1/*
2 * Double-precision SVE log(x) function.
3 *
4 * Copyright (c) 2020-2023, 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
12#define P(i) sv_f64 (__v_log_data.poly[i])
13#define N (1 << V_LOG_TABLE_BITS)
14#define Off (0x3fe6900900000000)
15#define MaxTop (0x7ff)
16#define MinTop (0x001)
17#define ThreshTop (0x7fe) /* MaxTop - MinTop.  */
18
19static svfloat64_t NOINLINE
20special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp)
21{
22  return sv_call_f64 (log, x, y, cmp);
23}
24
25/* SVE port of AdvSIMD log algorithm.
26   Maximum measured error is 2.17 ulp:
27   SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2
28					 want 0x1.ffffff1cca045p-2.  */
29svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg)
30{
31  svuint64_t ix = svreinterpret_u64 (x);
32  svuint64_t top = svlsr_x (pg, ix, 52);
33  svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop));
34
35  /* x = 2^k z; where z is in range [Off,2*Off) and exact.
36     The range is split into N subintervals.
37     The ith subinterval contains z and c is near its center.  */
38  svuint64_t tmp = svsub_x (pg, ix, Off);
39  /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N.
40     The actual value of i is double this due to table layout.  */
41  svuint64_t i
42      = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1);
43  svint64_t k
44      = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift.  */
45  svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
46  svfloat64_t z = svreinterpret_f64 (iz);
47  /* Lookup in 2 global lists (length N).  */
48  svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
49  svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
50
51  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
52  svfloat64_t r = svmad_x (pg, invc, z, -1);
53  svfloat64_t kd = svcvt_f64_x (pg, k);
54  /* hi = r + log(c) + k*Ln2.  */
55  svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2);
56  /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi.  */
57  svfloat64_t r2 = svmul_x (pg, r, r);
58  svfloat64_t y = svmla_x (pg, P (2), r, P (3));
59  svfloat64_t p = svmla_x (pg, P (0), r, P (1));
60  y = svmla_x (pg, y, r2, P (4));
61  y = svmla_x (pg, p, r2, y);
62
63  if (unlikely (svptest_any (pg, cmp)))
64    return special_case (x, svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp);
65  return svmla_x (pg, hi, r2, y);
66}
67
68PL_SIG (SV, D, 1, log, 0.01, 11.1)
69PL_TEST_ULP (SV_NAME_D1 (log), 1.68)
70PL_TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000)
71PL_TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000)
72PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000)
73PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000)
74PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000)
75PL_TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000)
76PL_TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000)
77