1/* Single-precision vector (SVE) exp 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
22static const struct data
23{
24 float poly[5];
25 float inv_ln2, ln2_hi, ln2_lo, shift, thres;
26} data = {
27 /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
28 compatibility with polynomial helpers. */
29 .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f,
30 0x1.0e4020p-7f },
31 .inv_ln2 = 0x1.715476p+0f,
32 .ln2_hi = 0x1.62e4p-1f,
33 .ln2_lo = 0x1.7f7d1cp-20f,
34 /* 1.5*2^17 + 127. */
35 .shift = 0x1.903f8p17f,
36 /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
37 correctly by FEXPA. */
38 .thres = 0x1.5d5e2ap+6f,
39};
40
41#define C(i) sv_f32 (d->poly[i])
42#define ExponentBias 0x3f800000
43
44static svfloat32_t NOINLINE
45special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
46{
47 return sv_call_f32 (f: expf, x, y, cmp: special);
48}
49
50/* Optimised single-precision SVE exp function.
51 Worst-case error is 1.04 ulp:
52 SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
53 want 0x1.ba74bap+4. */
54svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
55{
56 const struct data *d = ptr_barrier (&data);
57
58 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
59 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
60
61 /* Load some constants in quad-word chunks to minimise memory access (last
62 lane is wasted). */
63 svfloat32_t invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->inv_ln2);
64
65 /* n = round(x/(ln2/N)). */
66 svfloat32_t z = svmla_lane (sv_f32 (x: d->shift), x, invln2_and_ln2, 0);
67 svfloat32_t n = svsub_x (pg, z, d->shift);
68
69 /* r = x - n*ln2/N. */
70 svfloat32_t r = svmls_lane (x, n, invln2_and_ln2, 1);
71 r = svmls_lane (r, n, invln2_and_ln2, 2);
72
73 /* scale = 2^(n/N). */
74 svbool_t is_special_case = svacgt (pg, x, d->thres);
75 svfloat32_t scale = svexpa (svreinterpret_u32 (z));
76
77 /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */
78 svfloat32_t p12 = svmla_x (pg, C (1), C (2), r);
79 svfloat32_t p34 = svmla_x (pg, C (3), C (4), r);
80 svfloat32_t r2 = svmul_x (pg, r, r);
81 svfloat32_t p14 = svmla_x (pg, p12, p34, r2);
82 svfloat32_t p0 = svmul_x (pg, r, C (0));
83 svfloat32_t poly = svmla_x (pg, p0, r2, p14);
84
85 if (__glibc_unlikely (svptest_any (pg, is_special_case)))
86 return special_case (x, y: svmla_x (pg, scale, scale, poly), special: is_special_case);
87
88 return svmla_x (pg, scale, scale, poly);
89}
90

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