1 | /* Double-precision vector (SVE) 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 "sv_math.h" |
21 | #include "poly_sve_f64.h" |
22 | |
23 | static const struct data |
24 | { |
25 | double poly[9]; |
26 | double half_pi_hi, half_pi_lo, inv_half_pi, range_val, shift; |
27 | } data = { |
28 | /* Polynomial generated with FPMinimax. */ |
29 | .poly = { 0x1.5555555555556p-2, 0x1.1111111110a63p-3, 0x1.ba1ba1bb46414p-5, |
30 | 0x1.664f47e5b5445p-6, 0x1.226e5e5ecdfa3p-7, 0x1.d6c7ddbf87047p-9, |
31 | 0x1.7ea75d05b583ep-10, 0x1.289f22964a03cp-11, |
32 | 0x1.4e4fd14147622p-12, }, |
33 | .half_pi_hi = 0x1.921fb54442d18p0, |
34 | .half_pi_lo = 0x1.1a62633145c07p-54, |
35 | .inv_half_pi = 0x1.45f306dc9c883p-1, |
36 | .range_val = 0x1p23, |
37 | .shift = 0x1.8p52, |
38 | }; |
39 | |
40 | static svfloat64_t NOINLINE |
41 | special_case (svfloat64_t x, svfloat64_t y, svbool_t special) |
42 | { |
43 | return sv_call_f64 (f: tan, x, y, cmp: special); |
44 | } |
45 | |
46 | /* Vector approximation for double-precision tan. |
47 | Maximum measured error is 3.48 ULP: |
48 | _ZGVsMxv_tan(0x1.4457047ef78d8p+20) got -0x1.f6ccd8ecf7dedp+37 |
49 | want -0x1.f6ccd8ecf7deap+37. */ |
50 | svfloat64_t SV_NAME_D1 (tan) (svfloat64_t x, svbool_t pg) |
51 | { |
52 | const struct data *dat = ptr_barrier (&data); |
53 | |
54 | /* Invert condition to catch NaNs and Infs as well as large values. */ |
55 | svbool_t special = svnot_z (pg, svaclt (pg, x, dat->range_val)); |
56 | |
57 | /* q = nearest integer to 2 * x / pi. */ |
58 | svfloat64_t shift = sv_f64 (x: dat->shift); |
59 | svfloat64_t q = svmla_x (pg, shift, x, dat->inv_half_pi); |
60 | q = svsub_x (pg, q, shift); |
61 | svint64_t qi = svcvt_s64_x (pg, q); |
62 | |
63 | /* Use q to reduce x to r in [-pi/4, pi/4], by: |
64 | r = x - q * pi/2, in extended precision. */ |
65 | svfloat64_t r = x; |
66 | svfloat64_t half_pi = svld1rq (svptrue_b64 (), &dat->half_pi_hi); |
67 | r = svmls_lane (r, q, half_pi, 0); |
68 | r = svmls_lane (r, q, half_pi, 1); |
69 | /* Further reduce r to [-pi/8, pi/8], to be reconstructed using double angle |
70 | formula. */ |
71 | r = svmul_x (pg, r, 0.5); |
72 | |
73 | /* Approximate tan(r) using order 8 polynomial. |
74 | tan(x) is odd, so polynomial has the form: |
75 | tan(x) ~= x + C0 * x^3 + C1 * x^5 + C3 * x^7 + ... |
76 | Hence we first approximate P(r) = C1 + C2 * r^2 + C3 * r^4 + ... |
77 | Then compute the approximation by: |
78 | tan(r) ~= r + r^3 * (C0 + r^2 * P(r)). */ |
79 | svfloat64_t r2 = svmul_x (pg, r, r); |
80 | svfloat64_t r4 = svmul_x (pg, r2, r2); |
81 | svfloat64_t r8 = svmul_x (pg, r4, r4); |
82 | /* Use offset version coeff array by 1 to evaluate from C1 onwards. */ |
83 | svfloat64_t p = sv_estrin_7_f64_x (pg, x: r2, x2: r4, x4: r8, poly: dat->poly + 1); |
84 | p = svmad_x (pg, p, r2, dat->poly[0]); |
85 | p = svmla_x (pg, r, r2, svmul_x (pg, p, r)); |
86 | |
87 | /* Recombination uses double-angle formula: |
88 | tan(2x) = 2 * tan(x) / (1 - (tan(x))^2) |
89 | and reciprocity around pi/2: |
90 | tan(x) = 1 / (tan(pi/2 - x)) |
91 | to assemble result using change-of-sign and conditional selection of |
92 | numerator/denominator dependent on odd/even-ness of q (hence quadrant). */ |
93 | svbool_t use_recip |
94 | = svcmpeq (pg, svand_x (pg, svreinterpret_u64 (qi), 1), 0); |
95 | |
96 | svfloat64_t n = svmad_x (pg, p, p, -1); |
97 | svfloat64_t d = svmul_x (pg, p, 2); |
98 | svfloat64_t swap = n; |
99 | n = svneg_m (n, use_recip, d); |
100 | d = svsel (use_recip, swap, d); |
101 | if (__glibc_unlikely (svptest_any (pg, special))) |
102 | return special_case (x, y: svdiv_x (svnot_z (pg, special), n, d), special); |
103 | return svdiv_x (pg, n, d); |
104 | } |
105 | |