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 P(i) sv_f64 (__v_log_data.poly[i])
23#define N (1 << V_LOG_TABLE_BITS)
24#define Off (0x3fe6900900000000)
25#define MaxTop (0x7ff)
26#define MinTop (0x001)
27#define ThreshTop (0x7fe) /* MaxTop - MinTop. */
28
29static svfloat64_t NOINLINE
30special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
31{
32 return sv_call_f64 (f: log, x, y, cmp);
33}
34
35/* SVE port of AdvSIMD log algorithm.
36 Maximum measured error is 2.17 ulp:
37 SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
38 want 0x1.ffffff1cca045p-2. */
39svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
40{
41 svuint64_t ix = svreinterpret_u64 (x);
42 svuint64_t top = svlsr_x (pg, ix, 52);
43 svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop));
44
45 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
46 The range is split into N subintervals.
47 The ith subinterval contains z and c is near its center. */
48 svuint64_t tmp = svsub_x (pg, ix, Off);
49 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
50 The actual value of i is double this due to table layout. */
51 svuint64_t i
52 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
53 svint64_t k
54 = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */
55 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
56 svfloat64_t z = svreinterpret_f64 (iz);
57 /* Lookup in 2 global lists (length N). */
58 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
59 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
60
61 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
62 svfloat64_t r = svmad_x (pg, invc, z, -1);
63 svfloat64_t kd = svcvt_f64_x (pg, k);
64 /* hi = r + log(c) + k*Ln2. */
65 svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
66 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
67 svfloat64_t r2 = svmul_x (pg, r, r);
68 svfloat64_t y = svmla_x (pg, P (2), r, P (3));
69 svfloat64_t p = svmla_x (pg, P (0), r, P (1));
70 y = svmla_x (pg, y, r2, P (4));
71 y = svmla_x (pg, p, r2, y);
72
73 if (__glibc_unlikely (svptest_any (pg, cmp)))
74 return special_case (x, y: svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp);
75 return svmla_x (pg, hi, r2, y);
76}
77

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