63 lines
1.9 KiB
C
63 lines
1.9 KiB
C
/*
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* Double-precision vector atan(x) function.
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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 "sv_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if SV_SUPPORTED
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#include "sv_atan_common.h"
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/* Useful constants. */
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#define PiOver2 sv_f64 (0x1.921fb54442d18p+0)
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#define AbsMask (0x7fffffffffffffff)
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/* Fast implementation of SVE atan.
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Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using
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z=1/x and shift = pi/2. Largest errors are close to 1. The maximum observed
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error is 2.27 ulps:
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__sv_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1
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want 0x1.9225645bdd7c3p-1. */
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sv_f64_t
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__sv_atan_x (sv_f64_t x, const svbool_t pg)
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{
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/* No need to trigger special case. Small cases, infs and nans
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are supported by our approximation technique. */
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sv_u64_t ix = sv_as_u64_f64 (x);
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sv_u64_t sign = svand_n_u64_x (pg, ix, ~AbsMask);
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/* Argument reduction:
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y := arctan(x) for x < 1
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y := pi/2 + arctan(-1/x) for x > 1
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Hence, use z=-1/a if x>=1, otherwise z=a. */
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svbool_t red = svacgt_n_f64 (pg, x, 1.0);
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/* Avoid dependency in abs(x) in division (and comparison). */
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sv_f64_t z = svsel_f64 (red, svdiv_f64_x (pg, sv_f64 (-1.0), x), x);
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/* Use absolute value only when needed (odd powers of z). */
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sv_f64_t az = svabs_f64_x (pg, z);
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az = svneg_f64_m (az, red, az);
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sv_f64_t y = __sv_atan_common (pg, red, z, az, PiOver2);
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/* y = atan(x) if x>0, -atan(-x) otherwise. */
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y = sv_as_f64_u64 (sveor_u64_x (pg, sv_as_u64_f64 (y), sign));
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return y;
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}
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PL_ALIAS (__sv_atan_x, _ZGVsMxv_atan)
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PL_SIG (SV, D, 1, atan, -3.1, 3.1)
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PL_TEST_ULP (__sv_atan, 1.78)
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PL_TEST_INTERVAL (__sv_atan, -10.0, 10.0, 50000)
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PL_TEST_INTERVAL (__sv_atan, -1.0, 1.0, 40000)
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PL_TEST_INTERVAL (__sv_atan, 0.0, 1.0, 40000)
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PL_TEST_INTERVAL (__sv_atan, 1.0, 100.0, 40000)
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PL_TEST_INTERVAL (__sv_atan, 1e6, 1e32, 40000)
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#endif
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