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