1 /*
2 * Double-precision SVE log(x) function.
3 *
4 * Copyright (c) 2020-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 #define N (1 << V_LOG_TABLE_BITS)
13 #define Max (0x7ff0000000000000)
14 #define Min (0x0010000000000000)
15 #define Thresh (0x7fe0000000000000) /* Max - Min. */
16
17 static const struct data
18 {
19 double c0, c2;
20 double c1, c3;
21 double ln2, c4;
22 uint64_t off;
23 } data = {
24 .c0 = -0x1.ffffffffffff7p-2,
25 .c1 = 0x1.55555555170d4p-2,
26 .c2 = -0x1.0000000399c27p-2,
27 .c3 = 0x1.999b2e90e94cap-3,
28 .c4 = -0x1.554e550bd501ep-3,
29 .ln2 = 0x1.62e42fefa39efp-1,
30 .off = 0x3fe6900900000000,
31 };
32
33 static svfloat64_t NOINLINE
special_case(svfloat64_t hi,svuint64_t tmp,svfloat64_t y,svfloat64_t r2,svbool_t special,const struct data * d)34 special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
35 svbool_t special, const struct data *d)
36 {
37 svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
38 return sv_call_f64 (log, x, svmla_x (svptrue_b64 (), hi, r2, y), special);
39 }
40
41 /* Double-precision SVE log routine.
42 Maximum measured error is 2.64 ulp:
43 SV_NAME_D1 (log)(0x1.95e54bc91a5e2p+184) got 0x1.fffffffe88cacp+6
44 want 0x1.fffffffe88cafp+6. */
SV_NAME_D1(log)45 svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
46 {
47 const struct data *d = ptr_barrier (&data);
48
49 svuint64_t ix = svreinterpret_u64 (x);
50 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
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 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
61 svfloat64_t z = svreinterpret_f64 (iz);
62 /* Lookup in 2 global lists (length N). */
63 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
64 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
65
66 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
67 svfloat64_t kd = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
68 /* hi = r + log(c) + k*Ln2. */
69 svfloat64_t ln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->ln2);
70 svfloat64_t r = svmad_x (pg, invc, z, -1);
71 svfloat64_t hi = svmla_lane_f64 (logc, kd, ln2_and_c4, 0);
72 hi = svadd_x (pg, r, hi);
73
74 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
75 svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
76 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
77 svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
78 svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
79 y = svmla_lane_f64 (y, r2, ln2_and_c4, 1);
80 y = svmla_x (pg, p, r2, y);
81
82 if (unlikely (svptest_any (pg, special)))
83 return special_case (hi, tmp, y, r2, special, d);
84 return svmla_x (pg, hi, r2, y);
85 }
86
87 TEST_SIG (SV, D, 1, log, 0.01, 11.1)
88 TEST_ULP (SV_NAME_D1 (log), 2.15)
89 TEST_DISABLE_FENV (SV_NAME_D1 (log))
90 TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000)
91 TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000)
92 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000)
93 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000)
94 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000)
95 TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000)
96 TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000)
97 CLOSE_SVE_ATTR
98