1 /*
2 * Double-precision vector e^(x+tail) 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 "v_math.h"
9 #include "math_config.h"
10 #if V_SUPPORTED
11 #include "v_exp_tail.h"
12
13 #define C1 v_f64 (C1_scal)
14 #define C2 v_f64 (C2_scal)
15 #define C3 v_f64 (C3_scal)
16 #define InvLn2 v_f64 (InvLn2_scal)
17 #define Ln2hi v_f64 (Ln2hi_scal)
18 #define Ln2lo v_f64 (Ln2lo_scal)
19
20 #define IndexMask v_u64 (IndexMask_scal)
21 #define Shift v_f64 (Shift_scal)
22 #define Thres v_f64 (Thres_scal)
23
24 VPCS_ATTR
25 static v_f64_t
specialcase(v_f64_t s,v_f64_t y,v_f64_t n)26 specialcase (v_f64_t s, v_f64_t y, v_f64_t n)
27 {
28 v_f64_t absn = v_abs_f64 (n);
29
30 /* 2^(n/N) may overflow, break it up into s1*s2. */
31 v_u64_t b = v_cond_u64 (n <= v_f64 (0.0)) & v_u64 (0x6000000000000000);
32 v_f64_t s1 = v_as_f64_u64 (v_u64 (0x7000000000000000) - b);
33 v_f64_t s2 = v_as_f64_u64 (v_as_u64_f64 (s) - v_u64 (0x3010000000000000) + b);
34 v_u64_t cmp = v_cond_u64 (absn > v_f64 (1280.0 * N));
35 v_f64_t r1 = s1 * s1;
36 v_f64_t r0 = v_fma_f64 (y, s2, s2) * s1;
37 return v_as_f64_u64 ((cmp & v_as_u64_f64 (r1)) | (~cmp & v_as_u64_f64 (r0)));
38 }
39
40 VPCS_ATTR
V_NAME(exp_tail)41 v_f64_t V_NAME (exp_tail) (v_f64_t x, v_f64_t xtail)
42 {
43 v_f64_t n, r, s, y, z;
44 v_u64_t cmp, u, e, i;
45
46 cmp = v_cond_u64 (v_abs_f64 (x) > Thres);
47
48 /* n = round(x/(ln2/N)). */
49 z = v_fma_f64 (x, InvLn2, Shift);
50 u = v_as_u64_f64 (z);
51 n = z - Shift;
52
53 /* r = x - n*ln2/N. */
54 r = x;
55 r = v_fma_f64 (-Ln2hi, n, r);
56 r = v_fma_f64 (-Ln2lo, n, r);
57
58 e = u << (52 - V_EXP_TAIL_TABLE_BITS);
59 i = u & IndexMask;
60
61 /* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */
62 y = v_fma_f64 (C3, r, C2);
63 y = v_fma_f64 (y, r, C1);
64 y = v_fma_f64 (y, r, v_f64 (1.0));
65 y = v_fma_f64 (y, r, xtail);
66
67 /* s = 2^(n/N). */
68 u = v_lookup_u64 (Tab, i);
69 s = v_as_f64_u64 (u + e);
70
71 if (unlikely (v_any_u64 (cmp)))
72 return specialcase (s, y, n);
73 return v_fma_f64 (y, s, s);
74 }
75 #endif
76