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atan2(3) [osx man page]

ATAN2(3)						   BSD Library Functions Manual 						  ATAN2(3)

NAME
atan2 -- arc tangent function of two variables SYNOPSIS
#include <math.h> double atan2(double y, double x); long double atan2l(long double y, long double x); float atan2f(float y, float x); DESCRIPTION
The atan2() function computes the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value. SPECIAL VALUES
atan2(+-0, -0) returns +-pi. atan2(+-0, +0) returns +-0. atan2(+-0, x) returns +-pi for x < 0. atan2(+-0, x) returns +-0 for x > 0. atan2(y, +-0) returns +pi/2 for y > 0. atan2(y, +-0) returns -pi/2 for y < 0. atan2(+-y, -infinity) returns +-pi for finite y > 0. atan2(+-y, +infinity) returns +-0 for finite y > 0. atan2(+-infinity, x) returns +-pi/2 for finite x. atan2(+-infinity, -infinity) returns +-3*pi/4. atan2(+-infinity, +infinity) returns +-pi/4. NOTES
The atan2() function is used mostly to convert from rectangular (x,y) to polar (r,theta) coordinates that must satisfy x = r*cos theta and y = r*sin theta. In general, conversions to polar coordinates should be computed thus: r := hypot(x,y); ... := sqrt(x*x+y*y) theta := atan2(y,x). VECTOR OPERATIONS
If you need to apply the atan2() function to SIMD vectors or arrays, using the following functions provided by the Accelerate.framework may give significantly better performance: #include <Accelerate/Accelerate.h> vFloat atan2f(vFloat y, vFloat x); void vvatan2f(float *z, const float *y, const float *x, const int *n); void vvatan2(double *z, const double *y, const double *x, const int *n); SEE ALSO
acos(3), asin(3), atan(3), cos(3), cosh(3), sin(3), sinh(3), tan(3), tanh(3), math(3), STANDARDS
The atan2() function conforms to ISO/IEC 9899:2011. BSD
December 11, 2006 BSD

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ATAN2(3)						   BSD Library Functions Manual 						  ATAN2(3)

NAME
atan2, atan2f -- arc tangent function of two variables LIBRARY
Math Library (libm, -lm) SYNOPSIS
#include <math.h> double atan2(double y, double x); float atan2f(float y, float x); DESCRIPTION
The atan2() and atan2f() functions compute the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value. RETURN VALUES
The atan2() function, if successful, returns the arc tangent of y/x in the range [-pi, +pi] radians. If both x and y are zero, the global variable errno is set to EDOM. On the VAX: atan2(y, x) := atan(y/x) if x > 0, sign(y)*(pi - atan(|y/x|)) if x < 0, 0 if x = y = 0, or sign(y)*pi/2 if x = 0 y. NOTES
The function atan2() defines "if x > 0," atan2(0, 0) = 0 on a VAX despite that previously atan2(0, 0) may have generated an error message. The reasons for assigning a value to atan2(0, 0) are these: 1. Programs that test arguments to avoid computing atan2(0, 0) must be indifferent to its value. Programs that require it to be invalid are vulnerable to diverse reactions to that invalidity on diverse computer systems. 2. The atan2() function is used mostly to convert from rectangular (x,y) to polar (r,theta) coordinates that must satisfy x = r*cos theta and y = r*sin theta. These equations are satisfied when (x=0,y=0) is mapped to (r=0,theta=0) on a VAX. In general, conver- sions to polar coordinates should be computed thus: r := hypot(x,y); ... := sqrt(x*x+y*y) theta := atan2(y,x). 3. The foregoing formulas need not be altered to cope in a reasonable way with signed zeros and infinities on a machine that conforms to IEEE 754; the versions of hypot(3) and atan2() provided for such a machine are designed to handle all cases. That is why atan2(+-0, -0) = +-pi for instance. In general the formulas above are equivalent to these: r := sqrt(x*x+y*y); if r = 0 then x := copysign(1,x); SEE ALSO
acos(3), asin(3), atan(3), cos(3), cosh(3), math(3), sin(3), sinh(3), tan(3), tanh(3) STANDARDS
The atan2() function conforms to ANSI X3.159-1989 (``ANSI C89''). BSD
May 2, 1991 BSD
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