1 /* ix87 specific implementation of arcsinh.
2 Copyright (C) 1996-2021 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
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.
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.
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/>. */
19 #include <machine/asm.h>
20 #include <libm-alias-double.h>
27 ASM_SIZE_DIRECTIVE(huge)
30 ASM_SIZE_DIRECTIVE(one)
33 ASM_SIZE_DIRECTIVE(limit)
36 #define MO(op) op##@GOTOFF(%edx)
44 movl $0x7fffffff, %eax
46 andl $0x80000000, %ecx
50 jz 7f // x in ±Inf or NaN
53 cmpl $0x3e300000, %eax
55 fldln2 // log(2) : |x|
56 cmpl $0x41b00000, %eax
62 cmpl $0x40000000, %eax
65 // 2^-28 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2)))
66 fld %st // |x| : |x| : log(2)
67 fmul %st(1) // |x|^2 : |x| : log(2)
68 fld %st // |x|^2 : |x|^2 : |x| : log(2)
69 faddl MO(one) // 1+|x|^2 : |x|^2 : |x| : log(2)
70 fsqrt // sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
71 faddl MO(one) // 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
72 fdivrp // |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2)
73 faddp // |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2)
92 // |x| < 2^-28 => y = x (inexact iff |x| != 0.0)
101 faddl MO(huge) // huge+x : x
103 cmpl $0x00100000, %eax
106 cfi_adjust_cfa_offset (8)
111 cfi_adjust_cfa_offset (-8)
114 // |x| > 2^28 => y = sign(x) * (log(|x|) + log(2))
117 fldln2 // log(2) : log(|x|)
118 faddp // log(|x|)+log(2)
123 // |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1)))
125 5: fld %st // |x| : |x| : log(2)
126 fadd %st, %st(1) // |x| : 2*|x| : log(2)
127 fld %st // |x| : |x| : 2*|x| : log(2)
128 fmul %st(1) // |x|^2 : |x| : 2*|x| : log(2)
129 faddl MO(one) // 1+|x|^2 : |x| : 2*|x| : log(2)
130 fsqrt // sqrt(1+|x|^2) : |x| : 2*|x| : log(2)
131 faddp // |x|+sqrt(1+|x|^2) : 2*|x| : log(2)
132 fdivrl MO(one) // 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2)
133 faddp // 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2)
134 fyl2x // log(2*|x|+1/(|x|+sqrt(1+|x|^2)))
139 libm_alias_double (__asinh, asinh)