cacosf, cacos, cacosl - cppreference.com (original) (raw)

1-3) Computes the complex arc cosine of z with branch cuts outside the interval [−1,+1] along the real axis.

1. 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

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 References
• 7 See also

[edit] Parameters

[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 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

[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 = π + _i_ln(_i_z + √1-z2
)

For any z, acos(z) = π - acos(-z)

[edit] 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)); }

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