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csqrtf, csqrt, csqrtl

Defined in header `<complex.h>`
float complex csqrtf( float complex z );	(1)	(since C99)
double complex csqrt( double complex z );	(2)	(since C99)
long double complex csqrtl( long double complex z );	(3)	(since C99)
Defined in header `<tgmath.h>`
#define sqrt( z )	(4)	(since C99)

1-3) Computes the complex square root of z with branch cut along the negative real axis.

4) Type-generic macro: If z has type long double complex, csqrtl is called. if z has type double complex, csqrt is called, if z has type float complex, csqrtf is called. If z is real or integer, then the macro invokes the corresponding real function (sqrtf, sqrt, sqrtl). If z is imaginary, the corresponding complex number version is called.

Parameters

complex argument

Return value

If no errors occur, returns the square root of z, in the range of the right half-plane, including the imaginary axis ([0; +∞) along the real axis and (−∞; +∞) along the imaginary axis.).

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

The function is continuous onto the branch cut taking into account the sign of imaginary part
csqrt(conj(z)) == conj(csqrt(z))
If z is ±0+0i, the result is +0+0i
If z is x+∞i, the result is +∞+∞i even if x is NaN
If z is x+NaNi, the result is NaN+NaNi (unless x is ±∞) and FE_INVALID may be raised
If z is -∞+yi, the result is +0+∞i for finite positive y
If z is +∞+yi, the result is +∞+0i) for finite positive y
If z is -∞+NaNi, the result is NaN±∞ (sign of imaginary part unspecified)
If z is +∞+NaNi, the result is +∞+NaNi
If z is NaN+yi, the result is NaN+NaNi and FE_INVALID may be raised
If z is NaN+NaNi, the result is NaN+NaNi

Example

#include <stdio.h>
#include <complex.h>
 
int main(void)
{
    double complex z1 = csqrt(-4);
    printf("Square root of -4 is %.1f%+.1fi\n", creal(z1), cimag(z1));
 
    double complex z2 = csqrt(conj(-4)); // or, in C11, CMPLX(-4, -0.0)
    printf("Square root of -4-0i, the other side of the cut, is "
           "%.1f%+.1fi\n", creal(z2), cimag(z2));
}

Output:

Square root of -4 is 0.0+2.0i
Square root of -4-0i, the other side of the cut, is 0.0-2.0i

References

C11 standard (ISO/IEC 9899:2011):

7.3.8.3 The csqrt functions (p: 196)
7.25 Type-generic math <tgmath.h> (p: 373-375)
G.6.4.2 The csqrt functions (p: 544)
G.7 Type-generic math <tgmath.h> (p: 545)

C99 standard (ISO/IEC 9899:1999):

7.3.8.3 The csqrt functions (p: 178)
7.22 Type-generic math <tgmath.h> (p: 335-337)
G.6.4.2 The csqrt functions (p: 479)
G.7 Type-generic math <tgmath.h> (p: 480)