# catanf, catan, catanl

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< c‎ | numeric‎ | complex

Defined in header `<complex.h>` |  |
float complex catanf( float complex z ); | (1) | (since C99)
double complex catan( double complex z ); | (2) | (since C99)
long double complex catanl( long double complex z ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define atan( z ) | (4) | (since C99)

1-3) Computes the complex arc tangent of `z` with branch cuts outside the interval [−i,+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.

### Parameters

z | - | complex argument

### 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 [−π/2; +π/2] along the real axis.

Errors and special cases are handled as if the operation is implemented by -I * catanh(I*z).

### 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 (-∞i,-i) and (+i,+∞i) of the imaginary axis.

The mathematical definition of the principal value of inverse tangent is atan z = -

1
2

i [ln(1 - iz) - ln (1 + iz]

### Example

Run this code

    #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

### 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)

### See also

casin casinf casinl (C99)(C99)(C99) | computes the complex arc sine (function)
cacos cacosf cacosl (C99)(C99)(C99) | computes the complex arc cosine (function)
ctan ctanf ctanl (C99)(C99)(C99) | computes the complex tangent (function)
atan atanf atanl (C99)(C99) | computes arc tangent (arctan(x)) (function)

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