1 /*
2 * Single-precision vector tan(x) function.
3 *
4 * Copyright (c) 2020-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 static const struct data
13 {
14 float pio2_1, pio2_2, pio2_3, invpio2;
15 float c1, c3, c5;
16 float c0, c2, c4, range_val, shift;
17 } data = {
18 /* Coefficients generated using:
19 poly = fpminimax((tan(sqrt(x))-sqrt(x))/x^(3/2),
20 deg,
21 [|single ...|],
22 [a*a;b*b]);
23 optimize relative error
24 final prec : 23 bits
25 deg : 5
26 a : 0x1p-126 ^ 2
27 b : ((pi) / 0x1p2) ^ 2
28 dirty rel error: 0x1.f7c2e4p-25
29 dirty abs error: 0x1.f7c2ecp-25. */
30 .c0 = 0x1.55555p-2, .c1 = 0x1.11166p-3,
31 .c2 = 0x1.b88a78p-5, .c3 = 0x1.7b5756p-6,
32 .c4 = 0x1.4ef4cep-8, .c5 = 0x1.0e1e74p-7,
33
34 .pio2_1 = 0x1.921fb6p+0f, .pio2_2 = -0x1.777a5cp-25f,
35 .pio2_3 = -0x1.ee59dap-50f, .invpio2 = 0x1.45f306p-1f,
36 .range_val = 0x1p15f, .shift = 0x1.8p+23f
37 };
38
39 static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t cmp)40 special_case (svfloat32_t x, svfloat32_t y, svbool_t cmp)
41 {
42 return sv_call_f32 (tanf, x, y, cmp);
43 }
44
45 /* Fast implementation of SVE tanf.
46 Maximum error is 3.45 ULP:
47 SV_NAME_F1 (tan)(-0x1.e5f0cap+13) got 0x1.ff9856p-1
48 want 0x1.ff9850p-1. */
SV_NAME_F1(tan)49 svfloat32_t SV_NAME_F1 (tan) (svfloat32_t x, const svbool_t pg)
50 {
51 const struct data *d = ptr_barrier (&data);
52
53 svfloat32_t odd_coeffs = svld1rq (svptrue_b32 (), &d->c1);
54 svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->pio2_1);
55
56 /* n = rint(x/(pi/2)). */
57 svfloat32_t n = svrintn_x (pg, svmul_lane (x, pi_vals, 3));
58 /* n is already a signed integer, simply convert it. */
59 svint32_t in = svcvt_s32_x (pg, n);
60 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
61 svint32_t alt = svand_x (pg, in, 1);
62 svbool_t pred_alt = svcmpne (pg, alt, 0);
63 /* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
64 svfloat32_t r;
65 r = svmls_lane (x, n, pi_vals, 0);
66 r = svmls_lane (r, n, pi_vals, 1);
67 r = svmls_lane (r, n, pi_vals, 2);
68
69 /* If x lives in an interval, where |tan(x)|
70 - is finite, then use a polynomial approximation of the form
71 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
72 - grows to infinity then use symmetries of tangent and the identity
73 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
74 the same polynomial approximation of tan as above. */
75
76 /* Perform additional reduction if required. */
77 svfloat32_t z = svneg_m (r, pred_alt, r);
78
79 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4],
80 using Estrin on z^2. */
81 svfloat32_t z2 = svmul_x (svptrue_b32 (), r, r);
82 svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, odd_coeffs, 0);
83 svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, odd_coeffs, 1);
84 svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, odd_coeffs, 2);
85
86 svfloat32_t z4 = svmul_x (pg, z2, z2);
87 svfloat32_t p = svmla_x (pg, p01, z4, p23);
88
89 svfloat32_t z8 = svmul_x (pg, z4, z4);
90 p = svmla_x (pg, p, z8, p45);
91
92 svfloat32_t y = svmla_x (pg, z, p, svmul_x (pg, z, z2));
93
94 /* No need to pass pg to specialcase here since cmp is a strict subset,
95 guaranteed by the cmpge above. */
96
97 /* Determine whether input is too large to perform fast regression. */
98 svbool_t cmp = svacge (pg, x, d->range_val);
99 if (unlikely (svptest_any (pg, cmp)))
100 return special_case (x, svdivr_x (pg, y, 1.0f), cmp);
101
102 svfloat32_t inv_y = svdivr_x (pg, y, 1.0f);
103 return svsel (pred_alt, inv_y, y);
104 }
105
106 TEST_SIG (SV, F, 1, tan, -3.1, 3.1)
107 TEST_ULP (SV_NAME_F1 (tan), 2.96)
108 TEST_DISABLE_FENV (SV_NAME_F1 (tan))
109 TEST_INTERVAL (SV_NAME_F1 (tan), -0.0, -0x1p126, 100)
110 TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-149, 0x1p-126, 4000)
111 TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-126, 0x1p-23, 50000)
112 TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p-23, 0.7, 50000)
113 TEST_INTERVAL (SV_NAME_F1 (tan), 0.7, 1.5, 50000)
114 TEST_INTERVAL (SV_NAME_F1 (tan), 1.5, 100, 50000)
115 TEST_INTERVAL (SV_NAME_F1 (tan), 100, 0x1p17, 50000)
116 TEST_INTERVAL (SV_NAME_F1 (tan), 0x1p17, inf, 50000)
117 CLOSE_SVE_ATTR
118