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perl 5.0 alpha 5
[perl5.git] / lib / bigint.pl
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1package bigint;
2
3# arbitrary size integer math package
4#
5# by Mark Biggar
6#
7# Canonical Big integer value are strings of the form
8# /^[+-]\d+$/ with leading zeros suppressed
9# Input values to these routines may be strings of the form
10# /^\s*[+-]?[\d\s]+$/.
11# Examples:
12# '+0' canonical zero value
13# ' -123 123 123' canonical value '-123123123'
14# '1 23 456 7890' canonical value '+1234567890'
15# Output values always always in canonical form
16#
17# Actual math is done in an internal format consisting of an array
18# whose first element is the sign (/^[+-]$/) and whose remaining
19# elements are base 100000 digits with the least significant digit first.
20# The string 'NaN' is used to represent the result when input arguments
21# are not numbers, as well as the result of dividing by zero
22#
23# routines provided are:
24#
25# bneg(BINT) return BINT negation
26# babs(BINT) return BINT absolute value
27# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0)
28# badd(BINT,BINT) return BINT addition
29# bsub(BINT,BINT) return BINT subtraction
30# bmul(BINT,BINT) return BINT multiplication
31# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
32# bmod(BINT,BINT) return BINT modulus
33# bgcd(BINT,BINT) return BINT greatest common divisor
34# bnorm(BINT) return BINT normalization
35#
36\f
37# normalize string form of number. Strip leading zeros. Strip any
38# white space and add a sign, if missing.
39# Strings that are not numbers result the value 'NaN'.
40sub main'bnorm { #(num_str) return num_str
41 local($_) = @_;
42 s/\s+//g; # strip white space
43 if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
79072805 44 substr($_,$[,0) = '+' unless $1; # Add missing sign
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45 s/^-0/+0/;
46 $_;
47 } else {
48 'NaN';
49 }
50}
51
52# Convert a number from string format to internal base 100000 format.
53# Assumes normalized value as input.
54sub internal { #(num_str) return int_num_array
55 local($d) = @_;
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56 ($is,$il) = (substr($d,$[,1),length($d)-2);
57 substr($d,$[,1) = '';
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58 ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
59}
60
61# Convert a number from internal base 100000 format to string format.
62# This routine scribbles all over input array.
63sub external { #(int_num_array) return num_str
64 $es = shift;
65 grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad
66 &'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
67}
68
69# Negate input value.
70sub main'bneg { #(num_str) return num_str
71 local($_) = &'bnorm(@_);
72 vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
73 s/^H/N/;
74 $_;
75}
76
77# Returns the absolute value of the input.
78sub main'babs { #(num_str) return num_str
79 &abs(&'bnorm(@_));
80}
81
82sub abs { # post-normalized abs for internal use
83 local($_) = @_;
84 s/^-/+/;
85 $_;
86}
87\f
88# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
89sub main'bcmp { #(num_str, num_str) return cond_code
79072805 90 local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
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91 if ($x eq 'NaN') {
92 undef;
93 } elsif ($y eq 'NaN') {
94 undef;
95 } else {
96 &cmp($x,$y);
97 }
98}
99
100sub cmp { # post-normalized compare for internal use
101 local($cx, $cy) = @_;
102 $cx cmp $cy
103 &&
104 (
105 ord($cy) <=> ord($cx)
106 ||
107 ($cx cmp ',') * (length($cy) <=> length($cx) || $cy cmp $cx)
108 );
109}
110
111sub main'badd { #(num_str, num_str) return num_str
79072805 112 local(*x, *y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
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113 if ($x eq 'NaN') {
114 'NaN';
115 } elsif ($y eq 'NaN') {
116 'NaN';
117 } else {
118 @x = &internal($x); # convert to internal form
119 @y = &internal($y);
120 local($sx, $sy) = (shift @x, shift @y); # get signs
121 if ($sx eq $sy) {
122 &external($sx, &add(*x, *y)); # if same sign add
123 } else {
124 ($x, $y) = (&abs($x),&abs($y)); # make abs
125 if (&cmp($y,$x) > 0) {
126 &external($sy, &sub(*y, *x));
127 } else {
128 &external($sx, &sub(*x, *y));
129 }
130 }
131 }
132}
133
134sub main'bsub { #(num_str, num_str) return num_str
79072805 135 &'badd($_[$[],&'bneg($_[$[+1]));
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136}
137
138# GCD -- Euclids algorithm Knuth Vol 2 pg 296
139sub main'bgcd { #(num_str, num_str) return num_str
79072805 140 local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
68decaef 141 if ($x eq 'NaN' || $y eq 'NaN') {
5303340c 142 'NaN';
68decaef 143 } else {
