1 /*
2 * Double-precision SVE log10(x) function.
3 *
4 * Copyright (c) 2022-2024, 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 Min 0x0010000000000000
13 #define Max 0x7ff0000000000000
14 #define Thres 0x7fe0000000000000 /* Max - Min. */
15 #define N (1 << V_LOG10_TABLE_BITS)
16
17 static const struct data
18 {
19 double c0, c2;
20 double c1, c3;
21 double invln10, log10_2;
22 double c4;
23 uint64_t off;
24 } data = {
25 .c0 = -0x1.bcb7b1526e506p-3,
26 .c1 = 0x1.287a7636be1d1p-3,
27 .c2 = -0x1.bcb7b158af938p-4,
28 .c3 = 0x1.63c78734e6d07p-4,
29 .c4 = -0x1.287461742fee4p-4,
30 .invln10 = 0x1.bcb7b1526e50ep-2,
31 .log10_2 = 0x1.34413509f79ffp-2,
32 .off = 0x3fe6900900000000,
33 };
34
35 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)36 special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2,
37 svbool_t special, const struct data *d)
38 {
39 svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off));
40 return sv_call_f64 (log10, x, svmla_x (svptrue_b64 (), hi, r2, y), special);
41 }
42
43 /* Double-precision SVE log10 routine.
44 Maximum measured error is 2.46 ulps.
45 SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6
46 want 0x1.fffbdf6eaa667p-6. */
SV_NAME_D1(log10)47 svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg)
48 {
49 const struct data *d = ptr_barrier (&data);
50
51 svuint64_t ix = svreinterpret_u64 (x);
52 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
53
54 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
55 The range is split into N subintervals.
56 The ith subinterval contains z and c is near its center. */
57 svuint64_t tmp = svsub_x (pg, ix, d->off);
58 svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS);
59 i = svand_x (pg, i, (N - 1) << 1);
60 svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
61 svfloat64_t z = svreinterpret_f64 (
62 svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
63
64 /* log(x) = k*log(2) + log(c) + log(z/c). */
65 svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i);
66 svfloat64_t logc
67 = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i);
68
69 /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1):
70 r = z/c - 1 (we look up precomputed 1/c)
71 log(z/c) ~= P(r). */
72 svfloat64_t r = svmad_x (pg, invc, z, -1.0);
73
74 /* hi = log(c) + k*log(2). */
75 svfloat64_t invln10_log10_2 = svld1rq_f64 (svptrue_b64 (), &d->invln10);
76 svfloat64_t w = svmla_lane_f64 (logc, r, invln10_log10_2, 0);
77 svfloat64_t hi = svmla_lane_f64 (w, k, invln10_log10_2, 1);
78
79 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
80 svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1);
81 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
82 svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1);
83 svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0);
84 y = svmla_x (pg, y, r2, d->c4);
85 y = svmla_x (pg, p, r2, y);
86
87 if (unlikely (svptest_any (pg, special)))
88 return special_case (hi, tmp, y, r2, special, d);
89 return svmla_x (pg, hi, r2, y);
90 }
91
92 TEST_SIG (SV, D, 1, log10, 0.01, 11.1)
93 TEST_ULP (SV_NAME_D1 (log10), 1.97)
94 TEST_DISABLE_FENV (SV_NAME_D1 (log10))
95 TEST_INTERVAL (SV_NAME_D1 (log10), -0.0, -0x1p126, 100)
96 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000)
97 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000)
98 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-23, 1.0, 50000)
99 TEST_INTERVAL (SV_NAME_D1 (log10), 1.0, 100, 50000)
100 TEST_INTERVAL (SV_NAME_D1 (log10), 100, inf, 50000)
101 CLOSE_SVE_ATTR
102