1/*	$NetBSD: n_sqrt.S,v 1.12 2024/05/07 15:15:10 riastradh 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#ifdef WEAK_ALIAS
36WEAK_ALIAS(_sqrtl, sqrt)
37WEAK_ALIAS(sqrtl, sqrt)
38#endif
39
40/*
41 * double sqrt(arg)   revised August 15,1982
42 * double arg;
43 * if(arg<0.0) { _errno = EDOM; return(<a reserved operand>); }
44 * if arg is a reserved operand it is returned as it is
45 * W. Kahan's magic square root
46 * coded by Heidi Stettner and revised by Emile LeBlanc 8/18/82
47 *
48 * entry points:_d_sqrt		address of double arg is on the stack
49 *		_sqrt		double arg is on the stack
50 */
51	.set	EDOM,33
52
53ENTRY(d_sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
54	movq	*4(%ap),%r0
55	jbr  	dsqrt2
56END(d_sqrt)
57
58ENTRY(sqrt, 0x003c)		# save %r5,%r4,%r3,%r2
59	movq    4(%ap),%r0
60
61dsqrt2:	bicw3	$0x807f,%r0,%r2	# check exponent of input
62	jeql	noexp		# biased exponent is zero -> 0.0 or reserved
63	bsbb	__libm_dsqrt_r5_lcl
64noexp:	ret
65END(sqrt)
66
67/* **************************** internal procedure */
68
69	.hidden __libm_dsqrt_r5
70ALTENTRY(__libm_dsqrt_r5)
71	halt
72	halt
73__libm_dsqrt_r5_lcl:
74				/* ENTRY POINT FOR cdabs and cdsqrt	*/
75				/* returns double square root scaled by	*/
76				/* 2^%r6	*/
77
78	movd	%r0,%r4
79	jleq	nonpos		# argument is not positive
80	movzwl	%r4,%r2
81	ashl	$-1,%r2,%r0
82	addw2	$0x203c,%r0	# %r0 has magic initial approximation
83/*
84 * Do two steps of Heron's rule
85 * ((arg/guess) + guess) / 2 = better guess
86 */
87	divf3	%r0,%r4,%r2
88	addf2	%r2,%r0
89	subw2	$0x80,%r0	# divide by two
90
91	divf3	%r0,%r4,%r2
92	addf2	%r2,%r0
93	subw2	$0x80,%r0	# divide by two
94
95/* Scale argument and approximation to prevent over/underflow */
96
97	bicw3	$0x807f,%r4,%r1
98	subw2	$0x4080,%r1		# %r1 contains scaling factor
99	subw2	%r1,%r4
100	movl	%r0,%r2
101	subw2	%r1,%r2
102
103/* Cubic step
104 *
105 * b = a + 2*a*(n-a*a)/(n+3*a*a) where b is better approximation,
106 * a is approximation, and n is the original argument.
107 * (let s be scale factor in the following comments)
108 */
109	clrl	%r1
110	clrl	%r3
111	muld2	%r0,%r2			# %r2:%r3 = a*a/s
112	subd2	%r2,%r4			# %r4:%r5 = n/s - a*a/s
113	addw2	$0x100,%r2		# %r2:%r3 = 4*a*a/s
114	addd2	%r4,%r2			# %r2:%r3 = n/s + 3*a*a/s
115	muld2	%r0,%r4			# %r4:%r5 = a*n/s - a*a*a/s
116	divd2	%r2,%r4			# %r4:%r5 = a*(n-a*a)/(n+3*a*a)
117	addw2	$0x80,%r4		# %r4:%r5 = 2*a*(n-a*a)/(n+3*a*a)
118	addd2	%r4,%r0			# %r0:%r1 = a + 2*a*(n-a*a)/(n+3*a*a)
119	rsb				# DONE!
120nonpos:
121	jneq	negarg
122	ret				# argument and root are zero
123negarg:
124	pushl	$EDOM
125	calls	$1,_C_LABEL(infnan)	# generate the reserved op fault
126	ret
127
128ENTRY(sqrtf, 0)
129	cvtfd	4(%ap),-(%sp)
130	calls	$2,_C_LABEL(sqrt)
131	cvtdf	%r0,%r0
132	ret
133END(sqrtf)
134