1/* ix87 specific implementation of exp(x)-1.
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	/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
20
21#include <sysdep.h>
22#include <machine/asm.h>
23#include <i386-math-asm.h>
24#include <libm-alias-double.h>
25
26	.section .rodata
27
28	.align ALIGNARG(4)
29	.type minus1,@object
30minus1:	.double -1.0
31	ASM_SIZE_DIRECTIVE(minus1)
32	.type one,@object
33one:	.double 1.0
34	ASM_SIZE_DIRECTIVE(one)
35	.type l2e,@object
36l2e:	.tfloat 1.442695040888963407359924681002
37	ASM_SIZE_DIRECTIVE(l2e)
38
39DEFINE_DBL_MIN
40
41#ifdef PIC
42#define MO(op) op##@GOTOFF(%edx)
43#else
44#define MO(op) op
45#endif
46
47	.text
48ENTRY(__expm1)
49	movzwl	4+6(%esp), %eax
50	xorb	$0x80, %ah	// invert sign bit (now 1 is "positive")
51	cmpl	$0xc086, %eax	// is num >= 704?
52	jae	HIDDEN_JUMPTARGET (__exp)
53
54	fldl	4(%esp)		// x
55	fxam			// Is NaN, +-Inf or +-0?
56	xorb	$0x80, %ah
57	cmpl	$0xc043, %eax	// is num <= -38.0?
58	fstsw	%ax
59	movb	$0x45, %ch
60	jb	4f
61
62	// Below -38.0 (may be -NaN or -Inf).
63	andb	%ah, %ch
64#ifdef	PIC
65	LOAD_PIC_REG (dx)
66#endif
67	cmpb	$0x01, %ch
68	je	5f		// If -NaN, jump.
69	jmp	2f		// -large, possibly -Inf.
70
714:	// In range -38.0 to 704.0 (may be +-0 but not NaN or +-Inf).
72	andb	%ah, %ch
73	cmpb	$0x40, %ch
74	je	3f		// If +-0, jump.
75#ifdef	PIC
76	LOAD_PIC_REG (dx)
77#endif
78
795:	fldt	MO(l2e)		// log2(e) : x
80	fmulp			// log2(e)*x
81	fld	%st		// log2(e)*x : log2(e)*x
82	// Set round-to-nearest temporarily.
83	subl	$8, %esp
84	cfi_adjust_cfa_offset (8)
85	fstcw	4(%esp)
86	movl	$0xf3ff, %ecx
87	andl	4(%esp), %ecx
88	movl	%ecx, (%esp)
89	fldcw	(%esp)
90	frndint			// int(log2(e)*x) : log2(e)*x
91	fldcw	4(%esp)
92	addl	$8, %esp
93	cfi_adjust_cfa_offset (-8)
94	fsubr	%st, %st(1)	// int(log2(e)*x) : fract(log2(e)*x)
95	fxch			// fract(log2(e)*x) : int(log2(e)*x)
96	f2xm1			// 2^fract(log2(e)*x)-1 : int(log2(e)*x)
97	fscale			// 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
98	fxch			// int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
99	fldl	MO(one)		// 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
100	fscale			// 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
101	fsubrl	MO(one)		// 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
102	fstp	%st(1)		// 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
103	fsubrp	%st, %st(1)	// 2^(log2(e)*x)
104	DBL_CHECK_FORCE_UFLOW
105	ret
106
1072:	fstp	%st
108	fldl	MO(minus1)	// Set result to -1.0.
1093:	ret
110END(__expm1)
111libm_alias_double (__expm1, expm1)
112