cacosf

float complex       cacosf( float complex z );

double complex      cacos( double complex z );

long double complex cacosl( long double complex z );

#define acos( z )

Parameters

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 is π/2-0i
• If z is ±0+NaNi, the result is π/2+NaNi
• If z is x+∞i (for any finite x), the result is π/2-∞i
• If z is x+NaNi (for any nonzero finite x), the result is NaN+NaNi and FE_INVALID may be raised.
• If z is -∞+yi (for any positive finite y), the result is π-∞i
• If z is -∞+yi (for any positive finite y), the result is +0-∞i
• If z is -∞+∞i, the result is 3π/4-∞i
• If z is +∞+∞i, the result is π/4-∞i
• If z is ±∞+NaNi, the result is NaN±∞i (the sign of the imaginary part is unspecified)
• If z is NaN+yi (for any finite y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+∞i, the result is NaN-∞i
• If z is NaN+NaNi, the result is NaN+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 =

π + iln(iz + √1-z2
)

For any z, acos(z) = π - acos(-z).

Example

#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));
}

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