1 /* ix87 specific implementation of arcsinh.
2 Copyright (C) 1996-1997, 2005, 2011-2012 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <http://www.gnu.org/licenses/>. */
20 #include <machine/asm.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_acoshf)
41 cmpl $0x3f800000, %ecx
42 jl 5f // < 1 => invalid
44 flds 4(%esp) // x : log(2)
45 cmpl $0x47000000, %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 fld %st // x-1 : x-1 : log(2)
56 fmul %st(1) // (x-1)^2 : x-1 : log(2)
57 fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
58 fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
59 fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
60 faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
65 fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
68 2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
69 fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
72 // x > 2^14 => y = log(x) + log(2)
75 fldln2 // log(2) : log(x)
76 faddp // log(x)+log(2)
79 // 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
81 4: fld %st // x : x : log(2)
82 fadd %st, %st(1) // x : 2*x : log(2)
83 fld %st // x : x : 2*x : log(2)
84 fmul %st(1) // x^2 : x : 2*x : log(2)
85 fsubl MO(one) // x^2-1 : x : 2*x : log(2)
86 fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
87 faddp // x+sqrt(x^2-1) : 2*x : log(2)
88 fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
89 fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
90 fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
99 strong_alias (__ieee754_acoshf, __acoshf_finite)