1 | /* Single-precision SVE log1p |
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 | #include "poly_sve_f32.h" |
22 | |
23 | static const struct data |
24 | { |
25 | float poly[8]; |
26 | float ln2, exp_bias; |
27 | uint32_t four, three_quarters; |
28 | } data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as |
29 | this can be fmov-ed directly instead of including it in |
30 | the main load-and-mla polynomial schedule. */ |
31 | 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f, |
32 | -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f, |
33 | 0x1.abcb6p-4f, -0x1.6f0d5ep-5f}, |
34 | .ln2 = 0x1.62e43p-1f, |
35 | .exp_bias = 0x1p-23f, |
36 | .four = 0x40800000, |
37 | .three_quarters = 0x3f400000}; |
38 | |
39 | #define SignExponentMask 0xff800000 |
40 | |
41 | static svfloat32_t NOINLINE |
42 | special_case (svfloat32_t x, svfloat32_t y, svbool_t special) |
43 | { |
44 | return sv_call_f32 (f: log1pf, x, y, cmp: special); |
45 | } |
46 | |
47 | /* Vector log1pf approximation using polynomial on reduced interval. Worst-case |
48 | error is 1.27 ULP very close to 0.5. |
49 | _ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2 |
50 | want 0x1.9f323ep-2. */ |
51 | svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg) |
52 | { |
53 | const struct data *d = ptr_barrier (&data); |
54 | /* x < -1, Inf/Nan. */ |
55 | svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000); |
56 | special = svorn_z (pg, special, svcmpge (pg, x, -1)); |
57 | |
58 | /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m |
59 | is in [-0.25, 0.5]): |
60 | log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). |
61 | |
62 | We approximate log1p(m) with a polynomial, then scale by |
63 | k*log(2). Instead of doing this directly, we use an intermediate |
64 | scale factor s = 4*k*log(2) to ensure the scale is representable |
65 | as a normalised fp32 number. */ |
66 | svfloat32_t m = svadd_x (pg, x, 1); |
67 | |
68 | /* Choose k to scale x to the range [-1/4, 1/2]. */ |
69 | svint32_t k |
70 | = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters), |
71 | sv_s32 (SignExponentMask)); |
72 | |
73 | /* Scale x by exponent manipulation. */ |
74 | svfloat32_t m_scale = svreinterpret_f32 ( |
75 | svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k))); |
76 | |
77 | /* Scale up to ensure that the scale factor is representable as normalised |
78 | fp32 number, and scale m down accordingly. */ |
79 | svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four)); |
80 | m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (x: -1), s, 0.25)); |
81 | |
82 | /* Evaluate polynomial on reduced interval. */ |
83 | svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale), |
84 | ms4 = svmul_x (pg, ms2, ms2); |
85 | svfloat32_t p = sv_estrin_7_f32_x (pg, x: m_scale, x2: ms2, x4: ms4, poly: d->poly); |
86 | p = svmad_x (pg, m_scale, p, -0.5); |
87 | p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p)); |
88 | |
89 | /* The scale factor to be applied back at the end - by multiplying float(k) |
90 | by 2^-23 we get the unbiased exponent of k. */ |
91 | svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias); |
92 | |
93 | /* Apply the scaling back. */ |
94 | svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2); |
95 | |
96 | if (__glibc_unlikely (svptest_any (pg, special))) |
97 | return special_case (x, y, special); |
98 | |
99 | return y; |
100 | } |
101 | |