4.4BSD/usr/src/lib/libm/vax/cbrt.s

# 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. All advertising materials mentioning features or use of this software
#    must display the following acknowledgement:
#	This product includes software developed by the University of
#	California, Berkeley and its contributors.
# 4. 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
#
	.data
	.align	2
_sccsid:
.asciz	"@(#)cbrt.s	1.1 (Berkeley) 5/23/85; 8.1 (ucb.elefunt) 6/4/93"

# 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)
	.globl	_cbrt
	.globl	_d_cbrt
	.globl  _dcbrt_
	.text
	.align	1

_cbrt:
_d_cbrt:
	.word	0x00fc		# save r2 to r7
	movq	4(ap),r0	# r0 = argument x
	jmp 	dcbrt2
_dcbrt_:
	.word	0x00fc		# save r2 to r7
	movq	*4(ap),r0	# r0 = argument x

dcbrt2:	bicw3	$0x807f,r0,r2	# biased exponent of x
	jeql	return		# dcbrt(0)=0  dcbrt(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 dcbrt with bias/3
	addl2	B,r2		# restore bias, diminish fraction
	rotl	$16,r2,r2	# r2=|q|=|dcbrt| 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