1 /*
2 * Double-precision vector acosh(x) function.
3 * Copyright (c) 2023-2024, Arm Limited.
4 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
5 */
6
7 #include "v_math.h"
8 #include "test_sig.h"
9 #include "test_defs.h"
10
11 #define WANT_V_LOG1P_K0_SHORTCUT 1
12 #include "v_log1p_inline.h"
13
14 const static struct data
15 {
16 struct v_log1p_data log1p_consts;
17 uint64x2_t one, thresh;
18 } data = {
19 .log1p_consts = V_LOG1P_CONSTANTS_TABLE,
20 .one = V2 (0x3ff0000000000000),
21 .thresh = V2 (0x1ff0000000000000) /* asuint64(0x1p511) - asuint64(1). */
22 };
23
24 static float64x2_t NOINLINE VPCS_ATTR
special_case(float64x2_t x,float64x2_t y,uint64x2_t special,const struct v_log1p_data * d)25 special_case (float64x2_t x, float64x2_t y, uint64x2_t special,
26 const struct v_log1p_data *d)
27 {
28 return v_call_f64 (acosh, x, log1p_inline (y, d), special);
29 }
30
31 /* Vector approximation for double-precision acosh, based on log1p.
32 The largest observed error is 3.02 ULP in the region where the
33 argument to log1p falls in the k=0 interval, i.e. x close to 1:
34 _ZGVnN2v_acosh(0x1.00798aaf80739p+0) got 0x1.f2d6d823bc9dfp-5
35 want 0x1.f2d6d823bc9e2p-5. */
V_NAME_D1(acosh)36 VPCS_ATTR float64x2_t V_NAME_D1 (acosh) (float64x2_t x)
37 {
38 const struct data *d = ptr_barrier (&data);
39 uint64x2_t special
40 = vcgeq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (x), d->one), d->thresh);
41 float64x2_t special_arg = x;
42
43 #if WANT_SIMD_EXCEPT
44 if (unlikely (v_any_u64 (special)))
45 x = vbslq_f64 (special, vreinterpretq_f64_u64 (d->one), x);
46 #endif
47
48 float64x2_t xm1 = vsubq_f64 (x, v_f64 (1.0));
49 float64x2_t y = vaddq_f64 (x, v_f64 (1.0));
50 y = vmulq_f64 (y, xm1);
51 y = vsqrtq_f64 (y);
52 y = vaddq_f64 (xm1, y);
53
54 if (unlikely (v_any_u64 (special)))
55 return special_case (special_arg, y, special, &d->log1p_consts);
56 return log1p_inline (y, &d->log1p_consts);
57 }
58
59 TEST_SIG (V, D, 1, acosh, 1.0, 10.0)
60 TEST_ULP (V_NAME_D1 (acosh), 2.53)
61 TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (acosh), WANT_SIMD_EXCEPT)
62 TEST_INTERVAL (V_NAME_D1 (acosh), 1, 0x1p511, 90000)
63 TEST_INTERVAL (V_NAME_D1 (acosh), 0x1p511, inf, 10000)
64 TEST_INTERVAL (V_NAME_D1 (acosh), 0, 1, 1000)
65 TEST_INTERVAL (V_NAME_D1 (acosh), -0, -inf, 10000)
66