# tanh, tanhf, tanhl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float tanhf( float arg ); | (1) | (since C99)
double tanh( double arg ); | (2) |
long double tanhl( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define tanh( arg ) | (4) | (since C99)

1-3) Computes the hyperbolic tangent of `arg`.
4) Type-generic macro: If the argument has type long double, `tanhl` is called. Otherwise, if the argument has integer type or the type double, `tanh` is called. Otherwise, `tanhf` is called. If the argument is complex, then the macro invokes the corresponding complex function (ctanhf, ctanh, ctanhl).

### Parameters

arg | - | floating point value representing a hyperbolic angle

### Return value

If no errors occur, the hyperbolic tangent of `arg` (tanh(arg), or

earg -e-arg
earg +e-arg

) is returned.

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 implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is ±0, ±0 is returned
- If the argument is ±∞, ±1 is returned
- if the argument is NaN, NaN is returned

### Notes

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

Run this code

    #include <stdio.h>
    #include <math.h>

    int main(void)
    {
        printf("tanh(1) = %f\ntanh(-1) = %f\n", tanh(1), tanh(-1));
        printf("tanh(0.1)*sinh(0.2)-cosh(0.2) = %f\n", tanh(0.1) * sinh(0.2) - cosh(0.2));
        // special values
        printf("tanh(+0) = %f\ntanh(-0) = %f\n", tanh(0.0), tanh(-0.0));
    }

Output:

    tanh(1) = 0.761594
    tanh(-1) = -0.761594
    tanh(0.1)*sinh(0.2)-cosh(0.2) = -1.000000
    tanh(+0) = 0.000000
    tanh(-0) = -0.000000

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.5.6 The tanh functions (p: 242)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.2.6 The tanh functions (p: 520)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.5.6 The tanh functions (p: 222-223)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.2.6 The tanh functions (p: 457)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.3.3 The tanh function

### See also

sinh sinhf sinhl (C99)(C99) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
cosh coshf coshl (C99)(C99) | computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function)
atanh atanhf atanhl (C99)(C99)(C99) | computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)
ctanh ctanhf ctanhl (C99)(C99)(C99) | computes the complex hyperbolic tangent (function)

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