ccoshf, ccosh, ccoshl - cppreference.com (original) (raw)

Defined in header <complex.h>
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 <tgmath.h>
#define cosh( z ) (4) (since C99)

1-3) Computes the complex hyperbolic cosine of z.

  1. 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.

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[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,

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

[edit] See also