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/*
* Double-precision vector sinh(x) function.
* Copyright (c) 2022, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "mathlib.h"
#include "pl_sig.h"
#define AbsMask 0x7fffffffffffffff
#define Half 0x3fe0000000000000
#define OFlowBound \
0x40862e42fefa39f0 /* 0x1.62e42fefa39fp+9, above which using expm1 results \
in NaN. */
#if V_SUPPORTED
/* Approximation for vector double-precision sinh(x) using expm1.
sinh(x) = (exp(x) - exp(-x)) / 2.
The greatest observed error is 2.57 ULP:
sinh(0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2
want 0x1.ab34e59d678d9p-2. */
VPCS_ATTR v_f64_t V_NAME (sinh) (v_f64_t x)
{
v_u64_t ix = v_as_u64_f64 (x);
v_u64_t iax = ix & AbsMask;
v_f64_t ax = v_as_f64_u64 (iax);
v_u64_t sign = ix & ~AbsMask;
v_f64_t halfsign = v_as_f64_u64 (sign | Half);
v_u64_t special = v_cond_u64 (iax >= OFlowBound);
/* Fall back to the scalar variant for all lanes if any of them should trigger
an exception. */
if (unlikely (v_any_u64 (special)))
return v_call_f64 (sinh, x, x, v_u64 (-1));
/* Up to the point that expm1 overflows, we can use it to calculate sinh
using a slight rearrangement of the definition of asinh. This allows us to
retain acceptable accuracy for very small inputs. */
v_f64_t t = V_NAME (expm1) (ax);
return (t + t / (t + 1)) * halfsign;
}
VPCS_ALIAS
PL_SIG (V, D, 1, sinh, -10.0, 10.0)
#endif
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