1 /*
2 * Double-precision vector log(x) function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include "mathlib.h"
10 #include "v_math.h"
11 #include "v_log.h"
12 #if V_SUPPORTED
13
14 /* Worst-case error: 1.17 + 0.5 ulp. */
15
16 static const f64_t Poly[] = {
17 /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
18 -0x1.ffffffffffff7p-2,
19 0x1.55555555170d4p-2,
20 -0x1.0000000399c27p-2,
21 0x1.999b2e90e94cap-3,
22 -0x1.554e550bd501ep-3,
23 };
24
25 #define A0 v_f64 (Poly[0])
26 #define A1 v_f64 (Poly[1])
27 #define A2 v_f64 (Poly[2])
28 #define A3 v_f64 (Poly[3])
29 #define A4 v_f64 (Poly[4])
30 #define Ln2 v_f64 (0x1.62e42fefa39efp-1)
31 #define N (1 << V_LOG_TABLE_BITS)
32 #define OFF v_u64 (0x3fe6900900000000)
33
34 struct entry
35 {
36 v_f64_t invc;
37 v_f64_t logc;
38 };
39
40 static inline struct entry
lookup(v_u64_t i)41 lookup (v_u64_t i)
42 {
43 struct entry e;
44 #ifdef SCALAR
45 e.invc = __v_log_data[i].invc;
46 e.logc = __v_log_data[i].logc;
47 #else
48 e.invc[0] = __v_log_data[i[0]].invc;
49 e.logc[0] = __v_log_data[i[0]].logc;
50 e.invc[1] = __v_log_data[i[1]].invc;
51 e.logc[1] = __v_log_data[i[1]].logc;
52 #endif
53 return e;
54 }
55
56 VPCS_ATTR
57 __attribute__ ((noinline)) static v_f64_t
specialcase(v_f64_t x,v_f64_t y,v_u64_t cmp)58 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
59 {
60 return v_call_f64 (log, x, y, cmp);
61 }
62
63 VPCS_ATTR
64 v_f64_t
V_NAME(log)65 V_NAME(log) (v_f64_t x)
66 {
67 v_f64_t z, r, r2, p, y, kd, hi;
68 v_u64_t ix, iz, tmp, top, i, cmp;
69 v_s64_t k;
70 struct entry e;
71
72 ix = v_as_u64_f64 (x);
73 top = ix >> 48;
74 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
75
76 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
77 The range is split into N subintervals.
78 The ith subinterval contains z and c is near its center. */
79 tmp = ix - OFF;
80 i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
81 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
82 iz = ix - (tmp & v_u64 (0xfffULL << 52));
83 z = v_as_f64_u64 (iz);
84 e = lookup (i);
85
86 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
87 r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
88 kd = v_to_f64_s64 (k);
89
90 /* hi = r + log(c) + k*Ln2. */
91 hi = v_fma_f64 (kd, Ln2, e.logc + r);
92 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
93 r2 = r * r;
94 y = v_fma_f64 (A3, r, A2);
95 p = v_fma_f64 (A1, r, A0);
96 y = v_fma_f64 (A4, r2, y);
97 y = v_fma_f64 (y, r2, p);
98 y = v_fma_f64 (y, r2, hi);
99
100 if (unlikely (v_any_u64 (cmp)))
101 return specialcase (x, y, cmp);
102 return y;
103 }
104 VPCS_ALIAS
105 #endif
106