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/*
* Double-precision vector tanh(x) function.
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "v_math.h"
#include "estrin.h"
#include "mathlib.h"
#include "pl_sig.h"
#include "pl_test.h"
#if V_SUPPORTED
#define AbsMask v_u64 (0x7fffffffffffffff)
#define InvLn2 v_f64 (0x1.71547652b82fep0)
#define MLn2hi v_f64 (-0x1.62e42fefa39efp-1)
#define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56)
#define Shift v_f64 (0x1.8p52)
#define C(i) v_f64 (__expm1_poly[i])
#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4). */
#define TinyBound 0x3e40000000000000 /* asuint64 (0x1p-27). */
#define One v_u64 (0x3ff0000000000000)
static inline v_f64_t
expm1_inline (v_f64_t x)
{
/* Helper routine for calculating exp(x) - 1. Vector port of the helper from
the scalar variant of tanh. */
/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift;
v_s64_t i = v_to_s64_f64 (j);
v_f64_t f = v_fma_f64 (j, MLn2hi, x);
f = v_fma_f64 (j, MLn2lo, f);
/* Approximate expm1(f) using polynomial. */
v_f64_t f2 = f * f;
v_f64_t f4 = f2 * f2;
v_f64_t p = v_fma_f64 (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
/* t = 2 ^ i. */
v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One);
/* expm1(x) = p * t + (t - 1). */
return v_fma_f64 (p, t, t - 1);
}
static NOINLINE v_f64_t
special_case (v_f64_t x, v_f64_t y, v_u64_t special)
{
return v_call_f64 (tanh, x, y, special);
}
/* Vector approximation for double-precision tanh(x), using a simplified
version of expm1. The greatest observed error is 2.75 ULP:
__v_tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
want -0x1.ba31ba4691ab4p-3. */
VPCS_ATTR v_f64_t V_NAME (tanh) (v_f64_t x)
{
v_u64_t ix = v_as_u64_f64 (x);
v_u64_t ia = ix & AbsMask;
/* Trigger special-cases for tiny, boring and infinity/NaN. */
v_u64_t special = v_cond_u64 ((ia - TinyBound) > (BoringBound - TinyBound));
v_f64_t u;
/* To trigger fp exceptions correctly, set special lanes to a neutral value.
They will be fixed up later by the special-case handler. */
if (unlikely (v_any_u64 (special)))
u = v_sel_f64 (special, v_f64 (1), x) * 2;
else
u = x * 2;
/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
v_f64_t q = expm1_inline (u);
v_f64_t y = q / (q + 2);
if (unlikely (v_any_u64 (special)))
return special_case (x, y, special);
return y;
}
VPCS_ALIAS
PL_SIG (V, D, 1, tanh, -10.0, 10.0)
PL_TEST_ULP (V_NAME (tanh), 2.26)
PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (tanh))
PL_TEST_INTERVAL (V_NAME (tanh), 0, TinyBound, 1000)
PL_TEST_INTERVAL (V_NAME (tanh), -0, -TinyBound, 1000)
PL_TEST_INTERVAL (V_NAME (tanh), TinyBound, BoringBound, 100000)
PL_TEST_INTERVAL (V_NAME (tanh), -TinyBound, -BoringBound, 100000)
PL_TEST_INTERVAL (V_NAME (tanh), BoringBound, inf, 1000)
PL_TEST_INTERVAL (V_NAME (tanh), -BoringBound, -inf, 1000)
#endif
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