1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Single-precision vector tan(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2021-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "v_math.h"
9*f3087befSAndrew Turner #include "v_poly_f32.h"
10*f3087befSAndrew Turner #include "test_sig.h"
11*f3087befSAndrew Turner #include "test_defs.h"
12*f3087befSAndrew Turner
13*f3087befSAndrew Turner static const struct data
14*f3087befSAndrew Turner {
15*f3087befSAndrew Turner float32x4_t poly[6];
16*f3087befSAndrew Turner float pi_consts[4];
17*f3087befSAndrew Turner float32x4_t shift;
18*f3087befSAndrew Turner #if !WANT_SIMD_EXCEPT
19*f3087befSAndrew Turner float32x4_t range_val;
20*f3087befSAndrew Turner #endif
21*f3087befSAndrew Turner } data = {
22*f3087befSAndrew Turner /* Coefficients generated using FPMinimax. */
23*f3087befSAndrew Turner .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f),
24*f3087befSAndrew Turner V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) },
25*f3087befSAndrew Turner /* Stores constants: (-pi/2)_high, (-pi/2)_mid, (-pi/2)_low, and 2/pi. */
26*f3087befSAndrew Turner .pi_consts
27*f3087befSAndrew Turner = { -0x1.921fb6p+0f, 0x1.777a5cp-25f, 0x1.ee59dap-50f, 0x1.45f306p-1f },
28*f3087befSAndrew Turner .shift = V4 (0x1.8p+23f),
29*f3087befSAndrew Turner #if !WANT_SIMD_EXCEPT
30*f3087befSAndrew Turner .range_val = V4 (0x1p15f),
31*f3087befSAndrew Turner #endif
32*f3087befSAndrew Turner };
33*f3087befSAndrew Turner
34*f3087befSAndrew Turner #define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */
35*f3087befSAndrew Turner #define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */
36*f3087befSAndrew Turner #define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */
37*f3087befSAndrew Turner
38*f3087befSAndrew Turner /* Special cases (fall back to scalar calls). */
39*f3087befSAndrew Turner static float32x4_t VPCS_ATTR NOINLINE
special_case(float32x4_t x,float32x4_t y,uint32x4_t cmp)40*f3087befSAndrew Turner special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
41*f3087befSAndrew Turner {
42*f3087befSAndrew Turner return v_call_f32 (tanf, x, y, cmp);
43*f3087befSAndrew Turner }
44*f3087befSAndrew Turner
45*f3087befSAndrew Turner /* Use a full Estrin scheme to evaluate polynomial. */
46*f3087befSAndrew Turner static inline float32x4_t
eval_poly(float32x4_t z,const struct data * d)47*f3087befSAndrew Turner eval_poly (float32x4_t z, const struct data *d)
48*f3087befSAndrew Turner {
49*f3087befSAndrew Turner float32x4_t z2 = vmulq_f32 (z, z);
50*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT
51*f3087befSAndrew Turner /* Tiny z (<= 0x1p-31) will underflow when calculating z^4.
52*f3087befSAndrew Turner If fp exceptions are to be triggered correctly,
53*f3087befSAndrew Turner sidestep this by fixing such lanes to 0. */
54*f3087befSAndrew Turner uint32x4_t will_uflow
55*f3087befSAndrew Turner = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound);
56*f3087befSAndrew Turner if (unlikely (v_any_u32 (will_uflow)))
57*f3087befSAndrew Turner z2 = vbslq_f32 (will_uflow, v_f32 (0), z2);
58*f3087befSAndrew Turner #endif
59*f3087befSAndrew Turner float32x4_t z4 = vmulq_f32 (z2, z2);
60*f3087befSAndrew Turner return v_estrin_5_f32 (z, z2, z4, d->poly);
61*f3087befSAndrew Turner }
62*f3087befSAndrew Turner
63*f3087befSAndrew Turner /* Fast implementation of AdvSIMD tanf.
