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

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# Copyright (c) 1987, 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	8.1	(ucb.elefunt) 6/4/93"

# double cbrt(double arg)
# W. Kahan, 10/13/80. revised 1/13/84 for keeping sign symmetry
# Re-coded in tahoe assembly language by Z. Alex Liu (7/13/87)
# Max error less than 0.667 ULPs _if_ +,-,*,/ were all correctly rounded...
	.globl	_cbrt
	.globl	_d_cbrt
	.globl	_dcbrt_
	.text
	.align	2
_cbrt:
_d_cbrt:
	.word	0x01fc		# save r2-r8
	movl	4(fp),r0	# r0:r1 = x
	movl	8(fp),r1
	brb	1f
_dcbrt_:
	.word	0x01fc		# save r2-r8
	movl	4(fp),r8
	movl	(r8),r0
	movl	4(r8),r1	# r0:r1 = x

1:	andl3	$0x7f800000,r0,r2	# biased exponent of x
	beql	return		# dcbrt(0)=0  dcbrt(res)=res. operand
	andl3	$0x80000000,r0,r8	# r8 has sign(x)
	xorl2	r8,r0		# r0 is abs(x)
	movl	r0,r2		# r2 has abs(x)
	divl2	$3,r2		# rough dcbrt with bias/3
	addl2	B,r2		# restore bias, diminish fraction
	ldf	r2		# acc = |q|=|dcbrt| to 5 bits
	mulf	r2		# acc = qq
	divf	r0		# acc = qq/|x|
	mulf	r2		# acc = qqq/|x|
	addf	C		# acc = C+qqq/|x|
	stf	r3		# r3 = s = C+qqq/|x|
	ldf	D		# acc = D
	divf	r3		# acc = D/s
	addf	E		# acc = E+D/s
	addf	r3		# acc = s+E+D/s
	stf	r3		# r3 = s+E+D/s
	ldf	F		# acc = F
	divf	r3		# acc = F/(s+E+D/s)
	addf	G		# acc = G+F/(s+E+D/s)
	mulf	r2		# acc = q*(G+F/(s+E+D/s)) = new q to 23 bits
	stf	r2		# r2 = q*(G+F/(s+E+D/s)) = new q to 23 bits
	clrl	r3		# r2:r3 = q as double float
	ldd	r2		# acc = q as double float
	muld	r2		# acc = qq exactly
	std	r4		# r4:r5 = qq exactly
	ldd	r0		# acc = |x|
	divd	r4		# acc = |x|/(q*q) rounded
	std	r0		# r0:r1 = |x|/(q*q) rounded
	subd	r2		# acc = |x|/(q*q)-q exactly
	std	r6		# r6:r7 = |x|/(q*q)-q exactly
	movl    r2,r4
	clrl	r5		# r4:r5 = q as double float
	addl2	$0x800000,r4	# r4:r5 = 2*q
	ldd	r4		# acc = 2*q
	addd	r0		# acc = 2*q+|x|/(q*q)
	std	r4		# r4:r5 = 2*q+|x|/(q*q)
	ldd	r6		# acc = |x|/(q*q)-q
	divd	r4		# acc = (|x|/(q*q)-q)/(2*q+|x|/(q*q))
	muld	r2		# acc = q*(|x|/(q*q)-q)/(2*q+|x|/(q*q))
	addd	r2		# acc = q+q*(|x|/(q*q)-q)/(2*q+|x|/(q*q))
	std	r0		# r0:r1 = |result|
	orl2	r8,r0		# restore the sign bit
return: ret			# error less than 0.667ULPs?

	.data
	.align	2
B :	.long	721142941	#(86-0.03306235651)*(2^23)
	.align	2
C:	.long	0x400af8b0	#.float	0f0.5428571429	# 19/35
	.align	2
D:	.long	0xc0348ef1	#.float	0f-0.7053061224	# -864/1225
	.align	2
E:	.long	0x40b50750	#.float	0f1.414285714	# 99/70
	.align	2
F:	.long	0x40cdb6db	#.float	0f1.607142857	# 45/28
	.align	2
G:	.long	0x3fb6db6e	#.float	0f0.3571428571	# 5/14