1 /*
2 * Double-precision SVE 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 "sv_math.h"
8 #include "pl_sig.h"
9 #include "pl_test.h"
10
11 #define WANT_SV_LOG1P_K0_SHORTCUT 1
12 #include "sv_log1p_inline.h"
13
14 #define BigBoundTop 0x5fe /* top12 (asuint64 (0x1p511)). */
15 #define OneTop 0x3ff
16
17 static NOINLINE svfloat64_t
special_case(svfloat64_t x,svfloat64_t y,svbool_t special)18 special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
19 {
20 return sv_call_f64 (acosh, x, y, special);
21 }
22
23 /* SVE approximation for double-precision acosh, based on log1p.
24 The largest observed error is 3.19 ULP in the region where the
25 argument to log1p falls in the k=0 interval, i.e. x close to 1:
26 SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2
27 want 0x1.ed23399f51373p-2. */
SV_NAME_D1(acosh)28 svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg)
29 {
30 svuint64_t itop = svlsr_x (pg, svreinterpret_u64 (x), 52);
31 /* (itop - OneTop) >= (BigBoundTop - OneTop). */
32 svbool_t special = svcmpge (pg, svsub_x (pg, itop, OneTop), sv_u64 (0x1ff));
33
34 svfloat64_t xm1 = svsub_x (pg, x, 1);
35 svfloat64_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1));
36 svfloat64_t y = sv_log1p_inline (svadd_x (pg, xm1, svsqrt_x (pg, u)), pg);
37
38 /* Fall back to scalar routine for special lanes. */
39 if (unlikely (svptest_any (pg, special)))
40 return special_case (x, y, special);
41
42 return y;
43 }
44
45 PL_SIG (SV, D, 1, acosh, 1.0, 10.0)
46 PL_TEST_ULP (SV_NAME_D1 (acosh), 2.69)
47 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 1, 0x1p511, 90000)
48 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0x1p511, inf, 10000)
49 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), 0, 1, 1000)
50 PL_TEST_INTERVAL (SV_NAME_D1 (acosh), -0, -inf, 10000)
51