1072a4ba8SAndrew Turner /*
2072a4ba8SAndrew Turner * Double-precision SVE log10(x) function.
3072a4ba8SAndrew Turner *
4072a4ba8SAndrew Turner * Copyright (c) 2022-2023, Arm Limited.
5072a4ba8SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6072a4ba8SAndrew Turner */
7072a4ba8SAndrew Turner
8072a4ba8SAndrew Turner #include "sv_math.h"
9072a4ba8SAndrew Turner #include "pl_sig.h"
10072a4ba8SAndrew Turner #include "pl_test.h"
11*5a02ffc3SAndrew Turner #include "poly_sve_f64.h"
12072a4ba8SAndrew Turner
13*5a02ffc3SAndrew Turner #define Min 0x0010000000000000
14*5a02ffc3SAndrew Turner #define Max 0x7ff0000000000000
15*5a02ffc3SAndrew Turner #define Thres 0x7fe0000000000000 /* Max - Min. */
16*5a02ffc3SAndrew Turner #define Off 0x3fe6900900000000
17072a4ba8SAndrew Turner #define N (1 << V_LOG10_TABLE_BITS)
18072a4ba8SAndrew Turner
19*5a02ffc3SAndrew Turner static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t special)20*5a02ffc3SAndrew Turner special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
21072a4ba8SAndrew Turner {
22072a4ba8SAndrew Turner return sv_call_f64 (log10, x, y, special);
23072a4ba8SAndrew Turner }
24072a4ba8SAndrew Turner
25*5a02ffc3SAndrew Turner /* SVE log10 algorithm.
26*5a02ffc3SAndrew Turner Maximum measured error is 2.46 ulps.
27*5a02ffc3SAndrew Turner SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6
28072a4ba8SAndrew Turner want 0x1.fffbdf6eaa667p-6. */
SV_NAME_D1(log10)29*5a02ffc3SAndrew Turner svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg)
30072a4ba8SAndrew Turner {
31*5a02ffc3SAndrew Turner svuint64_t ix = svreinterpret_u64 (x);
32*5a02ffc3SAndrew Turner svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres);
33072a4ba8SAndrew Turner
34*5a02ffc3SAndrew Turner /* x = 2^k z; where z is in range [Off,2*Off) and exact.
35072a4ba8SAndrew Turner The range is split into N subintervals.
36072a4ba8SAndrew Turner The ith subinterval contains z and c is near its center. */
37*5a02ffc3SAndrew Turner svuint64_t tmp = svsub_x (pg, ix, Off);
38*5a02ffc3SAndrew Turner svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS);
39*5a02ffc3SAndrew Turner i = svand_x (pg, i, (N - 1) << 1);
40*5a02ffc3SAndrew Turner svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52));
41*5a02ffc3SAndrew Turner svfloat64_t z = svreinterpret_f64 (
42*5a02ffc3SAndrew Turner svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)));
43072a4ba8SAndrew Turner
44072a4ba8SAndrew Turner /* log(x) = k*log(2) + log(c) + log(z/c). */
45*5a02ffc3SAndrew Turner svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i);
46*5a02ffc3SAndrew Turner svfloat64_t logc
47*5a02ffc3SAndrew Turner = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i);
48072a4ba8SAndrew Turner
49072a4ba8SAndrew Turner /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1):
50072a4ba8SAndrew Turner r = z/c - 1 (we look up precomputed 1/c)
51072a4ba8SAndrew Turner log(z/c) ~= P(r). */
52*5a02ffc3SAndrew Turner svfloat64_t r = svmad_x (pg, invc, z, -1.0);
53072a4ba8SAndrew Turner
54072a4ba8SAndrew Turner /* hi = log(c) + k*log(2). */
55*5a02ffc3SAndrew Turner svfloat64_t w = svmla_x (pg, logc, r, __v_log10_data.invln10);
56*5a02ffc3SAndrew Turner svfloat64_t hi = svmla_x (pg, w, k, __v_log10_data.log10_2);
57072a4ba8SAndrew Turner
58072a4ba8SAndrew Turner /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
59*5a02ffc3SAndrew Turner svfloat64_t r2 = svmul_x (pg, r, r);
60*5a02ffc3SAndrew Turner svfloat64_t y = sv_pw_horner_4_f64_x (pg, r, r2, __v_log10_data.poly);
61072a4ba8SAndrew Turner
62*5a02ffc3SAndrew Turner if (unlikely (svptest_any (pg, special)))
63*5a02ffc3SAndrew Turner return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y),
64*5a02ffc3SAndrew Turner special);
65*5a02ffc3SAndrew Turner return svmla_x (pg, hi, r2, y);
66072a4ba8SAndrew Turner }
67072a4ba8SAndrew Turner
68072a4ba8SAndrew Turner PL_SIG (SV, D, 1, log10, 0.01, 11.1)
69*5a02ffc3SAndrew Turner PL_TEST_ULP (SV_NAME_D1 (log10), 1.97)
70*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), -0.0, -0x1p126, 100)
71*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000)
72*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000)
73*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-23, 1.0, 50000)
74*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), 1.0, 100, 50000)
75*5a02ffc3SAndrew Turner PL_TEST_INTERVAL (SV_NAME_D1 (log10), 100, inf, 50000)
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