3 .\" Copyright (C) 2003, 2006, 2009
4 .\" Free Software Foundation, Inc.
5 .\" Written by Werner Lemberg (wl@gnu.org)
7 .\" This file is part of groff.
9 .\" groff is free software; you can redistribute it and/or modify it under
10 .\" the terms of the GNU General Public License as published by the Free
11 .\" Software Foundation, either version 3 of the License, or
12 .\" (at your option) any later version.
14 .\" groff is distributed in the hope that it will be useful, but WITHOUT ANY
15 .\" WARRANTY; without even the implied warranty of MERCHANTABILITY or
16 .\" FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
19 .\" You should have received a copy of the GNU General Public License
20 .\" along with this program. If not, see <http://www.gnu.org/licenses/>.
24 .\" This file provides macros for addition, multiplication, and division of
25 .\" 62bit signed integers. Its main application is to `scale' 31bit values,
26 .\" namely, to perform the operation `a * b / c' accurately.
28 .\" Note that it is the duty of the user to check whether the input values
29 .\" fit within 31 bits (this is the range [-1073741824,1073741823]).
36 .\" .add31to62 <x> <y> <z>
38 .\" Add a 31bit signed integer to a signed 62bit integer. Result is a
39 .\" signed 62bit integer:
41 .\" <x> + (<y>h * 2^30 + <y>l) = <z>h * 2^30 + <z>l
44 .\" in: \n[<x>], \n[<y>h], \n[<y>l]
46 .\" out: \n[<z>h], \n[<z>l]
48 .\" Example: .add31to62 p q r
50 .\" -> input registers: \n[p], \n[qh], \n[ql]
51 .\" output registers: \n[rh], \n[rl]
54 . nr 62bit-lo2 (\\n[\\$2l])
55 . nr 62bit-hi2 (\\n[\\$2h])
57 . nr 62bit-i ((\\n[\\$1] + \\n[62bit-lo2]) / 1073741824)
58 . nr \\$3l ((\\n[\\$1] + \\n[62bit-lo2]) % 1073741824)
60 . ie ((\\n[62bit-lo2] > 0) & (\\n[\\$3l] < 0)) \{\
61 . nr \\$3l +1073741824
65 . if ((\\n[62bit-lo2] < 0) & (\\n[\\$3l] > 0)) \{\
66 . nr \\$3l -1073741824
70 . nr \\$3h (\\n[62bit-hi2] + \\n[62bit-i])
74 .\" .mult31by31 <x> <y> <z>
76 .\" Multiply two 31bit signed integers. Result is a 62bit signed
79 .\" <x> * <y> = <z>h * 2^30 + <z>l
82 .\" in: \n[<x>], \n[<y>]
84 .\" out: \n[<z>h], \n[<z>l]
86 .\" Example: .mult31by31 a b c
88 .\" -> input registers: \n[a], \n[b]
89 .\" output registers: \n[ch], \n[cl]
92 . nr 62bit-1 (\\n[\\$1])
93 . nr 62bit-2 (\\n[\\$2])
96 . if !\\n[62bit-1] \{\
97 . nr 62bit-sign -(\\n[62bit-sign])
98 . nr 62bit-1 -(\\n[62bit-1])
100 . if !\\n[62bit-2] \{\
101 . nr 62bit-sign -(\\n[62bit-sign])
102 . nr 62bit-2 -(\\n[62bit-2])
105 . nr 62bit-lo1 (\\n[62bit-1] % 32768)
106 . nr 62bit-hi1 (\\n[62bit-1] / 32768)
107 . nr 62bit-lo2 (\\n[62bit-2] % 32768)
108 . nr 62bit-hi2 (\\n[62bit-2] / 32768)
110 . nr 62bit-lo3 (\\n[62bit-lo1] * \\n[62bit-lo2] % 1073741824)
111 . nr 62bit-i1 (\\n[62bit-lo1] * \\n[62bit-hi2] % 1073741824)
112 . nr 62bit-i2 (\\n[62bit-lo2] * \\n[62bit-hi1] % 1073741824)
113 . nr 62bit-hi3 (\\n[62bit-hi1] * \\n[62bit-hi2] % 1073741824)
115 . nr 62bit-i1 (\\n[62bit-i1] + \\n[62bit-i2] % 1073741824)
116 . \" check carry overflow of 62bit-i1 + 62bit-i2
117 . if (\\n[62bit-i1] < \\n[62bit-i2]) \
118 . nr 62bit-hi3 +32768
120 . nr 62bit-hi3 +(\\n[62bit-i1] / 32768)
121 . \" multiply by 32768 in small steps to avoid overflow
123 . while \\n-[62bit-i] \
124 . nr 62bit-i1 (\\n[62bit-i1] * 2 % 1073741824)
126 . nr 62bit-lo3 (\\n[62bit-lo3] + \\n[62bit-i1] % 1073741824)
127 . \" check carry overflow of 62bit-i1 + lo
128 . if (\\n[62bit-lo3] < \\n[62bit-i1]) \
131 . if !\\n[62bit-sign] \{\
132 . nr 62bit-lo3 -(\\n[62bit-lo3])
133 . nr 62bit-hi3 -(\\n[62bit-hi3])
135 . nr \\$3l \\n[62bit-lo3]
136 . nr \\$3h \\n[62bit-hi3]
140 .\" .div62by31 <x> <y> <z>
142 .\" Divide a signed 62bit integer by a 31bit integer. Result is a
143 .\" 31bit signed integer:
145 .\" (<x>h * 2^30 + <x>l) / <y> = <z>
148 .\" in: \n[<x>h], \n[<x>l], \n[<y>]
152 .\" Example: .div62by31 foo bar baz
154 .\" -> input registers: \n[fooh] \n[fool] \n[bar]
155 .\" output register: \n[baz]
158 . nr 62bit-lo1 \\n[\\$1l]
159 . nr 62bit-hi1 \\n[\\$1h]
160 . nr 62bit-2 \\n[\\$2]
164 . if ((\\n[62bit-lo1] < 0) : (\\n[62bit-hi1] < 0)) \{\
165 . nr 62bit-sign -(\\n[62bit-sign])
166 . nr 62bit-lo1 -(\\n[62bit-lo1])
167 . nr 62bit-hi1 -(\\n[62bit-hi1])
169 . if !\\n[62bit-2] \{\
170 . nr 62bit-sign -(\\n[62bit-sign])
171 . nr 62bit-2 -(\\n[62bit-2])
175 . while \\n-[62bit-i] \{\
176 . nr 62bit-hi1 (\\n[62bit-hi1] * 2 % 1073741824)
177 . nr 62bit-3 (\\n[62bit-3] * 2)
178 . nr 62bit-hi1 +(\\n[62bit-lo1] / 536870912)
180 . if (\\n[62bit-hi1] >= \\n[62bit-2]) \{\
181 . nr 62bit-hi1 -\\n[62bit-2]
184 . nr 62bit-lo1 (\\n[62bit-lo1] * 2 % 1073741824)
187 . if !\\n[62bit-sign] \
188 . nr 62bit-3 -(\\n[62bit-3])
189 . nr \\$3 \\n[62bit-3]