64*f3087befSAndrew Turner Maximum error is 3.45 ULP:
65*f3087befSAndrew Turner __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
66*f3087befSAndrew Turner want 0x1.ff9850p-1. */
V_NAME_F1(tan)67*f3087befSAndrew Turner float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tan) (float32x4_t x)
68*f3087befSAndrew Turner {
69*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data);
70*f3087befSAndrew Turner float32x4_t special_arg = x;
71*f3087befSAndrew Turner
72*f3087befSAndrew Turner /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast
73*f3087befSAndrew Turner regression. */
74*f3087befSAndrew Turner #if WANT_SIMD_EXCEPT
75*f3087befSAndrew Turner uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x));
76*f3087befSAndrew Turner /* If fp exceptions are to be triggered correctly, also special-case tiny
77*f3087befSAndrew Turner input, as this will load to overflow later. Fix any special lanes to 1 to
78*f3087befSAndrew Turner prevent any exceptions being triggered. */
79*f3087befSAndrew Turner uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh);
80*f3087befSAndrew Turner if (unlikely (v_any_u32 (special)))
81*f3087befSAndrew Turner x = vbslq_f32 (special, v_f32 (1.0f), x);
82*f3087befSAndrew Turner #else
83*f3087befSAndrew Turner /* Otherwise, special-case large and special values. */
84*f3087befSAndrew Turner uint32x4_t special = vcageq_f32 (x, d->range_val);
85*f3087befSAndrew Turner #endif
86*f3087befSAndrew Turner
87*f3087befSAndrew Turner /* n = rint(x/(pi/2)). */
88*f3087befSAndrew Turner float32x4_t pi_consts = vld1q_f32 (d->pi_consts);
89*f3087befSAndrew Turner float32x4_t q = vfmaq_laneq_f32 (d->shift, x, pi_consts, 3);
90*f3087befSAndrew Turner float32x4_t n = vsubq_f32 (q, d->shift);
91*f3087befSAndrew Turner /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
92*f3087befSAndrew Turner uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1));
93*f3087befSAndrew Turner
94*f3087befSAndrew Turner /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */
95*f3087befSAndrew Turner float32x4_t r;
96*f3087befSAndrew Turner r = vfmaq_laneq_f32 (x, n, pi_consts, 0);
97*f3087befSAndrew Turner r = vfmaq_laneq_f32 (r, n, pi_consts, 1);
98*f3087befSAndrew Turner r = vfmaq_laneq_f32 (r, n, pi_consts, 2);
99*f3087befSAndrew Turner
100*f3087befSAndrew Turner /* If x lives in an interval, where |tan(x)|
101*f3087befSAndrew Turner - is finite, then use a polynomial approximation of the form
102*f3087befSAndrew Turner tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
103*f3087befSAndrew Turner - grows to infinity then use symmetries of tangent and the identity
104*f3087befSAndrew Turner tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
105*f3087befSAndrew Turner the same polynomial approximation of tan as above. */
106*f3087befSAndrew Turner
107*f3087befSAndrew Turner /* Invert sign of r if odd quadrant. */
108*f3087befSAndrew Turner float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1)));
109*f3087befSAndrew Turner
110*f3087befSAndrew Turner /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
111*f3087befSAndrew Turner float32x4_t z2 = vmulq_f32 (r, r);
112*f3087befSAndrew Turner float32x4_t p = eval_poly (z2, d);
113*f3087befSAndrew Turner float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p);
114*f3087befSAndrew Turner
115*f3087befSAndrew Turner /* Compute reciprocal and apply if required. */
116*f3087befSAndrew Turner float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y);
117*f3087befSAndrew Turner
118*f3087befSAndrew Turner if (unlikely (v_any_u32 (special)))
119*f3087befSAndrew Turner return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special);
120*f3087befSAndrew Turner return vbslq_f32 (pred_alt, inv_y, y);
121*f3087befSAndrew Turner }
122*f3087befSAndrew Turner
123*f3087befSAndrew Turner HALF_WIDTH_ALIAS_F1 (tan)
124*f3087befSAndrew Turner
125*f3087befSAndrew Turner TEST_SIG (V, F, 1, tan, -3.1, 3.1)
126*f3087befSAndrew Turner TEST_ULP (V_NAME_F1 (tan), 2.96)
127*f3087befSAndrew Turner TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (tan), WANT_SIMD_EXCEPT)
128*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0, 0x1p-31, 5000)
129*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p-31, 0x1p15, 500000)
130*f3087befSAndrew Turner TEST_SYM_INTERVAL (V_NAME_F1 (tan), 0x1p15, inf, 5000)
131