catanf, catan, catanl
From cppreference.com
Defined in header
<complex.h>
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(1) | (since C99) | |
(2) | (since C99) | |
(3) | (since C99) | |
Defined in header
<tgmath.h>
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#define atan( z )
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(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.
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[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 |
[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):
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- 7.3.5.3 The catan functions (p: 191)
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- 7.25 Type-generic math <tgmath.h> (p: 373-375)
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- G.7 Type-generic math <tgmath.h> (p: 545)
- C99 standard (ISO/IEC 9899:1999):
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- 7.3.5.3 The catan functions (p: 173)
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- 7.22 Type-generic math <tgmath.h> (p: 335-337)
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- G.7 Type-generic math <tgmath.h> (p: 480)
[edit] See also
(C99)(C99)(C99)
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computes the complex arc sine (function) |
(C99)(C99)(C99)
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computes the complex arc cosine (function) |
(C99)(C99)(C99)
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computes the complex tangent (function) |
(C99)(C99)
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computes arc tangent (arctan(x)) (function) |
C++ documentation for atan
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