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).  */
17static inline float
18eval_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