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