csinhf, csinh, csinhl
From cppreference.com
C
Concurrency support (C11)
Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
Defined in header
<complex.h>
Defined in header
<tgmath.h>
#define sinh( z )
(4)
(since C99)
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.Contents
[edit] Parameters
z
-
complex argument
[edit] Return value
If no errors occur, complex hyperbolic sine 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,
- csinh(conj (z)) == conj (csinh(z))
- csinh(z) == -csinh(-z)
- If
zis+0+0i, the result is+0+0i - If
zis+0+∞i, the result is±0+NaNi(the sign of the real part is unspecified) and FE_INVALID is raised - If
zis+0+NaNi, the result is±0+NaNi - If
zisx+∞i(for any positive finite x), the result isNaN+NaNiand FE_INVALID is raised - If
zisx+NaNi(for any positive finite x), the result isNaN+NaNiand FE_INVALID may be raised - If
zis+∞+0i, the result is+∞+0i - If
zis+∞+yi(for any positive finite y), the result is+∞cis(y) - If
zis+∞+∞i, the result is±∞+NaNi(the sign of the real part is unspecified) and FE_INVALID is raised - If
zis+∞+NaNi, the result is±∞+NaNi(the sign of the real part is unspecified) - If
zisNaN+0i, the result isNaN+0i - If
zisNaN+yi(for any finite nonzero y), the result isNaN+NaNiand FE_INVALID may be raised - If
zisNaN+NaNi, the result isNaN+NaNi
where cis(y) is cos(y) + i sin(y)
[edit] Notes
Mathematical definition of hyperbolic sine is sinh z = ez
-e-z
-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
[edit] 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)
[edit] References
- C11 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)
- C99 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)
[edit] See also
C++ documentation for sinh