1 /*
2 * Single-precision vector acosh(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 "pl_sig.h"
9 #include "pl_test.h"
10
11 #define WANT_V_LOG1P_K0_SHORTCUT 1
12 #include "v_log1p_inline.h"
13
14 #define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
15
16 #if V_SUPPORTED
17
18 static NOINLINE VPCS_ATTR v_f64_t
special_case(v_f64_t x)19 special_case (v_f64_t x)
20 {
21 return v_call_f64 (acosh, x, x, v_u64 (-1));
22 }
23
24 /* Vector approximation for double-precision acosh, based on log1p.
25 The largest observed error is 3.02 ULP in the region where the
26 argument to log1p falls in the k=0 interval, i.e. x close to 1:
27 __v_acosh(0x1.00798aaf80739p+0) got 0x1.f2d6d823bc9dfp-5
28 want 0x1.f2d6d823bc9e2p-5. */
V_NAME(acosh)29 VPCS_ATTR v_f64_t V_NAME (acosh) (v_f64_t x)
30 {
31 v_u64_t itop = v_as_u64_f64 (x) >> 52;
32 v_u64_t special = v_cond_u64 ((itop - OneTop) >= (BigBoundTop - OneTop));
33
34 /* Fall back to scalar routine for all lanes if any of them are special. */
35 if (unlikely (v_any_u64 (special)))
36 return special_case (x);
37
38 v_f64_t xm1 = x - 1;
39 v_f64_t u = xm1 * (x + 1);
40 return log1p_inline (xm1 + v_sqrt_f64 (u));
41 }
42 VPCS_ALIAS
43
44 PL_SIG (V, D, 1, acosh, 1.0, 10.0)
45 PL_TEST_ULP (V_NAME (acosh), 2.53)
46 PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (acosh))
47 PL_TEST_INTERVAL (V_NAME (acosh), 1, 0x1p511, 90000)
48 PL_TEST_INTERVAL (V_NAME (acosh), 0x1p511, inf, 10000)
49 PL_TEST_INTERVAL (V_NAME (acosh), 0, 1, 1000)
50 PL_TEST_INTERVAL (V_NAME (acosh), -0, -inf, 10000)
51 #endif
52