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

catanf, catan, catanl - cppreference.com

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

#define atan( z )

(4) (since C99)

1-3) Computes the complex arc tangent of z with branch cuts outside the interval [âi,+i] along the imaginary axis.

4)

Type-generic macro: If

z

has type

long double complex

catanl

is called. if

z

has type

double complex

catan

is called, if

z

has type

float complex

catanf

is called. If

z

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

atanf

atan

atanl

). If

z

is imaginary, then the macro invokes the corresponding real version of the function

atanh

, implementing the formula

atan(iy) = i atanh(y)

, and the return type of the macro is imaginary.

[edit] Parameters [edit] Return value

If no errors occur, complex arc tangent 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 * catanh(I*z).

[edit] Notes

Inverse tangent (or arc tangent) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-âi,-i) and (+i,+âi) of the imaginary axis.

The mathematical definition of the principal value of inverse tangent is

atan z = - i [ln(1 - iz) - ln (1 + iz] [edit] Example

#include <stdio.h>
#include <float.h>
#include <complex.h>
 
int main(void)
{
    double complex z = catan(2*I);
    printf("catan(+0+2i) = %f%+fi\n", creal(z), cimag(z));
 
    double complex z2 = catan(-conj(2*I)); // or CMPLX(-0.0, 2)
    printf("catan(-0+2i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
 
    double complex z3 = 2*catan(2*I*DBL_MAX); // or CMPLX(0, INFINITY)
    printf("2*catan(+0+i*Inf) = %f%+fi\n", creal(z3), cimag(z3));
}

Output:

catan(+0+2i) = 1.570796+0.549306i
catan(-0+2i) (the other side of the cut) = -1.570796+0.549306i
2*catan(+0+i*Inf) = 3.141593+0.000000i

[edit] References

C11 standard (ISO/IEC 9899:2011):

7.3.5.3 The catan functions (p: 191)

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):

7.3.5.3 The catan functions (p: 173)

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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