1/*
2 * Single-precision vector e^x function.
3 *
4 * Copyright (c) 2019-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "mathlib.h"
9#include "v_math.h"
10
11static const float Poly[] = {
12  /*  maxerr: 0.36565 +0.5 ulp.  */
13  0x1.6a6000p-10f,
14  0x1.12718ep-7f,
15  0x1.555af0p-5f,
16  0x1.555430p-3f,
17  0x1.fffff4p-2f,
18};
19#define C0 v_f32 (Poly[0])
20#define C1 v_f32 (Poly[1])
21#define C2 v_f32 (Poly[2])
22#define C3 v_f32 (Poly[3])
23#define C4 v_f32 (Poly[4])
24
25#define Shift v_f32 (0x1.8p23f)
26#define InvLn2 v_f32 (0x1.715476p+0f)
27#define Ln2hi v_f32 (0x1.62e4p-1f)
28#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
29
30static float32x4_t VPCS_ATTR NOINLINE
31specialcase (float32x4_t poly, float32x4_t n, uint32x4_t e, float32x4_t absn)
32{
33  /* 2^n may overflow, break it up into s1*s2.  */
34  uint32x4_t b = (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
35  float32x4_t s1 = vreinterpretq_f32_u32 (v_u32 (0x7f000000) + b);
36  float32x4_t s2 = vreinterpretq_f32_u32 (e - b);
37  uint32x4_t cmp = absn > v_f32 (192.0f);
38  float32x4_t r1 = s1 * s1;
39  float32x4_t r0 = poly * s1 * s2;
40  return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1))
41				| (~cmp & vreinterpretq_u32_f32 (r0)));
42}
43
44float32x4_t VPCS_ATTR
45_ZGVnN4v_expf_1u (float32x4_t x)
46{
47  float32x4_t n, r, scale, poly, absn, z;
48  uint32x4_t cmp, e;
49
50  /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
51     x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
52#if 1
53  z = vfmaq_f32 (Shift, x, InvLn2);
54  n = z - Shift;
55  r = vfmaq_f32 (x, n, -Ln2hi);
56  r = vfmaq_f32 (r, n, -Ln2lo);
57  e = vreinterpretq_u32_f32 (z) << 23;
58#else
59  z = x * InvLn2;
60  n = vrndaq_f32 (z);
61  r = vfmaq_f32 (x, n, -Ln2hi);
62  r = vfmaq_f32 (r, n, -Ln2lo);
63  e = vreinterpretq_u32_s32 (vcvtaq_s32_f32 (z)) << 23;
64#endif
65  scale = vreinterpretq_f32_u32 (e + v_u32 (0x3f800000));
66  absn = vabsq_f32 (n);
67  cmp = absn > v_f32 (126.0f);
68  poly = vfmaq_f32 (C1, C0, r);
69  poly = vfmaq_f32 (C2, poly, r);
70  poly = vfmaq_f32 (C3, poly, r);
71  poly = vfmaq_f32 (C4, poly, r);
72  poly = vfmaq_f32 (v_f32 (1.0f), poly, r);
73  poly = vfmaq_f32 (v_f32 (1.0f), poly, r);
74  if (unlikely (v_any_u32 (cmp)))
75    return specialcase (poly, n, e, absn);
76  return scale * poly;
77}
78