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/*
* Single-precision vector atan(x) function.
*
* Copyright (c) 2021-2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "pl_sig.h"
#if V_SUPPORTED
#include "atanf_common.h"
#define PiOver2 v_f32 (0x1.921fb6p+0f)
#define AbsMask v_u32 (0x7fffffff)
/* Fast implementation of vector atanf based on
atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps:
v_atanf(0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */
VPCS_ATTR
v_f32_t V_NAME (atanf) (v_f32_t x)
{
/* No need to trigger special case. Small cases, infs and nans
are supported by our approximation technique. */
v_u32_t ix = v_as_u32_f32 (x);
v_u32_t sign = ix & ~AbsMask;
/* Argument reduction:
y := arctan(x) for x < 1
y := pi/2 + arctan(-1/x) for x > 1
Hence, use z=-1/a if x>=1, otherwise z=a. */
v_u32_t red = v_cagt_f32 (x, v_f32 (1.0));
/* Avoid dependency in abs(x) in division (and comparison). */
v_f32_t z = v_sel_f32 (red, v_div_f32 (v_f32 (-1.0f), x), x);
v_f32_t shift = v_sel_f32 (red, PiOver2, v_f32 (0.0f));
/* Use absolute value only when needed (odd powers of z). */
v_f32_t az = v_abs_f32 (z);
az = v_sel_f32 (red, -az, az);
/* Calculate the polynomial approximation. */
v_f32_t y = eval_poly (z, az, shift);
/* y = atan(x) if x>0, -atan(-x) otherwise. */
y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign);
return y;
}
VPCS_ALIAS
PL_SIG (V, F, 1, atan, -10.0, 10.0)
#endif
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