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3548a4f0 JR |
1 | /* Single-precision AdvSIMD log1p |
2 | ||
3 | Copyright (C) 2023 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_f32.h" | |
22 | ||
23 | const static struct data | |
24 | { | |
25 | float32x4_t poly[8], ln2; | |
26 | uint32x4_t tiny_bound, minus_one, four, thresh; | |
27 | int32x4_t three_quarters; | |
28 | } data = { | |
29 | .poly = { /* Generated using FPMinimax in [-0.25, 0.5]. First two coefficients | |
30 | (1, -0.5) are not stored as they can be generated more | |
31 | efficiently. */ | |
32 | V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f), | |
33 | V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f), | |
34 | V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) }, | |
35 | .ln2 = V4 (0x1.62e43p-1f), | |
36 | .tiny_bound = V4 (0x34000000), /* asuint32(0x1p-23). ulp=0.5 at 0x1p-23. */ | |
37 | .thresh = V4 (0x4b800000), /* asuint32(INFINITY) - tiny_bound. */ | |
38 | .minus_one = V4 (0xbf800000), | |
39 | .four = V4 (0x40800000), | |
40 | .three_quarters = V4 (0x3f400000) | |
41 | }; | |
42 | ||
43 | static inline float32x4_t | |
44 | eval_poly (float32x4_t m, const float32x4_t *p) | |
45 | { | |
46 | /* Approximate log(1+m) on [-0.25, 0.5] using split Estrin scheme. */ | |
47 | float32x4_t p_12 = vfmaq_f32 (v_f32 (-0.5), m, p[0]); | |
48 | float32x4_t p_34 = vfmaq_f32 (p[1], m, p[2]); | |
49 | float32x4_t p_56 = vfmaq_f32 (p[3], m, p[4]); | |
50 | float32x4_t p_78 = vfmaq_f32 (p[5], m, p[6]); | |
51 | ||
52 | float32x4_t m2 = vmulq_f32 (m, m); | |
53 | float32x4_t p_02 = vfmaq_f32 (m, m2, p_12); | |
54 | float32x4_t p_36 = vfmaq_f32 (p_34, m2, p_56); | |
55 | float32x4_t p_79 = vfmaq_f32 (p_78, m2, p[7]); | |
56 | ||
57 | float32x4_t m4 = vmulq_f32 (m2, m2); | |
58 | float32x4_t p_06 = vfmaq_f32 (p_02, m4, p_36); | |
59 | return vfmaq_f32 (p_06, m4, vmulq_f32 (m4, p_79)); | |
60 | } | |
61 | ||
62 | static float32x4_t NOINLINE VPCS_ATTR | |
63 | special_case (float32x4_t x, float32x4_t y, uint32x4_t special) | |
64 | { | |
65 | return v_call_f32 (log1pf, x, y, special); | |
66 | } | |
67 | ||
68 | /* Vector log1pf approximation using polynomial on reduced interval. Accuracy | |
69 | is roughly 2.02 ULP: | |
70 | log1pf(0x1.21e13ap-2) got 0x1.fe8028p-3 want 0x1.fe802cp-3. */ | |
71 | VPCS_ATTR float32x4_t V_NAME_F1 (log1p) (float32x4_t x) | |
72 | { | |
73 | const struct data *d = ptr_barrier (&data); | |
74 | ||
75 | uint32x4_t ix = vreinterpretq_u32_f32 (x); | |
76 | uint32x4_t ia = vreinterpretq_u32_f32 (vabsq_f32 (x)); | |
77 | uint32x4_t special_cases | |
78 | = vorrq_u32 (vcgeq_u32 (vsubq_u32 (ia, d->tiny_bound), d->thresh), | |
79 | vcgeq_u32 (ix, d->minus_one)); | |
80 | float32x4_t special_arg = x; | |
81 | ||
82 | #if WANT_SIMD_EXCEPT | |
83 | if (__glibc_unlikely (v_any_u32 (special_cases))) | |
84 | /* Side-step special lanes so fenv exceptions are not triggered | |
85 | inadvertently. */ | |
86 | x = v_zerofy_f32 (x, special_cases); | |
87 | #endif | |
88 | ||
89 | /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m | |
90 | is in [-0.25, 0.5]): | |
91 | log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). | |
92 | ||
93 | We approximate log1p(m) with a polynomial, then scale by | |
94 | k*log(2). Instead of doing this directly, we use an intermediate | |
95 | scale factor s = 4*k*log(2) to ensure the scale is representable | |
96 | as a normalised fp32 number. */ | |
97 | ||
98 | float32x4_t m = vaddq_f32 (x, v_f32 (1.0f)); | |
99 | ||
100 | /* Choose k to scale x to the range [-1/4, 1/2]. */ | |
101 | int32x4_t k | |
102 | = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d->three_quarters), | |
103 | v_s32 (0xff800000)); | |
104 | uint32x4_t ku = vreinterpretq_u32_s32 (k); | |
105 | ||
106 | /* Scale x by exponent manipulation. */ | |
107 | float32x4_t m_scale | |
108 | = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku)); | |
109 | ||
110 | /* Scale up to ensure that the scale factor is representable as normalised | |
111 | fp32 number, and scale m down accordingly. */ | |
112 | float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d->four, ku)); | |
113 | m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s)); | |
114 | ||
115 | /* Evaluate polynomial on the reduced interval. */ | |
116 | float32x4_t p = eval_poly (m_scale, d->poly); | |
117 | ||
118 | /* The scale factor to be applied back at the end - by multiplying float(k) | |
119 | by 2^-23 we get the unbiased exponent of k. */ | |
120 | float32x4_t scale_back = vcvtq_f32_s32 (vshrq_n_s32 (k, 23)); | |
121 | ||
122 | /* Apply the scaling back. */ | |
123 | float32x4_t y = vfmaq_f32 (p, scale_back, d->ln2); | |
124 | ||
125 | if (__glibc_unlikely (v_any_u32 (special_cases))) | |
126 | return special_case (special_arg, y, special_cases); | |
127 | return y; | |
128 | } |