1 /*
2 * Double-precision vector log(x) function - inline version
3 *
4 * Copyright (c) 2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "math_config.h"
10
11 #ifndef SV_LOG_INLINE_POLY_ORDER
12 # error Cannot use inline log helper without specifying poly order (options are 4 or 5)
13 #endif
14
15 #if SV_LOG_INLINE_POLY_ORDER == 4
16 # define POLY \
17 { \
18 -0x1.ffffffffcbad3p-2, 0x1.555555578ed68p-2, -0x1.0000d3a1e7055p-2, \
19 0x1.999392d02a63ep-3 \
20 }
21 #elif SV_LOG_INLINE_POLY_ORDER == 5
22 # define POLY \
23 { \
24 -0x1.ffffffffffff7p-2, 0x1.55555555170d4p-2, -0x1.0000000399c27p-2, \
25 0x1.999b2e90e94cap-3, -0x1.554e550bd501ep-3 \
26 }
27 #else
28 # error Can only choose order 4 or 5 for log poly
29 #endif
30
31 struct sv_log_inline_data
32 {
33 double poly[SV_LOG_INLINE_POLY_ORDER];
34 double ln2;
35 uint64_t off, sign_exp_mask;
36 };
37
38 #define SV_LOG_CONSTANTS \
39 { \
40 .poly = POLY, .ln2 = 0x1.62e42fefa39efp-1, \
41 .sign_exp_mask = 0xfff0000000000000, .off = 0x3fe6900900000000 \
42 }
43
44 #define P(i) sv_f64 (d->poly[i])
45 #define N (1 << V_LOG_TABLE_BITS)
46
47 static inline svfloat64_t
sv_log_inline(svbool_t pg,svfloat64_t x,const struct sv_log_inline_data * d)48 sv_log_inline (svbool_t pg, svfloat64_t x, const struct sv_log_inline_data *d)
49 {
50 svuint64_t ix = svreinterpret_u64 (x);
51
52 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
53 The range is split into N subintervals.
54 The ith subinterval contains z and c is near its center. */
55 svuint64_t tmp = svsub_x (pg, ix, d->off);
56 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
57 The actual value of i is double this due to table layout. */
58 svuint64_t i
59 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
60 svint64_t k
61 = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */
62 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
63 svfloat64_t z = svreinterpret_f64 (iz);
64
65 /* Lookup in 2 global lists (length N). */
66 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
67 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
68
69 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
70 svfloat64_t r = svmad_x (pg, invc, z, -1);
71 svfloat64_t kd = svcvt_f64_x (pg, k);
72 /* hi = r + log(c) + k*Ln2. */
73 svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
74 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
75 svfloat64_t r2 = svmul_x (pg, r, r);
76 svfloat64_t y = svmla_x (pg, P (2), r, P (3));
77 svfloat64_t p = svmla_x (pg, P (0), r, P (1));
78 #if SV_LOG_INLINE_POLY_ORDER == 5
79 y = svmla_x (pg, P (4), r2);
80 #endif
81 y = svmla_x (pg, p, r2, y);
82 return svmla_x (pg, hi, r2, y);
83 }
84