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在头文件<math.h>中定义



float complex       clogf( float complex z );

(1)

(since C99)

double complex      clog( double complex z );

(2)

(since C99)

long double complex clogl( long double complex z );

(3)

(since C99)

Defined in header <tgmath.h>



#define log( z )

(4)

(since C99)

1-3）计算沿着负实轴的分支切割的复数自然（base- e）对数z。

4）类型 - 通用宏：如果z有类型long double complex，clogl被调用。如果z有类型double complex，clog称为，如果z有类型float complex，clogf称为。如果z是真实的或整数，则宏调用相应的实函数（logf，log，logl）。如果z是虚构的，则调用相应的复数版本。

参数

z

-

复杂的论点

返回值

如果没有出现错误，则复数自然对数z返回，在沿虚轴的间隔-iπ，+iπ中的条带范围内，并且在实轴上数学上无界。

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，

  • 考虑到虚部的符号，该功能在分支切割上是连续的

  • clog(conj(z)) == conj(clog(z))

  • 如果z是-0+0i，结果是-∞+πi并且FE_DIVBYZERO被提出

  • 如果z是+0+0i，结果是-∞+0i并且FE_DIVBYZERO被提出

  • 如果z是x+∞i（对于任何有限的x），结果是+∞+πi/2

  • 如果z是x+NaNi（对于任何有限的x），结果是NaN+NaNi并FE_INVALID可能会提出

  • 如果z是-∞+yi（对于任何有限的正y），结果是-∞+πi

  • 如果z是+∞+yi（对于任何有限的正y），结果是-∞+0i

  • 如果z是-∞+∞i，结果是+∞+3πi/4

  • 如果z是+∞+∞i，结果是+∞+πi/4

  • 如果z是±∞+NaNi，结果是+∞+NaNi

  • 如果z是NaN+yi（对于任何有限的y），结果是NaN+NaNi并且FE_INVALID可能会被提出

  • 如果z是NaN+∞i，结果是+∞+NaNi

  • 如果z是NaN+NaNi，结果是NaN+NaNi

笔记

具有极坐标分量（r，θ）的复数z的自然对数等于ln r + i（θ+2nπ），其中主值ln r +iθ

例

#include <stdio.h>#include <math.h>#include <complex.h>
 int main(void){
    double complex z = clog(I); // r = 1, θ = pi/2    printf("2*log(i) = %.1f%+fi\n", creal(2*z), cimag(2*z));
 
    double complex z2 = clog(sqrt(2)/2 + sqrt(2)/2*I); // r = 1, θ = pi/4    printf("4*log(sqrt(2)/2+sqrt(2)i/2) = %.1f%+fi\n", creal(4*z2), cimag(4*z2));
 
    double complex z3 = clog(-1); // r = 1, θ = pi    printf("log(-1+0i) = %.1f%+fi\n", creal(z3), cimag(z3));
 
    double complex z4 = clog(conj(-1)); // or clog(CMPLX(-1, -0.0)) in C11    printf("log(-1-0i) (the other side of the cut) = %.1f%+fi\n", creal(z4), cimag(z4));}

输出：

2*log(i) = 0.0+3.141593i4*log(sqrt(2)/2+sqrt(2)i/2) = 0.0+3.141593ilog(-1+0i) = 0.0+3.141593ilog(-1-0i) (the other side of the cut) = 0.0-3.141593i

参考

  • C11标准（ISO / IEC 9899：2011）：

    • 7.3.7.2堵塞功能（p：195）

    • 7.25类型通用数学<tgmath.h>（p：373-375）

    • G.6.3.2堵塞功能（p：543-544）

    • G.7类型 - 通用数学<tgmath.h>（p：545）

  • C99标准（ISO / IEC 9899：1999）：

    • 7.3.7.2堵塞功能（p：176-177）

    • 7.22类型通用数学<tgmath.h>（p：335-337）

    • G.6.3.2堵塞功能（p：478-479）

    • G.7类型 - 通用数学<tgmath.h>（p：480）

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