casinf, casin, casinl
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 asin( z )
(4)
(since C99)
1-3) Computes the complex arc sine of
z with branch cuts outside the interval [−1,+1] along the real axis.4) Type-generic macro: If
z has type long double complex , casinl is called. if z has type double complex , casin is called, if z has type float complex , casinf is called. If z is real or integer, then the macro invokes the corresponding real function (asinf, asin , asinl). If z is imaginary, then the macro invokes the corresponding real version of the function asinh , implementing the formula \(\small \arcsin({\rm i}y) = {\rm i}{\rm arsinh}(y)\)arcsin(iy) = i arsinh(y), and the return type of the macro is imaginary.[edit] Parameters
z
-
complex argument
[edit] Return value
If no errors occur, complex arc sine of z is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.
Errors and special cases are handled as if the operation is implemented by -I * casinh (I*z)
[edit] Notes
Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.
The mathematical definition of the principal value of arc sine is \(\small \arcsin z = -{\rm i}\ln({\rm i}z+\sqrt{1-z^2})\)arcsin z = -iln(iz + √1-z2
)
π
2
[edit] Example
Run this code
#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = casin(-2); printf ("casin(-2+0i) = %f%+fi\n", creal (z), cimag (z)); double complex z2 = casin(conj (-2)); // or CMPLX(-2, -0.0) printf ("casin(-2-0i) (the other side of the cut) = %f%+fi\n", creal (z2), cimag (z2)); // for any z, asin(z) = acos(-z) - pi/2 double pi = acos (-1); double complex z3 = csin (cacos (conj (-2))-pi/2); printf ("csin(cacos(-2-0i)-pi/2) = %f%+fi\n", creal (z3), cimag (z3)); }
Output:
casin(-2+0i) = -1.570796+1.316958i casin(-2-0i) (the other side of the cut) = -1.570796-1.316958i csin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i
[edit] References
- C11 standard (ISO/IEC 9899:2011):
- 7.3.5.2 The casin functions (p: 190)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- G.7 Type-generic math <tgmath.h> (p: 545)
- C99 standard (ISO/IEC 9899:1999):
- 7.3.5.2 The casin functions (p: 172)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- G.7 Type-generic math <tgmath.h> (p: 480)
[edit] See also
C++ documentation for asin