1*f3087befSAndrew Turner /*
2*f3087befSAndrew Turner * Double-precision SVE atanh(x) function.
3*f3087befSAndrew Turner *
4*f3087befSAndrew Turner * Copyright (c) 2023-2024, Arm Limited.
5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*f3087befSAndrew Turner */
7*f3087befSAndrew Turner
8*f3087befSAndrew Turner #include "sv_math.h"
9*f3087befSAndrew Turner #include "test_sig.h"
10*f3087befSAndrew Turner #include "test_defs.h"
11*f3087befSAndrew Turner
12*f3087befSAndrew Turner #define WANT_SV_LOG1P_K0_SHORTCUT 0
13*f3087befSAndrew Turner #include "sv_log1p_inline.h"
14*f3087befSAndrew Turner
15*f3087befSAndrew Turner #define One (0x3ff0000000000000)
16*f3087befSAndrew Turner #define Half (0x3fe0000000000000)
17*f3087befSAndrew Turner
18*f3087befSAndrew Turner static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t special)19*f3087befSAndrew Turner special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
20*f3087befSAndrew Turner {
21*f3087befSAndrew Turner return sv_call_f64 (atanh, x, y, special);
22*f3087befSAndrew Turner }
23*f3087befSAndrew Turner
24*f3087befSAndrew Turner /* SVE approximation for double-precision atanh, based on log1p.
25*f3087befSAndrew Turner The greatest observed error is 2.81 ULP:
26*f3087befSAndrew Turner _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
27*f3087befSAndrew Turner want 0x1.ffd8ff31b501cp-6. */
SV_NAME_D1(atanh)28*f3087befSAndrew Turner svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
29*f3087befSAndrew Turner {
30*f3087befSAndrew Turner
31*f3087befSAndrew Turner svfloat64_t ax = svabs_x (pg, x);
32*f3087befSAndrew Turner svuint64_t iax = svreinterpret_u64 (ax);
33*f3087befSAndrew Turner svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
34*f3087befSAndrew Turner svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
35*f3087befSAndrew Turner
36*f3087befSAndrew Turner /* It is special if iax >= 1. */
37*f3087befSAndrew Turner svbool_t special = svacge (pg, x, 1.0);
38*f3087befSAndrew Turner
39*f3087befSAndrew Turner /* Computation is performed based on the following sequence of equality:
40*f3087befSAndrew Turner (1+x)/(1-x) = 1 + 2x/(1-x). */
41*f3087befSAndrew Turner svfloat64_t y;
42*f3087befSAndrew Turner y = svadd_x (pg, ax, ax);
43*f3087befSAndrew Turner y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax));
44*f3087befSAndrew Turner /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */
45*f3087befSAndrew Turner y = sv_log1p_inline (y, pg);
46*f3087befSAndrew Turner
47*f3087befSAndrew Turner if (unlikely (svptest_any (pg, special)))
48*f3087befSAndrew Turner return special_case (x, svmul_x (pg, halfsign, y), special);
49*f3087befSAndrew Turner return svmul_x (pg, halfsign, y);
50*f3087befSAndrew Turner }
51*f3087befSAndrew Turner
52*f3087befSAndrew Turner TEST_SIG (SV, D, 1, atanh, -1.0, 1.0)
53*f3087befSAndrew Turner TEST_ULP (SV_NAME_D1 (atanh), 3.32)
54*f3087befSAndrew Turner TEST_DISABLE_FENV (SV_NAME_D1 (atanh))
55*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000)
56*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000)
57*f3087befSAndrew Turner TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 1, inf, 100)
58*f3087befSAndrew Turner /* atanh is asymptotic at 1, which is the default control value - have to set
59*f3087befSAndrew Turner -c 0 specially to ensure fp exceptions are triggered correctly (choice of
60*f3087befSAndrew Turner control lane is irrelevant if fp exceptions are disabled). */
61*f3087befSAndrew Turner TEST_CONTROL_VALUE (SV_NAME_D1 (atanh), 0)
62*f3087befSAndrew Turner CLOSE_SVE_ATTR
63