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
11 static 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
30 static float32x4_t VPCS_ATTR NOINLINE
specialcase(float32x4_t poly,float32x4_t n,uint32x4_t e,float32x4_t absn)31 specialcase (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
44 float32x4_t VPCS_ATTR
_ZGVnN4v_expf_1u(float32x4_t x)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