catanf, catan, catanl

C

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Technical Specifications

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
Power and exponential functions
cexp clog	cpow csqrt
Trigonometric functions
ccos csin ctan	cacos casin catan
Hyperbolic functions
ccosh csinh ctanh	cacosh casinh catanh

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 [/2; +/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

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)