1/* Double-precision vector (AdvSIMD) log10 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_LOG10_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 invln10, log10_2, ln2;
31 uint64x2_t sign_exp_mask;
32} data = {
33 /* Computed from log coefficients divided by log(10) then rounded to double
34 precision. */
35 .poly = { V2 (-0x1.bcb7b1526e506p-3), V2 (0x1.287a7636be1d1p-3),
36 V2 (-0x1.bcb7b158af938p-4), V2 (0x1.63c78734e6d07p-4),
37 V2 (-0x1.287461742fee4p-4) },
38 .ln2 = V2 (0x1.62e42fefa39efp-1),
39 .invln10 = V2 (0x1.bcb7b1526e50ep-2),
40 .log10_2 = V2 (0x1.34413509f79ffp-2),
41 .min_norm = V2 (0x0010000000000000), /* asuint64(0x1p-1022). */
42 .special_bound = V4 (0x7fe00000), /* asuint64(inf) - min_norm. */
43 .sign_exp_mask = V2 (0xfff0000000000000),
44};
45
46#define Off v_u64 (0x3fe6900900000000)
47#define IndexMask (N - 1)
48
49#define T(s, i) __v_log10_data.s[i]
50
51struct entry
52{
53 float64x2_t invc;
54 float64x2_t log10c;
55};
56
57static inline struct entry
58lookup (uint64x2_t i)
59{
60 struct entry e;
61 uint64_t i0 = (i[0] >> (52 - V_LOG10_TABLE_BITS)) & IndexMask;
62 uint64_t i1 = (i[1] >> (52 - V_LOG10_TABLE_BITS)) & IndexMask;
63 float64x2_t e0 = vld1q_f64 (&__v_log10_data.table[i0].invc);
64 float64x2_t e1 = vld1q_f64 (&__v_log10_data.table[i1].invc);
65 e.invc = vuzp1q_f64 (e0, e1);
66 e.log10c = vuzp2q_f64 (e0, e1);
67 return e;
68}
69
70static float64x2_t VPCS_ATTR NOINLINE
71special_case (float64x2_t x, float64x2_t y, float64x2_t hi, float64x2_t r2,
72 uint32x2_t special)
73{
74 return v_call_f64 (log10, x, vfmaq_f64 (hi, r2, y), vmovl_u32 (special));
75}
76
77/* Fast implementation of double-precision vector log10
78 is a slight modification of double-precision vector log.
79 Max ULP error: < 2.5 ulp (nearest rounding.)
80 Maximum measured at 2.46 ulp for x in [0.96, 0.97]
81 _ZGVnN2v_log10(0x1.13192407fcb46p+0) got 0x1.fff6be3cae4bbp-6
82 want 0x1.fff6be3cae4b9p-6. */
83float64x2_t VPCS_ATTR V_NAME_D1 (log10) (float64x2_t x)
84{
85 const struct data *d = ptr_barrier (&data);
86 uint64x2_t ix = vreinterpretq_u64_f64 (x);
87 uint32x2_t special = vcge_u32 (vsubhn_u64 (ix, d->min_norm),
88 vget_low_u32 (d->special_bound));
89
90 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
91 The range is split into N subintervals.
92 The ith subinterval contains z and c is near its center. */
93 uint64x2_t tmp = vsubq_u64 (ix, Off);
94 int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52);
95 uint64x2_t iz = vsubq_u64 (ix, vandq_u64 (tmp, d->sign_exp_mask));
96 float64x2_t z = vreinterpretq_f64_u64 (iz);
97
98 struct entry e = lookup (tmp);
99
100 /* log10(x) = log1p(z/c-1)/log(10) + log10(c) + k*log10(2). */
101 float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc);
102 float64x2_t kd = vcvtq_f64_s64 (k);
103
104 /* hi = r / log(10) + log10(c) + k*log10(2).
105 Constants in v_log10_data.c are computed (in extended precision) as
106 e.log10c := e.logc * ivln10. */
107 float64x2_t w = vfmaq_f64 (e.log10c, r, d->invln10);
108
109 /* y = log10(1+r) + n * log10(2). */
110 float64x2_t hi = vfmaq_f64 (w, kd, d->log10_2);
111
112 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
113 float64x2_t r2 = vmulq_f64 (r, r);
114 float64x2_t y = v_pw_horner_4_f64 (r, r2, d->poly);
115
116 if (__glibc_unlikely (v_any_u32h (special)))
117 return special_case (x, y, hi, r2, special);
118 return vfmaq_f64 (hi, r2, y);
119}
120

source code of glibc/sysdeps/aarch64/fpu/log10_advsimd.c