static ex atan2_eval(const ex & y, const ex & x)
{
- if (y.info(info_flags::numeric) && x.info(info_flags::numeric)) {
+ if (y.is_zero()) {
- if (y.is_zero()) {
+ // atan(0, 0) -> 0
+ if (x.is_zero())
+ return _ex0;
- // atan(0, 0) -> 0
- if (x.is_zero())
- return _ex0;
+ // atan(0, x), x real and positive -> 0
+ if (x.info(info_flags::positive))
+ return _ex0;
- // atan(0, x), x real and positive -> 0
- if (x.info(info_flags::positive))
- return _ex0;
+ // atan(0, x), x real and negative -> -Pi
+ if (x.info(info_flags::negative))
+ return _ex_1*Pi;
+ }
- // atan(0, x), x real and negative -> -Pi
- if (x.info(info_flags::negative))
- return _ex_1*Pi;
- }
+ if (x.is_zero()) {
- if (x.is_zero()) {
+ // atan(y, 0), y real and positive -> Pi/2
+ if (y.info(info_flags::positive))
+ return _ex1_2*Pi;
- // atan(y, 0), y real and positive -> Pi/2
- if (y.info(info_flags::positive))
- return _ex1_2*Pi;
+ // atan(y, 0), y real and negative -> -Pi/2
+ if (y.info(info_flags::negative))
+ return _ex_1_2*Pi;
+ }
- // atan(y, 0), y real and negative -> -Pi/2
- if (y.info(info_flags::negative))
- return _ex_1_2*Pi;
- }
+ if (y.is_equal(x)) {
- if (y.is_equal(x)) {
+ // atan(y, y), y real and positive -> Pi/4
+ if (y.info(info_flags::positive))
+ return _ex1_4*Pi;
- // atan(y, y), y real and positive -> Pi/4
- if (y.info(info_flags::positive))
- return _ex1_4*Pi;
+ // atan(y, y), y real and negative -> -3/4*Pi
+ if (y.info(info_flags::negative))
+ return numeric(-3, 4)*Pi;
+ }
- // atan(y, y), y real and negative -> -3/4*Pi
- if (y.info(info_flags::negative))
- return numeric(-3, 4)*Pi;
- }
+ if (y.is_equal(-x)) {
- if (y.is_equal(-x)) {
+ // atan(y, -y), y real and positive -> 3*Pi/4
+ if (y.info(info_flags::positive))
+ return numeric(3, 4)*Pi;
- // atan(y, -y), y real and positive -> 3*Pi/4
- if (y.info(info_flags::positive))
- return numeric(3, 4)*Pi;
+ // atan(y, -y), y real and negative -> -Pi/4
+ if (y.info(info_flags::negative))
+ return _ex_1_4*Pi;
+ }
- // atan(y, -y), y real and negative -> -Pi/4
- if (y.info(info_flags::negative))
- return _ex_1_4*Pi;
- }
+ // atan(float, float) -> float
+ if (is_a<numeric>(y) && is_a<numeric>(x) && !y.info(info_flags::crational)
+ && !x.info(info_flags::crational))
+ return atan(ex_to<numeric>(y), ex_to<numeric>(x));
- // atan(float, float) -> float
- if (!y.info(info_flags::crational) && !x.info(info_flags::crational))
- return atan(ex_to<numeric>(y), ex_to<numeric>(x));
-
- // atan(real, real) -> atan(y/x) +/- Pi
- if (y.info(info_flags::real) && x.info(info_flags::real)) {
- if (x.info(info_flags::positive))
- return atan(y/x);
- else if(y.info(info_flags::positive))
- return atan(y/x)+Pi;
- else
- return atan(y/x)-Pi;
- }
+ // atan(real, real) -> atan(y/x) +/- Pi
+ if (y.info(info_flags::real) && x.info(info_flags::real)) {
+ if (x.info(info_flags::positive))
+ return atan(y/x);
+ else if(y.info(info_flags::positive))
+ return atan(y/x)+Pi;
+ else
+ return atan(y/x)-Pi;
}
return atan2(y, x).hold();