1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
|
/*
* Single-precision SVE 2^x function.
*
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "poly_sve_f32.h"
#include "pl_sig.h"
#include "pl_test.h"
static const struct data
{
float poly[5];
float shift, thres;
} data = {
/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
compatibility with polynomial helpers. */
.poly = { 0x1.62e422p-1f, 0x1.ebf9bcp-3f, 0x1.c6bd32p-5f, 0x1.3ce9e4p-7f,
0x1.59977ap-10f },
/* 1.5*2^17 + 127. */
.shift = 0x1.903f8p17f,
/* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
correctly by FEXPA. */
.thres = 0x1.5d5e2ap+6f,
};
static svfloat32_t NOINLINE
special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
{
return sv_call_f32 (exp2f, x, y, special);
}
/* Single-precision SVE exp2f routine. Implements the same algorithm
as AdvSIMD exp2f.
Worst case error is 1.04 ULPs.
SV_NAME_F1 (exp2)(0x1.943b9p-1) got 0x1.ba7eb2p+0
want 0x1.ba7ebp+0. */
svfloat32_t SV_NAME_F1 (exp2) (svfloat32_t x, const svbool_t pg)
{
const struct data *d = ptr_barrier (&data);
/* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
x = n + r, with r in [-1/2, 1/2]. */
svfloat32_t shift = sv_f32 (d->shift);
svfloat32_t z = svadd_x (pg, x, shift);
svfloat32_t n = svsub_x (pg, z, shift);
svfloat32_t r = svsub_x (pg, x, n);
svbool_t special = svacgt (pg, x, d->thres);
svfloat32_t scale = svexpa (svreinterpret_u32 (z));
/* Polynomial evaluation: poly(r) ~ exp2(r)-1.
Evaluate polynomial use hybrid scheme - offset ESTRIN by 1 for
coefficients 1 to 4, and apply most significant coefficient directly. */
svfloat32_t r2 = svmul_x (pg, r, r);
svfloat32_t p14 = sv_pairwise_poly_3_f32_x (pg, r, r2, d->poly + 1);
svfloat32_t p0 = svmul_x (pg, r, d->poly[0]);
svfloat32_t poly = svmla_x (pg, p0, r2, p14);
if (unlikely (svptest_any (pg, special)))
return special_case (x, svmla_x (pg, scale, scale, poly), special);
return svmla_x (pg, scale, scale, poly);
}
PL_SIG (SV, F, 1, exp2, -9.9, 9.9)
PL_TEST_ULP (SV_NAME_F1 (exp2), 0.55)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 0, Thres, 40000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, 1, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), 1, Thres, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), Thres, inf, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, -0x1p-23, 40000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p-23, -1, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, -0x1p23, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0x1p23, -inf, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -0, ScaleThres, 40000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), ScaleThres, -1, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), -1, ScaleThres, 50000)
PL_TEST_INTERVAL (SV_NAME_F1 (exp2), ScaleThres, -inf, 50000)
|