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067a3415 JR |
1 | /* Double-precision vector (SVE) log10 function |
2 | ||
dff8da6b | 3 | Copyright (C) 2023-2024 Free Software Foundation, Inc. |
067a3415 JR |
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 | #include "poly_sve_f64.h" | |
22 | ||
23 | #define Min 0x0010000000000000 | |
24 | #define Max 0x7ff0000000000000 | |
25 | #define Thres 0x7fe0000000000000 /* Max - Min. */ | |
26 | #define Off 0x3fe6900900000000 | |
27 | #define N (1 << V_LOG10_TABLE_BITS) | |
28 | ||
29 | static svfloat64_t NOINLINE | |
30 | special_case (svfloat64_t x, svfloat64_t y, svbool_t special) | |
31 | { | |
32 | return sv_call_f64 (log10, x, y, special); | |
33 | } | |
34 | ||
35 | /* SVE log10 algorithm. | |
36 | Maximum measured error is 2.46 ulps. | |
37 | SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 | |
38 | want 0x1.fffbdf6eaa667p-6. */ | |
39 | svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg) | |
40 | { | |
41 | svuint64_t ix = svreinterpret_u64 (x); | |
42 | svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres); | |
43 | ||
44 | /* x = 2^k z; where z is in range [Off,2*Off) and exact. | |
45 | The range is split into N subintervals. | |
46 | The ith subinterval contains z and c is near its center. */ | |
47 | svuint64_t tmp = svsub_x (pg, ix, Off); | |
48 | svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS); | |
49 | i = svand_x (pg, i, (N - 1) << 1); | |
50 | svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); | |
51 | svfloat64_t z = svreinterpret_f64 ( | |
52 | svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52))); | |
53 | ||
54 | /* log(x) = k*log(2) + log(c) + log(z/c). */ | |
55 | svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i); | |
56 | svfloat64_t logc | |
57 | = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i); | |
58 | ||
59 | /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): | |
60 | r = z/c - 1 (we look up precomputed 1/c) | |
61 | log(z/c) ~= P(r). */ | |
62 | svfloat64_t r = svmad_x (pg, invc, z, -1.0); | |
63 | ||
64 | /* hi = log(c) + k*log(2). */ | |
65 | svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10); | |
66 | svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2); | |
67 | ||
68 | /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ | |
69 | svfloat64_t r2 = svmul_x (pg, r, r); | |
70 | svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log10_data.poly); | |
71 | ||
72 | if (__glibc_unlikely (svptest_any (pg, special))) | |
73 | return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y), | |
74 | special); | |
75 | return svmla_x (pg, hi, r2, y); | |
76 | } |