1*412f47f9SXin Li /*
2*412f47f9SXin Li * Double-precision SVE atanh(x) function.
3*412f47f9SXin Li *
4*412f47f9SXin Li * Copyright (c) 2023, Arm Limited.
5*412f47f9SXin Li * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*412f47f9SXin Li */
7*412f47f9SXin Li
8*412f47f9SXin Li #include "sv_math.h"
9*412f47f9SXin Li #include "pl_sig.h"
10*412f47f9SXin Li #include "pl_test.h"
11*412f47f9SXin Li
12*412f47f9SXin Li #define WANT_SV_LOG1P_K0_SHORTCUT 0
13*412f47f9SXin Li #include "sv_log1p_inline.h"
14*412f47f9SXin Li
15*412f47f9SXin Li #define One (0x3ff0000000000000)
16*412f47f9SXin Li #define Half (0x3fe0000000000000)
17*412f47f9SXin Li
18*412f47f9SXin Li static svfloat64_t NOINLINE
special_case(svfloat64_t x,svfloat64_t y,svbool_t special)19*412f47f9SXin Li special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
20*412f47f9SXin Li {
21*412f47f9SXin Li return sv_call_f64 (atanh, x, y, special);
22*412f47f9SXin Li }
23*412f47f9SXin Li
24*412f47f9SXin Li /* SVE approximation for double-precision atanh, based on log1p.
25*412f47f9SXin Li The greatest observed error is 2.81 ULP:
26*412f47f9SXin Li _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
27*412f47f9SXin Li want 0x1.ffd8ff31b501cp-6. */
SV_NAME_D1(atanh)28*412f47f9SXin Li svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
29*412f47f9SXin Li {
30*412f47f9SXin Li
31*412f47f9SXin Li svfloat64_t ax = svabs_x (pg, x);
32*412f47f9SXin Li svuint64_t iax = svreinterpret_u64 (ax);
33*412f47f9SXin Li svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
34*412f47f9SXin Li svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));
35*412f47f9SXin Li
36*412f47f9SXin Li /* It is special if iax >= 1. */
37*412f47f9SXin Li // svbool_t special = svcmpge (pg, iax, One);
38*412f47f9SXin Li svbool_t special = svacge (pg, x, 1.0);
39*412f47f9SXin Li
40*412f47f9SXin Li /* Computation is performed based on the following sequence of equality:
41*412f47f9SXin Li (1+x)/(1-x) = 1 + 2x/(1-x). */
42*412f47f9SXin Li svfloat64_t y;
43*412f47f9SXin Li y = svadd_x (pg, ax, ax);
44*412f47f9SXin Li y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax));
45*412f47f9SXin Li /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */
46*412f47f9SXin Li y = sv_log1p_inline (y, pg);
47*412f47f9SXin Li
48*412f47f9SXin Li if (unlikely (svptest_any (pg, special)))
49*412f47f9SXin Li return special_case (x, svmul_x (pg, halfsign, y), special);
50*412f47f9SXin Li return svmul_x (pg, halfsign, y);
51*412f47f9SXin Li }
52*412f47f9SXin Li
53*412f47f9SXin Li PL_SIG (SV, D, 1, atanh, -1.0, 1.0)
54*412f47f9SXin Li PL_TEST_ULP (SV_NAME_D1 (atanh), 3.32)
55*412f47f9SXin Li /* atanh is asymptotic at 1, which is the default control value - have to set
56*412f47f9SXin Li -c 0 specially to ensure fp exceptions are triggered correctly (choice of
57*412f47f9SXin Li control lane is irrelevant if fp exceptions are disabled). */
58*412f47f9SXin Li PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000, 0)
59*412f47f9SXin Li PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000, 0)
60*412f47f9SXin Li PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 1, inf, 100, 0)
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