cexpf, cexp, cexpl

 

C

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Technical Specifications

Symbol index

 

Numerics

Common mathematical functions

Floating-point environment (C99)

Pseudo-random number generation

Complex number arithmetic (C99)

Type-generic math (C99)

 

Complex number arithmetic

Types and the imaginary constant
complex (C99) _Complex_I (C99)     CMPLX (C11)	imaginary (C99) _Imaginary_I (C99) I (C99)
Manipulation
cimag (C99) creal (C99) carg (C99)	cabs (C99) conj (C99) cproj (C99)
Power and exponential functions
cexp (C99) clog (C99)	cpow (C99) csqrt (C99)
Trigonometric functions
ccos (C99) csin (C99) ctan (C99)	cacos (C99) casin (C99) catan (C99)
Hyperbolic functions
ccosh (C99) csinh (C99) ctanh (C99)	cacosh (C99) casinh (C99) catanh (C99)

 

Defined in header <complex.h>
float complex       cexpf( float complex z );	(1)	(since C99)
double complex      cexp( double complex z );	(2)	(since C99)
long double complex cexpl( long double complex z );	(3)	(since C99)
Defined in header <tgmath.h>
#define exp( z )	(4)	(since C99)

1-3) Computes the complex base-e exponential of z.

4) Type-generic macro: If z has type long double complex, cexpl is called. if z has type double complex, cexp is called, if z has type float complex, cexpf is called. If z is real or integer, then the macro invokes the corresponding real function (expf, exp, expl). If z is imaginary, the corresponding complex argument version is called.

Parameters

z

-

complex argument

Return value

If no errors occur, e raised to the power of z, \(\small e^z\)ez is returned.

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• cexp(conj(z)) == conj(cexp(z))
• If z is ±0+0i, the result is 1+0i
• If z is x+∞i (for any finite x), the result is NaN+NaNi and FE_INVALID is raised.
• If z is x+NaNi (for any finite x), the result is NaN+NaNi and FE_INVALID may be raised.
• If z is +∞+0i, the result is +∞+0i
• If z is -∞+yi (for any finite y), the result is +0cis(y)
• If z is +∞+yi (for any finite nonzero y), the result is +∞cis(y)
• If z is -∞+∞i, the result is ±0±0i (signs are unspecified)
• If z is +∞+∞i, the result is ±∞+NaNi and FE_INVALID is raised (the sign of the real part is unspecified)
• If z is -∞+NaNi, the result is ±0±0i (signs are unspecified)
• If z is +∞+NaNi, the result is ±∞+NaNi (the sign of the real part is unspecified)
• If z is NaN+0i, the result is NaN+0i
• If z is NaN+yi (for any nonzero y), the result is NaN+NaNi and FE_INVALID may be raised
• If z is NaN+NaNi, the result is NaN+NaNi

where \(\small{\rm cis}(y)\)cis(y) is \(\small \cos(y)+{\rm i}\sin(y)\)cos(y) + i sin(y)

Notes

The complex exponential function \(\small e^z\)ez for \(\small z = x + {\rm i}y\)z = x+iy equals \(\small e^x {\rm cis}(y)\)ex cis(y), or, \(\small e^x (\cos(y)+{\rm i}\sin(y))\)ex (cos(y) + i sin(y))

The exponential function is an entire function in the complex plane and has no branch cuts.

Example

Run this code

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    double PI = acos(-1);
    double complex z = cexp(I * PI); // Euler's formula
    printf("exp(i*pi) = %.1f%+.1fi\n", creal(z), cimag(z));
 
}

Output:

exp(i*pi) = -1.0+0.0i

References

• C11 standard (ISO/IEC 9899:2011):

• 7.3.7.1 The cexp functions (p: 194)

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

• G.6.3.1 The cexp functions (p: 543)

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

• C99 standard (ISO/IEC 9899:1999):

• 7.3.7.1 The cexp functions (p: 176)

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

• G.6.3.1 The cexp functions (p: 478)

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

See also

clogclogfclogl (C99)(C99)(C99)	computes the complex natural logarithm (function)
expexpfexpl (C99)(C99)	computes e raised to the given power (\({\small e^x}\)ex) (function)
C++ documentation for exp