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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 <machine/asm.h>
#include <libm-alias-finite.h>
.section .rodata.cst8,"aM",@progbits,8
.p2align 3
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
.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(__ieee754_acosh)
movl 8(%esp), %ecx
cmpl $0x3ff00000, %ecx
jl 5f // < 1 => invalid
fldln2 // log(2)
fldl 4(%esp) // x : log(2)
cmpl $0x41b00000, %ecx
ja 3f // x > 2^28
#ifdef PIC
LOAD_PIC_REG (dx)
#endif
cmpl $0x40000000, %ecx
ja 4f // x > 2
// 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
fsubl MO(one) // x-1 : log(2)
fabs // acosh(1) is +0 in all rounding modes
fld %st // x-1 : x-1 : log(2)
fmul %st(1) // (x-1)^2 : x-1 : log(2)
fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
fcoml MO(limit)
fnstsw
sahf
ja 2f
fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
ret
2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
ret
// x > 2^28 => y = log(x) + log(2)
.align ALIGNARG(4)
3: fyl2x // log(x)
fldln2 // log(2) : log(x)
faddp // log(x)+log(2)
ret
// 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
.align ALIGNARG(4)
4: 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)
fsubl MO(one) // x^2-1 : x : 2*x : log(2)
fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
faddp // x+sqrt(x^2-1) : 2*x : log(2)
fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
ret
// x < 1 (or -NaN) => NaN
.align ALIGNARG(4)
5: fldl 4(%esp)
fsub %st
fdiv %st, %st(0)
ret
END(__ieee754_acosh)
libm_alias_finite (__ieee754_acosh, __acosh)
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