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在头文件<math.h>中定义



float       atan2f( float y, float x );

(1)

(since C99)

double      atan2( double y, double x );

(2)


long double atan2l( long double y, long double x );

(3)

(since C99)

Defined in header <tgmath.h>



#define atan2( arg )

(4)

(since C99)

1-3)y/x使用参数符号计算反正切以确定正确的象限。

4)类型 - 通用宏:如果参数具有类型long doubleatan2l则被调用。否则,如果参数具有整数类型或类型doubleatan2则调用该参数。否则,atan2f被调用。

参数

x,y

-

浮点值

返回值

如果没有错误发生,则y/x(arctan(

| y |

|:----|

| x |

))在-π范围内; +π弧度,返回。

Y参数

返回值

X参数

如果发生域错误,则返回实现定义的值。

如果由于下溢而发生范围错误,则返回正确的结果(舍入后)。

错误处理

按照math_errhandling中的指定报告错误。

如果xy都为零,则可能会出现域错误。

如果实现支持IEEE浮点运算(IEC 60559),

  • 如果xy都为零,则不会发生域错误

  • 如果xy都是零,则范围错误也不会发生

  • 如果y为零,则不会发生极点错误

  • 如果y±0x为负或-0±π返回

  • 如果y±0并且x是肯定的+0±0则返回

  • 如果y±∞并且x是有限的,±π/2则返回

  • 如果y±∞x-∞±3π/4返回

  • 如果y±∞x+∞±π/4返回

  • 如果x±0y为负数,-π/2则返回

  • 如果x±0y为正,+π/2则返回

  • 如果x-∞并且y是有限且肯定的,则返回

  • 如果x-∞并且y是有限且负面的,则返回

  • 如果x+∞并且y是有限且肯定的,+0则返回

  • 如果x+∞并且y是有限且负面的,-0则返回

  • 如果x是NaN或yNaN,则返回NaN

笔记

atan2(y, x)相当于carg(x + I*y)

POSIX指定在发生下溢时y/x返回值,如果不支持,则返回不大于DBL_MIN,FLT_MIN和LDBL_MIN的实现定义值。

#include <stdio.h>#include <math.h>
 int main(void){    // normal usage: the signs of the two arguments determine the quadrant    // atan2(1,1) = +pi/4, Quad I    printf("(+1,+1) cartesian is (%f,%f) polar\n", hypot( 1, 1), atan2( 1, 1));    // atan2(1, -1) = +3pi/4, Quad II    printf("(+1,-1) cartesian is (%f,%f) polar\n", hypot( 1,-1), atan2( 1,-1));    // atan2(-1,-1) = -3pi/4, Quad III    printf("(-1,-1) cartesian is (%f,%f) polar\n", hypot(-1,-1), atan2(-1,-1));    // atan2(-1,-1) = -pi/4, Quad IV    printf("(-1,+1) cartesian is (%f,%f) polar\n", hypot(-1, 1), atan2(-1, 1)); 
    // special values    printf("atan2(0, 0) = %f atan2(0, -0)=%f\n", atan2(0,0), atan2(0,-0.0));    printf("atan2(7, 0) = %f atan2(7, -0)=%f\n", atan2(7,0), atan2(7,-0.0));}

输出:

(+1,+1) cartesian is (1.414214,0.785398) polar(+1,-1) cartesian is (1.414214,2.356194) polar(-1,-1) cartesian is (1.414214,-2.356194) polar(-1,+1) cartesian is (1.414214,-0.785398) polaratan2(0, 0) = 0.000000 atan2(0, -0)=3.141593atan2(7, 0) = 1.570796 atan2(7, -0)=1.570796

参考

  • C11标准(ISO / IEC 9899:2011):

    • 7.12.4.4 atan2函数(p:239)

    • 7.25类型通用数学<tgmath.h>(p:373-375)

    • F.10.1.4 atan2函数(p:519)

  • C99标准(ISO / IEC 9899:1999):

    • 7.12.4.4 atan2函数(p:219)

    • 7.22类型通用数学<tgmath.h>(p:335-337)

    • F.9.1.4 atan2函数(p:456)

  • C89 / C90标准(ISO / IEC 9899:1990):

    • 4.5.2.4 atan2函数

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