cacosf, cacos, cacosl
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 acos( z )
(4)
(since C99)
1-3) Computes the complex arc cosine of
z with branch cuts outside the interval [−1,+1] along the real axis.4) Type-generic macro: If
z has type long double complex , cacosl is called. if z has type double complex , cacos is called, if z has type float complex , cacosf is called. If z is real or integer, then the macro invokes the corresponding real function (acosf, acos , acosl). If z is imaginary, then the macro invokes the corresponding complex number version.Contents
[edit] Parameters
z
-
complex argument
[edit] Return value
If no errors occur, complex arc cosine of z is returned, in the range a strip unbounded along the imaginary axis and in the interval [0; π] along the real axis.
[edit] Error handling and special values
Errors are reported consistent with math_errhandling.
If the implementation supports IEEE floating-point arithmetic,
- cacos(conj (z)) == conj (cacos(z))
- If
zis±0+0i, the result isπ/2-0i - If
zis±0+NaNi, the result isπ/2+NaNi - If
zisx+∞i(for any finite x), the result isπ/2-∞i - If
zisx+NaNi(for any nonzero finite x), the result isNaN+NaNiand FE_INVALID may be raised. - If
zis-∞+yi(for any positive finite y), the result isπ-∞i - If
zis+∞+yi(for any positive finite y), the result is+0-∞i - If
zis-∞+∞i, the result is3π/4-∞i - If
zis+∞+∞i, the result isπ/4-∞i - If
zis±∞+NaNi, the result isNaN±∞i(the sign of the imaginary part is unspecified) - If
zisNaN+yi(for any finite y), the result isNaN+NaNiand FE_INVALID may be raised - If
zisNaN+∞i, the result isNaN-∞i - If
zisNaN+NaNi, the result isNaN+NaNi
[edit] Notes
Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventially placed at the line segments (-∞,-1) and (1,∞) of the real axis.
The mathematical definition of the principal value of arc cosine is acos z = 1
2
π + iln(iz + √1-z2)
For any z, acos(z) = π - acos(-z)
[edit] Example
Run this code
#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = cacos(-2); printf ("cacos(-2+0i) = %f%+fi\n", creal (z), cimag (z)); double complex z2 = cacos(conj (-2)); // or CMPLX(-2, -0.0) printf ("cacos(-2-0i) (the other side of the cut) = %f%+fi\n", creal (z2), cimag (z2)); // for any z, acos(z) = pi - acos(-z) double pi = acos (-1); double complex z3 = ccos (pi-z2); printf ("ccos(pi - cacos(-2-0i) = %f%+fi\n", creal (z3), cimag (z3)); }
Output:
cacos(-2+0i) = 3.141593-1.316958i cacos(-2-0i) (the other side of the cut) = 3.141593+1.316958i ccos(pi - cacos(-2-0i) = 2.000000+0.000000i
[edit] References
- C11 standard (ISO/IEC 9899:2011):
- 7.3.5.1 The cacos functions (p: 190)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- G.6.1.1 The cacos functions (p: 539)
- G.7 Type-generic math <tgmath.h> (p: 545)
- C99 standard (ISO/IEC 9899:1999):
- 7.3.5.1 The cacos functions (p: 172)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- G.6.1.1 The cacos functions (p: 474)
- G.7 Type-generic math <tgmath.h> (p: 480)
[edit] See also
C++ documentation for acos