1 /*
2 * Double-precision SVE sinh(x) function.
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "sv_poly_f64.h"
10 #include "test_sig.h"
11 #include "test_defs.h"
12
13 static 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
39 static inline svfloat64_t
expm1_inline(svfloat64_t x,svbool_t pg)40 expm1_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
65 static svfloat64_t NOINLINE
special_case(svfloat64_t x,svbool_t pg)66 special_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. */
SV_NAME_D1(sinh)76 svfloat64_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
99 TEST_SIG (SV, D, 1, sinh, -10.0, 10.0)
100 TEST_ULP (SV_NAME_D1 (sinh), 2.08)
101 TEST_DISABLE_FENV (SV_NAME_D1 (sinh))
102 TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0, 0x1p-26, 1000)
103 TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p-26, 0x1p9, 500000)
104 TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p9, inf, 1000)
105 CLOSE_SVE_ATTR
106