1*5a02ffc3SAndrew Turner /*
2*5a02ffc3SAndrew Turner * Single-precision vector atanh(x) function.
3*5a02ffc3SAndrew Turner *
4*5a02ffc3SAndrew Turner * Copyright (c) 2023, Arm Limited.
5*5a02ffc3SAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
6*5a02ffc3SAndrew Turner */
7*5a02ffc3SAndrew Turner
8*5a02ffc3SAndrew Turner #include "sv_math.h"
9*5a02ffc3SAndrew Turner #include "mathlib.h"
10*5a02ffc3SAndrew Turner #include "pl_sig.h"
11*5a02ffc3SAndrew Turner #include "pl_test.h"
12*5a02ffc3SAndrew Turner
13*5a02ffc3SAndrew Turner #include "sv_log1pf_inline.h"
14*5a02ffc3SAndrew Turner
15*5a02ffc3SAndrew Turner #define One (0x3f800000)
16*5a02ffc3SAndrew Turner #define Half (0x3f000000)
17*5a02ffc3SAndrew Turner
18*5a02ffc3SAndrew Turner static svfloat32_t NOINLINE
special_case(svfloat32_t x,svfloat32_t y,svbool_t special)19*5a02ffc3SAndrew Turner special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
20*5a02ffc3SAndrew Turner {
21*5a02ffc3SAndrew Turner return sv_call_f32 (atanhf, x, y, special);
22*5a02ffc3SAndrew Turner }
23*5a02ffc3SAndrew Turner
24*5a02ffc3SAndrew Turner /* Approximation for vector single-precision atanh(x) using modified log1p.
25*5a02ffc3SAndrew Turner The maximum error is 2.28 ULP:
26*5a02ffc3SAndrew Turner _ZGVsMxv_atanhf(0x1.ff1194p-5) got 0x1.ffbbbcp-5
27*5a02ffc3SAndrew Turner want 0x1.ffbbb6p-5. */
SV_NAME_F1(atanh)28*5a02ffc3SAndrew Turner svfloat32_t SV_NAME_F1 (atanh) (svfloat32_t x, const svbool_t pg)
29*5a02ffc3SAndrew Turner {
30*5a02ffc3SAndrew Turner svfloat32_t ax = svabs_x (pg, x);
31*5a02ffc3SAndrew Turner svuint32_t iax = svreinterpret_u32 (ax);
32*5a02ffc3SAndrew Turner svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax);
33*5a02ffc3SAndrew Turner svfloat32_t halfsign = svreinterpret_f32 (svorr_x (pg, sign, Half));
34*5a02ffc3SAndrew Turner svbool_t special = svcmpge (pg, iax, One);
35*5a02ffc3SAndrew Turner
36*5a02ffc3SAndrew Turner /* Computation is performed based on the following sequence of equality:
37*5a02ffc3SAndrew Turner * (1+x)/(1-x) = 1 + 2x/(1-x). */
38*5a02ffc3SAndrew Turner svfloat32_t y = svadd_x (pg, ax, ax);
39*5a02ffc3SAndrew Turner y = svdiv_x (pg, y, svsub_x (pg, sv_f32 (1), ax));
40*5a02ffc3SAndrew Turner /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */
41*5a02ffc3SAndrew Turner y = sv_log1pf_inline (y, pg);
42*5a02ffc3SAndrew Turner
43*5a02ffc3SAndrew Turner if (unlikely (svptest_any (pg, special)))
44*5a02ffc3SAndrew Turner return special_case (x, svmul_x (pg, halfsign, y), special);
45*5a02ffc3SAndrew Turner
46*5a02ffc3SAndrew Turner return svmul_x (pg, halfsign, y);
47*5a02ffc3SAndrew Turner }
48*5a02ffc3SAndrew Turner
49*5a02ffc3SAndrew Turner PL_SIG (SV, F, 1, atanh, -1.0, 1.0)
50*5a02ffc3SAndrew Turner PL_TEST_ULP (SV_NAME_F1 (atanh), 2.59)
51*5a02ffc3SAndrew Turner /* atanh is asymptotic at 1, which is the default control value - have to set
52*5a02ffc3SAndrew Turner -c 0 specially to ensure fp exceptions are triggered correctly (choice of
53*5a02ffc3SAndrew Turner control lane is irrelevant if fp exceptions are disabled). */
54*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 0, 0x1p-12, 1000, 0)
55*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 0x1p-12, 1, 20000, 0)
56*5a02ffc3SAndrew Turner PL_TEST_SYM_INTERVAL_C (SV_NAME_F1 (atanh), 1, inf, 1000, 0)
57