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
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