xref: /freebsd/contrib/arm-optimized-routines/pl/math/v_acosh_3u5.c (revision 9f23cbd6cae82fd77edfad7173432fa8dccd0a95)
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
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.  */
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