1 /*
2 * Double-precision vector log2 function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "v_math.h"
9 #include "include/mathlib.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12
13 #if V_SUPPORTED
14
15 #define InvLn2 v_f64 (0x1.71547652b82fep0)
16 #define N (1 << V_LOG2_TABLE_BITS)
17 #define OFF v_u64 (0x3fe6900900000000)
18 #define P(i) v_f64 (__v_log2_data.poly[i])
19
20 struct entry
21 {
22 v_f64_t invc;
23 v_f64_t log2c;
24 };
25
26 static inline struct entry
lookup(v_u64_t i)27 lookup (v_u64_t i)
28 {
29 struct entry e;
30 #ifdef SCALAR
31 e.invc = __v_log2_data.tab[i].invc;
32 e.log2c = __v_log2_data.tab[i].log2c;
33 #else
34 e.invc[0] = __v_log2_data.tab[i[0]].invc;
35 e.log2c[0] = __v_log2_data.tab[i[0]].log2c;
36 e.invc[1] = __v_log2_data.tab[i[1]].invc;
37 e.log2c[1] = __v_log2_data.tab[i[1]].log2c;
38 #endif
39 return e;
40 }
41
42 VPCS_ATTR
43 NOINLINE static v_f64_t
specialcase(v_f64_t x,v_f64_t y,v_u64_t cmp)44 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
45 {
46 return v_call_f64 (log2, x, y, cmp);
47 }
48
49 /* Double-precision vector log2 routine. Implements the same algorithm as vector
50 log10, with coefficients and table entries scaled in extended precision.
51 The maximum observed error is 2.58 ULP:
52 __v_log2(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
53 want 0x1.fffb34198d9ddp-5. */
54 VPCS_ATTR
V_NAME(log2)55 v_f64_t V_NAME (log2) (v_f64_t x)
56 {
57 v_u64_t ix = v_as_u64_f64 (x);
58 v_u64_t top = ix >> 48;
59 v_u64_t special
60 = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
61
62 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
63 The range is split into N subintervals.
64 The ith subinterval contains z and c is near its center. */
65 v_u64_t tmp = ix - OFF;
66 v_u64_t i = (tmp >> (52 - V_LOG2_TABLE_BITS)) % N;
67 v_s64_t k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift. */
68 v_u64_t iz = ix - (tmp & v_u64 (0xfffULL << 52));
69 v_f64_t z = v_as_f64_u64 (iz);
70 struct entry e = lookup (i);
71
72 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
73
74 v_f64_t r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
75 v_f64_t kd = v_to_f64_s64 (k);
76 v_f64_t w = v_fma_f64 (r, InvLn2, e.log2c);
77
78 v_f64_t r2 = r * r;
79 v_f64_t p_23 = v_fma_f64 (P (3), r, P (2));
80 v_f64_t p_01 = v_fma_f64 (P (1), r, P (0));
81 v_f64_t y = v_fma_f64 (P (4), r2, p_23);
82 y = v_fma_f64 (r2, y, p_01);
83 y = v_fma_f64 (r2, y, kd + w);
84
85 if (unlikely (v_any_u64 (special)))
86 return specialcase (x, y, special);
87 return y;
88 }
89 VPCS_ALIAS
90
91 PL_SIG (V, D, 1, log2, 0.01, 11.1)
92 PL_TEST_ULP (V_NAME (log2), 2.09)
93 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (log2))
94 PL_TEST_INTERVAL (V_NAME (log2), -0.0, -0x1p126, 100)
95 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-149, 0x1p-126, 4000)
96 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-126, 0x1p-23, 50000)
97 PL_TEST_INTERVAL (V_NAME (log2), 0x1p-23, 1.0, 50000)
98 PL_TEST_INTERVAL (V_NAME (log2), 1.0, 100, 50000)
99 PL_TEST_INTERVAL (V_NAME (log2), 100, inf, 50000)
100 #endif
101