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/*
* Double-precision polynomial evaluation function for SVE atan(x) and
* atan2(y,x).
*
* Copyright (c) 2021-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "math_config.h"
#include "sv_math.h"
#define P(i) sv_f64 (__atan_poly_data.poly[i])
/* Polynomial used in fast SVE atan(x) and atan2(y,x) implementations
The order 19 polynomial P approximates (atan(sqrt(x))-sqrt(x))/x^(3/2). */
static inline sv_f64_t
__sv_atan_common (svbool_t pg, svbool_t red, sv_f64_t z, sv_f64_t az,
sv_f64_t shift)
{
/* Use full Estrin scheme for P(z^2) with deg(P)=19. */
sv_f64_t z2 = svmul_f64_x (pg, z, z);
/* Level 1. */
sv_f64_t P_1_0 = sv_fma_f64_x (pg, P (1), z2, P (0));
sv_f64_t P_3_2 = sv_fma_f64_x (pg, P (3), z2, P (2));
sv_f64_t P_5_4 = sv_fma_f64_x (pg, P (5), z2, P (4));
sv_f64_t P_7_6 = sv_fma_f64_x (pg, P (7), z2, P (6));
sv_f64_t P_9_8 = sv_fma_f64_x (pg, P (9), z2, P (8));
sv_f64_t P_11_10 = sv_fma_f64_x (pg, P (11), z2, P (10));
sv_f64_t P_13_12 = sv_fma_f64_x (pg, P (13), z2, P (12));
sv_f64_t P_15_14 = sv_fma_f64_x (pg, P (15), z2, P (14));
sv_f64_t P_17_16 = sv_fma_f64_x (pg, P (17), z2, P (16));
sv_f64_t P_19_18 = sv_fma_f64_x (pg, P (19), z2, P (18));
/* Level 2. */
sv_f64_t x2 = svmul_f64_x (pg, z2, z2);
sv_f64_t P_3_0 = sv_fma_f64_x (pg, P_3_2, x2, P_1_0);
sv_f64_t P_7_4 = sv_fma_f64_x (pg, P_7_6, x2, P_5_4);
sv_f64_t P_11_8 = sv_fma_f64_x (pg, P_11_10, x2, P_9_8);
sv_f64_t P_15_12 = sv_fma_f64_x (pg, P_15_14, x2, P_13_12);
sv_f64_t P_19_16 = sv_fma_f64_x (pg, P_19_18, x2, P_17_16);
/* Level 3. */
sv_f64_t x4 = svmul_f64_x (pg, x2, x2);
sv_f64_t P_7_0 = sv_fma_f64_x (pg, P_7_4, x4, P_3_0);
sv_f64_t P_15_8 = sv_fma_f64_x (pg, P_15_12, x4, P_11_8);
/* Level 4. */
sv_f64_t x8 = svmul_f64_x (pg, x4, x4);
sv_f64_t y = sv_fma_f64_x (pg, P_19_16, x8, P_15_8);
y = sv_fma_f64_x (pg, y, x8, P_7_0);
/* Finalize. y = shift + z + z^3 * P(z^2). */
sv_f64_t z3 = svmul_f64_x (pg, z2, az);
y = sv_fma_f64_x (pg, y, z3, az);
/* Apply shift as indicated by `red` predicate. */
y = svadd_f64_m (red, y, shift);
return y;
}
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