1 /*
2 * Double-precision vector atanh(x) function.
3 *
4 * Copyright (c) 2022-2023, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "v_math.h"
9 #include "pl_sig.h"
10 #include "pl_test.h"
11
12 #define WANT_V_LOG1P_K0_SHORTCUT 0
13 #include "v_log1p_inline.h"
14
15 const static struct data
16 {
17 struct v_log1p_data log1p_consts;
18 uint64x2_t one, half;
19 } data = { .log1p_consts = V_LOG1P_CONSTANTS_TABLE,
20 .one = V2 (0x3ff0000000000000),
21 .half = V2 (0x3fe0000000000000) };
22
23 static float64x2_t VPCS_ATTR NOINLINE
special_case(float64x2_t x,float64x2_t y,uint64x2_t special)24 special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
25 {
26 return v_call_f64 (atanh, x, y, special);
27 }
28
29 /* Approximation for vector double-precision atanh(x) using modified log1p.
30 The greatest observed error is 3.31 ULP:
31 _ZGVnN2v_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
32 want 0x1.ffd8ff31b501cp-6. */
33 VPCS_ATTR
V_NAME_D1(atanh)34 float64x2_t V_NAME_D1 (atanh) (float64x2_t x)
35 {
36 const struct data *d = ptr_barrier (&data);
37
38 float64x2_t ax = vabsq_f64 (x);
39 uint64x2_t ia = vreinterpretq_u64_f64 (ax);
40 uint64x2_t sign = veorq_u64 (vreinterpretq_u64_f64 (x), ia);
41 uint64x2_t special = vcgeq_u64 (ia, d->one);
42 float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->half));
43
44 #if WANT_SIMD_EXCEPT
45 ax = v_zerofy_f64 (ax, special);
46 #endif
47
48 float64x2_t y;
49 y = vaddq_f64 (ax, ax);
50 y = vdivq_f64 (y, vsubq_f64 (v_f64 (1), ax));
51 y = log1p_inline (y, &d->log1p_consts);
52
53 if (unlikely (v_any_u64 (special)))
54 return special_case (x, vmulq_f64 (y, halfsign), special);
55 return vmulq_f64 (y, halfsign);
56 }
57
58 PL_SIG (V, D, 1, atanh, -1.0, 1.0)
59 PL_TEST_EXPECT_FENV (V_NAME_D1 (atanh), WANT_SIMD_EXCEPT)
60 PL_TEST_ULP (V_NAME_D1 (atanh), 3.32)
61 /* atanh is asymptotic at 1, which is the default control value - have to set
62 -c 0 specially to ensure fp exceptions are triggered correctly (choice of
63 control lane is irrelevant if fp exceptions are disabled). */
64 PL_TEST_SYM_INTERVAL_C (V_NAME_D1 (atanh), 0, 0x1p-23, 10000, 0)
65 PL_TEST_SYM_INTERVAL_C (V_NAME_D1 (atanh), 0x1p-23, 1, 90000, 0)
66 PL_TEST_SYM_INTERVAL_C (V_NAME_D1 (atanh), 1, inf, 100, 0)
67