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-finite.h>
22 .section .rodata.cst8,"aM",@progbits,8
27 ASM_SIZE_DIRECTIVE(one)
30 ASM_SIZE_DIRECTIVE(limit)
33 #define MO(op) op##@GOTOFF(%edx)
39 ENTRY(__ieee754_acosh)
41 cmpl $0x3ff00000, %ecx
42 jl 5f // < 1 => invalid
44 fldl 4(%esp) // x : log(2)
45 cmpl $0x41b00000, %ecx
50 cmpl $0x40000000, %ecx
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)
66 fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
69 2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
70 fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
73 // x > 2^28 => y = log(x) + log(2)
76 fldln2 // log(2) : log(x)
77 faddp // log(x)+log(2)
80 // 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
82 4: 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)))
94 // x < 1 (or -NaN) => NaN
101 libm_alias_finite (__ieee754_acosh, __acosh)