1 /*
2 * Double-precision SVE atanh(x) function.
3 *
4 * Copyright (c) 2023-2024, Arm Limited.
5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6 */
7
8 #include "sv_math.h"
9 #include "test_sig.h"
10 #include "test_defs.h"
11
12 #define WANT_SV_LOG1P_K0_SHORTCUT 0
13 #include "sv_log1p_inline.h"
14
15 #define One (0x3ff0000000000000)
16 #define Half (0x3fe0000000000000)
17
18 static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t special)19 special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
20 {
21 return sv_call_f64 (atanh, x, y, special);
22 }
23
24 /* SVE approximation for double-precision atanh, based on log1p.
25 The greatest observed error is 2.81 ULP:
26 _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
27 want 0x1.ffd8ff31b501cp-6. */
SV_NAME_D1(atanh)28 svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
29 {
30
31 svfloat64_t ax = svabs_x (pg, x);
32 svuint64_t iax = svreinterpret_u64 (ax);
33 svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
34 svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
35
36 /* It is special if iax >= 1. */
37 svbool_t special = svacge (pg, x, 1.0);
38
39 /* Computation is performed based on the following sequence of equality:
40 (1+x)/(1-x) = 1 + 2x/(1-x). */
41 svfloat64_t y;
42 y = svadd_x (pg, ax, ax);
43 y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax));
44 /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */
45 y = sv_log1p_inline (y, pg);
46
47 if (unlikely (svptest_any (pg, special)))
48 return special_case (x, svmul_x (pg, halfsign, y), special);
49 return svmul_x (pg, halfsign, y);
50 }
51
52 TEST_SIG (SV, D, 1, atanh, -1.0, 1.0)
53 TEST_ULP (SV_NAME_D1 (atanh), 3.32)
54 TEST_DISABLE_FENV (SV_NAME_D1 (atanh))
55 TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000)
56 TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000)
57 TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 1, inf, 100)
58 /* atanh is asymptotic at 1, which is the default control value - have to set
59 -c 0 specially to ensure fp exceptions are triggered correctly (choice of
60 control lane is irrelevant if fp exceptions are disabled). */
61 TEST_CONTROL_VALUE (SV_NAME_D1 (atanh), 0)
62 CLOSE_SVE_ATTR
63