cacosf, cacos, cacosl
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 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.Parameters
z | - | complex argument |
Return value
If no errors occur, complex arc cosine of z
is returned, in the range [0 ; ∞) along the real axis and in the range [−iπ ; iπ] along the imaginary axis.
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
z
is±0+0i
, the result isπ/2-0i
- If
z
is±0+NaNi
, the result isπ/2+NaNi
- If
z
isx+∞i
(for any finite x), the result isπ/2-∞i
- If
z
isx+NaNi
(for any nonzero finite x), the result isNaN+NaNi
and FE_INVALID may be raised. - If
z
is-∞+yi
(for any positive finite y), the result isπ-∞i
- If
z
is+∞+yi
(for any positive finite y), the result is+0-∞i
- If
z
is-∞+∞i
, the result is3π/4-∞i
- If
z
is+∞+∞i
, the result isπ/4-∞i
- If
z
is±∞+NaNi
, the result isNaN±∞i
(the sign of the imaginary part is unspecified) - If
z
isNaN+yi
(for any finite y), the result isNaN+NaNi
and FE_INVALID may be raised - If
z
isNaN+∞i
, the result isNaN-∞i
- If
z
isNaN+NaNi
, the result isNaN+NaNi
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 |
)
For any z, acos(z) = π - acos(-z)
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
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)
See also
(C99)(C99)(C99) |
computes the complex arc sine (function) |
(C99)(C99)(C99) |
computes the complex arc tangent (function) |
(C99)(C99)(C99) |
computes the complex cosine (function) |
(C99)(C99) |
computes arc cosine (arccos(x)) (function) |