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perl 5.002gamma: utils/h2xs.PL
[perl5.git] / lib / Math / BigInt.pm
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1package Math::BigInt;
2
3%OVERLOAD = (
4 # Anonymous subroutines:
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5'+' => sub {new Math::BigInt &badd},
6'-' => sub {new Math::BigInt
a0d0e21e 7 $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])},
748a9306 8'<=>' => sub {new Math::BigInt
a0d0e21e 9 $_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])},
748a9306 10'cmp' => sub {new Math::BigInt
a0d0e21e 11 $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
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12'*' => sub {new Math::BigInt &bmul},
13'/' => sub {new Math::BigInt
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14 $_[2]? scalar bdiv($_[1],${$_[0]}) :
15 scalar bdiv(${$_[0]},$_[1])},
748a9306 16'%' => sub {new Math::BigInt
a0d0e21e 17 $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])},
748a9306 18'**' => sub {new Math::BigInt
a0d0e21e 19 $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])},
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20'neg' => sub {new Math::BigInt &bneg},
21'abs' => sub {new Math::BigInt &babs},
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22
23qw(
24"" stringify
250+ numify) # Order of arguments unsignificant
26);
27
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28$NaNOK=1;
29
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30sub new {
31 my $foo = bnorm($_[1]);
748a9306 32 die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN";
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33 bless \$foo;
34}
35sub stringify { "${$_[0]}" }
36sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
37 # comparing to direct compilation based on
38 # stringify
39
40# arbitrary size integer math package
41#
42# by Mark Biggar
43#
44# Canonical Big integer value are strings of the form
45# /^[+-]\d+$/ with leading zeros suppressed
46# Input values to these routines may be strings of the form
47# /^\s*[+-]?[\d\s]+$/.
48# Examples:
49# '+0' canonical zero value
50# ' -123 123 123' canonical value '-123123123'
51# '1 23 456 7890' canonical value '+1234567890'
52# Output values always always in canonical form
53#
54# Actual math is done in an internal format consisting of an array
55# whose first element is the sign (/^[+-]$/) and whose remaining
56# elements are base 100000 digits with the least significant digit first.
57# The string 'NaN' is used to represent the result when input arguments
58# are not numbers, as well as the result of dividing by zero
59#
60# routines provided are:
61#
62# bneg(BINT) return BINT negation
63# babs(BINT) return BINT absolute value
64# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0)
65# badd(BINT,BINT) return BINT addition
66# bsub(BINT,BINT) return BINT subtraction
67# bmul(BINT,BINT) return BINT multiplication
68# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
69# bmod(BINT,BINT) return BINT modulus
70# bgcd(BINT,BINT) return BINT greatest common divisor
71# bnorm(BINT) return BINT normalization
72#
73
74$zero = 0;
75
76\f
77# normalize string form of number. Strip leading zeros. Strip any
78# white space and add a sign, if missing.
79# Strings that are not numbers result the value 'NaN'.
80
81sub bnorm { #(num_str) return num_str
82 local($_) = @_;
83 s/\s+//g; # strip white space
84 if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
85 substr($_,$[,0) = '+' unless $1; # Add missing sign
86 s/^-0/+0/;
87 $_;
88 } else {
89 'NaN';
90 }
91}
92
93# Convert a number from string format to internal base 100000 format.
94# Assumes normalized value as input.
95sub internal { #(num_str) return int_num_array
96 local($d) = @_;
97 ($is,$il) = (substr($d,$[,1),length($d)-2);
98 substr($d,$[,1) = '';
99 ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
100}
101
102# Convert a number from internal base 100000 format to string format.
103# This routine scribbles all over input array.
104sub external { #(int_num_array) return num_str
105 $es = shift;
106 grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad
107 &bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
108}
109
110# Negate input value.
111sub bneg { #(num_str) return num_str
112 local($_) = &bnorm(@_);
113 vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
114 s/^H/N/;
115 $_;
116}
117
118# Returns the absolute value of the input.
