1 /* ix87 specific implementation of arcsinh.
2 Copyright (C) 1996-2019 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
20 #include <machine/asm.h>
21 #include <libm-alias-float.h>
28 ASM_SIZE_DIRECTIVE(huge)
31 ASM_SIZE_DIRECTIVE(one)
34 ASM_SIZE_DIRECTIVE(limit)
37 #define MO(op) op##@GOTOFF(%edx)
45 movl $0x7fffffff, %eax
47 andl $0x80000000, %ecx
51 jz 7f // x in ±Inf or NaN
54 cmpl $0x38000000, %eax
56 fldln2 // log(2) : |x|
57 cmpl $0x47000000, %eax
63 cmpl $0x40000000, %eax
66 // 2^-14 <= |x| <= 2 => y = sign(x)*log1p(|x|+|x|^2/(1+sqrt(1+|x|^2)))
67 fld %st // |x| : |x| : log(2)
68 fmul %st(1) // |x|^2 : |x| : log(2)
69 fld %st // |x|^2 : |x|^2 : |x| : log(2)
70 faddl MO(one) // 1+|x|^2 : |x|^2 : |x| : log(2)
71 fsqrt // sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
72 faddl MO(one) // 1+sqrt(1+|x|^2) : |x|^2 : |x| : log(2)
73 fdivrp // |x|^2/(1+sqrt(1+|x|^2)) : |x| : log(2)
74 faddp // |x|+|x|^2/(1+sqrt(1+|x|^2)) : log(2)
93 // |x| < 2^-14 => y = x (inexact iff |x| != 0.0)
102 faddl MO(huge) // huge+x : x
104 cmpl $0x00800000, %eax
107 cfi_adjust_cfa_offset (4)
112 cfi_adjust_cfa_offset (-4)
115 // |x| > 2^14 => y = sign(x) * (log(|x|) + log(2))
118 fldln2 // log(2) : log(|x|)
119 faddp // log(|x|)+log(2)
124 // |x| > 2 => y = sign(x) * log(2*|x| + 1/(|x|+sqrt(x*x+1)))
126 5: fld %st // |x| : |x| : log(2)
127 fadd %st, %st(1) // |x| : 2*|x| : log(2)
128 fld %st // |x| : |x| : 2*|x| : log(2)
129 fmul %st(1) // |x|^2 : |x| : 2*|x| : log(2)
130 faddl MO(one) // 1+|x|^2 : |x| : 2*|x| : log(2)
131 fsqrt // sqrt(1+|x|^2) : |x| : 2*|x| : log(2)
132 faddp // |x|+sqrt(1+|x|^2) : 2*|x| : log(2)
133 fdivrl MO(one) // 1/(|x|+sqrt(1+|x|^2)) : 2*|x| : log(2)
134 faddp // 2*|x|+1/(|x|+sqrt(1+|x|^2)) : log(2)
135 fyl2x // log(2*|x|+1/(|x|+sqrt(1+|x|^2)))
140 libm_alias_float (__asinh, asinh)