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/* ix87 specific implementation of exp(x)-1.
Copyright (C) 1996-2023 Free Software Foundation, Inc.
This file is part of the GNU C Library.
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
<https://www.gnu.org/licenses/>. */
/* Using: e^x - 1 = 2^(x * log2(e)) - 1 */
#include <sysdep.h>
#include <machine/asm.h>
#include <i386-math-asm.h>
#include <libm-alias-double.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: .quad 0xb8aa3b295c17f0bc /* 1.442695040888963407359924681002 */
.short 0x3fff
ASM_SIZE_DIRECTIVE(l2e)
DEFINE_DBL_MIN
#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)
DBL_CHECK_FORCE_UFLOW
ret
2: fstp %st
fldl MO(minus1) // Set result to -1.0.
3: ret
END(__expm1)
libm_alias_double (__expm1, expm1)
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