amath  1.8.5
Simple command line calculator
cacot.c
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1 /*-
2  * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
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29 
30 #include "prim.h"
31 
32 /**
33  * @brief Inverse cotangent of complex number
34  * @details
35  * Inverse cotangent expressed using complex logarithms:
36  * <pre>
37  * arccot z = i/2 * (log(1 - i/z) - log(1 + i/z))
38  * </pre>
39  * More info is available at Wikipedia: <BR>
40  * https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
41  */
42 complex cacot(complex z)
43 {
44  complex one = cpack(1.0, 0.0);
45  complex two = cpack(2.0, 0.0);
46  complex i = cpack(0.0, 1.0);
47  complex iz = cdiv(i, z);
48  complex p = clog(csub(one, iz));
49  complex q = clog(cadd(one, iz));
50  complex w = cmul(cdiv(i, two), csub(p, q));
51  return w;
52 }
complex clog(complex z)
Natural logarithm of a complex number.
Definition: clog.c:42
complex csub(complex a, complex z)
Subtraction of two complex numbers.
Definition: prim.c:130
complex cadd(complex a, complex z)
Addition of two complex numbers.
Definition: prim.c:120
complex cdiv(complex a, complex z)
Division of two complex numbers.
Definition: prim.c:159
complex cpack(double x, double y)
Pack two real numbers into a complex number.
Definition: prim.c:68
complex cmul(complex a, complex z)
Multiplication of two complex numbers.
Definition: prim.c:140
complex cacot(complex z)
Inverse cotangent of complex number.
Definition: cacot.c:42