1/*
2 * Single-precision vector e^x function.
3 *
4 * Copyright (c) 2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
6 */
7
8#include "mathlib.h"
9#include "v_math.h"
10#if V_SUPPORTED
11
12static const float Poly[] = {
13  /*  maxerr: 0.36565 +0.5 ulp.  */
14  0x1.6a6000p-10f,
15  0x1.12718ep-7f,
16  0x1.555af0p-5f,
17  0x1.555430p-3f,
18  0x1.fffff4p-2f,
19};
20#define C0 v_f32 (Poly[0])
21#define C1 v_f32 (Poly[1])
22#define C2 v_f32 (Poly[2])
23#define C3 v_f32 (Poly[3])
24#define C4 v_f32 (Poly[4])
25
26#define Shift v_f32 (0x1.8p23f)
27#define InvLn2 v_f32 (0x1.715476p+0f)
28#define Ln2hi v_f32 (0x1.62e4p-1f)
29#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
30
31VPCS_ATTR
32static v_f32_t
33specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
34{
35  /* 2^n may overflow, break it up into s1*s2.  */
36  v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
37  v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
38  v_f32_t s2 = v_as_f32_u32 (e - b);
39  v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));
40  v_f32_t r1 = s1 * s1;
41  v_f32_t r0 = poly * s1 * s2;
42  return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
43}
44
45VPCS_ATTR
46v_f32_t
47V_NAME(expf_1u) (v_f32_t x)
48{
49  v_f32_t n, r, scale, poly, absn, z;
50  v_u32_t cmp, e;
51
52  /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
53     x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
54#if 1
55  z = v_fma_f32 (x, InvLn2, Shift);
56  n = z - Shift;
57  r = v_fma_f32 (n, -Ln2hi, x);
58  r = v_fma_f32 (n, -Ln2lo, r);
59  e = v_as_u32_f32 (z) << 23;
60#else
61  z = x * InvLn2;
62  n = v_round_f32 (z);
63  r = v_fma_f32 (n, -Ln2hi, x);
64  r = v_fma_f32 (n, -Ln2lo, r);
65  e = v_as_u32_s32 (v_round_s32 (z)) << 23;
66#endif
67  scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
68  absn = v_abs_f32 (n);
69  cmp = v_cond_u32 (absn > v_f32 (126.0f));
70  poly = v_fma_f32 (C0, r, C1);
71  poly = v_fma_f32 (poly, r, C2);
72  poly = v_fma_f32 (poly, r, C3);
73  poly = v_fma_f32 (poly, r, C4);
74  poly = v_fma_f32 (poly, r, v_f32 (1.0f));
75  poly = v_fma_f32 (poly, r, v_f32 (1.0f));
76  if (unlikely (v_any_u32 (cmp)))
77    return specialcase (poly, n, e, absn);
78  return scale * poly;
79}
80#endif
81