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
z | - | 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
isx+∞i
, the result is+∞+∞i
even if x is NaN - If
z
isx+NaNi
, the result isNaN+NaNi
(unless x is ±∞) andFE_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 isNaN±∞i
(sign of imaginary part unspecified) - If
z
is+∞+NaNi
, the result is+∞+NaNi
- If
z
isNaN+yi
, the result isNaN+NaNi
andFE_INVALID
may be raised - If
z
isNaN+NaNi
, the result isNaN+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)
See also
(C99)(C99)(C99) | computes the complex power function (function) |
(C99)(C99) | computes square root (√x) (function) |
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