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.
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
25 /* Please note that we use double value for 1.0. This number
26 has an exact representation and so we don't get accuracy
27 problems. The advantage is that the code is simpler. */
30 ASM_SIZE_DIRECTIVE(one)
31 /* It is not important that this constant is precise. It is only
32 a value which is known to be on the safe side for using the
33 fyl2xp1 instruction. */
36 ASM_SIZE_DIRECTIVE(limit)
39 #define MO(op) op##@GOTOFF(%edx)
45 ENTRY(__ieee754_acoshl)
49 jl 5f // < 1 => invalid
51 fldt 4(%esp) // x : log(2)
60 // 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
61 fsubl MO(one) // x-1 : log(2)
62 fabs // acosh(1) is +0 in all rounding modes
63 fld %st // x-1 : x-1 : log(2)
64 fmul %st(1) // (x-1)^2 : x-1 : log(2)
65 fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
66 fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
67 fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
68 faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
73 fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
76 2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
77 fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
80 // x > 2^34 => y = log(x) + log(2)
83 fldln2 // log(2) : log(x)
84 faddp // log(x)+log(2)
87 // 2^34 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
89 4: fld %st // x : x : log(2)
90 fadd %st, %st(1) // x : 2*x : log(2)
91 fld %st // x : x : 2*x : log(2)
92 fmul %st(1) // x^2 : x : 2*x : log(2)
93 fsubl MO(one) // x^2-1 : x : 2*x : log(2)
94 fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
95 faddp // x+sqrt(x^2-1) : 2*x : log(2)
96 fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
97 fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
98 fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
106 END(__ieee754_acoshl)
107 libm_alias_finite (__ieee754_acoshl, __acoshl)