1 /*
2 * Single-precision polynomial evaluation function for scalar and vector
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 "estrinf.h"
14
15 #if V_SUPPORTED
16
17 #include "v_math.h"
18
19 #define FLT_T v_f32_t
20 #define P(i) v_f32 (__atanf_poly_data.poly[i])
21
22 #else
23
24 #define FLT_T float
25 #define P(i) __atanf_poly_data.poly[i]
26
27 #endif
28
29 /* Polynomial used in fast atanf(x) and atan2f(y,x) implementations
30 The order 7 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
31 static inline FLT_T
eval_poly(FLT_T z,FLT_T az,FLT_T shift)32 eval_poly (FLT_T z, FLT_T az, FLT_T shift)
33 {
34 /* Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
35 a standard implementation using z8 creates spurious underflow
36 in the very last fma (when z^8 is small enough).
37 Therefore, we split the last fma into a mul and and an fma.
38 Horner and single-level Estrin have higher errors that exceed
39 threshold. */
40 FLT_T z2 = z * z;
41 FLT_T z4 = z2 * z2;
42
43 /* Then assemble polynomial. */
44 FLT_T y = FMA (z4, z4 * ESTRIN_3_ (z2, z4, P, 4), ESTRIN_3 (z2, z4, P));
45
46 /* Finalize:
47 y = shift + z * P(z^2). */
48 return FMA (y, z2 * az, az) + shift;
49 }
50
51 #endif // PL_MATH_ATANF_COMMON_H
52