#ifndef lint#static char	*sccsid = "@(#)sqrt.s	4.1	(ULTRIX)	7/17/90";#endif lint/************************************************************************ *									* *			Copyright (c) 1986 by				* *		Digital Equipment Corporation, Maynard, MA		* *			All rights reserved.				* *									* *   This software is furnished under a license and may be used and	* *   copied  only  in accordance with the terms of such license and	* *   with the  inclusion  of  the  above  copyright  notice.   This	* *   software  or  any  other copies thereof may not be provided or	* *   otherwise made available to any other person.  No title to and	* *   ownership of the software is hereby transferred.			* *									* *   This software is  derived  from  software  received  from  the	* *   University    of   California,   Berkeley,   and   from   Bell	* *   Laboratories.  Use, duplication, or disclosure is  subject  to	* *   restrictions  under  license  agreements  with  University  of	* *   California and with AT&T.						* *									* *   The information in this software is subject to change  without	* *   notice  and should not be construed as a commitment by Digital	* *   Equipment Corporation.						* *									* *   Digital assumes no responsibility for the use  or  reliability	* *   of its software on equipment which is not supplied by Digital.	* *									* ************************************************************************//**************************************************************************			Modification History* 002	Tim N	6/14/89*	Added setting of errno to EDOM on neg args.**	David Metsky, 12/18/86* 001	Adapted from sqrt.s 1.1 (Berkeley) 8/21/85**************************************************************************//* @(#)sqrt.s	1.1 (Berkeley) 8/21/85 * * double sqrt(arg)   revised August 15,1982 * double arg; * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); } * if arg is a reserved operand it is returned as it is * W. Kahan's magic square root * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82 * * entry points:_d_sqrt		address of double arg is on the stack *		_sqrt		double arg is on the stack */	.text	.align	1	.globl	_sqrt	.globl	_d_sqrt	.globl	libm$dsqrt_r5	.set	EDOM,33_d_sqrt:	.word	0x003c          # save r5,r4,r3,r2	movq	*4(ap),r0	jmp  	dsqrt2_sqrt:	.word	0x003c          # save r5,r4,r3,r2	movq    4(ap),r0dsqrt2:	bicw3	$0x807f,r0,r2	# check exponent of input	jeql	noexp		# biased exponent is zero -> 0.0 or reserved	bsbb	libm$dsqrt_r5noexp:	ret/* **************************** internal procedure */libm$dsqrt_r5:			# ENTRY POINT FOR cdabs and cdsqrt				# returns double square root scaled by				# 2^r6	movd	r0,r4	jleq	nonpos		# argument is not positive	movzwl	r4,r2	ashl	$-1,r2,r0	addw2	$0x203c,r0	# r0 has magic initial approximation/* * Do two steps of Heron's rule * ((arg/guess) + guess) / 2 = better guess */	divf3	r0,r4,r2	addf2	r2,r0	subw2	$0x80,r0	# divide by two	divf3	r0,r4,r2	addf2	r2,r0	subw2	$0x80,r0	# divide by two/* Scale argument and approximation to prevent over/underflow */	bicw3	$0x807f,r4,r1	subw2	$0x4080,r1		# r1 contains scaling factor	subw2	r1,r4	movl	r0,r2	subw2	r1,r2/* Cubic step * * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation, * a is approximation, and n is the original argument. * (let s be scale factor in the following comments) */	clrl	r1	clrl	r3	muld2	r0,r2			# r2:r3 = a*a/s	subd2	r2,r4			# r4:r5 = n/s - a*a/s	addw2	$0x100,r2		# r2:r3 = 4*a*a/s	addd2	r4,r2			# r2:r3 = n/s + 3*a*a/s	muld2	r0,r4			# r4:r5 = a*n/s - a*a*a/s	divd2	r2,r4			# r4:r5 = a*(n-a*a)/(n+3*a*a)	addw2	$0x80,r4		# r4:r5 = 2*a*(n-a*a)/(n+3*a*a)	addd2	r4,r0			# r0:r1 = a + 2*a*(n-a*a)/(n+3*a*a)	rsb				# DONE!nonpos:	jneq	negarg	ret			# argument and root are zeronegarg:	movl	$EDOM,_errno	# old code was: pushl	$EDOM	movl	$0,r0		# generate the reserved op fault	ret