1/* Single-precision vector (Advanced SIMD) tan function
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_f32.h"
22
23static const struct data
24{
25 float32x4_t poly[6];
26 float pi_consts[4];
27 float32x4_t shift;
28#if !WANT_SIMD_EXCEPT
29 float32x4_t range_val;
30#endif
31} data = {
32 /* Coefficients generated using FPMinimax. */
33 .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
34 V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
35 /* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */
36 .pi_consts
37 = { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
38 .shift = V4 (0x1.8p+23f),
39#if !WANT_SIMD_EXCEPT
40 .range_val = V4 (0x1p15f),
41#endif
42};
43
44#define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */
45#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */
46#define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */
47
48/* Special cases (fall back to scalar calls). */
49static float32x4_t VPCS_ATTR NOINLINE
50special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
51{
52 return v_call_f32 (tanf, x, y, cmp);
53}
54
55/* Use a full Estrin scheme to evaluate polynomial. */
56static inline float32x4_t
57eval_poly (float32x4_t z, const struct data *d)
58{
59 float32x4_t z2 = vmulq_f32 (z, z);
60#if WANT_SIMD_EXCEPT
61 /* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
62 If fp exceptions are to be triggered correctly,
63 sidestep this by fixing such lanes to 0. */
64 uint32x4_t will_uflow
65 = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
66 if (__glibc_unlikely (v_any_u32 (will_uflow)))
67 z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
68#endif
69 float32x4_t z4 = vmulq_f32 (z2, z2);
70 return v_estrin_5_f32 (z, z2, z4, d->poly);
71}
72
73/* Fast implementation of AdvSIMD tanf.
74 Maximum error is 3.45 ULP:
75 __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
76 want 0x1.ff9850p-1. */
77float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tan) (float32x4_t x)
78{
79 const struct data *d = ptr_barrier (&data);
80 float32x4_t special_arg = x;
81
82 /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
83 regression. */
84#if WANT_SIMD_EXCEPT
85 uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
86 /* If fp exceptions are to be triggered correctly, also special-case tiny
87 input, as this will load to overflow later. Fix any special lanes to 1 to
88 prevent any exceptions being triggered. */
89 uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
90 if (__glibc_unlikely (v_any_u32 (special)))
91 x = vbslq_f32 (special, v_f32 (1.0f), x);
92#else
93 /* Otherwise, special-case large and special values. */
94 uint32x4_t special = vcageq_f32 (x, d->range_val);
95#endif
96
97 /* n = rint(x/(pi/2)). */
98 float32x4_t pi_consts = vld1q_f32 (d->pi_consts);
99 float32x4_t q = vfmaq_laneq_f32 (d->shift, x, pi_consts, 3);
100 float32x4_t n = vsubq_f32 (q, d->shift);
101 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
102 uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
103
104 /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
105 float32x4_t r;
106 r = vfmaq_laneq_f32 (x, n, pi_consts, 0);
107 r = vfmaq_laneq_f32 (r, n, pi_consts, 1);
108 r = vfmaq_laneq_f32 (r, n, pi_consts, 2);
109
110 /* If x lives in an interval, where |tan(x)|
111 - is finite, then use a polynomial approximation of the form
112 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
113 - grows to infinity then use symmetries of tangent and the identity
114 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
115 the same polynomial approximation of tan as above. */
116
117 /* Invert sign of r if odd quadrant. */
118 float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
119
120 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
121 float32x4_t z2 = vmulq_f32 (r, r);
122 float32x4_t p = eval_poly (z2, d);
123 float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
124
125 /* Compute reciprocal and apply if required. */
126 float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
127
128 if (__glibc_unlikely (v_any_u32 (special)))
129 return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
130 return vbslq_f32 (pred_alt, inv_y, y);
131}
132libmvec_hidden_def (V_NAME_F1 (tan))
133HALF_WIDTH_ALIAS_F1 (tan)
134

source code of glibc/sysdeps/aarch64/fpu/tanf_advsimd.c