csinhf, csinh, csinhl

 

C

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Concurrency support (哋它亢11)

Technical Specifications

Symbol index

 

Numerics

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)

 

Complex number arithmetic

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       csinhf( float complex z );	(1)	(since 哋它亢99)
double complex      csinh( double complex z );	(2)	(since 哋它亢99)
long double complex csinhl( long double complex z );	(3)	(since 哋它亢99)
Defined in header <tgmath.h>
#define sinh( z )	(4)	(since 哋它亢99)

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

4) Type-generic macro: If z has type long double complex, csinhl is called. if z has type double complex, csinh is called, if z has type float complex, csinhf is called. If z is real or integer, then the macro invokes the corresponding real function (sinhf, sinh, sinhl). If z is imaginary, then the macro invokes the corresponding real version of the function sin, implementing the formula sinh(iy) = i sin(y), and the return type is imaginary.

Parameters

z

-

complex argument

Return value

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

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

• csinh(conj(z)) == conj(csinh(z))
• csinh(z) == -csinh(-z)
• If z is +0+0i, the result is +0+0i
• If z is +0+∞i, the result is ±0+NaNi (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is +0+NaNi, the result is ±0+NaNi
• If z is x+∞i (for any positive finite x), the result is NaN+NaNi and FE_INVALID is raised
• If z is x+NaNi (for any positive finite 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 positive finite 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 +∞+NaNi, the result is ±∞+NaNi (the sign of the real part is unspecified)
• If z is NaN+0i, the result is NaN+0i
• If z is NaN+yi (for any finite nonzero 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 sine is sinh z =

ez -e-z

2

Hyperbolic sine 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 = csinh(1);  // behaves like real sinh along the real line
    printf("sinh(1+0i) = %f%+fi (sinh(1)=%f)\n", creal(z), cimag(z), sinh(1));
 
    double complex z2 = csinh(I); // behaves like sine along the imaginary line
    printf("sinh(0+1i) = %f%+fi ( sin(1)=%f)\n", creal(z2), cimag(z2), sin(1));
}

Output:

sinh(1+0i) = 1.175201+0.000000i (sinh(1)=1.175201)
sinh(0+1i) = 0.000000+0.841471i ( sin(1)=0.841471)

References

• 哋它亢11 standard (ISO/IEC 9899:2011):

• 7.3.6.5 The csinh functions (p: 194)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• G.6.2.5 The csinh functions (p: 541-542)

• G.7 Type-generic math <tgmath.h> (p: 545)

• 哋它亢99 standard (ISO/IEC 9899:1999):

• 7.3.6.5 The csinh functions (p: 175-176)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• G.6.2.5 The csinh functions (p: 476-477)

• G.7 Type-generic math <tgmath.h> (p: 480)

See also

ccoshccoshfccoshl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex hyperbolic cosine (function)
ctanhctanhfctanhl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex hyperbolic tangent (function)
casinhcasinhfcasinhl (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex arc hyperbolic sine (function)
sinhsinhfsinhl (哋它亢99)(哋它亢99)	computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)