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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../../cpp/../c/numeric/complex/ccosh.html below:

ccoshf, ccosh, ccoshl - cppreference.com

(1) (since C99) (2) (since C99) (3) (since C99)

#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.

[edit] Parameters [edit] Return value

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

[edit] 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+âi, the result is NaNÂ±0i (the sign of the imaginary part is unspecified) and FE_INVALID is raised
If z is +0+NaNi, the result is NaNÂ±0i (the sign of the imaginary part is unspecified)
If z is x+âi (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 +â+0i, the result is +â+0i
If z is +â+yi (for any finite non-zero y), the result is +âcis(y)
If z is +â+âi, the result is Â±â+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
If z is +â+NaN, the result is +â+NaN
If z is NaN+0i, the result is NaNÂ±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)

[edit] Notes

Mathematical definition of hyperbolic cosine is

cosh z =

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

[edit] 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)

[edit] 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)

[edit] See also

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