csinhf, csinh, csinhl - cppreference.com (original) (raw)

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

1. 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

• 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 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 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)

[edit] Notes

Mathematical definition of hyperbolic sine is sinh z =

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

#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