[thirdparty/glibc.git] / sysdeps / i386 / fpu / s_expm1.S

/* ix87 specific implementation of exp(x)-1.
   Copyright (C) 1996-2015 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
   Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
   Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */

	/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */

#include <sysdep.h>
#include <machine/asm.h>

	.section .rodata

	.align ALIGNARG(4)
	.type minus1,@object
minus1:	.double -1.0
	ASM_SIZE_DIRECTIVE(minus1)
	.type one,@object
one:	.double 1.0
	ASM_SIZE_DIRECTIVE(one)
	.type l2e,@object
l2e:	.tfloat 1.442695040888963407359924681002
	ASM_SIZE_DIRECTIVE(l2e)

#ifdef PIC
#define MO(op) op##@GOTOFF(%edx)
#else
#define MO(op) op
#endif

	.text
ENTRY(__expm1)
	movzwl	4+6(%esp), %eax
	xorb	$0x80, %ah	// invert sign bit (now 1 is "positive")
	cmpl	$0xc086, %eax	// is num >= 704?
	jae	HIDDEN_JUMPTARGET (__exp)

	fldl	4(%esp)		// x
	fxam			// Is NaN, +-Inf or +-0?
	xorb	$0x80, %ah
	cmpl	$0xc043, %eax	// is num <= -38.0?
	fstsw	%ax
	movb	$0x45, %ch
	jb	4f

	// Below -38.0 (may be -NaN or -Inf).
	andb	%ah, %ch
#ifdef	PIC
	LOAD_PIC_REG (dx)
#endif
	cmpb	$0x01, %ch
	je	5f		// If -NaN, jump.
	jmp	2f		// -large, possibly -Inf.

4:	// In range -38.0 to 704.0 (may be +-0 but not NaN or +-Inf).
	andb	%ah, %ch
	cmpb	$0x40, %ch
	je	3f		// If +-0, jump.
#ifdef	PIC
	LOAD_PIC_REG (dx)
#endif

5:	fldt	MO(l2e)		// log2(e) : x
	fmulp			// log2(e)*x
	fld	%st		// log2(e)*x : log2(e)*x
	// Set round-to-nearest temporarily.
	subl	$8, %esp
	cfi_adjust_cfa_offset (8)
	fstcw	4(%esp)
	movl	$0xf3ff, %ecx
	andl	4(%esp), %ecx
	movl	%ecx, (%esp)
	fldcw	(%esp)
	frndint			// int(log2(e)*x) : log2(e)*x
	fldcw	4(%esp)
	addl	$8, %esp
	cfi_adjust_cfa_offset (-8)
	fsubr	%st, %st(1)	// int(log2(e)*x) : fract(log2(e)*x)
	fxch			// fract(log2(e)*x) : int(log2(e)*x)
	f2xm1			// 2^fract(log2(e)*x)-1 : int(log2(e)*x)
	fscale			// 2^(log2(e)*x)-2^int(log2(e)*x) : int(log2(e)*x)
	fxch			// int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
	fldl	MO(one)		// 1 : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
	fscale			// 2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
	fsubrl	MO(one)		// 1-2^int(log2(e)*x) : int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
	fstp	%st(1)		// 1-2^int(log2(e)*x) : 2^(log2(e)*x)-2^int(log2(e)*x)
	fsubrp	%st, %st(1)	// 2^(log2(e)*x)
	ret

