1 /*
2 * Double-precision vector tanh(x) function.
3 * Copyright (c) 2023, Arm Limited.
4 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
5 */
6
7 #include "v_math.h"
8 #include "estrin.h"
9 #include "mathlib.h"
10 #include "pl_sig.h"
11 #include "pl_test.h"
12
13 #if V_SUPPORTED
14
15 #define AbsMask v_u64 (0x7fffffffffffffff)
16 #define InvLn2 v_f64 (0x1.71547652b82fep0)
17 #define MLn2hi v_f64 (-0x1.62e42fefa39efp-1)
18 #define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56)
19 #define Shift v_f64 (0x1.8p52)
20 #define C(i) v_f64 (__expm1_poly[i])
21
22 #define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4). */
23 #define TinyBound 0x3e40000000000000 /* asuint64 (0x1p-27). */
24 #define One v_u64 (0x3ff0000000000000)
25
26 static inline v_f64_t
expm1_inline(v_f64_t x)27 expm1_inline (v_f64_t x)
28 {
29 /* Helper routine for calculating exp(x) - 1. Vector port of the helper from
30 the scalar variant of tanh. */
31
32 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
33 v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift;
34 v_s64_t i = v_to_s64_f64 (j);
35 v_f64_t f = v_fma_f64 (j, MLn2hi, x);
36 f = v_fma_f64 (j, MLn2lo, f);
37
38 /* Approximate expm1(f) using polynomial. */
39 v_f64_t f2 = f * f;
40 v_f64_t f4 = f2 * f2;
41 v_f64_t p = v_fma_f64 (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
42
43 /* t = 2 ^ i. */
44 v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One);
45 /* expm1(x) = p * t + (t - 1). */
46 return v_fma_f64 (p, t, t - 1);
47 }
48
49 static NOINLINE v_f64_t
special_case(v_f64_t x,v_f64_t y,v_u64_t special)50 special_case (v_f64_t x, v_f64_t y, v_u64_t special)
51 {
52 return v_call_f64 (tanh, x, y, special);
53 }
54
55 /* Vector approximation for double-precision tanh(x), using a simplified
56 version of expm1. The greatest observed error is 2.75 ULP:
57 __v_tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
58 want -0x1.ba31ba4691ab4p-3. */
V_NAME(tanh)59 VPCS_ATTR v_f64_t V_NAME (tanh) (v_f64_t x)
60 {
61 v_u64_t ix = v_as_u64_f64 (x);
62 v_u64_t ia = ix & AbsMask;
63
64 /* Trigger special-cases for tiny, boring and infinity/NaN. */
65 v_u64_t special = v_cond_u64 ((ia - TinyBound) > (BoringBound - TinyBound));
66 v_f64_t u;
67
68 /* To trigger fp exceptions correctly, set special lanes to a neutral value.
69 They will be fixed up later by the special-case handler. */
70 if (unlikely (v_any_u64 (special)))
71 u = v_sel_f64 (special, v_f64 (1), x) * 2;
72 else
73 u = x * 2;
74
75 /* tanh(x) = (e^2x - 1) / (e^2x + 1). */
76 v_f64_t q = expm1_inline (u);
77 v_f64_t y = q / (q + 2);
78
79 if (unlikely (v_any_u64 (special)))
80 return special_case (x, y, special);
81 return y;
82 }
83 VPCS_ALIAS
84
85 PL_SIG (V, D, 1, tanh, -10.0, 10.0)
86 PL_TEST_ULP (V_NAME (tanh), 2.26)
87 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (tanh))
88 PL_TEST_INTERVAL (V_NAME (tanh), 0, TinyBound, 1000)
89 PL_TEST_INTERVAL (V_NAME (tanh), -0, -TinyBound, 1000)
90 PL_TEST_INTERVAL (V_NAME (tanh), TinyBound, BoringBound, 100000)
91 PL_TEST_INTERVAL (V_NAME (tanh), -TinyBound, -BoringBound, 100000)
92 PL_TEST_INTERVAL (V_NAME (tanh), BoringBound, inf, 1000)
93 PL_TEST_INTERVAL (V_NAME (tanh), -BoringBound, -inf, 1000)
94 #endif
95