1 /*
2 * Double-precision SVE log2 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 "pl_sig.h"
10 #include "pl_test.h"
11 #include "poly_sve_f64.h"
12
13 #define N (1 << V_LOG2_TABLE_BITS)
14 #define Off 0x3fe6900900000000
15 #define Max (0x7ff0000000000000)
16 #define Min (0x0010000000000000)
17 #define Thresh (0x7fe0000000000000) /* Max - Min. */
18
19 static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t cmp)20 special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
21 {
22 return sv_call_f64 (log2, x, y, cmp);
23 }
24
25 /* Double-precision SVE log2 routine.
26 Implements the same algorithm as AdvSIMD log10, with coefficients and table
27 entries scaled in extended precision.
28 The maximum observed error is 2.58 ULP:
29 SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
30 want 0x1.fffb34198d9ddp-5. */
SV_NAME_D1(log2)31 svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
32 {
33 svuint64_t ix = svreinterpret_u64 (x);
34 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
35
36 /* x = 2^k z; where z is in range [Off,2*Off) and exact.
37 The range is split into N subintervals.
38 The ith subinterval contains z and c is near its center. */
39 svuint64_t tmp = svsub_x (pg, ix, Off);
40 svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS);
41 i = svand_x (pg, i, (N - 1) << 1);
42 svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
43 svfloat64_t z = svreinterpret_f64 (
44 svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
45
46 svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i);
47 svfloat64_t log2c
48 = svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i);
49
50 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
51
52 svfloat64_t r = svmad_x (pg, invc, z, -1.0);
53 svfloat64_t w = svmla_x (pg, log2c, r, __v_log2_data.invln2);
54
55 svfloat64_t r2 = svmul_x (pg, r, r);
56 svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log2_data.poly);
57 w = svadd_x (pg, k, w);
58
59 if (unlikely (svptest_any (pg, special)))
60 return special_case (x, svmla_x (svnot_z (pg, special), w, r2, y),
61 special);
62 return svmla_x (pg, w, r2, y);
63 }
64
65 PL_SIG (SV, D, 1, log2, 0.01, 11.1)
66 PL_TEST_ULP (SV_NAME_D1 (log2), 2.09)
67 PL_TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000)
68 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000)
69 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000)
70 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000)
71 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000)
72 PL_TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000)
73