xref: /freebsd/contrib/arm-optimized-routines/pl/math/atan_common.h (revision 5ca8e32633c4ffbbcd6762e5888b6a4ba0708c6c)
1 /*
2  * Double-precision polynomial evaluation function for scalar
3  * atan(x) and atan2(y,x).
4  *
5  * Copyright (c) 2021-2023, Arm Limited.
6  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
7  */
8 
9 #include "math_config.h"
10 #include "poly_scalar_f64.h"
11 
12 /* Polynomial used in fast atan(x) and atan2(y,x) implementations
13    The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2).  */
14 static inline double
15 eval_poly (double z, double az, double shift)
16 {
17   /* Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of
18      full scheme to avoid underflow in x^16.  */
19   double z2 = z * z;
20   double x2 = z2 * z2;
21   double x4 = x2 * x2;
22   double x8 = x4 * x4;
23   double y = fma (estrin_11_f64 (z2, x2, x4, x8, __atan_poly_data.poly + 8),
24 		  x8, estrin_7_f64 (z2, x2, x4, __atan_poly_data.poly));
25 
26   /* Finalize. y = shift + z + z^3 * P(z^2).  */
27   y = fma (y, z2 * az, az);
28   y = y + shift;
29 
30   return y;
31 }
32 
33 #undef P
34