1*412f47f9SXin Li /*
2*412f47f9SXin Li * Double-precision SVE log(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2020-2023, 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
12*412f47f9SXin Li #define P(i) sv_f64 (__v_log_data.poly[i])
13*412f47f9SXin Li #define N (1 << V_LOG_TABLE_BITS)
14*412f47f9SXin Li #define Off (0x3fe6900900000000)
15*412f47f9SXin Li #define MaxTop (0x7ff)
16*412f47f9SXin Li #define MinTop (0x001)
17*412f47f9SXin Li #define ThreshTop (0x7fe) /* MaxTop - MinTop. */
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 (log, x, y, cmp);
23*412f47f9SXin Li }
24*412f47f9SXin Li
25*412f47f9SXin Li /* SVE port of AdvSIMD log algorithm.
26*412f47f9SXin Li Maximum measured error is 2.17 ulp:
27*412f47f9SXin Li SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
28*412f47f9SXin Li want 0x1.ffffff1cca045p-2. */
SV_NAME_D1(log)29*412f47f9SXin Li svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
30*412f47f9SXin Li {
31*412f47f9SXin Li svuint64_t ix = svreinterpret_u64 (x);
32*412f47f9SXin Li svuint64_t top = svlsr_x (pg, ix, 52);
33*412f47f9SXin Li svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop));
34*412f47f9SXin Li
35*412f47f9SXin Li /* x = 2^k z; where z is in range [Off,2*Off) and exact.
36*412f47f9SXin Li The range is split into N subintervals.
37*412f47f9SXin Li The ith subinterval contains z and c is near its center. */
38*412f47f9SXin Li svuint64_t tmp = svsub_x (pg, ix, Off);
39*412f47f9SXin Li /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
40*412f47f9SXin Li The actual value of i is double this due to table layout. */
41*412f47f9SXin Li svuint64_t i
42*412f47f9SXin Li = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
43*412f47f9SXin Li svint64_t k
44*412f47f9SXin Li = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */
45*412f47f9SXin Li svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
46*412f47f9SXin Li svfloat64_t z = svreinterpret_f64 (iz);
47*412f47f9SXin Li /* Lookup in 2 global lists (length N). */
48*412f47f9SXin Li svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
49*412f47f9SXin Li svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
50*412f47f9SXin Li
51*412f47f9SXin Li /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */
52*412f47f9SXin Li svfloat64_t r = svmad_x (pg, invc, z, -1);
53*412f47f9SXin Li svfloat64_t kd = svcvt_f64_x (pg, k);
54*412f47f9SXin Li /* hi = r + log(c) + k*Ln2. */
55*412f47f9SXin Li svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
56*412f47f9SXin Li /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */
57*412f47f9SXin Li svfloat64_t r2 = svmul_x (pg, r, r);
58*412f47f9SXin Li svfloat64_t y = svmla_x (pg, P (2), r, P (3));
59*412f47f9SXin Li svfloat64_t p = svmla_x (pg, P (0), r, P (1));
60*412f47f9SXin Li y = svmla_x (pg, y, r2, P (4));
61*412f47f9SXin Li y = svmla_x (pg, p, r2, y);
62*412f47f9SXin Li
63*412f47f9SXin Li if (unlikely (svptest_any (pg, cmp)))
64*412f47f9SXin Li return special_case (x, svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp);
65*412f47f9SXin Li return svmla_x (pg, hi, r2, y);
66*412f47f9SXin Li }
67*412f47f9SXin Li
68*412f47f9SXin Li PL_SIG (SV, D, 1, log, 0.01, 11.1)
69*412f47f9SXin Li PL_TEST_ULP (SV_NAME_D1 (log), 1.68)
70*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000)
71*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000)
72*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000)
73*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000)
74*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000)
75*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000)
76*412f47f9SXin Li PL_TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000)
77