52 lines
1.5 KiB
C
52 lines
1.5 KiB
C
/*
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* Single-precision vector acosh(x) function.
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* Copyright (c) 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 "v_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#define WANT_V_LOG1P_K0_SHORTCUT 1
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#include "v_log1p_inline.h"
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#define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
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#if V_SUPPORTED
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static NOINLINE VPCS_ATTR v_f64_t
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special_case (v_f64_t x)
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{
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return v_call_f64 (acosh, x, x, v_u64 (-1));
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}
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/* Vector approximation for double-precision acosh, based on log1p.
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The largest observed error is 3.02 ULP in the region where the
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argument to log1p falls in the k=0 interval, i.e. x close to 1:
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__v_acosh(0x1.00798aaf80739p+0) got 0x1.f2d6d823bc9dfp-5
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want 0x1.f2d6d823bc9e2p-5. */
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VPCS_ATTR v_f64_t V_NAME (acosh) (v_f64_t x)
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{
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v_u64_t itop = v_as_u64_f64 (x) >> 52;
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v_u64_t special = v_cond_u64 ((itop - OneTop) >= (BigBoundTop - OneTop));
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/* Fall back to scalar routine for all lanes if any of them are special. */
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if (unlikely (v_any_u64 (special)))
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return special_case (x);
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v_f64_t xm1 = x - 1;
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v_f64_t u = xm1 * (x + 1);
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return log1p_inline (xm1 + v_sqrt_f64 (u));
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}
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VPCS_ALIAS
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PL_SIG (V, D, 1, acosh, 1.0, 10.0)
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PL_TEST_ULP (V_NAME (acosh), 2.53)
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PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (acosh))
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PL_TEST_INTERVAL (V_NAME (acosh), 1, 0x1p511, 90000)
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PL_TEST_INTERVAL (V_NAME (acosh), 0x1p511, inf, 10000)
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PL_TEST_INTERVAL (V_NAME (acosh), 0, 1, 1000)
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PL_TEST_INTERVAL (V_NAME (acosh), -0, -inf, 10000)
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#endif
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