csqrtf, csqrt, csqrtl - cppreference.com (original) (raw)

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

1. 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.

Contents

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

[edit] Parameters

[edit] 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.)

[edit] 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±∞i (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

[edit] 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

[edit] 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)

[edit] See also