2:	fstp	%st
	fldl	MO(minus1)	// Set result to -1.0.
3:	ret
END(__expm1)
weak_alias (__expm1, expm1)
Commit	Line	Data
6bc31da0	1	/* ix87 specific implementation of exp(x)-1.
b168057a	2	Copyright (C) 1996-2015 Free Software Foundation, Inc.
6bc31da0 UD	3	This file is part of the GNU C Library.
	4	Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
	5	Based on code by John C. Bowman <bowman@ipp-garching.mpg.de>.
5290baf0	6	Corrections by H.J. Lu (hjl@gnu.ai.mit.edu), 1997.
6bc31da0 UD	7
6bc31da0 UD	8	The GNU C Library is free software; you can redistribute it and/or
41bdb6e2 AJ	9	modify it under the terms of the GNU Lesser General Public
	10	License as published by the Free Software Foundation; either
	11	version 2.1 of the License, or (at your option) any later version.
6bc31da0 UD	12
	13	The GNU C Library is distributed in the hope that it will be useful,
	14	but WITHOUT ANY WARRANTY; without even the implied warranty of
	15	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
41bdb6e2	16	Lesser General Public License for more details.
6bc31da0	17
41bdb6e2	18	You should have received a copy of the GNU Lesser General Public
59ba27a6 PE	19	License along with the GNU C Library; if not, see
59ba27a6 PE	20	<http://www.gnu.org/licenses/>. */
6bc31da0 UD	21
	22	/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
	23
b7805d0b	24	#include <sysdep.h>
6bc31da0 UD	25	#include <machine/asm.h>
6bc31da0 UD	26
6bc31da0	27	.section .rodata
622c86f4	28
6bc31da0	29	.align ALIGNARG(4)
b67e9372	30	.type minus1,@object
0d8733c4 UD	31	minus1: .double -1.0
0d8733c4 UD	32	ASM_SIZE_DIRECTIVE(minus1)
b67e9372	33	.type one,@object
6bc31da0 UD	34	one: .double 1.0
6bc31da0 UD	35	ASM_SIZE_DIRECTIVE(one)
b67e9372	36	.type l2e,@object
6bc31da0 UD	37	l2e: .tfloat 1.442695040888963407359924681002
	38	ASM_SIZE_DIRECTIVE(l2e)
	39
	40	#ifdef PIC
	41	#define MO(op) op##@GOTOFF(%edx)
	42	#else
	43	#define MO(op) op
	44	#endif
	45
	46	.text
	47	ENTRY(__expm1)
b7805d0b AS	48	movzwl 4+6(%esp), %eax
	49	xorb $0x80, %ah // invert sign bit (now 1 is "positive")
	50	cmpl $0xc086, %eax // is num >= 704?
	51	jae HIDDEN_JUMPTARGET (__exp)
	52
6bc31da0	53	fldl 4(%esp) // x
f17ac40d JM	54	fxam // Is NaN, +-Inf or +-0?
	55	xorb $0x80, %ah
	56	cmpl $0xc043, %eax // is num <= -38.0?
6bc31da0	57	fstsw %ax
c57abfa7	58	movb $0x45, %ch
f17ac40d JM	59	jb 4f
	60
	61	// Below -38.0 (may be -NaN or -Inf).
	62	andb %ah, %ch
	63	#ifdef PIC
	64	LOAD_PIC_REG (dx)
	65	#endif
	66	cmpb $0x01, %ch
	67	je 5f // If -NaN, jump.
	68	jmp 2f // -large, possibly -Inf.
	69
	70	4: // In range -38.0 to 704.0 (may be +-0 but not NaN or +-Inf).
c57abfa7 UD	71	andb %ah, %ch
	72	cmpb $0x40, %ch
	73	je 3f // If +-0, jump.
6bc31da0	74	#ifdef PIC
fee732e5	75	LOAD_PIC_REG (dx)
6bc31da0	76	#endif
6bc31da0	77
f17ac40d	78	5: fldt MO(l2e) // log2(e) : x
6bc31da0 UD	79	fmulp // log2(e)*x
6bc31da0 UD	80	fld %st // log2(e)x : log2(e)x
f88acd39 JM	81	// Set round-to-nearest temporarily.
	82	subl $8, %esp
	83	cfi_adjust_cfa_offset (8)
	84	fstcw 4(%esp)
	85	movl $0xf3ff, %ecx
	86	andl 4(%esp), %ecx
	87	movl %ecx, (%esp)
	88	fldcw (%esp)
6bc31da0	89	frndint // int(log2(e)x) : log2(e)x
f88acd39 JM	90	fldcw 4(%esp)
	91	addl $8, %esp
	92	cfi_adjust_cfa_offset (-8)
5290baf0	93	fsubr %st, %st(1) // int(log2(e)x) : fract(log2(e)x)
6bc31da0 UD	94	fxch // fract(log2(e)x) : int(log2(e)x)
	95	f2xm1 // 2^fract(log2(e)x)-1 : int(log2(e)x)
	96	fscale // 2^(log2(e)x)-2^int(log2(e)x) : int(log2(e)*x)
	97	fxch // int(log2(e)x) : 2^(log2(e)x)-2^int(log2(e)*x)
	98	fldl MO(one) // 1 : int(log2(e)x) : 2^(log2(e)x)-2^int(log2(e)*x)
5290baf0 UD	99	fscale // 2^int(log2(e)x) : int(log2(e)x) : 2^(log2(e)x)-2^int(log2(e)x)
	100	fsubrl MO(one) // 1-2^int(log2(e)x) : int(log2(e)x) : 2^(log2(e)x)-2^int(log2(e)x)
	101	fstp %st(1) // 1-2^int(log2(e)x) : 2^(log2(e)x)-2^int(log2(e)*x)
	102	fsubrp %st, %st(1) // 2^(log2(e)*x)
6bc31da0 UD	103	ret
6bc31da0 UD	104
f17ac40d	105	2: fstp %st
0d8733c4	106	fldl MO(minus1) // Set result to -1.0.
6bc31da0 UD	107	3: ret
	108	END(__expm1)
	109	weak_alias (__expm1, expm1)