1/* Double-precision vector (AdvSIMD) exp2 function
2
3 Copyright (C) 2023-2024 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20#include "v_math.h"
21#include "poly_advsimd_f64.h"
22
23#define N (1 << V_LOG2_TABLE_BITS)
24
25static const struct data
26{
27 uint64x2_t min_norm;
28 uint32x4_t special_bound;
29 float64x2_t poly[5];
30 float64x2_t invln2;
31 uint64x2_t sign_exp_mask;
32} data = {
33 /* Each coefficient was generated to approximate log(r) for |r| < 0x1.fp-9
34 and N = 128, then scaled by log2(e) in extended precision and rounded back
35 to double precision. */
36 .poly = { V2 (-0x1.71547652b83p-1), V2 (0x1.ec709dc340953p-2),
37 V2 (-0x1.71547651c8f35p-2), V2 (0x1.2777ebe12dda5p-2),
38 V2 (-0x1.ec738d616fe26p-3) },
39 .invln2 = V2 (0x1.71547652b82fep0),
40 .min_norm = V2 (0x0010000000000000), /* asuint64(0x1p-1022). */
41 .special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */
42 .sign_exp_mask = V2 (0xfff0000000000000),
43};
44
45#define Off v_u64 (0x3fe6900900000000)
46#define IndexMask (N - 1)
47
48struct entry
49{
50 float64x2_t invc;
51 float64x2_t log2c;
52};
53
54static inline struct entry
55lookup (uint64x2_t i)
56{
57 struct entry e;
58 uint64_t i0 = (i[0] >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
59 uint64_t i1 = (i[1] >> (52 - V_LOG2_TABLE_BITS)) & IndexMask;
60 float64x2_t e0 = vld1q_f64 (&__v_log2_data.table[i0].invc);
61 float64x2_t e1 = vld1q_f64 (&__v_log2_data.table[i1].invc);
62 e.invc = vuzp1q_f64 (e0, e1);
63 e.log2c = vuzp2q_f64 (e0, e1);
64 return e;
65}
66
67static float64x2_t VPCS_ATTR NOINLINE
68special_case (float64x2_t x, float64x2_t y, float64x2_t w, float64x2_t r2,
69 uint32x2_t special)
70{
71 return v_call_f64 (log2, x, vfmaq_f64 (w, r2, y), vmovl_u32 (special));
72}
73
74/* Double-precision vector log2 routine. Implements the same algorithm as
75 vector log10, with coefficients and table entries scaled in extended
76 precision. The maximum observed error is 2.58 ULP:
77 _ZGVnN2v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
78 want 0x1.fffb34198d9ddp-5. */
79float64x2_t VPCS_ATTR V_NAME_D1 (log2) (float64x2_t x)
80{
81 const struct data *d = ptr_barrier (&data);
82 uint64x2_t ix = vreinterpretq_u64_f64 (x);
83 uint32x2_t special = vcge_u32 (vsubhn_u64 (ix, d->min_norm),
84 vget_low_u32 (d->special_bound));
85
86 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
87 The range is split into N subintervals.
88 The ith subinterval contains z and c is near its center. */
89 uint64x2_t tmp = vsubq_u64 (ix, Off);
90 int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52);
91 uint64x2_t iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
92 float64x2_t z = vreinterpretq_f64_u64 (iz);
93
94 struct entry e = lookup (tmp);
95
96 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
97
98 float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
99 float64x2_t kd = vcvtq_f64_s64 (k);
100 float64x2_t w = vfmaq_f64 (e.log2c, r, d->invln2);
101
102 float64x2_t r2 = vmulq_f64 (r, r);
103 float64x2_t y = v_pw_horner_4_f64 (r, r2, d->poly);
104 w = vaddq_f64 (kd, w);
105
106 if (__glibc_unlikely (v_any_u32h (special)))
107 return special_case (x, y, w, r2, special);
108 return vfmaq_f64 (w, r2, y);
109}
110

source code of glibc/sysdeps/aarch64/fpu/log2_advsimd.c