ccoshf, ccosh, ccoshl

Types and the imaginary constant

complex (哋它亢99)
_Complex_I (哋它亢99)
CMPLX (哋它亢11)

imaginary (哋它亢99)
_Imaginary_I (哋它亢99)
I (哋它亢99)

Manipulation

cimag (哋它亢99)
creal (哋它亢99)
carg (哋它亢99)

cabs (哋它亢99)
conj (哋它亢99)
cproj (哋它亢99)

Power and exponential functions

cexp (哋它亢99)
clog (哋它亢99)

cpow (哋它亢99)
csqrt (哋它亢99)

Trigonometric functions

ccos (哋它亢99)
csin (哋它亢99)
ctan (哋它亢99)

cacos (哋它亢99)
casin (哋它亢99)
catan (哋它亢99)

Hyperbolic functions

ccosh (哋它亢99)
csinh (哋它亢99)
ctanh (哋它亢99)

cacosh (哋它亢99)
casinh (哋它亢99)
catanh (哋它亢99)

Defined in header `<complex.h>`
float complex ccoshf( float complex z );	(1)	(since 哋它亢99)
double complex ccosh( double complex z );	(2)	(since 哋它亢99)
long double complex ccoshl( long double complex z );	(3)	(since 哋它亢99)
Defined in header `<tgmath.h>`
#define cosh( z )	(4)	(since 哋它亢99)

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.

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 = e z +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

Run this code

#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

哋它亢11 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)

哋它亢99 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)

Language
Headers
Type support
Program utilities
Variadic function support
Error handling
Dynamic memory management
Strings library
Algorithms
Numerics
Date and time utilities
Input/output support
Localization support
Concurrency support (哋它亢11)
Technical Specifications
Symbol index

Common mathematical functions
Floating-point environment (哋它亢99)
Pseudo-random number generation
Complex number arithmetic (哋它亢99)
Type-generic math (哋它亢99)

csinhcsinhfcsinhl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex hyperbolic sine (function)
ctanhctanhfctanhl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex hyperbolic tangent (function)
cacoshcacoshfcacoshl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex arc hyperbolic cosine (function)
coshcoshfcoshl (哋它亢99)(哋它亢99)	computes hyperbolic cosine (\({\small\cosh{x} }\) $cosh(x)$ ) (function)