1 /*
2 * Double-precision polynomial evaluation function for scalar
3 * atan(x) and atan2(y,x).
4 *
5 * Copyright (c) 2021-2024, 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
eval_poly(double z,double az,double shift)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