1 | /* Double-precision vector (AdvSIMD) exp2 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 "v_math.h" |
21 | #include "poly_advsimd_f64.h" |
22 | |
23 | #define N (1 << V_EXP_TABLE_BITS) |
24 | #define IndexMask (N - 1) |
25 | #define BigBound 1022.0 |
26 | #define UOFlowBound 1280.0 |
27 | #define TinyBound 0x2000000000000000 /* asuint64(0x1p-511). */ |
28 | |
29 | static const struct data |
30 | { |
31 | float64x2_t poly[4]; |
32 | float64x2_t shift, scale_big_bound, scale_uoflow_bound; |
33 | } data = { |
34 | /* Coefficients are computed using Remez algorithm with |
35 | minimisation of the absolute error. */ |
36 | .poly = { V2 (0x1.62e42fefa3686p-1), V2 (0x1.ebfbdff82c241p-3), |
37 | V2 (0x1.c6b09b16de99ap-5), V2 (0x1.3b2abf5571ad8p-7) }, |
38 | .shift = V2 (0x1.8p52 / N), |
39 | .scale_big_bound = V2 (BigBound), |
40 | .scale_uoflow_bound = V2 (UOFlowBound), |
41 | }; |
42 | |
43 | static inline uint64x2_t |
44 | lookup_sbits (uint64x2_t i) |
45 | { |
46 | return (uint64x2_t){ __v_exp_data[i[0] & IndexMask], |
47 | __v_exp_data[i[1] & IndexMask] }; |
48 | } |
49 | |
50 | #if WANT_SIMD_EXCEPT |
51 | |
52 | # define Thres 0x2080000000000000 /* asuint64(512.0) - TinyBound. */ |
53 | |
54 | /* Call scalar exp2 as a fallback. */ |
55 | static float64x2_t VPCS_ATTR NOINLINE |
56 | special_case (float64x2_t x, float64x2_t y, uint64x2_t is_special) |
57 | { |
58 | return v_call_f64 (exp2, x, y, is_special); |
59 | } |
60 | |
61 | #else |
62 | |
63 | # define SpecialOffset 0x6000000000000000 /* 0x1p513. */ |
64 | /* SpecialBias1 + SpecialBias1 = asuint(1.0). */ |
65 | # define SpecialBias1 0x7000000000000000 /* 0x1p769. */ |
66 | # define SpecialBias2 0x3010000000000000 /* 0x1p-254. */ |
67 | |
68 | static inline float64x2_t VPCS_ATTR |
69 | special_case (float64x2_t s, float64x2_t y, float64x2_t n, |
70 | const struct data *d) |
71 | { |
72 | /* 2^(n/N) may overflow, break it up into s1*s2. */ |
73 | uint64x2_t b = vandq_u64 (vclezq_f64 (n), v_u64 (SpecialOffset)); |
74 | float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (v_u64 (SpecialBias1), b)); |
75 | float64x2_t s2 = vreinterpretq_f64_u64 ( |
76 | vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), v_u64 (SpecialBias2)), b)); |
77 | uint64x2_t cmp = vcagtq_f64 (n, d->scale_uoflow_bound); |
78 | float64x2_t r1 = vmulq_f64 (s1, s1); |
79 | float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, s2, y), s1); |
80 | return vbslq_f64 (cmp, r1, r0); |
81 | } |
82 | |
83 | #endif |
84 | |
85 | /* Fast vector implementation of exp2. |
86 | Maximum measured error is 1.65 ulp. |
87 | _ZGVnN2v_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1 |
88 | want 0x1.f8db0d4df721dp-1. */ |
89 | VPCS_ATTR |
90 | float64x2_t V_NAME_D1 (exp2) (float64x2_t x) |
91 | { |
92 | const struct data *d = ptr_barrier (&data); |
93 | uint64x2_t cmp; |
94 | #if WANT_SIMD_EXCEPT |
95 | uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); |
96 | cmp = vcgeq_u64 (vsubq_u64 (ia, v_u64 (TinyBound)), v_u64 (Thres)); |
97 | /* Mask special lanes and retain a copy of x for passing to special-case |
98 | handler. */ |
99 | float64x2_t xc = x; |
100 | x = v_zerofy_f64 (x, cmp); |
101 | #else |
102 | cmp = vcagtq_f64 (x, d->scale_big_bound); |
103 | #endif |
104 | |
105 | /* n = round(x/N). */ |
106 | float64x2_t z = vaddq_f64 (d->shift, x); |
107 | uint64x2_t u = vreinterpretq_u64_f64 (z); |
108 | float64x2_t n = vsubq_f64 (z, d->shift); |
109 | |
110 | /* r = x - n/N. */ |
111 | float64x2_t r = vsubq_f64 (x, n); |
112 | |
113 | /* s = 2^(n/N). */ |
114 | uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS); |
115 | u = lookup_sbits (u); |
116 | float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e)); |
117 | |
118 | /* y ~ exp2(r) - 1. */ |
119 | float64x2_t r2 = vmulq_f64 (r, r); |
120 | float64x2_t y = v_pairwise_poly_3_f64 (r, r2, d->poly); |
121 | y = vmulq_f64 (r, y); |
122 | |
123 | if (__glibc_unlikely (v_any_u64 (cmp))) |
124 | #if !WANT_SIMD_EXCEPT |
125 | return special_case (s, y, n, d); |
126 | #else |
127 | return special_case (xc, vfmaq_f64 (s, s, y), cmp); |
128 | #endif |
129 | return vfmaq_f64 (s, s, y); |
130 | } |
131 | |