如何使用计算反正切arc？实现示例

本文概述

• C
• C
• C

什么是反正切？

反正切是切线函数的反函数。它返回切线为给定数字的角度。

catan()是一个内置函数<complex.h>头文件, 返回复杂反正切(或反正切)任何常数, 它根据闭合区间中的反正切线将假想轴进行划分[-i, + i](我代表iota), 用于评估复杂的对象说Z在虚轴上, 而要确定是实数还是整数的复杂对象, 则在内部调用预定义方法, 如下所示：

语法如下：

atan(double arg);
atanf(float arg);
atanl(long double arg);
where arg is a floating-point value

catan(double complex z);
catanf(float complex z);
catanl( long double complex z);
where z is a Type – generic macro

参数：这些函数接受一个强制性参数ž指定反正切。该参数可以是double, float或long double数据类型.

返回值：该函数返回复弧切线/弧切线根据传递的参数类型。

下面的程序说明了上述方法：

程序1:该程序将说明函数晒黑(), atanf()和atanl()计算浮点参数的反正切的主值。如果由于下溢而导致量程错误, 则四舍五入后将返回正确的结果。

C

//C program to illustrate the use
//of functions atan(), atanf(), //and atanl()
#include <math.h>
#include <stdio.h>
  
//Driver Code
int main()
{
     //For function atan()
     printf ( "atan(1) = %lf, " , atan (1));
     printf ( " 4*atan(1)=%lf\n" , 4 * atan (1));
  
     printf ( "atan(-0.0) = %+lf, " , atan (-0.0));
     printf ( "atan(+0.0) = %+lf\n" , atan (0));
  
     //For special values INFINITY
     printf ( "atan(Inf) = %lf, " , atan (INFINITY));
     printf ( "2*atan(Inf) = %lf\n\n" , 2 * atan (INFINITY));
  
     //For function atanf()
     printf ( "atanf(1.1) = %f, " , atanf(1.1));
     printf ( "4*atanf(1.5)=%f\n" , 4 * atanf(1.5));
  
     printf ( "atanf(-0.3) = %+f, " , atanf(-0.3));
     printf ( "atanf(+0.3) = %+f\n" , atanf(0.3));
  
     //For special values INFINITY
     printf ( "atanf(Inf) = %f, " , atanf(INFINITY));
     printf ( "2*atanf(Inf) = %f\n\n" , 2 * atanf(INFINITY));
  
     //For function atanl()
     printf ( "atanl(1.1) = %Lf, " , atanl(1.1));
     printf ( "4*atanl(1.7)=%Lf\n" , 4 * atanl(1.7));
  
     printf ( "atanl(-1.3) = %+Lf, " , atanl(-1.3));
     printf ( "atanl(+0.3) = %+Lf\n" , atanl(0.3));
  
     //For special values INFINITY
     printf ( "atanl(Inf) = %Lf, " , atanl(INFINITY));
     printf ( "2*atanl(Inf) = %Lf\n\n" , 2 * atanl(INFINITY));
  
     return 0;
}

输出如下：

atan(1) = 0.785398, 4*atan(1)=3.141593
atan(-0.0) = -0.000000, atan(+0.0) = +0.000000
atan(Inf) = 1.570796, 2*atan(Inf) = 3.141593

atanf(1.1) = 0.832981, 4*atanf(1.5)=3.931175
atanf(-0.3) = -0.291457, atanf(+0.3) = +0.291457
atanf(Inf) = 1.570796, 2*atanf(Inf) = 3.141593

atanl(1.1) = 0.832981, 4*atanl(1.7)=4.156289
atanl(-1.3) = -0.915101, atanl(+0.3) = +0.291457
atanl(Inf) = 1.570796, 2*atanl(Inf) = 3.141593

程序2:该程序将说明函数catan(), catanf()和catanl()计算复数反正切的主值作为参数。

C

//C program to illustrate the use
//of functions catan(), catanf(), //and catanl()
#include <complex.h>
#include <float.h>
#include <stdio.h>
  
