1/*	$NetBSD: n_sqrt.S,v 1.7 2004/05/13 20:35:40 mhitch Exp $	*/
2/*
3 * Copyright (c) 1985, 1993
4 *	The Regents of the University of California.  All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 *    may be used to endorse or promote products derived from this software
16 *    without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 *
30 *	@(#)sqrt.s	8.1 (Berkeley) 6/4/93
31 */
32
33#include <machine/asm.h>
34
35/*
36 * double sqrt(arg)   revised August 15,1982
37 * double arg;
38 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); }
39 * if arg is a reserved operand it is returned as it is
40 * W. Kahan's magic square root
41 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82
42 *
43 * entry points:_d_sqrt		address of double arg is on the stack
44 *		_sqrt		double arg is on the stack
45 */
46	.set	EDOM,33
47
48ENTRY(d_sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
49	movq	*4(%ap),%r0
50	jbr  	dsqrt2
51
52ENTRY(sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
53	movq    4(%ap),%r0
54
55dsqrt2:	bicw3	$0x807f,%r0,%r2	# check exponent of input
56	jeql	noexp		# biased exponent is zero -> 0.0 or reserved
57	bsbb	__libm_dsqrt_r5_lcl
58noexp:	ret
59
60/* **************************** internal procedure */
61
62	.hidden __libm_dsqrt_r5
63ALTENTRY(__libm_dsqrt_r5)
64	halt
65	halt
66__libm_dsqrt_r5_lcl:
67				/* ENTRY POINT FOR cdabs and cdsqrt	*/
68				/* returns double square root scaled by	*/
69				/* 2^%r6	*/
70
71	movd	%r0,%r4
72	jleq	nonpos		# argument is not positive
73	movzwl	%r4,%r2
74	ashl	$-1,%r2,%r0
75	addw2	$0x203c,%r0	# %r0 has magic initial approximation
76/*
77 * Do two steps of Heron's rule
78 * ((arg/guess) + guess) / 2 = better guess
79 */
80	divf3	%r0,%r4,%r2
81	addf2	%r2,%r0
82	subw2	$0x80,%r0	# divide by two
83
84	divf3	%r0,%r4,%r2
85	addf2	%r2,%r0
86	subw2	$0x80,%r0	# divide by two
87
88/* Scale argument and approximation to prevent over/underflow */
89
90	bicw3	$0x807f,%r4,%r1
91	subw2	$0x4080,%r1		# %r1 contains scaling factor
92	subw2	%r1,%r4
93	movl	%r0,%r2
94	subw2	%r1,%r2
95
96/* Cubic step
97 *
98 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation,
99 * a is approximation, and n is the original argument.
100 * (let s be scale factor in the following comments)
101 */
102	clrl	%r1
103	clrl	%r3
104	muld2	%r0,%r2			# %r2:%r3 = a*a/s
105	subd2	%r2,%r4			# %r4:%r5 = n/s - a*a/s
106	addw2	$0x100,%r2		# %r2:%r3 = 4*a*a/s
107	addd2	%r4,%r2			# %r2:%r3 = n/s + 3*a*a/s
108	muld2	%r0,%r4			# %r4:%r5 = a*n/s - a*a*a/s
109	divd2	%r2,%r4			# %r4:%r5 = a*(n-a*a)/(n+3*a*a)
110	addw2	$0x80,%r4		# %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a)
111	addd2	%r4,%r0			# %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a)
112	rsb				# DONE!
113nonpos:
114	jneq	negarg
115	ret				# argument and root are zero
116negarg:
117	pushl	$EDOM
118	calls	$1,_C_LABEL(infnan)	# generate the reserved op fault
119	ret
120
121ENTRY(sqrtf, 0)
122	cvtfd	4(%ap),-(%sp)
123	calls	$2,_C_LABEL(sqrt)
124	cvtdf	%r0,%r0
125	ret
126