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: 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
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,v_u32_t cmp1,v_f32_t scale)30 specialcase (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
44 VPCS_ATTR
45 v_f32_t
V_NAME(exp2f)46 V_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 }
77 VPCS_ALIAS
78 #endif
79