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. |
4 | |
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. |
9 | |
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. |
14 | |
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/>. */ |
18 | |
19 | #include <machine/asm.h> |
20 | #include <libm-alias-finite.h> |
21 | |
22 | .section .rodata |
23 | |
24 | .align ALIGNARG(4) |
25 | /* Please note that we use double values for 0.5 and 1.0. These |
26 | numbers have exact representations and so we don't get accuracy |
27 | problems. The advantage is that the code is simpler. */ |
28 | .type half,@object |
29 | half: .double 0.5 |
30 | ASM_SIZE_DIRECTIVE(half) |
31 | .type one,@object |
32 | one: .double 1.0 |
33 | ASM_SIZE_DIRECTIVE(one) |
34 | /* It is not important that this constant is precise. It is only |
35 | a value which is known to be on the safe side for using the |
36 | fyl2xp1 instruction. */ |
37 | .type limit,@object |
38 | limit: .double 0.29 |
39 | ASM_SIZE_DIRECTIVE(limit) |
40 | .align ALIGNARG(4) |
41 | .type ln2_2,@object |
42 | ln2_2: .quad 0xb17217f7d1cf79ac /* 0.3465735902799726547086160 */ |
43 | .short 0x3ffd |
44 | ASM_SIZE_DIRECTIVE(ln2_2) |
45 | |
46 | #ifdef PIC |
47 | #define MO(op) op##@GOTOFF(%edx) |
48 | #else |
49 | #define MO(op) op |
50 | #endif |
51 | |
52 | .text |
53 | ENTRY(__ieee754_atanhl) |
54 | movl 12(%esp), %ecx |
55 | |
56 | movl %ecx, %eax |
57 | andl $0x7fff, %eax |
58 | cmpl $0x7fff, %eax |
59 | je 5f |
60 | cmpl $0x3fdf, %eax |
61 | jge 7f |
62 | // Exponent below -32; return x, with underflow if subnormal. |
63 | fldt 4(%esp) |
64 | cmpl $0, %eax |
65 | jne 8f |
66 | fld %st(0) |
67 | fmul %st(0) |
68 | fstp %st(0) |
69 | 8: ret |
70 | 7: |
71 | |
72 | #ifdef PIC |
73 | LOAD_PIC_REG (dx) |
74 | #endif |
75 | |
76 | andl $0x8000, %ecx // ECX == 0 iff X >= 0 |
77 | |
78 | fldt MO(ln2_2) // 0.5*ln2 |
79 | xorl %ecx, 12(%esp) |
80 | fldt 4(%esp) // |x| : 0.5*ln2 |
81 | fcoml MO(half) // |x| : 0.5*ln2 |
82 | fld %st(0) // |x| : |x| : 0.5*ln2 |
83 | fnstsw // |x| : |x| : 0.5*ln2 |
84 | sahf |
85 | jae 2f |
86 | fadd %st, %st(1) // |x| : 2*|x| : 0.5*ln2 |
87 | fld %st // |x| : |x| : 2*|x| : 0.5*ln2 |
88 | fsubrl MO(one) // 1-|x| : |x| : 2*|x| : 0.5*ln2 |
89 | fxch // |x| : 1-|x| : 2*|x| : 0.5*ln2 |
90 | fmul %st(2) // 2*|x|^2 : 1-|x| : 2*|x| : 0.5*ln2 |
91 | fdivp // (2*|x|^2)/(1-|x|) : 2*|x| : 0.5*ln2 |
92 | faddp // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2 |
93 | fcoml MO(limit) // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2 |
94 | fnstsw // 2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2 |
95 | sahf |
96 | jae 4f |
97 | fyl2xp1 // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|)) |
98 | jecxz 3f |
99 | fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x)) |
100 | 3: ret |
101 | |
102 | .align ALIGNARG(4) |
103 | 4: faddl MO(one) // 1+2*|x|+(2*|x|^2)/(1-|x|) : 0.5*ln2 |
104 | fyl2x // 0.5*ln2*ld(1+2*|x|+(2*|x|^2)/(1-|x|)) |
105 | jecxz 3f |
106 | fchs // 0.5*ln2*ld(1+2*x+(2*x^2)/(1-x)) |
107 | 3: ret |
108 | |
109 | .align ALIGNARG(4) |
110 | 2: faddl MO(one) // 1+|x| : |x| : 0.5*ln2 |
111 | fxch // |x| : 1+|x| : 0.5*ln2 |
112 | fsubrl MO(one) // 1-|x| : 1+|x| : 0.5*ln2 |
113 | fdivrp // (1+|x|)/(1-|x|) : 0.5*ln2 |
114 | fyl2x // 0.5*ln2*ld((1+|x|)/(1-|x|)) |
115 | jecxz 3f |
116 | fchs // 0.5*ln2*ld((1+x)/(1-x)) |
117 | 3: ret |
118 | |
119 | // x == NaN or ħInf |
120 | 5: cmpl $0x80000000, 8(%esp) |
121 | ja 6f |
122 | cmpl $0, 4(%esp) |
123 | je 7b |
124 | 6: fldt 4(%esp) |
125 | fadd %st(0) |
126 | ret |
127 | END(__ieee754_atanhl) |
128 | libm_alias_finite (__ieee754_atanhl, __atanhl) |
129 | |