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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。

参数

z

-

复杂的论点

返回值

如果没有出现错误，e提高到电源z， ez

返回。

错误处理和特殊值

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）。

Notes

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。

例

#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

参考

  • 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）

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