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/*
* Single-precision polynomial evaluation function for scalar and vector
* atan(x) and atan2(y,x).
*
* Copyright (c) 2021-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#ifndef PL_MATH_ATANF_COMMON_H
#define PL_MATH_ATANF_COMMON_H
#include "math_config.h"
#include "estrinf.h"
#if V_SUPPORTED
#include "v_math.h"
#define FLT_T v_f32_t
#define P(i) v_f32 (__atanf_poly_data.poly[i])
#else
#define FLT_T float
#define P(i) __atanf_poly_data.poly[i]
#endif
/* Polynomial used in fast atanf(x) and atan2f(y,x) implementations
The order 7 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
static inline FLT_T
eval_poly (FLT_T z, FLT_T az, FLT_T shift)
{
/* Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However,
a standard implementation using z8 creates spurious underflow
in the very last fma (when z^8 is small enough).
Therefore, we split the last fma into a mul and and an fma.
Horner and single-level Estrin have higher errors that exceed
threshold. */
FLT_T z2 = z * z;
FLT_T z4 = z2 * z2;
/* Then assemble polynomial. */
FLT_T y = FMA (z4, z4 * ESTRIN_3_ (z2, z4, P, 4), ESTRIN_3 (z2, z4, P));
/* Finalize:
y = shift + z * P(z^2). */
return FMA (y, z2 * az, az) + shift;
}
#endif // PL_MATH_ATANF_COMMON_H
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