cexpf, cexp, cexpl
From cppreference.com
Defined in header
<complex.h>
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(1) | (since C99) | |
(2) | (since C99) | |
(3) | (since C99) | |
Defined in header
<tgmath.h>
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#define exp( z )
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(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
z
is±0+0i
, the result is1+0i
- If
z
isx+∞i
(for any finite x), the result isNaN+NaNi
and FE_INVALID is raised. - If
z
isx+NaNi
(for any finite x), the result isNaN+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+0+cis(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
isNaN+0i
, the result isNaN+0i
- If
z
isNaN+yi
(for any nonzero y), the result isNaN+NaNi
and FE_INVALID may be raised - If
z
isNaN+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):
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- 7.3.7.1 The cexp functions (p: 194)
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- 7.25 Type-generic math <tgmath.h> (p: 373-375)
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- G.6.3.1 The cexp functions (p: 543)
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- 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)
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- G.6.3.1 The cexp functions (p: 478)
-
- G.7 Type-generic math <tgmath.h> (p: 480)
[edit] See also
(C99)(C99)(C99)
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computes the complex natural logarithm (function) |
(C99)(C99)
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computes e raised to the given power (ex) (function) |
C++ documentation for exp
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