1 | /* Single-precision vector (SVE) exp 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 | static const struct data |
23 | { |
24 | float poly[5]; |
25 | float inv_ln2, ln2_hi, ln2_lo, shift, thres; |
26 | } data = { |
27 | /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for |
28 | compatibility with polynomial helpers. */ |
29 | .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f, |
30 | 0x1.0e4020p-7f }, |
31 | .inv_ln2 = 0x1.715476p+0f, |
32 | .ln2_hi = 0x1.62e4p-1f, |
33 | .ln2_lo = 0x1.7f7d1cp-20f, |
34 | /* 1.5*2^17 + 127. */ |
35 | .shift = 0x1.903f8p17f, |
36 | /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled |
37 | correctly by FEXPA. */ |
38 | .thres = 0x1.5d5e2ap+6f, |
39 | }; |
40 | |
41 | #define C(i) sv_f32 (d->poly[i]) |
42 | #define ExponentBias 0x3f800000 |
43 | |
44 | static svfloat32_t NOINLINE |
45 | special_case (svfloat32_t x, svfloat32_t y, svbool_t special) |
46 | { |
47 | return sv_call_f32 (f: expf, x, y, cmp: special); |
48 | } |
49 | |
50 | /* Optimised single-precision SVE exp function. |
51 | Worst-case error is 1.04 ulp: |
52 | SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4 |
53 | want 0x1.ba74bap+4. */ |
54 | svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg) |
55 | { |
56 | const struct data *d = ptr_barrier (&data); |
57 | |
58 | /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] |
59 | x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ |
60 | |
61 | /* Load some constants in quad-word chunks to minimise memory access (last |
62 | lane is wasted). */ |
63 | svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2); |
64 | |
65 | /* n = round(x/(ln2/N)). */ |
66 | svfloat32_t z = svmla_lane (sv_f32 (x: d->shift), x, invln2_and_ln2, 0); |
67 | svfloat32_t n = svsub_x (pg, z, d->shift); |
68 | |
69 | /* r = x - n*ln2/N. */ |
70 | svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1); |
71 | r = svmls_lane (r, n, invln2_and_ln2, 2); |
72 | |
73 | /* scale = 2^(n/N). */ |
74 | svbool_t is_special_case = svacgt (pg, x, d->thres); |
75 | svfloat32_t scale = svexpa (svreinterpret_u32 (z)); |
76 | |
77 | /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */ |
78 | svfloat32_t p12 = svmla_x (pg, C (1), C (2), r); |
79 | svfloat32_t p34 = svmla_x (pg, C (3), C (4), r); |
80 | svfloat32_t r2 = svmul_x (pg, r, r); |
81 | svfloat32_t p14 = svmla_x (pg, p12, p34, r2); |
82 | svfloat32_t p0 = svmul_x (pg, r, C (0)); |
83 | svfloat32_t poly = svmla_x (pg, p0, r2, p14); |
84 | |
85 | if (__glibc_unlikely (svptest_any (pg, is_special_case))) |
86 | return special_case (x, y: svmla_x (pg, scale, scale, poly), special: is_special_case); |
87 | |
88 | return svmla_x (pg, scale, scale, poly); |
89 | } |
90 | |