1 /* Double-precision AdvSIMD log1p
3 Copyright (C) 2023-2024 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
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.
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.
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/>. */
21 #include "poly_advsimd_f64.h"
23 const static struct data
25 float64x2_t poly
[19], ln2
[2];
26 uint64x2_t hf_rt2_top
, one_m_hf_rt2_top
, umask
, inf
, minus_one
;
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)
51 #define BottomMask v_u64 (0xffffffff)
53 static float64x2_t VPCS_ATTR NOINLINE
54 special_case (float64x2_t x
, float64x2_t y
, uint64x2_t special
)
56 return v_call_f64 (log1p
, x
, y
, special
);
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
)
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
);
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
);
77 special
= vorrq_u64 (special
, vcleq_f64 (x
, v_f64 (-1)));
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).
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.
89 We therefore calculate log1p(x) by k*log2 + log1p(f) + c/m. */
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
);
100 = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u
, 52)), d
->one_top
);
101 float64x2_t k
= vcvtq_f64_s64 (ki
);
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));
108 /* Correction term c/m. */
109 float64x2_t cm
= vdivq_f64 (vsubq_f64 (x
, vsubq_f64 (m
, v_f64 (1))), m
);
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
);
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
);
124 if (__glibc_unlikely (v_any_u64 (special
)))
125 return special_case (vreinterpretq_f64_u64 (ix
), vfmaq_f64 (y
, f2
, p
),
128 return vfmaq_f64 (y
, f2
, p
);