/C

# catanf, catan, catanl

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)`.

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

```#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```
• 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

 casincasinfcasinl (C99)(C99)(C99) computes the complex arc sine (function) cacoscacosfcacosl (C99)(C99)(C99) computes the complex arc cosine (function) ctanctanfctanl (C99)(C99)(C99) computes the complex tangent (function) atanatanfatanl (C99)(C99) computes arc tangent (arctan(x)) (function)

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