1/* Single-precision SVE expm1
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_f32.h"
22
23/* Largest value of x for which expm1(x) should round to -1. */
24#define SpecialBound 0x1.5ebc4p+6f
25
26static const struct data
27{
28 /* These 4 are grouped together so they can be loaded as one quadword, then
29 used with _lane forms of svmla/svmls. */
30 float c2, c4, ln2_hi, ln2_lo;
31 float c0, c1, c3, inv_ln2, special_bound, shift;
32} data = {
33 /* Generated using fpminimax. */
34 .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3,
35 .c2 = 0x1.555736p-5, .c3 = 0x1.12287cp-7,
36 .c4 = 0x1.6b55a2p-10,
37
38 .special_bound = SpecialBound, .shift = 0x1.8p23f,
39 .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f,
40 .ln2_lo = 0x1.7f7d1cp-20f,
41};
42
43#define C(i) sv_f32 (d->c##i)
44
45static svfloat32_t NOINLINE
46special_case (svfloat32_t x, svbool_t pg)
47{
48 return sv_call_f32 (f: expm1f, x, y: x, cmp: pg);
49}
50
51/* Single-precision SVE exp(x) - 1. Maximum error is 1.52 ULP:
52 _ZGVsMxv_expm1f(0x1.8f4ebcp-2) got 0x1.e859dp-2
53 want 0x1.e859d4p-2. */
54svfloat32_t SV_NAME_F1 (expm1) (svfloat32_t x, svbool_t pg)
55{
56 const struct data *d = ptr_barrier (&data);
57
58 /* Large, NaN/Inf. */
59 svbool_t special = svnot_z (pg, svaclt (pg, x, d->special_bound));
60
61 if (__glibc_unlikely (svptest_any (pg, special)))
62 return special_case (x, pg);
63
64 /* This vector is reliant on layout of data - it contains constants
65 that can be used with _lane forms of svmla/svmls. Values are:
66 [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
67 svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
68
69 /* Reduce argument to smaller range:
70 Let i = round(x / ln2)
71 and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
72 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
73 where 2^i is exact because i is an integer. */
74 svfloat32_t j = svmla_x (pg, sv_f32 (x: d->shift), x, d->inv_ln2);
75 j = svsub_x (pg, j, d->shift);
76 svint32_t i = svcvt_s32_x (pg, j);
77
78 svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
79 f = svmls_lane (f, j, lane_constants, 3);
80
81 /* Approximate expm1(f) using polynomial.
82 Taylor expansion for expm1(x) has the form:
83 x + ax^2 + bx^3 + cx^4 ....
84 So we calculate the polynomial P(f) = a + bf + cf^2 + ...
85 and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
86 svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
87 svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
88 svfloat32_t f2 = svmul_x (pg, f, f);
89 svfloat32_t p = svmla_x (pg, p12, f2, p34);
90 p = svmla_x (pg, C (0), f, p);
91 p = svmla_x (pg, f, f2, p);
92
93 /* Assemble the result.
94 expm1(x) ~= 2^i * (p + 1) - 1
95 Let t = 2^i. */
96 svfloat32_t t = svreinterpret_f32 (
97 svadd_x (pg, svreinterpret_u32 (svlsl_x (pg, i, 23)), 0x3f800000));
98 return svmla_x (pg, svsub_x (pg, t, 1), p, t);
99}
100

source code of glibc/sysdeps/aarch64/fpu/expm1f_sve.c