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144 ($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
145 $x;
146 }
147}
148\f
68decaef 149# routine to add two base 1e5 numbers
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150# stolen from Knuth Vol 2 Algorithm A pg 231
151# there are separate routines to add and sub as per Kunth pg 233
152sub add { #(int_num_array, int_num_array) return int_num_array
153 local(*x, *y) = @_;
154 $car = 0;
155 for $x (@x) {
156 last unless @y || $car;
e334a159 157 $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5);
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158 }
159 for $y (@y) {
160 last unless $car;
68decaef 161 $y -= 1e5 if $car = (($y += $car) >= 1e5);
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162 }
163 (@x, @y, $car);
164}
165
68decaef 166# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
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167sub sub { #(int_num_array, int_num_array) return int_num_array
168 local(*sx, *sy) = @_;
169 $bar = 0;
170 for $sx (@sx) {
171 last unless @y || $bar;
e334a159 172 $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
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173 }
174 @sx;
175}
176
177# multiply two numbers -- stolen from Knuth Vol 2 pg 233
178sub main'bmul { #(num_str, num_str) return num_str
79072805 179 local(*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
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180 if ($x eq 'NaN') {
181 'NaN';
182 } elsif ($y eq 'NaN') {
183 'NaN';
184 } else {
185 @x = &internal($x);
186 @y = &internal($y);
187 local($signr) = (shift @x ne shift @y) ? '-' : '+';
188 @prod = ();
189 for $x (@x) {
79072805 190 ($car, $cty) = (0, $[);
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191 for $y (@y) {
192 $prod = $x * $y + $prod[$cty] + $car;
193 $prod[$cty++] =
68decaef 194 $prod - ($car = int($prod * 1e-5)) * 1e5;
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195 }
196 $prod[$cty] += $car if $car;
197 $x = shift @prod;
198 }
199 &external($signr, @x, @prod);
200 }
201}
202
203# modulus
204sub main'bmod { #(num_str, num_str) return num_str
79072805 205 (&'bdiv(@_))[$[+1];
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206}
207\f
208sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
79072805 209 local (*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
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210 return wantarray ? ('NaN','NaN') : 'NaN'
211 if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
212 return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
213 @x = &internal($x); @y = &internal($y);
79072805 214 $srem = $y[$[];
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215 $sr = (shift @x ne shift @y) ? '-' : '+';
216 $car = $bar = $prd = 0;
68decaef 217 if (($dd = int(1e5/($y[$#y]+1))) != 1) {
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218 for $x (@x) {
219 $x = $x * $dd + $car;
68decaef 220 $x -= ($car = int($x * 1e-5)) * 1e5;
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221 }
222 push(@x, $car); $car = 0;
223 for $y (@y) {
224 $y = $y * $dd + $car;
68decaef 225 $y -= ($car = int($y * 1e-5)) * 1e5;
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226 }
227 }
228 else {
229 push(@x, 0);
230 }
ed6116ce 231 @q = (); ($v2,$v1) = @y[-2,-1];
5303340c 232 while ($#x > $#y) {
ed6116ce 233 ($u2,$u1,$u0) = @x[-3..-1];
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234 $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
235 --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
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236 if ($q) {
237 ($car, $bar) = (0,0);
79072805 238 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
5303340c 239 $prd = $q * $y[$y] + $car;
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240 $prd -= ($car = int($prd * 1e-5)) * 1e5;
241 $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
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242 }
243 if ($x[$#x] < $car + $bar) {
244 $car = 0; --$q;
79072805 245 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
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246 $x[$x] -= 1e5
247 if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
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248 }
249 }
250 }
251 pop(@x); unshift(@q, $q);
252 }
253 if (wantarray) {
254 @d = ();
255 if ($dd != 1) {
256 $car = 0;
257 for $x (reverse @x) {
68decaef 258 $prd = $car * 1e5 + $x;
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259 $car = $prd - ($tmp = int($prd / $dd)) * $dd;
260 unshift(@d, $tmp);
261 }
262 }
263 else {
264 @d = @x;
265 }
266 (&external($sr, @q), &external($srem, @d, 0));
267 } else {
268 &external($sr, @q);
269 }
270}
2711;