119sub babs { #(num_str) return num_str
120 &abs(&bnorm(@_));
121}
122
123sub abs { # post-normalized abs for internal use
124 local($_) = @_;
125 s/^-/+/;
126 $_;
127}
128\f
129# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
130sub bcmp { #(num_str, num_str) return cond_code
131 local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
132 if ($x eq 'NaN') {
133 undef;
134 } elsif ($y eq 'NaN') {
135 undef;
136 } else {
137 &cmp($x,$y);
138 }
139}
140
141sub cmp { # post-normalized compare for internal use
142 local($cx, $cy) = @_;
143 $cx cmp $cy
144 &&
145 (
146 ord($cy) <=> ord($cx)
147 ||
148 ($cx cmp ',') * (length($cy) <=> length($cx) || $cy cmp $cx)
149 );
150}
151
152sub badd { #(num_str, num_str) return num_str
153 local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
154 if ($x eq 'NaN') {
155 'NaN';
156 } elsif ($y eq 'NaN') {
157 'NaN';
158 } else {
159 @x = &internal($x); # convert to internal form
160 @y = &internal($y);
161 local($sx, $sy) = (shift @x, shift @y); # get signs
162 if ($sx eq $sy) {
163 &external($sx, &add(*x, *y)); # if same sign add
164 } else {
165 ($x, $y) = (&abs($x),&abs($y)); # make abs
166 if (&cmp($y,$x) > 0) {
167 &external($sy, &sub(*y, *x));
168 } else {
169 &external($sx, &sub(*x, *y));
170 }
171 }
172 }
173}
174
175sub bsub { #(num_str, num_str) return num_str
176 &badd($_[$[],&bneg($_[$[+1]));
177}
178
179# GCD -- Euclids algorithm Knuth Vol 2 pg 296
180sub bgcd { #(num_str, num_str) return num_str
181 local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
182 if ($x eq 'NaN' || $y eq 'NaN') {
183 'NaN';
184 } else {
185 ($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0';
186 $x;
187 }
188}
189\f
190# routine to add two base 1e5 numbers
191# stolen from Knuth Vol 2 Algorithm A pg 231
192# there are separate routines to add and sub as per Kunth pg 233
193sub add { #(int_num_array, int_num_array) return int_num_array
194 local(*x, *y) = @_;
195 $car = 0;
196 for $x (@x) {
197 last unless @y || $car;
198 $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5);
199 }
200 for $y (@y) {
201 last unless $car;
202 $y -= 1e5 if $car = (($y += $car) >= 1e5);
203 }
204 (@x, @y, $car);
205}
206
207# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
208sub sub { #(int_num_array, int_num_array) return int_num_array
209 local(*sx, *sy) = @_;
210 $bar = 0;
211 for $sx (@sx) {
212 last unless @y || $bar;
213 $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
214 }
215 @sx;
216}
217
218# multiply two numbers -- stolen from Knuth Vol 2 pg 233
219sub bmul { #(num_str, num_str) return num_str
220 local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
221 if ($x eq 'NaN') {
222 'NaN';
223 } elsif ($y eq 'NaN') {
224 'NaN';
225 } else {
226 @x = &internal($x);
227 @y = &internal($y);
228 &external(&mul(*x,*y));
229 }
230}
231
232# multiply two numbers in internal representation
233# destroys the arguments, supposes that two arguments are different
234sub mul { #(*int_num_array, *int_num_array) return int_num_array
235 local(*x, *y) = (shift, shift);
236 local($signr) = (shift @x ne shift @y) ? '-' : '+';
237 @prod = ();
238 for $x (@x) {
239 ($car, $cty) = (0, $[);
240 for $y (@y) {
241 $prod = $x * $y + $prod[$cty] + $car;
242 $prod[$cty++] =
243 $prod - ($car = int($prod * 1e-5)) * 1e5;
244 }
245 $prod[$cty] += $car if $car;
246 $x = shift @prod;
247 }
248 ($signr, @x, @prod);
249}
250
251# modulus
252sub bmod { #(num_str, num_str) return num_str
253 (&bdiv(@_))[$[+1];
254}
255\f
256sub bdiv { #(dividend: num_str, divisor: num_str) return num_str
257 local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
258 return wantarray ? ('NaN','NaN') : 'NaN'
259 if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
260 return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
261 @x = &internal($x); @y = &internal($y);
262 $srem = $y[$[];
263 $sr = (shift @x ne shift @y) ? '-' : '+';
264 $car = $bar = $prd = 0;
265 if (($dd = int(1e5/($y[$#y]+1))) != 1) {
266 for $x (@x) {
267 $x = $x * $dd + $car;
268 $x -= ($car = int($x * 1e-5)) * 1e5;
269 }
270 push(@x, $car); $car = 0;
271 for $y (@y) {
272 $y = $y * $dd + $car;
273 $y -= ($car = int($y * 1e-5)) * 1e5;
274 }
275 }
276 else {
277 push(@x, 0);
278 }
279 @q = (); ($v2,$v1) = @y[-2,-1];
280 while ($#x > $#y) {
281 ($u2,$u1,$u0) = @x[-3..-1];
282 $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
283 --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
284 if ($q) {
285 ($car, $bar) = (0,0);
286 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
287 $prd = $q * $y[$y] + $car;
288 $prd -= ($car = int($prd * 1e-5)) * 1e5;
289 $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
290 }
291 if ($x[$#x] < $car + $bar) {
292 $car = 0; --$q;
293 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
294 $x[$x] -= 1e5
295 if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
296 }
297 }
298 }
299 pop(@x); unshift(@q, $q);
300 }
301 if (wantarray) {
302 @d = ();
303 if ($dd != 1) {
304 $car = 0;
305 for $x (reverse @x) {
306 $prd = $car * 1e5 + $x;
307 $car = $prd - ($tmp = int($prd / $dd)) * $dd;
308 unshift(@d, $tmp);
309 }
310 }
311 else {
312 @d = @x;
313 }
314 (&external($sr, @q), &external($srem, @d, $zero));
315 } else {
316 &external($sr, @q);
317 }
318}
319
320# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
321sub bpow { #(num_str, num_str) return num_str
322 local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
323 if ($x eq 'NaN') {
324 'NaN';
325 } elsif ($y eq 'NaN') {
326 'NaN';
327 } elsif ($x eq '+1') {
328 '+1';
329 } elsif ($x eq '-1') {
330 &bmod($x,2) ? '-1': '+1';
331 } elsif ($y =~ /^-/) {
332 'NaN';
333 } elsif ($x eq '+0' && $y eq '+0') {
334 'NaN';
335 } else {
336 @x = &internal($x);
337 local(@pow2)=@x;
338 local(@pow)=&internal("+1");
339 local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul
340 while ($y ne '+0') {
341 ($y,$res)=&bdiv($y,2);
342 if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);}
343 if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);}
344 }
345 &external(@pow);
346 }
347}
348
3491;