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