1*412f47f9SXin Li /*
2*412f47f9SXin Li * Double-precision SVE log2 function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2022-2024, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li #include "poly_sve_f64.h"
12*412f47f9SXin Li
13*412f47f9SXin Li #define N (1 << V_LOG2_TABLE_BITS)
14*412f47f9SXin Li #define Off 0x3fe6900900000000
15*412f47f9SXin Li #define Max (0x7ff0000000000000)
16*412f47f9SXin Li #define Min (0x0010000000000000)
17*412f47f9SXin Li #define Thresh (0x7fe0000000000000) /* Max - Min. */
18*412f47f9SXin Li
19*412f47f9SXin Li static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t cmp)20*412f47f9SXin Li special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
21*412f47f9SXin Li {
22*412f47f9SXin Li return sv_call_f64 (log2, x, y, cmp);
23*412f47f9SXin Li }
24*412f47f9SXin Li
25*412f47f9SXin Li /* Double-precision SVE log2 routine.
26*412f47f9SXin Li Implements the same algorithm as AdvSIMD log10, with coefficients and table
27*412f47f9SXin Li entries scaled in extended precision.
28*412f47f9SXin Li The maximum observed error is 2.58 ULP:
29*412f47f9SXin Li SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5
30*412f47f9SXin Li want 0x1.fffb34198d9ddp-5. */
SV_NAME_D1(log2)31*412f47f9SXin Li svfloat64_t SV_NAME_D1 (log2) (svfloat64_t x, const svbool_t pg)
32*412f47f9SXin Li {
33*412f47f9SXin Li svuint64_t ix = svreinterpret_u64 (x);
34*412f47f9SXin Li svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh);
35*412f47f9SXin Li
36*412f47f9SXin Li /* x = 2^k z; where z is in range [Off,2*Off) and exact.
37*412f47f9SXin Li The range is split into N subintervals.
38*412f47f9SXin Li The ith subinterval contains z and c is near its center. */
39*412f47f9SXin Li svuint64_t tmp = svsub_x (pg, ix, Off);
40*412f47f9SXin Li svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG2_TABLE_BITS);
41*412f47f9SXin Li i = svand_x (pg, i, (N - 1) << 1);
42*412f47f9SXin Li svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
43*412f47f9SXin Li svfloat64_t z = svreinterpret_f64 (
44*412f47f9SXin Li svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
45*412f47f9SXin Li
46*412f47f9SXin Li svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i);
47*412f47f9SXin Li svfloat64_t log2c
48*412f47f9SXin Li = svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i);
49*412f47f9SXin Li
50*412f47f9SXin Li /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */
51*412f47f9SXin Li
52*412f47f9SXin Li svfloat64_t r = svmad_x (pg, invc, z, -1.0);
53*412f47f9SXin Li svfloat64_t w = svmla_x (pg, log2c, r, __v_log2_data.invln2);
54*412f47f9SXin Li
55*412f47f9SXin Li svfloat64_t r2 = svmul_x (pg, r, r);
56*412f47f9SXin Li svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log2_data.poly);
57*412f47f9SXin Li w = svadd_x (pg, k, w);
58*412f47f9SXin Li
59*412f47f9SXin Li if (unlikely (svptest_any (pg, special)))
60*412f47f9SXin Li return special_case (x, svmla_x (svnot_z (pg, special), w, r2, y),
61*412f47f9SXin Li special);
62*412f47f9SXin Li return svmla_x (pg, w, r2, y);
63*412f47f9SXin Li }
64*412f47f9SXin Li
65*412f47f9SXin Li PL_SIG (SV, D, 1, log2, 0.01, 11.1)
66*412f47f9SXin Li PL_TEST_ULP (SV_NAME_D1 (log2), 2.09)
67*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000)
68*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000)
69*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000)
70*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000)
71*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000)
72*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000)
73