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
12 static const float Poly[] = {
13 /* maxerr: 0.878 ulp. */
14 0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f
15 };
16 #define C0 v_f32 (Poly[0])
17 #define C1 v_f32 (Poly[1])
18 #define C2 v_f32 (Poly[2])
19 #define C3 v_f32 (Poly[3])
20 #define C4 v_f32 (Poly[4])
21 #define C5 v_f32 (Poly[5])
22
23 #define Shift v_f32 (0x1.8p23f)
24 #define InvLn2 v_f32 (0x1.715476p+0f)
25 #define Ln2hi v_f32 (0x1.62e4p-1f)
26 #define Ln2lo v_f32 (0x1.7f7d1cp-20f)
27
28 VPCS_ATTR
29 static v_f32_t
specialcase(v_f32_t poly,v_f32_t n,v_u32_t e,v_f32_t absn)30 specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
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 (0x83000000);
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 cmp = v_cond_u32 (absn > v_f32 (192.0f));
37 v_f32_t r1 = s1 * s1;
38 v_f32_t r0 = poly * s1 * s2;
39 return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
40 }
41
42 VPCS_ATTR
43 v_f32_t
V_NAME(exp2f_1u)44 V_NAME(exp2f_1u) (v_f32_t x)
45 {
46 v_f32_t n, r, scale, poly, absn;
47 v_u32_t cmp, e;
48
49 /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
50 x = n + r, with r in [-1/2, 1/2]. */
51 #if 0
52 v_f32_t z;
53 z = x + Shift;
54 n = z - Shift;
55 r = x - n;
56 e = v_as_u32_f32 (z) << 23;
57 #else
58 n = v_round_f32 (x);
59 r = x - n;
60 e = v_as_u32_s32 (v_round_s32 (x)) << 23;
61 #endif
62 scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
63 absn = v_abs_f32 (n);
64 cmp = v_cond_u32 (absn > v_f32 (126.0f));
65 poly = v_fma_f32 (C0, r, C1);
66 poly = v_fma_f32 (poly, r, C2);
67 poly = v_fma_f32 (poly, r, C3);
68 poly = v_fma_f32 (poly, r, C4);
69 poly = v_fma_f32 (poly, r, C5);
70 poly = v_fma_f32 (poly, r, v_f32 (1.0f));
71 if (unlikely (v_any_u32 (cmp)))
72 return specialcase (poly, n, e, absn);
73 return scale * poly;
74 }
75 #endif
76