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在头文件<math.h>中定义 | ||
|---|---|---|
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)计算复杂碱基Ë指数的z。
4)类型 - 通用宏:如果z有类型long double complex,cexpl被调用。如果z有类型double complex,cexp称为,如果z有类型float complex,cexpf称为。如果z是真实的或整数,则宏调用相应的实函数(expf,exp,expl)。如果z是虚构的,则调用相应的复杂参数版本。
z | - | 复杂的论点 |
|---|
如果没有出现错误,e提高到电源z, ez
返回。
报告的错误与math_errhandling一致。
如果实现支持IEEE浮点运算,
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 +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 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
其中cis(y)是cos(y)+ i sin(y)。
复指数函数ez
对于z = x + iy等于ex
cis(y), or, ex
(cos(y) + i sin(y)).
指数函数是复平面中的一个完整函数,并且没有分支切割。
#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)); }输出:
exp(i*pi) = -1.0+0.0i
C11标准(ISO / IEC 9899:2011):
7.3.7.1 cexp函数(p:194)
7.25类型通用数学<tgmath.h>(p:373-375)
G.6.3.1 cexp函数(p:543)
G.7类型 - 通用数学<tgmath.h>(p:545)
C99标准(ISO / IEC 9899:1999):
7.3.7.1 cexp函数(p:176)
7.22类型通用数学<tgmath.h>(p:335-337)
G.6.3.1 cexp函数(p:478)
G.7类型 - 通用数学<tgmath.h>(p:480)