1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
|
/* Single-precision vector (Advanced SIMD) tan function
Copyright (C) 2023-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include "v_math.h"
#include "poly_advsimd_f32.h"
static const struct data
{
float32x4_t poly[6];
float32x4_t pi_consts;
float32x4_t shift;
#if !WANT_SIMD_EXCEPT
float32x4_t range_val;
#endif
} data = {
/* Coefficients generated using FPMinimax. */
.poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
/* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */
.pi_consts
= { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
.shift = V4 (0x1.8p+23f),
#if !WANT_SIMD_EXCEPT
.range_val = V4 (0x1p15f),
#endif
};
#define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */
#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */
#define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */
/* Special cases (fall back to scalar calls). */
static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
{
return v_call_f32 (tanf, x, y, cmp);
}
/* Use a full Estrin scheme to evaluate polynomial. */
static inline float32x4_t
eval_poly (float32x4_t z, const struct data *d)
{
float32x4_t z2 = vmulq_f32 (z, z);
#if WANT_SIMD_EXCEPT
/* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
If fp exceptions are to be triggered correctly,
sidestep this by fixing such lanes to 0. */
uint32x4_t will_uflow
= vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
if (__glibc_unlikely (v_any_u32 (will_uflow)))
z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
#endif
float32x4_t z4 = vmulq_f32 (z2, z2);
return v_estrin_5_f32 (z, z2, z4, d->poly);
}
/* Fast implementation of AdvSIMD tanf.
Maximum error is 3.45 ULP:
__v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
want 0x1.ff9850p-1. */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tan) (float32x4_t x)
{
const struct data *d = ptr_barrier (&data);
float32x4_t special_arg = x;
/* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
regression. */
#if WANT_SIMD_EXCEPT
uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
/* If fp exceptions are to be triggered correctly, also special-case tiny
input, as this will load to overflow later. Fix any special lanes to 1 to
prevent any exceptions being triggered. */
uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
if (__glibc_unlikely (v_any_u32 (special)))
x = vbslq_f32 (special, v_f32 (1.0f), x);
#else
/* Otherwise, special-case large and special values. */
uint32x4_t special = vcageq_f32 (x, d->range_val);
#endif
/* n = rint(x/(pi/2)). */
float32x4_t q = vfmaq_laneq_f32 (d->shift, x, d->pi_consts, 3);
float32x4_t n = vsubq_f32 (q, d->shift);
/* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
/* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
float32x4_t r;
r = vfmaq_laneq_f32 (x, n, d->pi_consts, 0);
r = vfmaq_laneq_f32 (r, n, d->pi_consts, 1);
r = vfmaq_laneq_f32 (r, n, d->pi_consts, 2);
/* If x lives in an interval, where |tan(x)|
- is finite, then use a polynomial approximation of the form
tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
- grows to infinity then use symmetries of tangent and the identity
tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
the same polynomial approximation of tan as above. */
/* Invert sign of r if odd quadrant. */
float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
/* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
float32x4_t z2 = vmulq_f32 (r, r);
float32x4_t p = eval_poly (z2, d);
float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
/* Compute reciprocal and apply if required. */
float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
if (__glibc_unlikely (v_any_u32 (special)))
return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
return vbslq_f32 (pred_alt, inv_y, y);
}
libmvec_hidden_def (V_NAME_F1 (tan))
HALF_WIDTH_ALIAS_F1 (tan)
|
