cpowf, cpow, cpowl

C

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Type support

Program utilities

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Error handling

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Input/output support

Localization support

Atomic operations (C11)

Thread support (C11)

Technical Specifications

Numerics

Common mathematical functions

Floating-point environment

Complex number arithmetics

Random number generation

Type-generic math

Complex number arithmetic

Types and the imaginary constant
complex _Complex_I CMPLX	imaginary _Imaginary_I I
Manipulation
cimag creal carg	cabs conj cproj
Power and exponential functions
cexp clog	cpow csqrt
Trigonometric functions
ccos csin ctan	cacos casin catan
Hyperbolic functions
ccosh csinh ctanh	cacosh casinh catanh

Defined in header <complex.h>
float complex cpowf( float complex x, float complex y );	(1)	(since C99)
double complex cpow( double complex x, double complex y );	(2)	(since C99)
long double complex cpowl( long double complex x, long double complex y );	(3)	(since C99)
Defined in header <tgmath.h>
#define pow( x, y )	(4)	(since C99)

1-3) Computes the complex power function xy
, with branch cut for the first parameter along the negative real axis.

4) Type-generic macro: If any argument has type long double complex, cpowl is called. if any argument has type double complex, cpow is called, if any argument has type float complex, cpowf is called. If the arguments are real or integer, then the macro invokes the corresponding real function (powf, pow, powl). If any argument is imaginary, the corresponding complex number version is called.

Parameters

x, y

-

complex argument

Return value

If no errors occur, the complex power xy
, is returned.

Errors and special cases are handled as if the operation is implemented by cexp(y*clog(x)), except that the implementation is allowed to treat special cases more carefully.

Example

Run this code

#include <stdio.h>
#include <complex.h>

int main(void)
{    
    double complex z = cpow(1.0+2.0*I, 2);
    printf("(1+2i)^2 =%.1f%+.1fi\n", creal(z), cimag(z));

    double complex z2 = cpow(-1, 0.5);
    printf("(-1+0i)^0.5 =%.1f%+.1fi\n", creal(z2), cimag(z2));

    double complex z3 = cpow(conj(-1), 0.5); // other side of the cut
    printf("(-1-0i)^0.5 =%.1f%+.1fi\n", creal(z3), cimag(z3));

    double complex z4 = cpow(I, I); // i^i = exp(-pi/2)
    printf("i^i =%f%+fi\n", creal(z4), cimag(z4));
}

Output:

(1+2i)^2 = -3.0+4.0i
(-1+0i)^0.5 = 0.0+1.0i
(-1-0i)^0.5 = 0.0-1.0i
i^i = 0.207880+0.000000i

References

• C11 standard (ISO/IEC 9899:2011):

• 7.3.8.2 The cpow functions (p: 195-196)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• G.6.4.1 The cpow functions (p: 544)

• G.7 Type-generic math <tgmath.h> (p: 545)

• C99 standard (ISO/IEC 9899:1999):

• 7.3.8.2 The cpow functions (p: 177)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• G.6.4.1 The cpow functions (p: 479)

• G.7 Type-generic math <tgmath.h> (p: 480)

See also

csqrtcsqrtfcsqrtl (C99)(C99)(C99)	computes the complex square root (function)
powpowfpowl (C99)(C99)	computes a number raised to the given power (xy) (function)