1 /* ix87 specific implementation of arctanh function.
2 Copyright (C) 1996-2024 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 <i386-math-asm.h>
21 #include <libm-alias-finite.h>
28 ASM_SIZE_DIRECTIVE(half)
31 ASM_SIZE_DIRECTIVE(one)
34 ASM_SIZE_DIRECTIVE(limit)
36 ln2_2: .quad 0xb17217f7d1cf79ac /* 0.3465735902799726547086160 */
38 ASM_SIZE_DIRECTIVE(ln2_2)
43 #define MO(op) op##@GOTOFF(%edx)
49 ENTRY(__ieee754_atanh)
53 andl $0x7fffffff, %eax
54 cmpl $0x7ff00000, %eax
62 andl $0x80000000, %ecx // ECX == 0 iff X >= 0
64 fldt MO(ln2_2) // 0.5*ln2
66 fldl 4(%esp) // |x| : 0.5*ln2
67 fcoml MO(half) // |x| : 0.5*ln2
68 fld %st // |x| : |x| : 0.5*ln2
69 fnstsw // |x| : |x| : 0.5*ln2
72 fadd %st, %st(1) // |x| : 2*|x| : 0.5*ln2
73 fld %st // |x| : |x| : 2*|x| : 0.5*ln2
74 fsubrl MO(one) // 1-|x| : |x| : 2*|x| : 0.5*ln2
75 fxch // |x| : 1-|x| : 2*|x| : 0.5*ln2
76 fmul %st(2) // 2*|x|^2 : 1-|x| : 2*|x| : 0.5*ln2
77 fdivp // (2*|x|^2)/(1-|x|) : 2*|x| : 0.5*ln2
78 faddp // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
79 fcoml MO(limit) // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
80 fnstsw // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
83 fyl2xp1 // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
84 DBL_CHECK_FORCE_UFLOW_NONNEG
86 fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
90 4: faddl MO(one) // 1+2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2
91 fyl2x // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|))
93 fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x))
97 2: faddl MO(one) // 1+|x| : |x| : 0.5*ln2
98 fxch // |x| : 1+|x| : 0.5*ln2
99 fsubrl MO(one) // 1-|x| : 1+|x| : 0.5*ln2
100 fdivrp // (1+|x|)/(1-|x|) : 0.5*ln2
101 fyl2x // 0.5*ln2*ld((1+|x|)/(1-|x|))
103 fchs // 0.5*ln2*ld((1+x)/(1-x))
113 libm_alias_finite (__ieee754_atanh, __atanh)