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
.
- Type-generic macro: If
z
has type long double complex,ccoshl
is called. ifz
has type double complex,ccosh
is called, ifz
has type float complex,ccoshf
is called. Ifz
is real or integer, then the macro invokes the corresponding real function (coshf, cosh, coshl). Ifz
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
- 1 Parameters
- 2 Return value
- 3 Error handling and special values
- 4 Notes
- 5 Example
- 6 References
- 7 See also
[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 is1+0i
- If
z
is+0+∞i
, the result isNaN±0i
(the sign of the imaginary part is unspecified) and FE_INVALID is raised - If
z
is+0+NaNi
, the result isNaN±0i
(the sign of the imaginary part is unspecified) - If
z
isx+∞i
(for any finite non-zero x), the result isNaN+NaNi
and FE_INVALID is raised - If
z
isx+NaNi
(for any finite non-zero x), the result isNaN+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
isNaN+0i
, the result isNaN±0i
(the sign of the imaginary part is unspecified) - If
z
isNaN+yi
(for any finite non-zero y), the result isNaN+NaNi
and FE_INVALID may be raised - If
z
isNaN+NaNi
, the result isNaN+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)