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在头文件<math.h>中定义



float complex       cacosf( float complex z );

(1)

(since C99)

double complex      cacos( double complex z );

(2)

(since C99)

long double complex cacosl( long double complex z );

(3)

(since C99)

Defined in header <tgmath.h>



#define acos( z )

(4)

(since C99)

1-3）z沿实轴计算在区间-1，+ 1之外的分支切口的复余弦余弦。

4）类型 - 通用宏：如果z有类型long double complex，cacosl被调用。如果z有类型double complex，cacos称为，如果z有类型float complex，cacosf称为。如果z是真实的或整数，则宏调用相应的实函数（acosf，acos，acosl）。如果z是虚构的，则宏调用相应的复数版本。

参数

z

-

复杂的论点

返回值

如果没有发生错误，z则返回复余弦反射余弦值，范围为[0; ∞）沿实轴和在范围- 我 π; i沿虚轴。

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，

  • cacos(conj(z)) == conj(cacos(z))

  • 如果z是±0+0i，结果是π/2-0i

  • 如果z是±0+NaNi，结果是π/2+NaNi

  • 如果z是x+∞i（对于任何有限的x），结果是π/2-∞i

  • 如果z是x+NaNi（对于任何非零有限x），结果是NaN+NaNi并且FE_INVALID可能会提出。

  • 如果z是-∞+yi（对于任何有限的y），结果是π-∞i

  • 如果z是-∞+yi（对于任何有限的y），结果是+0-∞i

  • 如果z是-∞+∞i，结果是3π/4-∞i

  • 如果z是+∞+∞i，结果是π/4-∞i

  • 如果z是±∞+NaNi，结果是NaN±∞i（虚数部分的符号未指定）

  • 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NaN-∞i

  • 如果z是NaN+NaNi，结果是NaN+NaNi

笔记

逆余弦（或反余弦）是一种多值函数，需要在复平面上进行分支切分。分支切口通常位于实轴的线段（-∞，-1）和（1，∞）处。反余弦主值的数学定义为acos z =

| 1 |

|:----|

| 2 |

π + _i_ln(_i_z + √1-z2

)

对于任何一个，acos（z）=π -  acos（-z）。

例

#include <stdio.h>#include <math.h>#include <complex.h>
 int main(void){
    double complex z = cacos(-2);    printf("cacos(-2+0i) = %f%+fi\n", creal(z), cimag(z));
 
    double complex z2 = cacos(conj(-2)); // or CMPLX(-2, -0.0)    printf("cacos(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2)); 
    // for any z, acos(z) = pi - acos(-z)
    double pi = acos(-1);
    double complex z3 = ccos(pi-z2);    printf("ccos(pi - cacos(-2-0i) = %f%+fi\n", creal(z3), cimag(z3));}

输出：

cacos(-2+0i) = 3.141593-1.316958icacos(-2-0i) (the other side of the cut) = 3.141593+1.316958iccos(pi - cacos(-2-0i) = 2.000000+0.000000i

参考

在头文件<math.h>中定义



float complex       cacoshf( float complex z );

(1)

(since C99)

double complex      cacosh( double complex z );

(2)

(since C99)

long double complex cacoshl( long double complex z );

(3)

(since C99)

Defined in header <tgmath.h>



#define acosh( z )

(4)

(since C99)

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