From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fcomplex%2Fcatan.html | 56 ++++++++++++++++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 devdocs/c/numeric%2Fcomplex%2Fcatan.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcatan.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcatan.html b/devdocs/c/numeric%2Fcomplex%2Fcatan.html new file mode 100644 index 00000000..c74f6eef --- /dev/null +++ b/devdocs/c/numeric%2Fcomplex%2Fcatan.html @@ -0,0 +1,56 @@ +

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).

+

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

#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

See also

+ + + + +
+
(C99)(C99)(C99)
 computes the complex arc sine
(function)
+
(C99)(C99)(C99)
 computes the complex arc cosine
(function)
+
(C99)(C99)(C99)
 computes the complex tangent
(function)
+
(C99)(C99)
 computes arc tangent (\({\small\arctan{x} }\)arctan(x))
(function)
C++ documentation for atan
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/complex/catan +

+
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