1/*
2 * Single-precision vector tan(x) function.
3 *
4 * Copyright (c) 2021-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "v_math.h"
9#include "poly_advsimd_f32.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12
13static const struct data
14{
15  float32x4_t poly[6];
16  float32x4_t pi_consts;
17  float32x4_t shift;
18#if !WANT_SIMD_EXCEPT
19  float32x4_t range_val;
20#endif
21} data = {
22  /* Coefficients generated using FPMinimax.  */
23  .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
24	    V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
25  /* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi.  */
26  .pi_consts
27  = { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
28  .shift = V4 (0x1.8p+23f),
29#if !WANT_SIMD_EXCEPT
30  .range_val = V4 (0x1p15f),
31#endif
32};
33
34#define RangeVal v_u32 (0x47000000)  /* asuint32(0x1p15f).  */
35#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f).  */
36#define Thresh v_u32 (0x16000000)    /* asuint32(RangeVal) - TinyBound.  */
37
38/* Special cases (fall back to scalar calls).  */
39static float32x4_t VPCS_ATTR NOINLINE
40special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
41{
42  return v_call_f32 (tanf, x, y, cmp);
43}
44
45/* Use a full Estrin scheme to evaluate polynomial.  */
46static inline float32x4_t
47eval_poly (float32x4_t z, const struct data *d)
48{
49  float32x4_t z2 = vmulq_f32 (z, z);
50#if WANT_SIMD_EXCEPT
51  /* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
52     If fp exceptions are to be triggered correctly,
53     sidestep this by fixing such lanes to 0.  */
54  uint32x4_t will_uflow
55      = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
56  if (unlikely (v_any_u32 (will_uflow)))
57    z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
58#endif
59  float32x4_t z4 = vmulq_f32 (z2, z2);
60  return v_estrin_5_f32 (z, z2, z4, d->poly);
61}
62
63/* Fast implementation of AdvSIMD tanf.
64   Maximum error is 3.45 ULP:
65   __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
66			    want 0x1.ff9850p-1.  */
67float32x4_t VPCS_ATTR V_NAME_F1 (tan) (float32x4_t x)
68{
69  const struct data *d = ptr_barrier (&data);
70  float32x4_t special_arg = x;
71
72  /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
73     regression.  */
74#if WANT_SIMD_EXCEPT
75  uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
76  /* If fp exceptions are to be triggered correctly, also special-case tiny
77     input, as this will load to overflow later. Fix any special lanes to 1 to
78     prevent any exceptions being triggered.  */
79  uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
80  if (unlikely (v_any_u32 (special)))
81    x = vbslq_f32 (special, v_f32 (1.0f), x);
82#else
83  /* Otherwise, special-case large and special values.  */
84  uint32x4_t special = vcageq_f32 (x, d->range_val);
85#endif
86
87  /* n = rint(x/(pi/2)).  */
88  float32x4_t q = vfmaq_laneq_f32 (d->shift, x, d->pi_consts, 3);
89  float32x4_t n = vsubq_f32 (q, d->shift);
90  /* Determine if x lives in an interval, where |tan(x)| grows to infinity.  */
91  uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
92
93  /* r = x - n * (pi/2)  (range reduction into -pi./4 .. pi/4).  */
94  float32x4_t r;
95  r = vfmaq_laneq_f32 (x, n, d->pi_consts, 0);
96  r = vfmaq_laneq_f32 (r, n, d->pi_consts, 1);
97  r = vfmaq_laneq_f32 (r, n, d->pi_consts, 2);
98
99  /* If x lives in an interval, where |tan(x)|
100     - is finite, then use a polynomial approximation of the form
101       tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
102     - grows to infinity then use symmetries of tangent and the identity
103       tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
104       the same polynomial approximation of tan as above.  */
105
106  /* Invert sign of r if odd quadrant.  */
107  float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
108
109  /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4].  */
110  float32x4_t z2 = vmulq_f32 (r, r);
111  float32x4_t p = eval_poly (z2, d);
112  float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
113
114  /* Compute reciprocal and apply if required.  */
115  float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
116
117  if (unlikely (v_any_u32 (special)))
118    return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
119  return vbslq_f32 (pred_alt, inv_y, y);
120}
121
122PL_SIG (V, F, 1, tan, -3.1, 3.1)
123PL_TEST_ULP (V_NAME_F1 (tan), 2.96)
124PL_TEST_EXPECT_FENV (V_NAME_F1 (tan), WANT_SIMD_EXCEPT)
125PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0, 0x1p-31, 5000)
126PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p-31, 0x1p15, 500000)
127PL_TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p15, inf, 5000)
128