1/*
2 * Single-precision vector e^x function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9#include "mathlib.h"
10#include "v_math.h"
11#if V_SUPPORTED
12
13static const float Poly[] = {
14 /* maxerr: 0.36565 +0.5 ulp. */
15 0x1.6a6000p-10f,
16 0x1.12718ep-7f,
17 0x1.555af0p-5f,
18 0x1.555430p-3f,
19 0x1.fffff4p-2f,
20};
21#define C0 v_f32 (Poly[0])
22#define C1 v_f32 (Poly[1])
23#define C2 v_f32 (Poly[2])
24#define C3 v_f32 (Poly[3])
25#define C4 v_f32 (Poly[4])
26
27#define Shift v_f32 (0x1.8p23f)
28#define InvLn2 v_f32 (0x1.715476p+0f)
29#define Ln2hi v_f32 (0x1.62e4p-1f)
30#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
31
32VPCS_ATTR
33static v_f32_t
34specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
35{
36 /* 2^n may overflow, break it up into s1*s2. */
37 v_u32_t b = v_cond_u32 (x: n <= v_f32 (x: 0.0f)) & v_u32 (x: 0x83000000);
38 v_f32_t s1 = v_as_f32_u32 (x: v_u32 (x: 0x7f000000) + b);
39 v_f32_t s2 = v_as_f32_u32 (x: e - b);
40 v_u32_t cmp = v_cond_u32 (x: absn > v_f32 (x: 192.0f));
41 v_f32_t r1 = s1 * s1;
42 v_f32_t r0 = poly * s1 * s2;
43 return v_as_f32_u32 (x: (cmp & v_as_u32_f32 (x: r1)) | (~cmp & v_as_u32_f32 (x: r0)));
44}
45
46VPCS_ATTR
47v_f32_t
48V_NAME(expf_1u) (v_f32_t x)
49{
50 v_f32_t n, r, scale, poly, absn, z;
51 v_u32_t cmp, e;
52
53 /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
54 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */
55#if 1
56 z = v_fma_f32 (x, InvLn2, Shift);
57 n = z - Shift;
58 r = v_fma_f32 (x: n, y: -Ln2hi, z: x);
59 r = v_fma_f32 (x: n, y: -Ln2lo, z: r);
60 e = v_as_u32_f32 (x: z) << 23;
61#else
62 z = x * InvLn2;
63 n = v_round_f32 (z);
64 r = v_fma_f32 (n, -Ln2hi, x);
65 r = v_fma_f32 (n, -Ln2lo, r);
66 e = v_as_u32_s32 (v_round_s32 (z)) << 23;
67#endif
68 scale = v_as_f32_u32 (x: e + v_u32 (x: 0x3f800000));
69 absn = v_abs_f32 (x: n);
70 cmp = v_cond_u32 (x: absn > v_f32 (x: 126.0f));
71 poly = v_fma_f32 (C0, y: r, C1);
72 poly = v_fma_f32 (x: poly, y: r, C2);
73 poly = v_fma_f32 (x: poly, y: r, C3);
74 poly = v_fma_f32 (x: poly, y: r, C4);
75 poly = v_fma_f32 (x: poly, y: r, z: v_f32 (x: 1.0f));
76 poly = v_fma_f32 (x: poly, y: r, z: v_f32 (x: 1.0f));
77 if (unlikely (v_any_u32 (cmp)))
78 return specialcase (poly, n, e, absn);
79 return scale * poly;
80}
81#endif
82

source code of libc/AOR_v20.02/math/v_expf_1u.c