1/* ix87 specific implementation of arcsinh.
2 Copyright (C) 1996-2022 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.cst8,"aM",@progbits,8
23
24 .p2align 3
25 .type one,@object
26one: .double 1.0
27 ASM_SIZE_DIRECTIVE(one)
28 .type limit,@object
29limit: .double 0.29
30 ASM_SIZE_DIRECTIVE(limit)
31
32#ifdef PIC
33#define MO(op) op##@GOTOFF(%edx)
34#else
35#define MO(op) op
36#endif
37
38 .text
39ENTRY(__ieee754_acosh)
40 movl 8(%esp), %ecx
41 cmpl $0x3ff00000, %ecx
42 jl 5f // < 1 => invalid
43 fldln2 // log(2)
44 fldl 4(%esp) // x : log(2)
45 cmpl $0x41b00000, %ecx
46 ja 3f // x > 2^28
47#ifdef PIC
48 LOAD_PIC_REG (dx)
49#endif
50 cmpl $0x40000000, %ecx
51 ja 4f // x > 2
52
53 // 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
54 fsubl MO(one) // x-1 : log(2)
55 fabs // acosh(1) is +0 in all rounding modes
56 fld %st // x-1 : x-1 : log(2)
57 fmul %st(1) // (x-1)^2 : x-1 : log(2)
58 fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
59 fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
60 fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
61 faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
62 fcoml MO(limit)
63 fnstsw
64 sahf
65 ja 2f
66 fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
67 ret
68
692: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
70 fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
71 ret
72
73 // x > 2^28 => y = log(x) + log(2)
74 .align ALIGNARG(4)
753: fyl2x // log(x)
76 fldln2 // log(2) : log(x)
77 faddp // log(x)+log(2)
78 ret
79
80 // 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
81 .align ALIGNARG(4)
824: fld %st // x : x : log(2)
83 fadd %st, %st(1) // x : 2*x : log(2)
84 fld %st // x : x : 2*x : log(2)
85 fmul %st(1) // x^2 : x : 2*x : log(2)
86 fsubl MO(one) // x^2-1 : x : 2*x : log(2)
87 fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
88 faddp // x+sqrt(x^2-1) : 2*x : log(2)
89 fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
90 fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
91 fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
92 ret
93
94 // x < 1 (or -NaN) => NaN
95 .align ALIGNARG(4)
965: fldl 4(%esp)
97 fsub %st
98 fdiv %st, %st(0)
99 ret
100END(__ieee754_acosh)
101libm_alias_finite (__ieee754_acosh, __acosh)
102

source code of glibc/sysdeps/i386/fpu/e_acosh.S