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Showing content from https://en.cppreference.com/w/cpp/language/../algorithm/../../cpp/../c/numeric/complex/casin.html below:

casinf, casin, casinl - cppreference.com

(1) (since C99) (2) (since C99) (3) (since C99)

#define asin( z )

(4) (since C99)

1-3) Computes the complex arc sine of z with branch cuts outside the interval [â1,+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 [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 [âÏ/2; +Ï/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 (-â,-1) and (1,â) 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 + â1-z2 )

For any z,

\(\small{ \arcsin(z) = \arccos(-z) - \frac{\pi}{2} }\)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));
}

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

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