1/*
2 * Single-precision vector 2^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: 1.962 ulp.  */
14  0x1.59977ap-10f,
15  0x1.3ce9e4p-7f,
16  0x1.c6bd32p-5f,
17  0x1.ebf9bcp-3f,
18  0x1.62e422p-1f,
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
28VPCS_ATTR
29static v_f32_t
30specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
31{
32  /* 2^n may overflow, break it up into s1*s2.  */
33  v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
34  v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
35  v_f32_t s2 = v_as_f32_u32 (e - b);
36  v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
37  v_u32_t r2 = v_as_u32_f32 (s1 * s1);
38  v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
39  /* Similar to r1 but avoids double rounding in the subnormal range.  */
40  v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
41  return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
42}
43
44VPCS_ATTR
45v_f32_t
46V_NAME(exp2f) (v_f32_t x)
47{
48  v_f32_t n, r, r2, scale, p, q, poly, absn;
49  v_u32_t cmp, e;
50
51  /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
52     x = n + r, with r in [-1/2, 1/2].  */
53#if 0
54  v_f32_t z;
55  z = x + Shift;
56  n = z - Shift;
57  r = x - n;
58  e = v_as_u32_f32 (z) << 23;
59#else
60  n = v_round_f32 (x);
61  r = x - n;
62  e = v_as_u32_s32 (v_round_s32 (x)) << 23;
63#endif
64  scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
65  absn = v_abs_f32 (n);
66  cmp = v_cond_u32 (absn > v_f32 (126.0f));
67  r2 = r * r;
68  p = v_fma_f32 (C0, r, C1);
69  q = v_fma_f32 (C2, r, C3);
70  q = v_fma_f32 (p, r2, q);
71  p = C4 * r;
72  poly = v_fma_f32 (q, r2, p);
73  if (unlikely (v_any_u32 (cmp)))
74    return specialcase (poly, n, e, absn, cmp, scale);
75  return v_fma_f32 (poly, scale, scale);
76}
77VPCS_ALIAS
78#endif
79