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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 complexccoshl被调用。如果z有类型double complexccosh称为,如果z有类型float complexccoshf称为。如果z是真实的或整数,则宏调用相应的实函数(coshfcoshcoshl)。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+0+0i,结果是1+0i

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

  • 如果z+0+NaNi,结果是NaN±0i(虚数部分的符号未指定)

  • 如果zx+∞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zx+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+∞+0i,结果是+∞+0i

  • 如果z+∞+yi(对于任何有限的非零y),结果是+∞+cis(y)

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

  • 如果z+∞+NaN,结果是+∞+NaN

  • 如果zNaN+0i,结果是NaN±0i(虚数部分的符号未指定)

  • 如果zNaN+yi(对于任何有限的非零y),结果是NaN+NaNiFE_INVALID可能会提高

  • 如果zNaN+NaNi,结果是NaN+NaNi

其中cis(y)是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。

#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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