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/*
* Single-precision vector acosh(x) function.
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "pl_sig.h"
#include "pl_test.h"
#define WANT_V_LOG1P_K0_SHORTCUT 1
#include "v_log1p_inline.h"
#define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
#if V_SUPPORTED
static NOINLINE VPCS_ATTR v_f64_t
special_case (v_f64_t x)
{
return v_call_f64 (acosh, x, x, v_u64 (-1));
}
/* Vector approximation for double-precision acosh, based on log1p.
The largest observed error is 3.02 ULP in the region where the
argument to log1p falls in the k=0 interval, i.e. x close to 1:
__v_acosh(0x1.00798aaf80739p+0) got 0x1.f2d6d823bc9dfp-5
want 0x1.f2d6d823bc9e2p-5. */
VPCS_ATTR v_f64_t V_NAME (acosh) (v_f64_t x)
{
v_u64_t itop = v_as_u64_f64 (x) >> 52;
v_u64_t special = v_cond_u64 ((itop - OneTop) >= (BigBoundTop - OneTop));
/* Fall back to scalar routine for all lanes if any of them are special. */
if (unlikely (v_any_u64 (special)))
return special_case (x);
v_f64_t xm1 = x - 1;
v_f64_t u = xm1 * (x + 1);
return log1p_inline (xm1 + v_sqrt_f64 (u));
}
VPCS_ALIAS
PL_SIG (V, D, 1, acosh, 1.0, 10.0)
PL_TEST_ULP (V_NAME (acosh), 2.53)
PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (acosh))
PL_TEST_INTERVAL (V_NAME (acosh), 1, 0x1p511, 90000)
PL_TEST_INTERVAL (V_NAME (acosh), 0x1p511, inf, 10000)
PL_TEST_INTERVAL (V_NAME (acosh), 0, 1, 1000)
PL_TEST_INTERVAL (V_NAME (acosh), -0, -inf, 10000)
#endif
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