//Driver Code
int main()
{
     //Given Complex Number
     double complex z1 = catan(2 * I);
  
     //Function catan()
     printf ( "catan(+0 + 2i) = %lf + %lfi\n" , creal(z1), cimag(z1));
  
     //Complex(0, + INFINITY)
     double complex z2 = 2
                         * catan(2 * I * DBL_MAX);
     printf ( "2*catan(+0 + i*Inf) = %lf%+lfi\n" , creal(z2), cimag(z2));
  
     printf ( "\n" );
  
     //Function catanf()
     float complex z3 = catanf(2 * I);
     printf ( "catanf(+0 + 2i) = %f + %fi\n" , crealf(z3), cimagf(z3));
  
     //Complex(0, + INFINITY)
     float complex z4 = 2
                        * catanf(2 * I * DBL_MAX);
     printf ( "2*catanf(+0 + i*Inf) = %f + %fi\n" , crealf(z4), cimagf(z4));
  
     printf ( "\n" );
  
     //Function catanl()
     long double complex z5 = catanl(2 * I);
     printf ( "catan(+0+2i) = %Lf%+Lfi\n" , creall(z5), cimagl(z5));
  
     //Complex(0, + INFINITY)
     long double complex z6 = 2
                              * catanl(2 * I * DBL_MAX);
     printf ( "2*catanl(+0 + i*Inf) = %Lf + %Lfi\n" , creall(z6), cimagl(z6));
}

输出如下：

catan(+0 + 2i) = 1.570796 + 0.549306i
2*catan(+0 + i*Inf) = 3.141593+0.000000i

catanf(+0 + 2i) = 1.570796 + 0.549306i
2*catanf(+0 + i*Inf) = 3.141593 + 0.000000i

catan(+0+2i) = 1.570796+0.549306i
2*catanl(+0 + i*Inf) = 3.141593 + 0.000000i

程序3:该程序将说明函数catanh(), catanhf()和catanhl()计算的复弧双曲正切ž沿实轴并在区间内[-i * PI / 2, + i * PI / 2]沿假想轴。

C

//C program to illustrate the use
//of functions  catanh(), catanhf(), //and catanhl()
#include <complex.h>
#include <stdio.h>
  
//Driver Code
int main()
{
     //Function catanh()
     double complex z1 = catanh(2);
     printf ( "catanh(+2+0i) = %lf%+lfi\n" , creal(z1), cimag(z1));
  
     //for any z, atanh(z) = atan(iz)/i
     //I denotes Imaginary
     //part of the complex number
     double complex z2 = catanh(1 + 2 * I);
     printf ( "catanh(1+2i) = %lf%+lfi\n\n" , creal(z2), cimag(z2));
  
     //Function catanhf()
     float complex z3 = catanhf(2);
     printf ( "catanhf(+2+0i) = %f%+fi\n" , crealf(z3), cimagf(z3));
  
     //for any z, atanh(z) = atan(iz)/i
     float complex z4 = catanhf(1 + 2 * I);
     printf ( "catanhf(1+2i) = %f%+fi\n\n" , crealf(z4), cimagf(z4));
  
     //Function catanh()
     long double complex z5 = catanhl(2);
     printf ( "catanhl(+2+0i) = %Lf%+Lfi\n" , creall(z5), cimagl(z5));
  
     //for any z, atanh(z) = atan(iz)/i
     long double complex z6 = catanhl(1 + 2 * I);
     printf ( "catanhl(1+2i) = %Lf%+Lfi\n\n" , creall(z6), cimagl(z6));
}

输出如下：

catanh(+2+0i) = 0.549306+1.570796i
catanh(1+2i) = 0.173287+1.178097i

catanhf(+2+0i) = 0.549306+1.570796i
catanhf(1+2i) = 0.173287+1.178097i

catanhl(+2+0i) = 0.549306+1.570796i
catanhl(1+2i) = 0.173287+1.178097i