cexpf, cexp, cexpl
From cppreference.com
| Defined in header <complex.h>
|
||
| (1) | (since C99) | |
| (2) | (since C99) | |
| (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.Contents |
[edit] Parameters
| z | - | complex argument |
[edit] Return value
If no errors occur, e raised to the power of z, ez
is returned.
[edit] 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
zis±0+0i, the result is1+0i - If
zisx+∞i(for any finite x), the result isNaN+NaNiand FE_INVALID is raised. - If
zisx+NaNi(for any finite x), the result isNaN+NaNiand FE_INVALID may be raised. - If
zis+∞+0i, the result is+∞+0i - If
zis-∞+yi(for any finite y), the result is+0+cis(y) - If
zis+∞+yi(for any finite nonzero y), the result is+∞+cis(y) - If
zis-∞+∞i, the result is±0±0i(signs are unspecified) - If
zis+∞+∞i, the result is±∞+NaNiand FE_INVALID is raised (the sign of the real part is unspecified) - If
zis-∞+NaNi, the result is±0±0i(signs are unspecified) - If
zis+∞+NaNi, the result is±∞+NaNi(the sign of the real part is unspecified) - If
zisNaN+0i, the result isNaN+0i - If
zisNaN+yi(for any nonzero y), the result isNaN+NaNiand FE_INVALID may be raised - If
zisNaN+NaNi, the result isNaN+NaNi
where cis(y) is cos(y) + i sin(y)
[edit] Notes
The complex exponential function ez
for z = x+iy equals to ex
cis(y), or, ex
(cos(y) + i sin(y))
The exponential function is an entire function in the complex plane and has no branch cuts.
[edit] Example
Run this code
Output:
exp(i*pi) = -1.0+0.0i
[edit] 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)
[edit] See also
| (C99)(C99)(C99) |
computes the complex natural logarithm (function) |
| (C99)(C99) |
computes e raised to the given power (ex) (function) |
| C++ documentation for exp
| |