1 /*
2 * Single-precision vector tan(x) function.
3 *
4 * Copyright (c) 2020-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #if SV_SUPPORTED
13
14 /* Constants. */
15 #define NegPio2_1 (sv_f32 (-0x1.921fb6p+0f))
16 #define NegPio2_2 (sv_f32 (0x1.777a5cp-25f))
17 #define NegPio2_3 (sv_f32 (0x1.ee59dap-50f))
18 #define InvPio2 (sv_f32 (0x1.45f306p-1f))
19 #define RangeVal (sv_f32 (0x1p15f))
20 #define Shift (sv_f32 (0x1.8p+23f))
21
22 #define poly(i) sv_f32 (__tanf_poly_data.poly_tan[i])
23
24 /* Use full Estrin's scheme to evaluate polynomial. */
25 static inline sv_f32_t
eval_poly(svbool_t pg,sv_f32_t z)26 eval_poly (svbool_t pg, sv_f32_t z)
27 {
28 sv_f32_t z2 = svmul_f32_x (pg, z, z);
29 sv_f32_t z4 = svmul_f32_x (pg, z2, z2);
30 sv_f32_t y_10 = sv_fma_f32_x (pg, z, poly (1), poly (0));
31 sv_f32_t y_32 = sv_fma_f32_x (pg, z, poly (3), poly (2));
32 sv_f32_t y_54 = sv_fma_f32_x (pg, z, poly (5), poly (4));
33 sv_f32_t y_32_10 = sv_fma_f32_x (pg, z2, y_32, y_10);
34 sv_f32_t y = sv_fma_f32_x (pg, z4, y_54, y_32_10);
35 return y;
36 }
37
38 static NOINLINE sv_f32_t
__sv_tanf_specialcase(sv_f32_t x,sv_f32_t y,svbool_t cmp)39 __sv_tanf_specialcase (sv_f32_t x, sv_f32_t y, svbool_t cmp)
40 {
41 return sv_call_f32 (tanf, x, y, cmp);
42 }
43
44 /* Fast implementation of SVE tanf.
45 Maximum error is 3.45 ULP:
46 __sv_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1
47 want 0x1.ff9850p-1. */
48 sv_f32_t
__sv_tanf_x(sv_f32_t x,const svbool_t pg)49 __sv_tanf_x (sv_f32_t x, const svbool_t pg)
50 {
51 /* Determine whether input is too large to perform fast regression. */
52 svbool_t cmp = svacge_f32 (pg, x, RangeVal);
53 svbool_t pred_minuszero = svcmpeq_f32 (pg, x, sv_f32 (-0.0));
54
55 /* n = rint(x/(pi/2)). */
56 sv_f32_t q = sv_fma_f32_x (pg, InvPio2, x, Shift);
57 sv_f32_t n = svsub_f32_x (pg, q, Shift);
58 /* n is already a signed integer, simply convert it. */
59 sv_s32_t in = sv_to_s32_f32_x (pg, n);
60 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
61 sv_s32_t alt = svand_s32_x (pg, in, sv_s32 (1));
62 svbool_t pred_alt = svcmpne_s32 (pg, alt, sv_s32 (0));
63
64 /* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
65 sv_f32_t r;
66 r = sv_fma_f32_x (pg, NegPio2_1, n, x);
67 r = sv_fma_f32_x (pg, NegPio2_2, n, r);
68 r = sv_fma_f32_x (pg, NegPio2_3, n, r);
69
70 /* If x lives in an interval, where |tan(x)|
71 - is finite, then use a polynomial approximation of the form
72 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
73 - grows to infinity then use symmetries of tangent and the identity
74 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
75 the same polynomial approximation of tan as above. */
76
77 /* Perform additional reduction if required. */
78 sv_f32_t z = svneg_f32_m (r, pred_alt, r);
79
80 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */
81 sv_f32_t z2 = svmul_f32_x (pg, z, z);
82 sv_f32_t p = eval_poly (pg, z2);
83 sv_f32_t y = sv_fma_f32_x (pg, svmul_f32_x (pg, z, z2), p, z);
84
85 /* Transform result back, if necessary. */
86 sv_f32_t inv_y = svdiv_f32_x (pg, sv_f32 (1.0f), y);
87 y = svsel_f32 (pred_alt, inv_y, y);
88
89 /* Fast reduction does not handle the x = -0.0 case well,
90 therefore it is fixed here. */
91 y = svsel_f32 (pred_minuszero, x, y);
92
93 /* No need to pass pg to specialcase here since cmp is a strict subset,
94 guaranteed by the cmpge above. */
95 if (unlikely (svptest_any (pg, cmp)))
96 return __sv_tanf_specialcase (x, y, cmp);
97 return y;
98 }
99
100 PL_ALIAS (__sv_tanf_x, _ZGVsMxv_tanf)
101
102 PL_SIG (SV, F, 1, tan, -3.1, 3.1)
103 PL_TEST_ULP (__sv_tanf, 2.96)
104 PL_TEST_INTERVAL (__sv_tanf, -0.0, -0x1p126, 100)
105 PL_TEST_INTERVAL (__sv_tanf, 0x1p-149, 0x1p-126, 4000)
106 PL_TEST_INTERVAL (__sv_tanf, 0x1p-126, 0x1p-23, 50000)
107 PL_TEST_INTERVAL (__sv_tanf, 0x1p-23, 0.7, 50000)
108 PL_TEST_INTERVAL (__sv_tanf, 0.7, 1.5, 50000)
109 PL_TEST_INTERVAL (__sv_tanf, 1.5, 100, 50000)
110 PL_TEST_INTERVAL (__sv_tanf, 100, 0x1p17, 50000)
111 PL_TEST_INTERVAL (__sv_tanf, 0x1p17, inf, 50000)
112 #endif
113