catanf, catan, catanl
From cppreference.com
C
Concurrency support (C11)
Complex number arithmetic
Types and the imaginary constant
Manipulation
Power and exponential functions
Trigonometric functions
Hyperbolic functions
Defined in header
<complex.h>
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.[edit] Parameters
z
-
complex argument
[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 [−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).
[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 (-∞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]
[edit] 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
[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
C++ documentation for atan