]>
git.ipfire.org Git - thirdparty/glibc.git/blob - sysdeps/aarch64/fpu/tanf_sve.c
1 /* Single-precision vector (SVE) tan function
3 Copyright (C) 2023 Free Software Foundation, Inc.
4 This file is part of the GNU C Library.
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.
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.
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/>. */
22 static const struct data
24 float pio2_1
, pio2_2
, pio2_3
, invpio2
;
26 float c0
, c2
, c4
, range_val
, shift
;
28 /* Coefficients generated using:
29 poly = fpminimax((tan(sqrt(x))-sqrt(x))/x^(3/2),
33 optimize relative error
37 b : ((pi) / 0x1p2) ^ 2
38 dirty rel error: 0x1.f7c2e4p-25
39 dirty abs error: 0x1.f7c2ecp-25. */
40 .c0
= 0x1.55555p
-2, .c1
= 0x1.11166p
-3,
41 .c2
= 0x1.b88a78p
-5, .c3
= 0x1.7b5756p
-6,
42 .c4
= 0x1.4ef4cep
-8, .c5
= 0x1.0e1e74p
-7,
44 .pio2_1
= 0x1.921fb6p
+0f
, .pio2_2
= -0x1.777a5cp
-25f
,
45 .pio2_3
= -0x1.ee59dap
-50f
, .invpio2
= 0x1.45f306p
-1f
,
46 .range_val
= 0x1p
15f
, .shift
= 0x1.8p
+23f
49 static svfloat32_t NOINLINE
50 special_case (svfloat32_t x
, svfloat32_t y
, svbool_t cmp
)
52 return sv_call_f32 (tanf
, x
, y
, cmp
);
55 /* Fast implementation of SVE tanf.
56 Maximum error is 3.45 ULP:
57 SV_NAME_F1 (tan)(-0x1.e5f0cap+13) got 0x1.ff9856p-1
58 want 0x1.ff9850p-1. */
59 svfloat32_t
SV_NAME_F1 (tan
) (svfloat32_t x
, const svbool_t pg
)
61 const struct data
*d
= ptr_barrier (&data
);
63 /* Determine whether input is too large to perform fast regression. */
64 svbool_t cmp
= svacge (pg
, x
, d
->range_val
);
66 svfloat32_t odd_coeffs
= svld1rq (svptrue_b32 (), &d
->c1
);
67 svfloat32_t pi_vals
= svld1rq (svptrue_b32 (), &d
->pio2_1
);
69 /* n = rint(x/(pi/2)). */
70 svfloat32_t q
= svmla_lane (sv_f32 (d
->shift
), x
, pi_vals
, 3);
71 svfloat32_t n
= svsub_x (pg
, q
, d
->shift
);
72 /* n is already a signed integer, simply convert it. */
73 svint32_t in
= svcvt_s32_x (pg
, n
);
74 /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */
75 svint32_t alt
= svand_x (pg
, in
, 1);
76 svbool_t pred_alt
= svcmpne (pg
, alt
, 0);
78 /* r = x - n * (pi/2) (range reduction into 0 .. pi/4). */
80 r
= svmls_lane (x
, n
, pi_vals
, 0);
81 r
= svmls_lane (r
, n
, pi_vals
, 1);
82 r
= svmls_lane (r
, n
, pi_vals
, 2);
84 /* If x lives in an interval, where |tan(x)|
85 - is finite, then use a polynomial approximation of the form
86 tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2).
87 - grows to infinity then use symmetries of tangent and the identity
88 tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use
89 the same polynomial approximation of tan as above. */
91 /* Perform additional reduction if required. */
92 svfloat32_t z
= svneg_m (r
, pred_alt
, r
);
94 /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4],
95 using Estrin on z^2. */
96 svfloat32_t z2
= svmul_x (pg
, z
, z
);
97 svfloat32_t p01
= svmla_lane (sv_f32 (d
->c0
), z2
, odd_coeffs
, 0);
98 svfloat32_t p23
= svmla_lane (sv_f32 (d
->c2
), z2
, odd_coeffs
, 1);
99 svfloat32_t p45
= svmla_lane (sv_f32 (d
->c4
), z2
, odd_coeffs
, 2);
101 svfloat32_t z4
= svmul_x (pg
, z2
, z2
);
102 svfloat32_t p
= svmla_x (pg
, p01
, z4
, p23
);
104 svfloat32_t z8
= svmul_x (pg
, z4
, z4
);
105 p
= svmla_x (pg
, p
, z8
, p45
);
107 svfloat32_t y
= svmla_x (pg
, z
, p
, svmul_x (pg
, z
, z2
));
109 /* Transform result back, if necessary. */
110 svfloat32_t inv_y
= svdivr_x (pg
, y
, 1.0f
);
112 /* No need to pass pg to specialcase here since cmp is a strict subset,
113 guaranteed by the cmpge above. */
114 if (__glibc_unlikely (svptest_any (pg
, cmp
)))
115 return special_case (x
, svsel (pred_alt
, inv_y
, y
), cmp
);
117 return svsel (pred_alt
, inv_y
, y
);