2 * Double-precision vector log(x) function.
4 * Copyright (c) 2019, Arm Limited.
5 * SPDX-License-Identifier: MIT
13 /* Worst-case error: 1.17 + 0.5 ulp. */
15 static const f64_t Poly[] = {
16 /* rel error: 0x1.6272e588p-56 in [ -0x1.fc1p-9 0x1.009p-8 ]. */
17 -0x1.ffffffffffff7p-2,
19 -0x1.0000000399c27p-2,
21 -0x1.554e550bd501ep-3,
24 #define A0 v_f64 (Poly[0])
25 #define A1 v_f64 (Poly[1])
26 #define A2 v_f64 (Poly[2])
27 #define A3 v_f64 (Poly[3])
28 #define A4 v_f64 (Poly[4])
29 #define Ln2 v_f64 (0x1.62e42fefa39efp-1)
30 #define N (1 << V_LOG_TABLE_BITS)
31 #define OFF v_u64 (0x3fe6900900000000)
39 static inline struct entry
44 e.invc = __v_log_data[i].invc;
45 e.logc = __v_log_data[i].logc;
47 e.invc[0] = __v_log_data[i[0]].invc;
48 e.logc[0] = __v_log_data[i[0]].logc;
49 e.invc[1] = __v_log_data[i[1]].invc;
50 e.logc[1] = __v_log_data[i[1]].logc;
56 __attribute__ ((noinline)) static v_f64_t
57 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
59 return v_call_f64 (log, x, y, cmp);
64 V_NAME(log) (v_f64_t x)
66 v_f64_t z, r, r2, p, y, kd, hi;
67 v_u64_t ix, iz, tmp, top, i, cmp;
71 ix = v_as_u64_f64 (x);
73 cmp = v_cond_u64 (top - v_u64 (0x0010) >= v_u64 (0x7ff0 - 0x0010));
75 /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
76 The range is split into N subintervals.
77 The ith subinterval contains z and c is near its center. */
79 i = (tmp >> (52 - V_LOG_TABLE_BITS)) % N;
80 k = v_as_s64_u64 (tmp) >> 52; /* arithmetic shift */
81 iz = ix - (tmp & v_u64 (0xfffULL << 52));
82 z = v_as_f64_u64 (iz);
85 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
86 r = v_fma_f64 (z, e.invc, v_f64 (-1.0));
87 kd = v_to_f64_s64 (k);
89 /* hi = r + log(c) + k*Ln2. */
90 hi = v_fma_f64 (kd, Ln2, e.logc + r);
91 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
93 y = v_fma_f64 (A3, r, A2);
94 p = v_fma_f64 (A1, r, A0);
95 y = v_fma_f64 (A4, r2, y);
96 y = v_fma_f64 (y, r2, p);
97 y = v_fma_f64 (y, r2, hi);
99 if (unlikely (v_any_u64 (cmp)))
100 return specialcase (x, y, cmp);