# ccoshf, ccosh, ccoshl

< c‎ | numeric‎ | complex

C
 Language Headers Type support Program utilities Variadic function support Error handling Dynamic memory management Date and time utilities Strings library Algorithms Numerics Input/output support Localization support Atomic operations (C11) Thread support (C11) Technical Specifications

Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
 ccosh csinh ctanh

 Defined in header  float complex       ccoshf( float complex z ); (1) (since C99) double complex      ccosh( double complex z ); (2) (since C99) long double complex ccoshl( long double complex z ); (3) (since C99) Defined in header  #define cosh( z ) (4) (since C99)
1-3) Computes the complex hyperbolic cosine of z.
4) Type-generic macro: If z has type long double complex, ccoshl is called. if z has type double complex, ccosh is called, if z has type float complex, ccoshf is called. If z is real or integer, then the macro invokes the corresponding real function (coshf, cosh, coshl). If z is imaginary, then the macro invokes the corresponding real version of the function cos, implementing the formula cosh(iy) = cos(y), and the return type is real.

## Contents

### Parameters

 z - complex argument

### Return value

If no errors occur, complex hyperbolic cosine of z is returned

### Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• ccosh(conj(z)) == conj(ccosh(z))
• ccosh(z) == ccosh(-z)
• If z is +0+0i, the result is 1+0i
• If z is +0+∞i, the result is NaN±0i (the sign of the imaginary part is unspecified) and FE_INVALID is raised
• If z is +0+NaNi, the result is NaN±0i (the sign of the imaginary part is unspecified)
• If z is x+∞i (for any finite non-zero x), the result is NaN+NaNi and FE_INVALID is raised
• If z is x+NaNi (for any finite non-zero x), the result is NaN+NaNi and FE_INVALID may be raised
• If z is +∞+0i, the result is +∞+0i
• If z is +∞+yi (for any finite non-zero y), the result is +∞cis(y)
• If z is +∞+∞i, the result is ±∞+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is +∞+NaN, the result is +∞+NaN
• If z is NaN+0i, the result is NaN±0i (the sign of the imaginary part is unspecified)
• If z is NaN+yi (for any finite non-zero y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+NaNi, the result is NaN+NaNi

where cis(y) is cos(y) + i sin(y)

### Notes

Mathematical definition of hyperbolic cosine is cosh z =
 ez+e-z 2

Hyperbolic cosine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi

### Example

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

int main(void)
{
double complex z = ccosh(1);  // behaves like real cosh along the real line
printf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n", creal(z), cimag(z), cosh(1));

double complex z2 = ccosh(I); // behaves like real cosine along the imaginary line
printf("cosh(0+1i) = %f%+fi ( cos(1)=%f)\n", creal(z2), cimag(z2), cos(1));
}

Output:

cosh(1+0i) = 1.543081+0.000000i (cosh(1)=1.543081)
cosh(0+1i) = 0.540302+0.000000i ( cos(1)=0.540302)

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.3.6.4 The ccosh functions (p: 193)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• G.6.2.4 The ccosh functions (p: 541)
• G.7 Type-generic math <tgmath.h> (p: 545)
• C99 standard (ISO/IEC 9899:1999):
• 7.3.6.4 The ccosh functions (p: 175)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• G.6.2.4 The ccosh functions (p: 476)
• G.7 Type-generic math <tgmath.h> (p: 480)