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      atan2, atan2f, atan2l

      From cppreference.com
      <c‎ |numeric‎ |math
       
       
       
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      Defined in header<math.h>
      float       atan2f(float y,float x);
      		 (1)(since C99)
      double      atan2(double y,double x);
      		 (2)
      longdouble atan2l(longdouble y,longdouble x);
      		 (3)(since C99)
      _Decimal32  atan2d32( _Decimal32 y, _Decimal32 x);
      		 (4)(since C23)
      _Decimal64  atan2d64( _Decimal64 y, _Decimal64 x);
      		 (5)(since C23)
      _Decimal128 atan2d128( _Decimal128 y, _Decimal128 x);
      		 (6)(since C23)
      Defined in header<tgmath.h>
      #define atan2( y, x )
      		 (7)(since C99)
      1-6) Computes the arc tangent ofy/ x using the signs of arguments to determine the correct quadrant.
      7) Type-generic macro: If any argument has typelongdouble,(3) (atan2l) is called. Otherwise, if any argument has integer type or has typedouble,(2) (atan2) is called. Otherwise,(1) (atan2f) is called.

      The functions(4-6) are declared if and only if the implementation predefines__STDC_IEC_60559_DFP__ (i.e. the implementation supports decimal floating-point numbers).

      		(since C23)

      Contents

      [edit]Parameters

      x, y - floating-point value

      [edit]Return value

      If no errors occur, the arc tangent ofy/ x (arctan(
      y
      x
      )      ) in the range[-π ; +π] radians, is returned.
      Y argument
      Return value
      math-atan2.png
      X argument

      If a domain error occurs, an implementation-defined value is returned.

      If a range error occurs due to underflow, the correct result (after rounding) is returned.

      [edit]Error handling

      Errors are reported as specified inmath_errhandling.

      Domain error may occur ifx andy are both zero.

      If the implementation supports IEEE floating-point arithmetic (IEC 60559):

      • Ifx andy are both zero, domain errordoes not occur;
      • Ifx andy are both zero, range error does not occur either;
      • Ify is zero, pole error does not occur;
      • Ify is±0 andx is negative or-0,±π is returned;
      • Ify is±0 andx is positive or+0,±0 is returned;
      • Ify is±∞ andx is finite,±π/2 is returned;
      • Ify is±∞ andx is-∞,±3π/4 is returned;
      • Ify is±∞ andx is+∞,±π/4 is returned;
      • Ifx is±0 andy is negative,-π/2 is returned;
      • Ifx is±0 andy is positive,+π/2 is returned;
      • Ifx is-∞ andy is finite and positive,+π is returned;
      • Ifx is-∞ andy is finite and negative,-π is returned;
      • Ifx is+∞ andy is finite and positive,+0 is returned;
      • Ifx is+∞ andy is finite and negative,-0 is returned;
      • If eitherx is NaN ory is NaN, NaN is returned.

      [edit]Notes

      atan2(y, x) is equivalent tocarg(x+ I*y).

      POSIX specifies that in case of underflow,y/ x is the value returned, and if that is not supported, an implementation-defined value no greater thanDBL_MIN,FLT_MIN, andLDBL_MIN is returned.

      [edit]Example

      Run this code
      #include <math.h>#include <stdio.h> int main(void){// normal usage: the signs of the two arguments determine the quadrant// atan2(1,1) = +pi/4, Quad Iprintf("(+1,+1) cartesian is (%f,%f) polar\n",hypot(1,1), atan2(1,1));// atan2(1, -1) = +3pi/4, Quad IIprintf("(+1,-1) cartesian is (%f,%f) polar\n",hypot(1,-1), atan2(1,-1));// atan2(-1,-1) = -3pi/4, Quad IIIprintf("(-1,-1) cartesian is (%f,%f) polar\n",hypot(-1,-1), atan2(-1,-1));// atan2(-1,-1) = -pi/4, Quad IVprintf("(-1,+1) cartesian is (%f,%f) polar\n",hypot(-1,1), atan2(-1,1)); // special valuesprintf("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));}

      Output:

      (+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

      [edit]References

      • C23 standard (ISO/IEC 9899:2024):
      • 7.12.4.4 The atan2 functions (p: TBD)
      • 7.25 Type-generic math <tgmath.h> (p: TBD)
      • F.10.1.4 The atan2 functions (p: TBD)
      • C17 standard (ISO/IEC 9899:2018):
      • 7.12.4.4 The atan2 functions (p: 174)
      • 7.25 Type-generic math <tgmath.h> (p: 272-273)
      • F.10.1.4 The atan2 functions (p: 378)
      • C11 standard (ISO/IEC 9899:2011):
      • 7.12.4.4 The atan2 functions (p: 239)
      • 7.25 Type-generic math <tgmath.h> (p: 373-375)
      • F.10.1.4 The atan2 functions (p: 519)
      • C99 standard (ISO/IEC 9899:1999):
      • 7.12.4.4 The atan2 functions (p: 219)
      • 7.22 Type-generic math <tgmath.h> (p: 335-337)
      • F.9.1.4 The atan2 functions (p: 456)
      • C89/C90 standard (ISO/IEC 9899:1990):
      • 4.5.2.4 The atan2 function

      [edit]See also

      (C99)(C99)
      		 computes arc sine (\({\small\arcsin{x} }\)arcsin(x))
      (function)[edit]
      (C99)(C99)
      		 computes arc cosine (\({\small\arccos{x} }\)arccos(x))
      (function)[edit]
      (C99)(C99)
      		 computes arc tangent (\({\small\arctan{x} }\)arctan(x))
      (function)[edit]
      (C99)(C99)(C99)
      		 computes the phase angle of a complex number
      (function)[edit]
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