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/*
* Double-precision SVE acosh(x) function.
* Copyright (c) 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"
#define WANT_SV_LOG1P_K0_SHORTCUT 1
#include "sv_log1p_inline.h"
#define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
#define OneTop 0x3ff
static NOINLINE svfloat64_t
special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
{
return sv_call_f64 (acosh, x, y, special);
}
/* SVE approximation for double-precision acosh, based on log1p.
The largest observed error is 3.19 ULP in the region where the
argument to log1p falls in the k=0 interval, i.e. x close to 1:
SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2
want 0x1.ed23399f51373p-2. */
svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg)
{
svuint64_t itop = svlsr_x (pg, svreinterpret_u64 (x), 52);
/* (itop - OneTop) >= (BigBoundTop - OneTop). */
svbool_t special = svcmpge (pg, svsub_x (pg, itop, OneTop), sv_u64 (0x1ff));
svfloat64_t xm1 = svsub_x (pg, x, 1);
svfloat64_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1));
svfloat64_t y = sv_log1p_inline (svadd_x (pg, xm1, svsqrt_x (pg, u)), pg);
/* Fall back to scalar routine for special lanes. */
if (unlikely (svptest_any (pg, special)))
return special_case (x, y, special);
return y;
}
PL_SIG (SV, D, 1, acosh, 1.0, 10.0)
PL_TEST_ULP (SV_NAME_D1 (acosh), 2.69)
PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 1, 0x1p511, 90000)
PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0x1p511, inf, 10000)
PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0, 1, 1000)
PL_TEST_INTERVAL (SV_NAME_D1 (acosh), -0, -inf, 10000)
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