1/* ix87 specific implementation of arctanh function.
2 Copyright (C) 1996-2022 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <machine/asm.h>
20#include <libm-alias-finite.h>
21
22 .section .rodata
23
24 .align ALIGNARG(4)
25 /* Please note that we use double values for 0.5 and 1.0. These
26 numbers have exact representations and so we don't get accuracy
27 problems. The advantage is that the code is simpler. */
28 .type half,@object
29half: .double 0.5
30 ASM_SIZE_DIRECTIVE(half)
31 .type one,@object
32one: .double 1.0
33 ASM_SIZE_DIRECTIVE(one)
34 /* It is not important that this constant is precise. It is only
35 a value which is known to be on the safe side for using the
36 fyl2xp1 instruction. */
37 .type limit,@object
38limit: .double 0.29
39 ASM_SIZE_DIRECTIVE(limit)
40 .align ALIGNARG(4)
41 .type ln2_2,@object
42ln2_2: .tfloat 0.3465735902799726547086160
43 ASM_SIZE_DIRECTIVE(ln2_2)
44
45#ifdef PIC
46#define MO(op) op##@GOTOFF(%edx)
47#else
48#define MO(op) op
49#endif
50
51 .text
52ENTRY(__ieee754_atanhl)
53 movl 12(%esp), %ecx
54
55 movl %ecx, %eax
56 andl $0x7fff, %eax
57 cmpl $0x7fff, %eax
58 je 5f
59 cmpl $0x3fdf, %eax
60 jge 7f
61 // Exponent below -32; return x, with underflow if subnormal.
62 fldt 4(%esp)
63 cmpl $0, %eax
64 jne 8f
65 fld %st(0)
66 fmul %st(0)
67 fstp %st(0)
688: ret
697:
70
71#ifdef PIC
72 LOAD_PIC_REG (dx)
73#endif
74
75 andl $0x8000, %ecx // ECX == 0 iff X >= 0
76
77 fldt MO(ln2_2) // 0.5*ln2
78 xorl %ecx, 12(%esp)
79 fldt 4(%esp) // |x| : 0.5*ln2
80 fcoml MO(half) // |x| : 0.5*ln2
81 fld %st(0) // |x| : |x| : 0.5*ln2
82 fnstsw // |x| : |x| : 0.5*ln2
83 sahf
84 jae 2f
85 fadd %st, %st(1) // |x| : 2*|x| : 0.5*ln2
86 fld %st // |x| : |x| : 2*|x| : 0.5*ln2
87 fsubrl MO(one) // 1-|x| : |x| : 2*|x| : 0.5*ln2
88 fxch // |x| : 1-|x| : 2*|x| : 0.5*ln2
89 fmul %st(2) // 2*|x|^2 : 1-|x| : 2*|x| : 0.5*ln2
90 fdivp // (2*|x|^2)/(1-|x|) : 2*|x| : 0.5*ln2
91 faddp // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
92 fcoml MO(limit) // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
93 fnstsw // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
94 sahf
95 jae 4f
96 fyl2xp1 // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
97 jecxz 3f
98 fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
993: ret
100
101 .align ALIGNARG(4)
1024: faddl MO(one) // 1+2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
103 fyl2x // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
104 jecxz 3f
105 fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
1063: ret
107
108 .align ALIGNARG(4)
1092: faddl MO(one) // 1+|x| : |x| : 0.5*ln2
110 fxch // |x| : 1+|x| : 0.5*ln2
111 fsubrl MO(one) // 1-|x| : 1+|x| : 0.5*ln2
112 fdivrp // (1+|x|)/(1-|x|) : 0.5*ln2
113 fyl2x // 0.5*ln2*ld((1+|x|)/(1-|x|))
114 jecxz 3f
115 fchs // 0.5*ln2*ld((1+x)/(1-x))
1163: ret
117
118 // x == NaN or ħInf
1195: cmpl $0x80000000, 8(%esp)
120 ja 6f
121 cmpl $0, 4(%esp)
122 je 7b
1236: fldt 4(%esp)
124 fadd %st(0)
125 ret
126END(__ieee754_atanhl)
127libm_alias_finite (__ieee754_atanhl, __atanhl)
128

source code of glibc/sysdeps/i386/fpu/e_atanhl.S