1 /*
2 * Single-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 #ifndef PL_MATH_ATANF_COMMON_H
10 #define PL_MATH_ATANF_COMMON_H
11
12 #include "math_config.h"
13 #include "poly_scalar_f32.h"
14
15 /* Polynomial used in fast atanf(x) and atan2f(y,x) implementations
16 The order 7 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
17 static inline float
eval_poly(float z,float az,float shift)18 eval_poly (float z, float az, float shift)
19 {
20 /* Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
21 a standard implementation using z8 creates spurious underflow
22 in the very last fma (when z^8 is small enough).
23 Therefore, we split the last fma into a mul and and an fma.
24 Horner and single-level Estrin have higher errors that exceed
25 threshold. */
26 float z2 = z * z;
27 float z4 = z2 * z2;
28
29 /* Then assemble polynomial. */
30 float y = fmaf (
31 z4, z4 * pairwise_poly_3_f32 (z2, z4, __atanf_poly_data.poly + 4),
32 pairwise_poly_3_f32 (z2, z4, __atanf_poly_data.poly));
33 /* Finalize:
34 y = shift + z * P(z^2). */
35 return fmaf (y, z2 * az, az) + shift;
36 }
37
38 #endif // PL_MATH_ATANF_COMMON_H
39