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/* $OpenBSD: n_cbrt.S,v 1.5 2013/07/05 21:10:50 miod Exp $ */
/* $NetBSD: n_cbrt.S,v 1.1 1995/10/10 23:40:26 ragge Exp $ */
/*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* @(#)cbrt.s 8.1 (Berkeley) 6/4/93
*/
#include <machine/asm.h>
/*
* double cbrt(double arg)
* W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry
* error check by E LeBlanc, 8/18/82
* Revised and tested by K.C. Ng, 5/2/85
* Max error less than 0.667 ulps (unit in the last places)
*/
.text
_ALIGN_TEXT
ENTRY(cbrt, R2|R3|R4|R5|R6|R7)
movq 4(%ap),%r0 # r0 = argument x
bicw3 $0x807f,%r0,%r2 # biased exponent of x
jeql return # cbrt(0)=0 cbrt(res)=res. operand
bicw3 $0x7fff,%r0,%ap # ap has sign(x)
xorw2 %ap,%r0 # r0 is abs(x)
movl %r0,%r2 # r2 has abs(x)
rotl $16,%r2,%r2 # r2 = |x| with bits unscrambled
divl2 $3,%r2 # rough cbrt with bias/3
addl2 B,%r2 # restore bias, diminish fraction
rotl $16,%r2,%r2 # r2=|q|=|cbrt| to 5 bits
mulf3 %r2,%r2,%r3 # r3 =qq
divf2 %r0,%r3 # r3 = qq/x
mulf2 %r2,%r3
addf2 C,%r3 # r3 = s = C + qqq/x
divf3 %r3,D,%r4 # r4 = D/s
addf2 E,%r4
addf2 %r4,%r3 # r3 = s + E + D/s
divf3 %r3,F,%r3 # r3 = F / (s + E + D/s)
addf2 G,%r3 # r3 = G + F / (s + E + D/s)
mulf2 %r3,%r2 # r2 = qr3 = new q to 23 bits
clrl %r3 # r2:r3 = q as double float
muld3 %r2,%r2,%r4 # r4:r5 = qq exactly
divd2 %r4,%r0 # r0:r1 = x/(q*q) rounded
subd3 %r2,%r0,%r6 # r6:r7 = x/(q*q) - q exactly
movq %r2,%r4 # r4:r5 = q
addw2 $0x80,%r4 # r4:r5 = 2 * q
addd2 %r0,%r4 # r4:r5 = 2*q + x/(q*q)
divd2 %r4,%r6 # r6:r7 = (x/(q*q)-q)/(2*q+x/(q*q))
muld2 %r2,%r6 # r6:r7 = q*(x/(q*q)-q)/(2*q+x/(q*q))
addd3 %r6,%r2,%r0 # r0:r1 = q + r6:r7
bisw2 %ap,%r0 # restore the sign bit
return:
ret # error less than 0.667 ulps
.data
.align 2
B : .long 721142941 # (86-0.03306235651)*(2^23)
C : .float 0f0.5428571429 # 19/35
D : .float 0f-0.7053061224 # -864/1225
E : .float 0f1.414285714 # 99/70
F : .float 0f1.607142857 # 45/28
G : .float 0f0.3571428571 # 5/14
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