casinf, casin, casinl

< c‎ | numeric‎ | complex
Defined in header <complex.h>
float complex       casinf( float complex z );
(1) (since C99)
double complex      casin( double complex z );
(2) (since C99)
long double complex casinl( long double complex z );
(3) (since C99)
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 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 arcsin z = -iln(iz + 1-z2

For any z, arcsin(z) = acos(-z) -

[edit] Example

#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));


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):
  • 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):
  • 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

computes the complex arc cosine
(function) [edit]
computes the complex arc tangent
(function) [edit]
computes the complex sine
(function) [edit]
computes arc sine (arcsin(x))
(function) [edit]