NAME

casin, casinf, casinl — complex arc sine functions

SYNOPSIS

#include <complex.h>

double complex casin(double complex z);
float complex casinf(float complex z);
long double complex casinl(long double complex z);


DESCRIPTION

^[CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2024 defers to the ISO C standard.

These functions shall compute the complex arc sine of z, with branch cuts outside the interval [-1, +1] along the real axis.

RETURN VALUE

These functions shall return the complex arc sine value, in the range of a strip mathematically unbounded along the imaginary axis and in the interval [-ℼ/2, +ℼ/2] along the real axis.

^[MXC] casin(conj(iz)), casinf(conjf(iz)), and casinl(conjl(iz)) shall return exactly the same value as conj(casin(iz)), conjf(casinf(iz)), and conjl(casinl(iz)), respectively, and casin(-iz), casinf(-iz), and casinl(-iz) shall return exactly the same value as -casin(iz), -casinf(iz), and -casinl(iz), respectively, including for the special values of iz below.

If iz is +0 + i0, -i (0 + i0) shall be returned.

If iz is x + iInf where x is positive-signed and finite, -i (+Inf + iℼ/2) shall be returned.

If iz is x + iNaN where x is finite, -i (NaN + iNaN) shall be returned and the invalid floating-point exception may be raised.

If iz is +Inf + iy where y is positive-signed and finite, -i (+Inf + i0) shall be returned.

If iz is +Inf + iInf, -i (+Inf + iℼ/4) shall be returned.

If iz is +Inf + iNaN, -i (+Inf + iNaN) shall be returned.

If iz is NaN + i0, -i (NaN + i0) shall be returned.

If iz is NaN + iy where y is non-zero and finite, -i (NaN + iNaN) shall be returned and the invalid floating-point exception may be raised.

If iz is NaN + iInf, -i (±Inf + iNaN) shall be returned; the sign of the imaginary part of the result is unspecified.

If iz is NaN + iNaN, -i (NaN + iNaN) shall be returned.

ERRORS

No errors are defined.

EXAMPLES

None.

APPLICATION USAGE

None.

RATIONALE

The MXC special cases for casin() are derived from those for casinh() by applying the formula casin(z) = -i casinh(iz).

FUTURE DIRECTIONS

None.

SEE ALSO

casinh, csin

XBD <complex.h>

CHANGE HISTORY

First released in Issue 6. Derived from the ISO/IEC 9899:1999 standard.

Issue 8

Austin Group Defect 1302 is applied, aligning these functions with the ISO/IEC 9899:2018 standard.