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/* Double-precision vector (Advanced SIMD) tanh function
Copyright (C) 2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "v_math.h"
#include "poly_advsimd_f64.h"
static const struct data
{
float64x2_t poly[11];
float64x2_t inv_ln2, ln2_hi, ln2_lo, shift;
uint64x2_t onef;
uint64x2_t thresh, tiny_bound;
} data = {
/* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */
.poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), },
.inv_ln2 = V2 (0x1.71547652b82fep0),
.ln2_hi = V2 (-0x1.62e42fefa39efp-1),
.ln2_lo = V2 (-0x1.abc9e3b39803fp-56),
.shift = V2 (0x1.8p52),
.onef = V2 (0x3ff0000000000000),
.tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */
/* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */
.thresh = V2 (0x01f241bf835f9d5f),
};
static inline float64x2_t
expm1_inline (float64x2_t x, const struct data *d)
{
/* 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. */
float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift);
int64x2_t i = vcvtq_s64_f64 (j);
float64x2_t f = vfmaq_f64 (x, j, d->ln2_hi);
f = vfmaq_f64 (f, j, d->ln2_lo);
/* Approximate expm1(f) using polynomial. */
float64x2_t f2 = vmulq_f64 (f, f);
float64x2_t f4 = vmulq_f64 (f2, f2);
float64x2_t p = vfmaq_f64 (
f, f2, v_estrin_10_f64 (f, f2, f4, vmulq_f64 (f4, f4), d->poly));
/* t = 2 ^ i. */
float64x2_t t = vreinterpretq_f64_u64 (
vaddq_u64 (vreinterpretq_u64_s64 (i << 52), d->onef));
/* expm1(x) = p * t + (t - 1). */
return vfmaq_f64 (vsubq_f64 (t, v_f64 (1)), p, t);
}
static float64x2_t NOINLINE VPCS_ATTR
special_case (float64x2_t x, float64x2_t y, uint64x2_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 2.77 ULP:
_ZGVnN2v_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3
want -0x1.bd6a21a163624p-3. */
float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x)
{
const struct data *d = ptr_barrier (&data);
uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
float64x2_t u = x;
/* Trigger special-cases for tiny, boring and infinity/NaN. */
uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia, d->tiny_bound), d->thresh);
#if WANT_SIMD_EXCEPT
/* To trigger fp exceptions correctly, set special lanes to a neutral value.
They will be fixed up later by the special-case handler. */
if (__glibc_unlikely (v_any_u64 (special)))
u = v_zerofy_f64 (u, special);
#endif
u = vaddq_f64 (u, u);
/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
float64x2_t q = expm1_inline (u, d);
float64x2_t qp2 = vaddq_f64 (q, v_f64 (2));
if (__glibc_unlikely (v_any_u64 (special)))
return special_case (x, vdivq_f64 (q, qp2), special);
return vdivq_f64 (q, qp2);
}
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