1 /* Double-precision SVE expm1
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/>. */
21 #include "poly_sve_f64.h"
23 #define SpecialBound 0x1.62b7d369a5aa9p+9
24 #define ExponentBias 0x3ff0000000000000
26 static const struct data
29 double shift
, inv_ln2
, special_bound
;
30 /* To be loaded in one quad-word. */
31 double ln2_hi
, ln2_lo
;
33 /* Generated using fpminimax. */
34 .poly
= { 0x1p
-1, 0x1.5555555555559p
-3, 0x1.555555555554bp
-5,
35 0x1.111111110f663p
-7, 0x1.6c16c16c1b5f3p
-10, 0x1.a01a01affa35dp
-13,
36 0x1.a01a018b4ecbbp
-16, 0x1.71ddf82db5bb4p
-19, 0x1.27e517fc0d54bp
-22,
37 0x1.af5eedae67435p
-26, 0x1.1f143d060a28ap
-29, },
39 .special_bound
= SpecialBound
,
40 .inv_ln2
= 0x1.71547652b82fep0
,
41 .ln2_hi
= 0x1.62e42fefa39efp
-1,
42 .ln2_lo
= 0x1.abc9e3b39803fp
-56,
46 static svfloat64_t NOINLINE
47 special_case (svfloat64_t x
, svfloat64_t y
, svbool_t pg
)
49 return sv_call_f64 (expm1
, x
, y
, pg
);
52 /* Double-precision vector exp(x) - 1 function.
53 The maximum error observed error is 2.18 ULP:
54 _ZGVsMxv_expm1(0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2
55 want 0x1.a8b9ea8d66e2p-2. */
56 svfloat64_t
SV_NAME_D1 (expm1
) (svfloat64_t x
, svbool_t pg
)
58 const struct data
*d
= ptr_barrier (&data
);
61 svbool_t special
= svnot_z (pg
, svaclt (pg
, x
, d
->special_bound
));
63 /* Reduce argument to smaller range:
64 Let i = round(x / ln2)
65 and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
66 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
67 where 2^i is exact because i is an integer. */
68 svfloat64_t shift
= sv_f64 (d
->shift
);
69 svfloat64_t n
= svsub_x (pg
, svmla_x (pg
, shift
, x
, d
->inv_ln2
), shift
);
70 svint64_t i
= svcvt_s64_x (pg
, n
);
71 svfloat64_t ln2
= svld1rq (svptrue_b64 (), &d
->ln2_hi
);
72 svfloat64_t f
= svmls_lane (x
, n
, ln2
, 0);
73 f
= svmls_lane (f
, n
, ln2
, 1);
75 /* Approximate expm1(f) using polynomial.
76 Taylor expansion for expm1(x) has the form:
77 x + ax^2 + bx^3 + cx^4 ....
78 So we calculate the polynomial P(f) = a + bf + cf^2 + ...
79 and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
80 svfloat64_t f2
= svmul_x (pg
, f
, f
);
81 svfloat64_t f4
= svmul_x (pg
, f2
, f2
);
82 svfloat64_t f8
= svmul_x (pg
, f4
, f4
);
84 = svmla_x (pg
, f
, f2
, sv_estrin_10_f64_x (pg
, f
, f2
, f4
, f8
, d
->poly
));
86 /* Assemble the result.
87 expm1(x) ~= 2^i * (p + 1) - 1
89 svint64_t u
= svadd_x (pg
, svlsl_x (pg
, i
, 52), ExponentBias
);
90 svfloat64_t t
= svreinterpret_f64 (u
);
92 /* expm1(x) ~= p * t + (t - 1). */
93 svfloat64_t y
= svmla_x (pg
, svsub_x (pg
, t
, 1), p
, t
);
95 if (__glibc_unlikely (svptest_any (pg
, special
)))
96 return special_case (x
, y
, special
);