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在头文件<math.h>中定义



float complex       ccoshf( float complex z );

(1)

(since C99)

double complex      ccosh( double complex z );

(2)

(since C99)

long double complex ccoshl( long double complex z );

(3)

(since C99)

Defined in header <tgmath.h>



#define cosh( z )

(4)

(since C99)

1-3）计算复数双曲余弦z。

4）类型 - 通用宏：如果z有类型long double complex，ccoshl被调用。如果z有类型double complex，ccosh称为，如果z有类型float complex，ccoshf称为。如果z是真实的或整数，则宏调用相应的实函数（coshf，cosh，coshl）。如果z是虚构的，则宏调用函数的相应实际版本cos，实现公式cosh（iy）= cos（y），并且返回类型是实数。

参数

z

-

复杂的论点

返回值

如果没有错误发生，z则返回复双曲余弦。

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，

  • ccosh(conj(z)) == conj(ccosh(z))

  • ccosh(z) == ccosh(-z)

  • 如果z是+0+0i，结果是1+0i

  • 如果z是+0+∞i，结果是NaN±0i（虚部的符号未指定）并被FE_INVALID提出

  • 如果z是+0+NaNi，结果是NaN±0i（虚数部分的符号未指定）

  • 如果z是x+∞i（对于任何有限的非零x），结果是NaN+NaNi并且FE_INVALID被提出

  • 如果z是x+NaNi（对于任何有限的非零x），结果是NaN+NaNi并且FE_INVALID可能会提高

  • 如果z是+∞+0i，结果是+∞+0i

  • 如果z是+∞+yi（对于任何有限的非零y），结果是+∞+cis(y)

  • 如果z是+∞+∞i，结果是±∞+NaNi（真实部分的符号未指定）并被FE_INVALID提出

  • 如果z是+∞+NaN，结果是+∞+NaN

  • 如果z是NaN+0i，结果是NaN±0i（虚数部分的符号未指定）

  • 如果z是NaN+yi（对于任何有限的非零y），结果是NaN+NaNi并FE_INVALID可能会提高

  • 如果z是NaN+NaNi，结果是NaN+NaNi

where cis(y) is cos(y) + i sin(y).

笔记

双曲余弦的数学定义是cosh z =

| ez+e-z |

|:----|

| 2 |

双曲余弦是复平面中的一个完整函数，并且没有分支切割。它是周期性的，相对于虚部，周期为2πi。

例

#include <stdio.h>#include <math.h>#include <complex.h>
 int main(void){
    double complex z = ccosh(1);  // behaves like real cosh along the real line    printf("cosh(1+0i) = %f%+fi (cosh(1)=%f)\n", creal(z), cimag(z), cosh(1));
 
    double complex z2 = ccosh(I); // behaves like real cosine along the imaginary line    printf("cosh(0+1i) = %f%+fi ( cos(1)=%f)\n", creal(z2), cimag(z2), cos(1));}

输出：

cosh(1+0i) = 1.543081+0.000000i (cosh(1)=1.543081)cosh(0+1i) = 0.540302+0.000000i ( cos(1)=0.540302)

参考

  • C11标准（ISO / IEC 9899：2011）：

    • 7.3.6.4 ccosh函数（p：193）

    • 7.25类型通用数学<tgmath.h>（p：373-375）

    • G.6.2.4 ccosh函数（p：541）

    • G.7类型 - 通用数学<tgmath.h>（p：545）

  • C99标准（ISO / IEC 9899：1999）：

    • 7.3.6.4 ccosh函数（p：175）

    • 7.22类型通用数学<tgmath.h>（p：335-337）

    • G.6.2.4 ccosh函数（p：476）

    • G.7类型 - 通用数学<tgmath.h>（p：480）

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