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在头文件<math.h>中定义



float complex       catanf( float complex z );

(1)

(since C99)

double complex      catan( double complex z );

(2)

(since C99)

long double complex catanl( long double complex z );

(3)

(since C99)

Defined in header <tgmath.h>



#define atan( z )

(4)

(since C99)

1-3)计算在z沿虚轴的间隔-i,+ i之外的分支切口的复数反正切。

4)类型 - 通用宏:如果z有类型long double complexcatanl被调用。如果z有类型double complexcatan称为,如果z有类型float complexcatanf称为。如果z是真实的或整数,则宏调用相应的实函数(atanfatanatanl)。如果z是虚构的,那么宏调用函数的相应实际版本atanh,实现公式atan(iy)= i atanh(y),并且宏的返回类型是虚构的。

参数

z

-

复杂的论点

返回值

如果没有出现错误,z则在沿虚轴无界且在-π/ 2区间内的条带范围内返回复正切正切; +π/ 2沿实轴。

错误和特殊情况被处理,就像操作被执行一样-I * catanh(I*z)

笔记

反正切(或反正切)是一种多值函数,需要在复平面上进行分支切割。通常将分支切口放置在虚轴的线段(-∞i,-i)和(+ i,+∞i)处。反正切的主值的数学定义是atan z =  -

| 1 |

|:----|

| 2 |

i ln(1 - iz) - ln (1 + iz

#include <stdio.h>#include <float.h>#include <complex.h>
 int main(void){
    double complex z = catan(2*I);    printf("catan(+0+2i) = %f%+fi\n", creal(z), cimag(z));
 
    double complex z2 = catan(-conj(2*I)); // or CMPLX(-0.0, 2)    printf("catan(-0+2i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
 
    double complex z3 = 2*catan(2*I*DBL_MAX); // or CMPLX(0, INFINITY)    printf("2*catan(+0+i*Inf) = %f%+fi\n", creal(z3), cimag(z3));}

输出:

catan(+0+2i) = 1.570796+0.549306icatan(-0+2i) (the other side of the cut) = -1.570796+0.549306i2*catan(+0+i*Inf) = 3.141593+0.000000i

参考

  • C11标准(ISO / IEC 9899:2011):

    • 7.3.5.3 catan函数(p:191)

    • 7.25类型通用数学<tgmath.h>(p:373-375)

    • G.7类型 - 通用数学<tgmath.h>(p:545)

  • C99标准(ISO / IEC 9899:1999):

    • 7.3.5.3 catan函数(p:173)

    • 7.22类型通用数学<tgmath.h>(p:335-337)

    • G.7类型 - 通用数学<tgmath.h>(p:480)

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