ccoshf, ccosh, ccoshl

 

C

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Technical Specifications

 

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

 

Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
Power and exponential functions
cexp clog	cpow csqrt
Trigonometric functions
ccos csin ctan	cacos casin catan
Hyperbolic functions
ccosh csinh ctanh	cacosh casinh catanh

 

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.

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 =

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

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

• 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)

See also

csinhcsinhfcsinhl (C99)(C99)(C99)	computes the complex hyperbolic sine (function)
ctanhctanhfctanhl (C99)(C99)(C99)	computes the complex hyperbolic tangent (function)
cacoshcacoshfcacoshl (C99)(C99)(C99)	computes the complex arc hyperbolic cosine (function)
coshcoshfcoshl (C99)(C99)	computes hyperbolic cosine (ch(x)) (function)
C++ documentation for cosh