1996-12-30 02:47:46 +01:00
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/* ix87 specific implementation of arcsinh.
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Copyright (C) 1996 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.
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The GNU C Library is free software; you can redistribute it and/or
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2001-07-06 06:58:11 +02:00
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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1996-12-30 02:47:46 +01:00
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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2001-07-06 06:58:11 +02:00
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Lesser General Public License for more details.
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1996-12-30 02:47:46 +01:00
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2001-07-06 06:58:11 +02:00
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA. */
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1996-12-30 02:47:46 +01:00
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#include <machine/asm.h>
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#ifdef __ELF__
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.section .rodata
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#else
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.text
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#endif
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.align ALIGNARG(4)
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ASM_TYPE_DIRECTIVE(one,@object)
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one: .double 1.0
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ASM_SIZE_DIRECTIVE(one)
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ASM_TYPE_DIRECTIVE(limit,@object)
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limit: .double 0.29
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ASM_SIZE_DIRECTIVE(limit)
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#ifdef PIC
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#define MO(op) op##@GOTOFF(%edx)
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#else
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#define MO(op) op
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#endif
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.text
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ENTRY(__ieee754_acosh)
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movl 8(%esp), %ecx
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cmpl $0x3ff00000, %ecx
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jl 5f // < 1 => invalid
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fldln2 // log(2)
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fldl 4(%esp) // x : log(2)
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cmpl $0x41b00000, %ecx
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ja 3f // x > 2^28
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#ifdef PIC
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call 1f
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1: popl %edx
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addl $_GLOBAL_OFFSET_TABLE_+[.-1b], %edx
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#endif
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cmpl $0x40000000, %ecx
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ja 4f // x > 2
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// 1 <= x <= 2 => y = log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
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fsubl MO(one) // x-1 : log(2)
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fld %st // x-1 : x-1 : log(2)
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fmul %st(1) // (x-1)^2 : x-1 : log(2)
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fadd %st(1) // x-1+(x-1)^2 : x-1 : log(2)
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fadd %st(1) // 2*(x-1)+(x-1)^2 : x-1 : log(2)
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fsqrt // sqrt(2*(x-1)+(x-1)^2) : x-1 : log(2)
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faddp // x-1+sqrt(2*(x-1)+(x-1)^2) : log(2)
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fcoml MO(limit)
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fnstsw
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sahf
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ja 2f
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fyl2xp1 // log1p(x-1+sqrt(2*(x-1)+(x-1)^2))
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ret
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2: faddl MO(one) // x+sqrt(2*(x-1)+(x-1)^2) : log(2)
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fyl2x // log(x+sqrt(2*(x-1)+(x-1)^2))
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ret
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// x > 2^28 => y = log(x) + log(2)
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.align ALIGNARG(4)
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3: fyl2x // log(x)
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fldln2 // log(2) : log(x)
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faddp // log(x)+log(2)
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ret
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// 2^28 > x > 2 => y = log(2*x - 1/(x+sqrt(x*x-1)))
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.align ALIGNARG(4)
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4: fld %st // x : x : log(2)
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fadd %st, %st(1) // x : 2*x : log(2)
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fld %st // x : x : 2*x : log(2)
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fmul %st(1) // x^2 : x : 2*x : log(2)
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fsubl MO(one) // x^2-1 : x : 2*x : log(2)
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fsqrt // sqrt(x^2-1) : x : 2*x : log(2)
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faddp // x+sqrt(x^2-1) : 2*x : log(2)
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fdivrl MO(one) // 1/(x+sqrt(x^2-1)) : 2*x : log(2)
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fsubrp // 2*x+1/(x+sqrt(x^2)-1) : log(2)
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fyl2x // log(2*x+1/(x+sqrt(x^2-1)))
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ret
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// x < 1 => NaN
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.align ALIGNARG(4)
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5: fldz
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fdiv %st, %st(0)
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ret
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END(__ieee754_acosh)
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