1/* Double-precision vector (SVE) log 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 "sv_math.h"
21
22#define N (1 << V_LOG_TABLE_BITS)
23#define Max (0x7ff0000000000000)
24#define Min (0x0010000000000000)
25#define Thresh (0x7fe0000000000000) /* Max - Min. */
26
27static const struct data
28{
29 double c0, c2;
30 double c1, c3;
31 double ln2, c4;
32 uint64_t off;
33} data = {
34 .c0 = -0x1.ffffffffffff7p-2,
35 .c1 = 0x1.55555555170d4p-2,
36 .c2 = -0x1.0000000399c27p-2,
37 .c3 = 0x1.999b2e90e94cap-3,
38 .c4 = -0x1.554e550bd501ep-3,
39 .ln2 = 0x1.62e42fefa39efp-1,
40 .off = 0x3fe6900900000000,
41};
42
43static svfloat64_t NOINLINE
44special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
45 svbool_t special, const struct data *d)
46{
47 svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
48 return sv_call_f64 (f: log, x, y: svmla_x (svptrue_b64 (), hi, r2, y), cmp: special);
49}
50
51/* Double-precision SVE log routine.
52 Maximum measured error is 2.64 ulp:
53 SV_NAME_D1 (log)(0x1.95e54bc91a5e2p+184) got 0x1.fffffffe88cacp+6
54 want 0x1.fffffffe88cafp+6. */
55svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
56{
57 const struct data *d = ptr_barrier (&data);
58
59 svuint64_t ix = svreinterpret_u64 (x);
60 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
61
62 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
63 The range is split into N subintervals.
64 The ith subinterval contains z and c is near its center. */
65 svuint64_t tmp = svsub_x (pg, ix, d->off);
66 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
67 The actual value of i is double this due to table layout. */
68 svuint64_t i
69 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
70 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
71 svfloat64_t z = svreinterpret_f64 (iz);
72 /* Lookup in 2 global lists (length N). */
73 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
74 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
75
76 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
77 svfloat64_t kd = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
78 /* hi = r + log(c) + k*Ln2. */
79 svfloat64_t ln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->ln2);
80 svfloat64_t r = svmad_x (pg, invc, z, -1);
81 svfloat64_t hi = svmla_lane_f64 (logc, kd, ln2_and_c4, 0);
82 hi = svadd_x (pg, r, hi);
83
84 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
85 svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
86 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
87 svfloat64_t y = svmla_lane_f64 (sv_f64 (x: d->c2), r, odd_coeffs, 1);
88 svfloat64_t p = svmla_lane_f64 (sv_f64 (x: d->c0), r, odd_coeffs, 0);
89 y = svmla_lane_f64 (y, r2, ln2_and_c4, 1);
90 y = svmla_x (pg, p, r2, y);
91
92 if (__glibc_unlikely (svptest_any (pg, special)))
93 return special_case (hi, tmp, y, r2, special, d);
94 return svmla_x (pg, hi, r2, y);
95}
96

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