1/*
2 * Double-precision SVE sinh(x) function.
3 *
4 * Copyright (c) 2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8#include "sv_math.h"
9#include "poly_sve_f64.h"
10#include "pl_sig.h"
11#include "pl_test.h"
12
13static const struct data
14{
15  float64_t poly[11];
16  float64_t inv_ln2, m_ln2_hi, m_ln2_lo, shift;
17  uint64_t halff;
18  int64_t onef;
19  uint64_t large_bound;
20} data = {
21  /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2].  */
22  .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5,
23	    0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10,
24	    0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16,
25	    0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22,
26	    0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, },
27
28  .inv_ln2 = 0x1.71547652b82fep0,
29  .m_ln2_hi = -0x1.62e42fefa39efp-1,
30  .m_ln2_lo = -0x1.abc9e3b39803fp-56,
31  .shift = 0x1.8p52,
32
33  .halff = 0x3fe0000000000000,
34  .onef = 0x3ff0000000000000,
35  /* 2^9. expm1 helper overflows for large input.  */
36  .large_bound = 0x4080000000000000,
37};
38
39static inline svfloat64_t
40expm1_inline (svfloat64_t x, svbool_t pg)
41{
42  const struct data *d = ptr_barrier (&data);
43
44  /* Reduce argument:
45     exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
46     where i = round(x / ln2)
47     and   f = x - i * ln2 (f in [-ln2/2, ln2/2]).  */
48  svfloat64_t j
49      = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift);
50  svint64_t i = svcvt_s64_x (pg, j);
51  svfloat64_t f = svmla_x (pg, x, j, d->m_ln2_hi);
52  f = svmla_x (pg, f, j, d->m_ln2_lo);
53  /* Approximate expm1(f) using polynomial.  */
54  svfloat64_t f2 = svmul_x (pg, f, f);
55  svfloat64_t f4 = svmul_x (pg, f2, f2);
56  svfloat64_t f8 = svmul_x (pg, f4, f4);
57  svfloat64_t p
58      = svmla_x (pg, f, f2, sv_estrin_10_f64_x (pg, f, f2, f4, f8, d->poly));
59  /* t = 2^i.  */
60  svfloat64_t t = svscale_x (pg, sv_f64 (1), i);
61  /* expm1(x) ~= p * t + (t - 1).  */
62  return svmla_x (pg, svsub_x (pg, t, 1.0), p, t);
63}
64
65static svfloat64_t NOINLINE
66special_case (svfloat64_t x, svbool_t pg)
67{
68  return sv_call_f64 (sinh, x, x, pg);
69}
70
71/* Approximation for SVE double-precision sinh(x) using expm1.
72   sinh(x) = (exp(x) - exp(-x)) / 2.
73   The greatest observed error is 2.57 ULP:
74   _ZGVsMxv_sinh (0x1.a008538399931p-2) got 0x1.ab929fc64bd66p-2
75				       want 0x1.ab929fc64bd63p-2.  */
76svfloat64_t SV_NAME_D1 (sinh) (svfloat64_t x, svbool_t pg)
77{
78  const struct data *d = ptr_barrier (&data);
79
80  svfloat64_t ax = svabs_x (pg, x);
81  svuint64_t sign
82      = sveor_x (pg, svreinterpret_u64 (x), svreinterpret_u64 (ax));
83  svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, d->halff));
84
85  svbool_t special = svcmpge (pg, svreinterpret_u64 (ax), d->large_bound);
86
87  /* Fall back to scalar variant for all lanes if any are special.  */
88  if (unlikely (svptest_any (pg, special)))
89    return special_case (x, pg);
90
91  /* Up to the point that expm1 overflows, we can use it to calculate sinh
92     using a slight rearrangement of the definition of sinh. This allows us to
93     retain acceptable accuracy for very small inputs.  */
94  svfloat64_t t = expm1_inline (ax, pg);
95  t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0)));
96  return svmul_x (pg, t, halfsign);
97}
98
99PL_SIG (SV, D, 1, sinh, -10.0, 10.0)
100PL_TEST_ULP (SV_NAME_D1 (sinh), 2.08)
101PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0, 0x1p-26, 1000)
102PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p-26, 0x1p9, 500000)
103PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p9, inf, 1000)
104