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 | |
23 | static const struct data |
24 | { |
25 | float32x4_t poly[6]; |
26 | float32x4_t pi_consts; |
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). */ |
49 | static float32x4_t VPCS_ATTR NOINLINE |
50 | special_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. */ |
56 | static inline float32x4_t |
57 | eval_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. */ |
77 | float32x4_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 q = vfmaq_laneq_f32 (d->shift, x, d->pi_consts, 3); |
99 | float32x4_t n = vsubq_f32 (q, d->shift); |
100 | /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ |
101 | uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1)); |
102 | |
103 | /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */ |
104 | float32x4_t r; |
105 | r = vfmaq_laneq_f32 (x, n, d->pi_consts, 0); |
106 | r = vfmaq_laneq_f32 (r, n, d->pi_consts, 1); |
107 | r = vfmaq_laneq_f32 (r, n, d->pi_consts, 2); |
108 | |
109 | /* If x lives in an interval, where |tan(x)| |
110 | - is finite, then use a polynomial approximation of the form |
111 | tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2). |
112 | - grows to infinity then use symmetries of tangent and the identity |
113 | tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use |
114 | the same polynomial approximation of tan as above. */ |
115 | |
116 | /* Invert sign of r if odd quadrant. */ |
117 | float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1))); |
118 | |
119 | /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */ |
120 | float32x4_t z2 = vmulq_f32 (r, r); |
121 | float32x4_t p = eval_poly (z2, d); |
122 | float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p); |
123 | |
124 | /* Compute reciprocal and apply if required. */ |
125 | float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y); |
126 | |
127 | if (__glibc_unlikely (v_any_u32 (special))) |
128 | return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special); |
129 | return vbslq_f32 (pred_alt, inv_y, y); |
130 | } |
131 | libmvec_hidden_def (V_NAME_F1 (tan)) |
132 | HALF_WIDTH_ALIAS_F1 (tan) |
133 | |