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