mirror of git://sourceware.org/git/glibc.git
110 lines
3.9 KiB
C
110 lines
3.9 KiB
C
/* Double-precision vector (Advanced SIMD) tanh function
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Copyright (C) 2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "v_math.h"
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#include "poly_advsimd_f64.h"
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static const struct data
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{
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float64x2_t poly[11];
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float64x2_t inv_ln2, ln2_hi, ln2_lo, shift;
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uint64x2_t onef;
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uint64x2_t thresh, tiny_bound;
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} data = {
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/* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */
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.poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5),
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V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10),
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V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16),
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V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22),
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V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), },
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.inv_ln2 = V2 (0x1.71547652b82fep0),
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.ln2_hi = V2 (-0x1.62e42fefa39efp-1),
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.ln2_lo = V2 (-0x1.abc9e3b39803fp-56),
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.shift = V2 (0x1.8p52),
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.onef = V2 (0x3ff0000000000000),
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.tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */
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/* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */
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.thresh = V2 (0x01f241bf835f9d5f),
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};
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static inline float64x2_t
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expm1_inline (float64x2_t x, const struct data *d)
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{
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/* Helper routine for calculating exp(x) - 1. Vector port of the helper from
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the scalar variant of tanh. */
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/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
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float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift);
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int64x2_t i = vcvtq_s64_f64 (j);
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float64x2_t f = vfmaq_f64 (x, j, d->ln2_hi);
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f = vfmaq_f64 (f, j, d->ln2_lo);
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/* Approximate expm1(f) using polynomial. */
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float64x2_t f2 = vmulq_f64 (f, f);
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float64x2_t f4 = vmulq_f64 (f2, f2);
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float64x2_t p = vfmaq_f64 (
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f, f2, v_estrin_10_f64 (f, f2, f4, vmulq_f64 (f4, f4), d->poly));
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/* t = 2 ^ i. */
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float64x2_t t = vreinterpretq_f64_u64 (
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vaddq_u64 (vreinterpretq_u64_s64 (i << 52), d->onef));
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/* expm1(x) = p * t + (t - 1). */
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return vfmaq_f64 (vsubq_f64 (t, v_f64 (1)), p, t);
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}
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static float64x2_t NOINLINE VPCS_ATTR
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special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
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{
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return v_call_f64 (tanh, x, y, special);
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}
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/* Vector approximation for double-precision tanh(x), using a simplified
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version of expm1. The greatest observed error is 2.77 ULP:
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_ZGVnN2v_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3
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want -0x1.bd6a21a163624p-3. */
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float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x)
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{
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const struct data *d = ptr_barrier (&data);
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uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x));
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float64x2_t u = x;
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/* Trigger special-cases for tiny, boring and infinity/NaN. */
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uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia, d->tiny_bound), d->thresh);
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#if WANT_SIMD_EXCEPT
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/* To trigger fp exceptions correctly, set special lanes to a neutral value.
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They will be fixed up later by the special-case handler. */
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if (__glibc_unlikely (v_any_u64 (special)))
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u = v_zerofy_f64 (u, special);
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#endif
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u = vaddq_f64 (u, u);
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/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
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float64x2_t q = expm1_inline (u, d);
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float64x2_t qp2 = vaddq_f64 (q, v_f64 (2));
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if (__glibc_unlikely (v_any_u64 (special)))
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return special_case (x, vdivq_f64 (q, qp2), special);
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return vdivq_f64 (q, qp2);
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}
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