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/*
* Single-precision vector atan(x) function.
*
* Copyright (c) 2021-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.h"
#if SV_SUPPORTED
#include "sv_atanf_common.h"
#define PiOver2 sv_f32 (0x1.921fb6p+0f)
#define AbsMask (0x7fffffff)
/* Fast implementation of SVE 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.
Largest observed error is 2.9 ULP, close to +/-1.0:
__sv_atanf(0x1.0468f6p+0) got -0x1.967f06p-1
want -0x1.967fp-1. */
sv_f32_t
__sv_atanf_x (sv_f32_t x, const svbool_t pg)
{
/* No need to trigger special case. Small cases, infs and nans
are supported by our approximation technique. */
sv_u32_t ix = sv_as_u32_f32 (x);
sv_u32_t sign = svand_n_u32_x (pg, 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. */
svbool_t red = svacgt_n_f32 (pg, x, 1.0f);
/* Avoid dependency in abs(x) in division (and comparison). */
sv_f32_t z = svsel_f32 (red, svdiv_f32_x (pg, sv_f32 (-1.0f), x), x);
/* Use absolute value only when needed (odd powers of z). */
sv_f32_t az = svabs_f32_x (pg, z);
az = svneg_f32_m (az, red, az);
sv_f32_t y = __sv_atanf_common (pg, red, z, az, PiOver2);
/* y = atan(x) if x>0, -atan(-x) otherwise. */
return sv_as_f32_u32 (sveor_u32_x (pg, sv_as_u32_f32 (y), sign));
}
PL_ALIAS (__sv_atanf_x, _ZGVsMxv_atanf)
PL_SIG (SV, F, 1, atan, -3.1, 3.1)
PL_TEST_ULP (__sv_atanf, 2.9)
PL_TEST_INTERVAL (__sv_atanf, -10.0, 10.0, 50000)
PL_TEST_INTERVAL (__sv_atanf, -1.0, 1.0, 40000)
PL_TEST_INTERVAL (__sv_atanf, 0.0, 1.0, 40000)
PL_TEST_INTERVAL (__sv_atanf, 1.0, 100.0, 40000)
PL_TEST_INTERVAL (__sv_atanf, 1e6, 1e32, 40000)
#endif
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