1 | /* Double-precision AdvSIMD 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 "v_math.h" |
21 | #include "poly_advsimd_f64.h" |
22 | |
23 | const static struct data |
24 | { |
25 | float64x2_t poly[19], ln2[2]; |
26 | uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask, inf, minus_one; |
27 | int64x2_t one_top; |
28 | } data = { |
29 | /* Generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */ |
30 | .poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2), |
31 | V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3), |
32 | V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3), |
33 | V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4), |
34 | V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4), |
35 | V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4), |
36 | V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4), |
37 | V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5), |
38 | V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4), |
39 | V2 (-0x1.cfa7385bdb37ep-6) }, |
40 | .ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) }, |
41 | /* top32(asuint64(sqrt(2)/2)) << 32. */ |
42 | .hf_rt2_top = V2 (0x3fe6a09e00000000), |
43 | /* (top32(asuint64(1)) - top32(asuint64(sqrt(2)/2))) << 32. */ |
44 | .one_m_hf_rt2_top = V2 (0x00095f6200000000), |
45 | .umask = V2 (0x000fffff00000000), |
46 | .one_top = V2 (0x3ff), |
47 | .inf = V2 (0x7ff0000000000000), |
48 | .minus_one = V2 (0xbff0000000000000) |
49 | }; |
50 | |
51 | #define BottomMask v_u64 (0xffffffff) |
52 | |
53 | static float64x2_t VPCS_ATTR NOINLINE |
54 | special_case (float64x2_t x, float64x2_t y, uint64x2_t special) |
55 | { |
56 | return v_call_f64 (log1p, x, y, special); |
57 | } |
58 | |
59 | /* Vector log1p approximation using polynomial on reduced interval. Routine is |
60 | a modification of the algorithm used in scalar log1p, with no shortcut for |
61 | k=0 and no narrowing for f and k. Maximum observed error is 2.45 ULP: |
62 | _ZGVnN2v_log1p(0x1.658f7035c4014p+11) got 0x1.fd61d0727429dp+2 |
63 | want 0x1.fd61d0727429fp+2 . */ |
64 | VPCS_ATTR float64x2_t V_NAME_D1 (log1p) (float64x2_t x) |
65 | { |
66 | const struct data *d = ptr_barrier (&data); |
67 | uint64x2_t ix = vreinterpretq_u64_f64 (x); |
68 | uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); |
69 | uint64x2_t special = vcgeq_u64 (ia, d->inf); |
70 | |
71 | #if WANT_SIMD_EXCEPT |
72 | special = vorrq_u64 (special, |
73 | vcgeq_u64 (ix, vreinterpretq_u64_f64 (v_f64 (-1)))); |
74 | if (__glibc_unlikely (v_any_u64 (special))) |
75 | x = v_zerofy_f64 (x, special); |
76 | #else |
77 | special = vorrq_u64 (special, vcleq_f64 (x, v_f64 (-1))); |
78 | #endif |
79 | |
80 | /* With x + 1 = t * 2^k (where t = f + 1 and k is chosen such that f |
81 | is in [sqrt(2)/2, sqrt(2)]): |
82 | log1p(x) = k*log(2) + log1p(f). |
83 | |
84 | f may not be representable exactly, so we need a correction term: |
85 | let m = round(1 + x), c = (1 + x) - m. |
86 | c << m: at very small x, log1p(x) ~ x, hence: |
87 | log(1+x) - log(m) ~ c/m. |
88 | |
89 | We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */ |
90 | |
91 | /* Obtain correctly scaled k by manipulation in the exponent. |
92 | The scalar algorithm casts down to 32-bit at this point to calculate k and |
93 | u_red. We stay in double-width to obtain f and k, using the same constants |
94 | as the scalar algorithm but shifted left by 32. */ |
95 | float64x2_t m = vaddq_f64 (x, v_f64 (1)); |
96 | uint64x2_t mi = vreinterpretq_u64_f64 (m); |
97 | uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top); |
98 | |
99 | int64x2_t ki |
100 | = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top); |
101 | float64x2_t k = vcvtq_f64_s64 (ki); |
102 | |
103 | /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ |
104 | uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top); |
105 | uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask)); |
106 | float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1)); |
107 | |
108 | /* Correction term c/m. */ |
109 | float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m); |
110 | |
111 | /* Approximate log1p(x) on the reduced input using a polynomial. Because |
112 | log1p(0)=0 we choose an approximation of the form: |
113 | x + C0*x^2 + C1*x^3 + C2x^4 + ... |
114 | Hence approximation has the form f + f^2 * P(f) |
115 | where P(x) = C0 + C1*x + C2x^2 + ... |
116 | Assembling this all correctly is dealt with at the final step. */ |
117 | float64x2_t f2 = vmulq_f64 (f, f); |
118 | float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly); |
119 | |
120 | float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]); |
121 | float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]); |
122 | float64x2_t y = vaddq_f64 (ylo, yhi); |
123 | |
124 | if (__glibc_unlikely (v_any_u64 (special))) |
125 | return special_case (vreinterpretq_f64_u64 (ix), vfmaq_f64 (y, f2, p), |
126 | special); |
127 | |
128 | return vfmaq_f64 (y, f2, p); |
129 | } |
130 | |