cexpf, cexp, cexpl

 

C

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Variadic function support

Error handling

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Strings library

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Numerics

Date and time utilities

Input/output support

Localization support

Concurrency support (哋它亢11)

Technical Specifications

Symbol index

 

Numerics

Common mathematical functions

Floating-point environment (哋它亢99)

Pseudo-random number generation

Complex number arithmetic (哋它亢99)

Type-generic math (哋它亢99)

 

Complex number arithmetic

Types and the imaginary constant
complex (哋它亢99) _Complex_I (哋它亢99)     CMPLX (哋它亢11)	imaginary (哋它亢99) _Imaginary_I (哋它亢99) I (哋它亢99)
Manipulation
cimag (哋它亢99) creal (哋它亢99) carg (哋它亢99)	cabs (哋它亢99) conj (哋它亢99) cproj (哋它亢99)
Power and exponential functions
cexp (哋它亢99) clog (哋它亢99)	cpow (哋它亢99) csqrt (哋它亢99)
Trigonometric functions
ccos (哋它亢99) csin (哋它亢99) ctan (哋它亢99)	cacos (哋它亢99) casin (哋它亢99) catan (哋它亢99)
Hyperbolic functions
ccosh (哋它亢99) csinh (哋它亢99) ctanh (哋它亢99)	cacosh (哋它亢99) casinh (哋它亢99) catanh (哋它亢99)

 

Defined in header <complex.h>
float complex       cexpf( float complex z );	(1)	(since 哋它亢99)
double complex      cexp( double complex z );	(2)	(since 哋它亢99)
long double complex cexpl( long double complex z );	(3)	(since 哋它亢99)
Defined in header <tgmath.h>
#define exp( z )	(4)	(since 哋它亢99)

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

• 哋它亢11 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)

• 哋它亢99 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 (哋它亢99)(哋它亢99)(哋它亢99)	computes the complex natural logarithm (function)
expexpfexpl (哋它亢99)(哋它亢99)	computes e raised to the given power (\({\small e^x}\)ex) (function)