2  * Double-precision scalar atan2(x) function.
4  * Copyright (c) 2021-2023, Arm Limited.
5  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
17 #define PiOver4 (0x1.921fb54442d18p-1)
25    and d for which P underflows, and is used to special-case such inputs.  */
35 /* Fast implementation of scalar atan2. Largest errors are when y and x are
37    atan2(-0x1.5915b1498e82fp+732, 0x1.54d11ef838826p+732)
38    got -0x1.954f42f1fa841p-1 want -0x1.954f42f1fa843p-1.  */
40 atan2 (double y, double x)  in atan2()  argument
43   uint64_t iy = asuint64 (y);  in atan2()
52   if (unlikely (isnan (y) && !xisnan))  in atan2()
53     return __math_invalid (y);  in atan2()
57   /* m = 2 * sign(x) + sign(y).  */  in atan2()
60   int64_t exp_diff = biased_exponent (x) - biased_exponent (y);  in atan2()
62   /* y = 0.  */  in atan2()
69 	  return y; /* atan(+-0,+anything)=+-0.  */  in atan2()
71 	  return Pi; /* atan(+0,-anything) = pi.  */  in atan2()
73 	  return -Pi; /* atan(-0,-anything) =-pi.  */  in atan2()
76   /* Special case for (x, y) either on or very close to the y axis. Either x =  in atan2()
77      0, or y is much larger than x (difference in exponents >=  in atan2()
79   if (unlikely (iax == 0 || exp_diff <= -POW8_EXP_UFLOW_BOUND))  in atan2()
80     return sign_y ? -PiOver2 : PiOver2;  in atan2()
82   /* Special case for either x is INF or (x, y) is very close to x axis and x is  in atan2()
94 	      return -PiOver4; /* atan(-INF,+INF).  */  in atan2()
96 	      return 3.0 * PiOver4; /* atan(+INF,-INF).  */  in atan2()
98 	      return -3.0 * PiOver4; /* atan(-INF,-INF).  */  in atan2()
108 	      return -0.0; /* atan(-...,+INF).  */  in atan2()
110 	      return Pi; /* atan(+...,-INF).  */  in atan2()
112 	      return -Pi; /* atan(-...,-INF).  */  in atan2()
116   /* y is INF.  */  in atan2()
118     return sign_y ? -PiOver2 : PiOver2;  in atan2()
127   double n = pred_aygtax ? -ax : ay;  in atan2()
134       /* If (x, y) is very close to x axis and x is positive, the polynomial  in atan2()
141       double shift = sign_x ? -2.0 : 0.0;  in atan2()
148   /* Account for the sign of x and y.  */  in atan2()
155 PL_TEST_INTERVAL (atan2, -10.0, 10.0, 50000)
156 PL_TEST_INTERVAL (atan2, -1.0, 1.0, 40000)