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 �Inf 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