanh( double arg ); | (2) | (since C99) |
long double atanhl( long double arg ); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define atanh( arg ) | (4) | (since C99) |
1-3) Computes the inverse hyperbolic tangent of arg.
4) Type-generic macro: If the argument has type long double, atanhl is called. Otherwise, if the argument has integer type or the type double, atanh is called. Otherwise, atanhf is called. If the argument is complex, then the macro invokes the corresponding complex function (catanhf, catanh, catanhl).
Parameters
arg | - | floating point value representing the area of a hyperbolic sector |
|---|
Return value
If no errors occur, the inverse hyperbolic tangent of arg (tanh-1
(arg), or artanh(arg)), is returned.
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
If a pole error occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned (with the correct sign).
If a range error occurs due to underflow, the correct result (after rounding) is returned.
Error handling
Errors are reported as specified in math_errhandling.
If the argument is not on the interval -1, +1, a range error occurs.
If the argument is ±1, a pole error occurs.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
if the argument is ±0, it is returned unmodified
if the argument is ±1, ±∞ is returned and
FE_DIVBYZEROis raised.if |arg|>1, NaN is returned and
FE_INVALIDis raised.if the argument is NaN, NaN is returned
Notes
Although the C standard names this function "arc hyperbolic tangent", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic tangent" (used by POSIX) or "area hyperbolic tangent".
POSIX specifies that in case of underflow, arg is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.
Example
#include <stdio.h>#include <math.h>#include <float.h>#include <errno.h>#include <fenv.h>#pragma STDC FENV_ACCESS ON
int main(void){ printf("atanh(0) = %f\natanh(-0) = %f\n", atanh(0), atanh(-0.0)); printf("atanh(0.9) = %f\n", atanh(0.9)); //error handling
errno = 0; feclearexcept(FE_ALL_EXCEPT); printf("atanh(-1) = %f\n", atanh(-1)); if(errno == ERANGE) perror(" errno == ERANGE"); if(fetestexcept(FE_DIVBYZERO)) puts(" FE_DIVBYZERO raised");}Possible output:
atanh(0) = 0.000000atanh(-0) = -0.000000atanh(0.9) = 1.472219atanh(-1) = -inf errno == ERANGE: Numerical result out of range FE_DIVBYZERO raised
References
C11 standard (ISO/IEC 9899:2011):
7.12.5.3 The atanh functions (p: 241)
7.25 Type-generic math <tgmath.h> (p: 373-375)
F.10.2.3 The atanh functions (p: 520)
C99 standard (ISO/IEC 9899:1999):
7.12.5.3 The atanh functions (p: 221-222)
7.22 Type-generic math <tgmath.h> (p: 335-337)
F.9.2.3 The atanh functions (p: 457)
See also
asinhasinhfasinhl (C99)(C99)(C99) | computes inverse hyperbolic sine (arsinh(x)) (function) |
|---|---|
acoshacoshfacoshl (C99)(C99)(C99) | computes inverse hyperbolic cosine (arcosh(x)) (function) |
tanhtanhftanhl (C99)(C99) | computes hyperbolic tangent (function) |
catanhcatanhfcatanhl (C99)(C99)(C99) | computes the complex arc hyperbolic tangent (function) |
| C++ documentation for atanh |