1/* ix87 specific implementation of arcsinh.
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-double.h>
21
22 .section .rodata
23
24 .align ALIGNARG(4)
25 .type huge,@object
26huge: .double 1e+300
27 ASM_SIZE_DIRECTIVE(huge)
28 .type one,@object
29one: .double 1.0
30 ASM_SIZE_DIRECTIVE(one)
31 .type limit,@object
32limit: .double 0.29
33 ASM_SIZE_DIRECTIVE(limit)
34
35#ifdef PIC
36#define MO(op) op##@GOTOFF(%edx)
37#else
38#define MO(op) op
39#endif
40
41 .text
42ENTRY(__asinh)
43 movl 8(%esp), %ecx
44 movl $0x7fffffff, %eax
45 andl %ecx, %eax
46 andl $0x80000000, %ecx
47 movl %eax, %edx
48 orl $0x800fffff, %edx
49 incl %edx
50 jz 7f // x in ħInf or NaN
51 xorl %ecx, 8(%esp)
52 fldl 4(%esp) // |x|
53 cmpl $0x3e300000, %eax
54 jb 2f // |x| < 2^-28
55 fldln2 // log(2) : |x|
56 cmpl $0x41b00000, %eax
57 fxch // |x| : log(2)
58 ja 3f // |x| > 2^28
59#ifdef PIC
60 LOAD_PIC_REG (dx)
61#endif
62 cmpl $0x40000000, %eax
63 ja 5f // |x| > 2
64
65 // 2^-28 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2)))
66 fld %st // |x| : |x| : log(2)
67 fmul %st(1) // |x|^2 : |x| : log(2)
68 fld %st // |x|^2 : |x|^2 : |x| : log(2)
69 faddl MO(one) // 1+|x|^2 : |x|^2 : |x| : log(2)
70 fsqrt // sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
71 faddl MO(one) // 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
72 fdivrp // |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2)
73 faddp // |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2)
74 fcoml MO(limit)
75 fnstsw
76 sahf
77 ja 6f
78 fyl2xp1
79 jecxz 4f
80 fchs
814: ret
82
837: fldl 4(%esp)
84 ret
85
866: faddl MO(one)
87 fyl2x
88 jecxz 4f
89 fchs
904: ret
91
92 // |x| < 2^-28 => y = x (inexact iff |x| != 0.0)
93 .align ALIGNARG(4)
942:
95#ifdef PIC
96 LOAD_PIC_REG (dx)
97#endif
98 jecxz 4f
99 fchs // x
1004: fld %st // x : x
101 faddl MO(huge) // huge+x : x
102 fstp %st(0) // x
103 cmpl $0x00100000, %eax
104 jae 8f
105 subl $8, %esp
106 cfi_adjust_cfa_offset (8)
107 fld %st(0)
108 fmul %st(0)
109 fstpl (%esp)
110 addl $8, %esp
111 cfi_adjust_cfa_offset (-8)
1128: ret
113
114 // |x| > 2^28 => y = sign(x) * (log(|x|) + log(2))
115 .align ALIGNARG(4)
1163: fyl2x // log(|x|)
117 fldln2 // log(2) : log(|x|)
118 faddp // log(|x|)+log(2)
119 jecxz 4f
120 fchs
1214: ret
122
123 // |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1)))
124 .align ALIGNARG(4)
1255: fld %st // |x| : |x| : log(2)
126 fadd %st, %st(1) // |x| : 2*|x| : log(2)
127 fld %st // |x| : |x| : 2*|x| : log(2)
128 fmul %st(1) // |x|^2 : |x| : 2*|x| : log(2)
129 faddl MO(one) // 1+|x|^2 : |x| : 2*|x| : log(2)
130 fsqrt // sqrt(1+|x|^2) : |x| : 2*|x| : log(2)
131 faddp // |x|+sqrt(1+|x|^2) : 2*|x| : log(2)
132 fdivrl MO(one) // 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2)
133 faddp // 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2)
134 fyl2x // log(2*|x|+1/(|x|+sqrt(1+|x|^2)))
135 jecxz 4f
136 fchs
1374: ret
138END(__asinh)
139libm_alias_double (__asinh, asinh)
140

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