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/*
* Single-precision vector atanh(x) function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "mathlib.h"
#include "pl_sig.h"
#include "pl_test.h"
#if V_SUPPORTED
#include "v_log1pf_inline.h"
#define AbsMask 0x7fffffff
#define Half 0x3f000000
#define One 0x3f800000
#define TinyBound 0x39800000 /* 0x1p-12, below which atanhf(x) rounds to x. */
/* Approximation for vector single-precision atanh(x) using modified log1p.
The maximum error is 3.08 ULP:
__v_atanhf(0x1.ff215p-5) got 0x1.ffcb7cp-5
want 0x1.ffcb82p-5. */
VPCS_ATTR v_f32_t V_NAME (atanhf) (v_f32_t x)
{
v_u32_t ix = v_as_u32_f32 (x);
v_f32_t halfsign
= v_as_f32_u32 (v_bsl_u32 (v_u32 (AbsMask), v_u32 (Half), ix));
v_u32_t iax = ix & AbsMask;
v_f32_t ax = v_as_f32_u32 (iax);
#if WANT_SIMD_EXCEPT
v_u32_t special = v_cond_u32 ((iax >= One) | (iax <= TinyBound));
/* Side-step special cases by setting those lanes to 0, which will trigger no
exceptions. These will be fixed up later. */
if (unlikely (v_any_u32 (special)))
ax = v_sel_f32 (special, v_f32 (0), ax);
#else
v_u32_t special = v_cond_u32 (iax >= One);
#endif
v_f32_t y = halfsign * log1pf_inline ((2 * ax) / (1 - ax));
if (unlikely (v_any_u32 (special)))
return v_call_f32 (atanhf, x, y, special);
return y;
}
VPCS_ALIAS
PL_SIG (V, F, 1, atanh, -1.0, 1.0)
PL_TEST_ULP (V_NAME (atanhf), 2.59)
PL_TEST_EXPECT_FENV (V_NAME (atanhf), WANT_SIMD_EXCEPT)
PL_TEST_INTERVAL_C (V_NAME (atanhf), 0, 0x1p-12, 500, 0)
PL_TEST_INTERVAL_C (V_NAME (atanhf), 0x1p-12, 1, 200000, 0)
PL_TEST_INTERVAL_C (V_NAME (atanhf), 1, inf, 1000, 0)
PL_TEST_INTERVAL_C (V_NAME (atanhf), -0, -0x1p-12, 500, 0)
PL_TEST_INTERVAL_C (V_NAME (atanhf), -0x1p-12, -1, 200000, 0)
PL_TEST_INTERVAL_C (V_NAME (atanhf), -1, -inf, 1000, 0)
#endif
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