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/* ix87 specific implementation of arcsinh.
Copyright (C) 1996-2024 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/>. */
#include <libm-alias-ldouble.h>
#include <machine/asm.h>
.section .rodata
.align ALIGNARG(4)
.type huge,@object
huge: .quad 0x89b634e7456ffa1d /* 1e+4930 */
.short 0x7ff8
ASM_SIZE_DIRECTIVE(huge)
.align ALIGNARG(4)
/* Please note that we use double value for 1.0. This number
has an exact representation and so we don't get accuracy
problems. The advantage is that the code is simpler. */
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
/* It is not important that this constant is precise. It is only
a value which is known to be on the safe side for using the
fyl2xp1 instruction. */
.type limit,@object
limit: .double 0.29
ASM_SIZE_DIRECTIVE(limit)
#ifdef PIC
#define MO(op) op##@GOTOFF(%edx)
#else
#define MO(op) op
#endif
.text
ENTRY(__asinhl)
movl 12(%esp), %ecx
movl $0x7fff, %eax
andl %ecx, %eax
andl $0x8000, %ecx
movl %eax, %edx
orl $0xffff8000, %edx
incl %edx
jz 7f // x in ±Inf or NaN
xorl %ecx, 12(%esp)
fldt 4(%esp) // |x|
cmpl $0x3fde, %eax
jb 2f // |x| < 2^-34
fldln2 // log(2) : |x|
cmpl $0x4020, %eax
fxch // |x| : log(2)
ja 3f // |x| > 2^34
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
cmpl $0x4000, %eax
ja 5f // |x| > 2
// 2^-34 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2)))
fld %st // |x| : |x| : log(2)
fmul %st(1) // |x|^2 : |x| : log(2)
fld %st // |x|^2 : |x|^2 : |x| : log(2)
faddl MO(one) // 1+|x|^2 : |x|^2 : |x| : log(2)
fsqrt // sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
faddl MO(one) // 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
fdivrp // |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2)
faddp // |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2)
fcoml MO(limit)
fnstsw
sahf
ja 6f
fyl2xp1
jecxz 4f
fchs
4: ret
7: fldt 4(%esp)
fadd %st
ret
6: faddl MO(one)
fyl2x
jecxz 4f
fchs
4: ret
// |x| < 2^-34 => y = x (inexact iff |x| != 0.0)
.align ALIGNARG(4)
2:
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
jecxz 4f
fchs // x
4: fld %st // x : x
fldt MO(huge) // huge : x : x
faddp // huge+x : x
fstp %st(0) // x
cmpl $0x0001, %eax
jae 8f
fld %st(0)
fmul %st(0)
fstp %st(0)
8: ret
// |x| > 2^34 => y = sign(x) * (log(|x|) + log(2))
.align ALIGNARG(4)
3: fyl2x // log(|x|)
fldln2 // log(2) : log(|x|)
faddp // log(|x|)+log(2)
jecxz 4f
fchs
4: ret
// |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1)))
.align ALIGNARG(4)
5: fld %st // |x| : |x| : log(2)
fadd %st, %st(1) // |x| : 2*|x| : log(2)
fld %st // |x| : |x| : 2*|x| : log(2)
fmul %st(1) // |x|^2 : |x| : 2*|x| : log(2)
faddl MO(one) // 1+|x|^2 : |x| : 2*|x| : log(2)
fsqrt // sqrt(1+|x|^2) : |x| : 2*|x| : log(2)
faddp // |x|+sqrt(1+|x|^2) : 2*|x| : log(2)
fdivrl MO(one) // 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2)
faddp // 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2)
fyl2x // log(2*|x|+1/(|x|+sqrt(1+|x|^2)))
jecxz 4f
fchs
4: ret
END(__asinhl)
libm_alias_ldouble (__asinh, asinh)
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