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1/* $Id: umul.S,v 1.4 1996/09/30 02:22:39 davem Exp $
2 * umul.S: This routine was taken from glibc-1.09 and is covered
3 * by the GNU Library General Public License Version 2.
4 */
5
6
7/*
8 * Unsigned multiply. Returns %o0 * %o1 in %o1%o0 (i.e., %o1 holds the
9 * upper 32 bits of the 64-bit product).
10 *
11 * This code optimizes short (less than 13-bit) multiplies. Short
12 * multiplies require 25 instruction cycles, and long ones require
13 * 45 instruction cycles.
14 *
15 * On return, overflow has occurred (%o1 is not zero) if and only if
16 * the Z condition code is clear, allowing, e.g., the following:
17 *
18 * call .umul
19 * nop
20 * bnz overflow (or tnz)
21 */
22
23 .globl .umul
24.umul:
25 or %o0, %o1, %o4
26 mov %o0, %y ! multiplier -> Y
27
28 andncc %o4, 0xfff, %g0 ! test bits 12..31 of *both* args
29 be Lmul_shortway ! if zero, can do it the short way
30 andcc %g0, %g0, %o4 ! zero the partial product and clear N and V
31
32 /*
33 * Long multiply. 32 steps, followed by a final shift step.
34 */
35 mulscc %o4, %o1, %o4 ! 1
36 mulscc %o4, %o1, %o4 ! 2
37 mulscc %o4, %o1, %o4 ! 3
38 mulscc %o4, %o1, %o4 ! 4
39 mulscc %o4, %o1, %o4 ! 5
40 mulscc %o4, %o1, %o4 ! 6
41 mulscc %o4, %o1, %o4 ! 7
42 mulscc %o4, %o1, %o4 ! 8
43 mulscc %o4, %o1, %o4 ! 9
44 mulscc %o4, %o1, %o4 ! 10
45 mulscc %o4, %o1, %o4 ! 11
46 mulscc %o4, %o1, %o4 ! 12
47 mulscc %o4, %o1, %o4 ! 13
48 mulscc %o4, %o1, %o4 ! 14
49 mulscc %o4, %o1, %o4 ! 15
50 mulscc %o4, %o1, %o4 ! 16
51 mulscc %o4, %o1, %o4 ! 17
52 mulscc %o4, %o1, %o4 ! 18
53 mulscc %o4, %o1, %o4 ! 19
54 mulscc %o4, %o1, %o4 ! 20
55 mulscc %o4, %o1, %o4 ! 21
56 mulscc %o4, %o1, %o4 ! 22
57 mulscc %o4, %o1, %o4 ! 23
58 mulscc %o4, %o1, %o4 ! 24
59 mulscc %o4, %o1, %o4 ! 25
60 mulscc %o4, %o1, %o4 ! 26
61 mulscc %o4, %o1, %o4 ! 27
62 mulscc %o4, %o1, %o4 ! 28
63 mulscc %o4, %o1, %o4 ! 29
64 mulscc %o4, %o1, %o4 ! 30
65 mulscc %o4, %o1, %o4 ! 31
66 mulscc %o4, %o1, %o4 ! 32
67 mulscc %o4, %g0, %o4 ! final shift
68
69
70 /*
71 * Normally, with the shift-and-add approach, if both numbers are
72 * positive you get the correct result. With 32-bit two's-complement
73 * numbers, -x is represented as
74 *
75 * x 32
76 * ( 2 - ------ ) mod 2 * 2
77 * 32
78 * 2
79 *
80 * (the `mod 2' subtracts 1 from 1.bbbb). To avoid lots of 2^32s,
81 * we can treat this as if the radix point were just to the left
82 * of the sign bit (multiply by 2^32), and get
83 *
84 * -x = (2 - x) mod 2
85 *
86 * Then, ignoring the `mod 2's for convenience:
87 *
88 * x * y = xy
89 * -x * y = 2y - xy
90 * x * -y = 2x - xy
91 * -x * -y = 4 - 2x - 2y + xy
92 *
93 * For signed multiplies, we subtract (x << 32) from the partial
94 * product to fix this problem for negative multipliers (see mul.s).
95 * Because of the way the shift into the partial product is calculated
96 * (N xor V), this term is automatically removed for the multiplicand,
97 * so we don't have to adjust.
98 *
99 * But for unsigned multiplies, the high order bit wasn't a sign bit,
100 * and the correction is wrong. So for unsigned multiplies where the
101 * high order bit is one, we end up with xy - (y << 32). To fix it
102 * we add y << 32.
103 */
104#if 0
105 tst %o1
106 bl,a 1f ! if %o1 < 0 (high order bit = 1),
107 add %o4, %o0, %o4 ! %o4 += %o0 (add y to upper half)
108
1091:
110 rd %y, %o0 ! get lower half of product
111 retl
112 addcc %o4, %g0, %o1 ! put upper half in place and set Z for %o1==0
113#else
114 /* Faster code from tege@sics.se. */
115 sra %o1, 31, %o2 ! make mask from sign bit
116 and %o0, %o2, %o2 ! %o2 = 0 or %o0, depending on sign of %o1
117 rd %y, %o0 ! get lower half of product
118 retl
119 addcc %o4, %o2, %o1 ! add compensation and put upper half in place
120#endif
121
122Lmul_shortway:
123 /*
124 * Short multiply. 12 steps, followed by a final shift step.
125 * The resulting bits are off by 12 and (32-12) = 20 bit positions,
126 * but there is no problem with %o0 being negative (unlike above),
127 * and overflow is impossible (the answer is at most 24 bits long).
128 */
129 mulscc %o4, %o1, %o4 ! 1
130 mulscc %o4, %o1, %o4 ! 2
131 mulscc %o4, %o1, %o4 ! 3
132 mulscc %o4, %o1, %o4 ! 4
133 mulscc %o4, %o1, %o4 ! 5
134 mulscc %o4, %o1, %o4 ! 6
135 mulscc %o4, %o1, %o4 ! 7
136 mulscc %o4, %o1, %o4 ! 8
137 mulscc %o4, %o1, %o4 ! 9
138 mulscc %o4, %o1, %o4 ! 10
139 mulscc %o4, %o1, %o4 ! 11
140 mulscc %o4, %o1, %o4 ! 12
141 mulscc %o4, %g0, %o4 ! final shift
142
143 /*
144 * %o4 has 20 of the bits that should be in the result; %y has
145 * the bottom 12 (as %y's top 12). That is:
146 *
147 * %o4 %y
148 * +----------------+----------------+
149 * | -12- | -20- | -12- | -20- |
150 * +------(---------+------)---------+
151 * -----result-----
152 *
153 * The 12 bits of %o4 left of the `result' area are all zero;
154 * in fact, all top 20 bits of %o4 are zero.
155 */
156
157 rd %y, %o5
158 sll %o4, 12, %o0 ! shift middle bits left 12
159 srl %o5, 20, %o5 ! shift low bits right 20
160 or %o5, %o0, %o0
161 retl
162 addcc %g0, %g0, %o1 ! %o1 = zero, and set Z
163
164 .globl .umul_patch
165.umul_patch:
166 umul %o0, %o1, %o0
167 retl
168 rd %y, %o1
169 nop