1 /* Double-precision vector (Advanced SIMD) sinh function
3 Copyright (C) 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 static const struct data
26 float64x2_t inv_ln2
, m_ln2
, shift
;
30 uint64x2_t tiny_bound
, thresh
;
32 uint64x2_t large_bound
;
35 /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */
36 .poly
= { V2 (0x1p
-1), V2 (0x1.5555555555559p
-3), V2 (0x1.555555555554bp
-5),
37 V2 (0x1.111111110f663p
-7), V2 (0x1.6c16c16c1b5f3p
-10),
38 V2 (0x1.a01a01affa35dp
-13), V2 (0x1.a01a018b4ecbbp
-16),
39 V2 (0x1.71ddf82db5bb4p
-19), V2 (0x1.27e517fc0d54bp
-22),
40 V2 (0x1.af5eedae67435p
-26), V2 (0x1.1f143d060a28ap
-29), },
42 .inv_ln2
= V2 (0x1.71547652b82fep0
),
43 .m_ln2
= (float64x2_t
) {-0x1.62e42fefa39efp
-1, -0x1.abc9e3b39803fp
-56},
44 .shift
= V2 (0x1.8p52
),
46 .halff
= V2 (0x3fe0000000000000),
47 .onef
= V2 (0x3ff0000000000000),
49 /* 2^-26, below which sinh(x) rounds to x. */
50 .tiny_bound
= V2 (0x3e50000000000000),
51 /* asuint(large_bound) - asuint(tiny_bound). */
52 .thresh
= V2 (0x0230000000000000),
54 /* 2^9. expm1 helper overflows for large input. */
55 .large_bound
= V2 (0x4080000000000000),
59 static inline float64x2_t
60 expm1_inline (float64x2_t x
)
62 const struct data
*d
= ptr_barrier (&data
);
65 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
66 where i = round(x / ln2)
67 and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */
68 float64x2_t j
= vsubq_f64 (vfmaq_f64 (d
->shift
, d
->inv_ln2
, x
), d
->shift
);
69 int64x2_t i
= vcvtq_s64_f64 (j
);
70 float64x2_t f
= vfmaq_laneq_f64 (x
, j
, d
->m_ln2
, 0);
71 f
= vfmaq_laneq_f64 (f
, j
, d
->m_ln2
, 1);
72 /* Approximate expm1(f) using polynomial. */
73 float64x2_t f2
= vmulq_f64 (f
, f
);
74 float64x2_t f4
= vmulq_f64 (f2
, f2
);
75 float64x2_t f8
= vmulq_f64 (f4
, f4
);
76 float64x2_t p
= vfmaq_f64 (f
, f2
, v_estrin_10_f64 (f
, f2
, f4
, f8
, d
->poly
));
78 float64x2_t t
= vreinterpretq_f64_u64 (
79 vreinterpretq_u64_s64 (vaddq_s64 (vshlq_n_s64 (i
, 52), d
->onef
)));
80 /* expm1(x) ~= p * t + (t - 1). */
81 return vfmaq_f64 (vsubq_f64 (t
, v_f64 (1.0)), p
, t
);
84 static float64x2_t NOINLINE VPCS_ATTR
85 special_case (float64x2_t x
)
87 return v_call_f64 (sinh
, x
, x
, v_u64 (-1));
90 /* Approximation for vector double-precision sinh(x) using expm1.
91 sinh(x) = (exp(x) - exp(-x)) / 2.
92 The greatest observed error is 2.57 ULP:
93 _ZGVnN2v_sinh (0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2
94 want 0x1.ab34e59d678d9p-2. */
95 float64x2_t VPCS_ATTR
V_NAME_D1 (sinh
) (float64x2_t x
)
97 const struct data
*d
= ptr_barrier (&data
);
99 float64x2_t ax
= vabsq_f64 (x
);
101 = veorq_u64 (vreinterpretq_u64_f64 (x
), vreinterpretq_u64_f64 (ax
));
102 float64x2_t halfsign
= vreinterpretq_f64_u64 (vorrq_u64 (sign
, d
->halff
));
105 uint64x2_t special
= vcgeq_u64 (
106 vsubq_u64 (vreinterpretq_u64_f64 (ax
), d
->tiny_bound
), d
->thresh
);
108 uint64x2_t special
= vcgeq_u64 (vreinterpretq_u64_f64 (ax
), d
->large_bound
);
111 /* Fall back to scalar variant for all lanes if any of them are special. */
112 if (__glibc_unlikely (v_any_u64 (special
)))
113 return special_case (x
);
115 /* Up to the point that expm1 overflows, we can use it to calculate sinh
116 using a slight rearrangement of the definition of sinh. This allows us to
117 retain acceptable accuracy for very small inputs. */
118 float64x2_t t
= expm1_inline (ax
);
119 t
= vaddq_f64 (t
, vdivq_f64 (t
, vaddq_f64 (t
, v_f64 (1.0))));
120 return vmulq_f64 (t
, halfsign
);