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

cacosf, cacos, cacosl - cppreference.com

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

#define acos( z )

(4) (since C99)

1-3) Computes the complex arc cosine 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

cacosl

is called. if

z

has type

double complex

cacos

is called, if

z

has type

float complex

cacosf

is called. If

z

is real or integer, then the macro invokes the corresponding real function (

acosf

acos

acosl

). If

z

is imaginary, then the macro invokes the corresponding complex number version.

[edit] Parameters [edit] Return value

If no errors occur, complex arc cosine of z is returned, in the range a strip unbounded along the imaginary axis and in the interval [0; Ï] along the real axis.

[edit] Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

cacos(conj(z)) == conj(cacos(z))
If z is Â±0+0i, the result is Ï/2-0i
If z is Â±0+NaNi, the result is Ï/2+NaNi
If z is x+âi (for any finite x), the result is Ï/2-âi
If z is x+NaNi (for any nonzero finite x), the result is NaN+NaNi and FE_INVALID may be raised.
If z is -â+yi (for any positive finite y), the result is Ï-âi
If z is +â+yi (for any positive finite y), the result is +0-âi
If z is -â+âi, the result is 3Ï/4-âi
If z is +â+âi, the result is Ï/4-âi
If z is Â±â+NaNi, the result is NaNÂ±âi (the sign of the imaginary part is unspecified)
If z is NaN+yi (for any finite y), the result is NaN+NaNi and FE_INVALID may be raised
If z is NaN+âi, the result is NaN-âi
If z is NaN+NaNi, the result is NaN+NaNi

[edit] Notes

Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventially placed at the line segments (-â,-1) and (1,â) of the real axis.

The mathematical definition of the principal value of arc cosine is

acos z = Ï + iln(iz + â1-z2 )

For any z, acos(z) = Ï - acos(-z)

[edit] Example

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    double complex z = cacos(-2);
    printf("cacos(-2+0i) = %f%+fi\n", creal(z), cimag(z));
 
    double complex z2 = cacos(conj(-2)); // or CMPLX(-2, -0.0)
    printf("cacos(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
 
    // for any z, acos(z) = pi - acos(-z)
    double pi = acos(-1);
    double complex z3 = ccos(pi-z2);
    printf("ccos(pi - cacos(-2-0i) = %f%+fi\n", creal(z3), cimag(z3));
}

Output:

cacos(-2+0i) = 3.141593-1.316958i
cacos(-2-0i) (the other side of the cut) = 3.141593+1.316958i
ccos(pi - cacos(-2-0i) = 2.000000+0.000000i

[edit] References

C11 standard (ISO/IEC 9899:2011):

7.3.5.1 The cacos functions (p: 190)

7.25 Type-generic math <tgmath.h> (p: 373-375)

G.6.1.1 The cacos functions (p: 539)

G.7 Type-generic math <tgmath.h> (p: 545)

C99 standard (ISO/IEC 9899:1999):

7.3.5.1 The cacos functions (p: 172)

7.22 Type-generic math <tgmath.h> (p: 335-337)

G.6.1.1 The cacos functions (p: 474)

G.7 Type-generic math <tgmath.h> (p: 480)

[edit] See also

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