4 '+' => sub {new Math::BigInt &badd},
5 '-' => sub {new Math::BigInt
6 $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])},
7 '<=>' => sub {$_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])},
8 'cmp' => sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
9 '*' => sub {new Math::BigInt &bmul},
10 '/' => sub {new Math::BigInt
11 $_[2]? scalar bdiv($_[1],${$_[0]}) :
12 scalar bdiv(${$_[0]},$_[1])},
13 '%' => sub {new Math::BigInt
14 $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])},
15 '**' => sub {new Math::BigInt
16 $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])},
17 'neg' => sub {new Math::BigInt &bneg},
18 'abs' => sub {new Math::BigInt &babs},
22 0+ numify) # Order of arguments unsignificant
29 my($foo) = bnorm(shift);
30 die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN";
33 sub stringify { "${$_[0]}" }
34 sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
35 # comparing to direct compilation based on
40 die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
41 overload::constant integer => sub {Math::BigInt->new(shift)};
47 # normalize string form of number. Strip leading zeros. Strip any
48 # white space and add a sign, if missing.
49 # Strings that are not numbers result the value 'NaN'.
51 sub bnorm { #(num_str) return num_str
53 s/\s+//g; # strip white space
54 if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
55 substr($_,$[,0) = '+' unless $1; # Add missing sign
63 # Convert a number from string format to internal base 100000 format.
64 # Assumes normalized value as input.
65 sub internal { #(num_str) return int_num_array
67 ($is,$il) = (substr($d,$[,1),length($d)-2);
69 ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
72 # Convert a number from internal base 100000 format to string format.
73 # This routine scribbles all over input array.
74 sub external { #(int_num_array) return num_str
76 grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad
77 &bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
81 sub bneg { #(num_str) return num_str
82 local($_) = &bnorm(@_);
83 return $_ if $_ eq '+0' or $_ eq 'NaN';
84 vec($_,0,8) ^= ord('+') ^ ord('-');
88 # Returns the absolute value of the input.
89 sub babs { #(num_str) return num_str
93 sub abs { # post-normalized abs for internal use
99 # Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
100 sub bcmp { #(num_str, num_str) return cond_code
101 local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
104 } elsif ($y eq 'NaN') {
111 sub cmp { # post-normalized compare for internal use
112 local($cx, $cy) = @_;
114 return 0 if ($cx eq $cy);
116 local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
120 return 1 if ($sy eq '-' || $cy eq '+0');
121 $ld = length($cx) - length($cy);
124 } else { # $sx eq '-'
125 return -1 if ($sy eq '+');
126 $ld = length($cy) - length($cx);
132 sub badd { #(num_str, num_str) return num_str
133 local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
136 } elsif ($y eq 'NaN') {
139 @x = &internal($x); # convert to internal form
141 local($sx, $sy) = (shift @x, shift @y); # get signs
143 &external($sx, &add(*x, *y)); # if same sign add
145 ($x, $y) = (&abs($x),&abs($y)); # make abs
146 if (&cmp($y,$x) > 0) {
147 &external($sy, &sub(*y, *x));
149 &external($sx, &sub(*x, *y));
155 sub bsub { #(num_str, num_str) return num_str
156 &badd($_[$[],&bneg($_[$[+1]));
159 # GCD -- Euclids algorithm Knuth Vol 2 pg 296
160 sub bgcd { #(num_str, num_str) return num_str
161 local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
162 if ($x eq 'NaN' || $y eq 'NaN') {
165 ($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0';
170 # routine to add two base 1e5 numbers
171 # stolen from Knuth Vol 2 Algorithm A pg 231
172 # there are separate routines to add and sub as per Kunth pg 233
173 sub add { #(int_num_array, int_num_array) return int_num_array
177 last unless @y || $car;
178 $x -= 1e5 if $car = (($x += (@y ? shift(@y) : 0) + $car) >= 1e5) ? 1 : 0;
182 $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
187 # subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
188 sub sub { #(int_num_array, int_num_array) return int_num_array
189 local(*sx, *sy) = @_;
192 last unless @sy || $bar;
193 $sx += 1e5 if $bar = (($sx -= (@sy ? shift(@sy) : 0) + $bar) < 0);
198 # multiply two numbers -- stolen from Knuth Vol 2 pg 233
199 sub bmul { #(num_str, num_str) return num_str
200 local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
203 } elsif ($y eq 'NaN') {
208 &external(&mul(*x,*y));
212 # multiply two numbers in internal representation
213 # destroys the arguments, supposes that two arguments are different
214 sub mul { #(*int_num_array, *int_num_array) return int_num_array
215 local(*x, *y) = (shift, shift);
216 local($signr) = (shift @x ne shift @y) ? '-' : '+';
219 ($car, $cty) = (0, $[);
221 $prod = $x * $y + ($prod[$cty] || 0) + $car;
223 $prod - ($car = int($prod * 1e-5)) * 1e5;
225 $prod[$cty] += $car if $car;
232 sub bmod { #(num_str, num_str) return num_str
236 sub bdiv { #(dividend: num_str, divisor: num_str) return num_str
237 local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
238 return wantarray ? ('NaN','NaN') : 'NaN'
239 if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
240 return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
241 @x = &internal($x); @y = &internal($y);
243 $sr = (shift @x ne shift @y) ? '-' : '+';
244 $car = $bar = $prd = 0;
245 if (($dd = int(1e5/($y[$#y]+1))) != 1) {
247 $x = $x * $dd + $car;
248 $x -= ($car = int($x * 1e-5)) * 1e5;
250 push(@x, $car); $car = 0;
252 $y = $y * $dd + $car;
253 $y -= ($car = int($y * 1e-5)) * 1e5;
259 @q = (); ($v2,$v1) = @y[-2,-1];
262 ($u2,$u1,$u0) = @x[-3..-1];
264 $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
265 --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
267 ($car, $bar) = (0,0);
268 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
269 $prd = $q * $y[$y] + $car;
270 $prd -= ($car = int($prd * 1e-5)) * 1e5;
271 $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
273 if ($x[$#x] < $car + $bar) {
275 for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
277 if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
281 pop(@x); unshift(@q, $q);
287 for $x (reverse @x) {
288 $prd = $car * 1e5 + $x;
289 $car = $prd - ($tmp = int($prd / $dd)) * $dd;
296 (&external($sr, @q), &external($srem, @d, $zero));
302 # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
303 sub bpow { #(num_str, num_str) return num_str
304 local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
307 } elsif ($y eq 'NaN') {
309 } elsif ($x eq '+1') {
311 } elsif ($x eq '-1') {
312 &bmod($x,2) ? '-1': '+1';
313 } elsif ($y =~ /^-/) {
315 } elsif ($x eq '+0' && $y eq '+0') {
320 local(@pow)=&internal("+1");
321 local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul
323 ($y,$res)=&bdiv($y,2);
324 if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);}
325 if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);}
336 Math::BigInt - Arbitrary size integer math package
341 $i = Math::BigInt->new($string);
343 $i->bneg return BINT negation
344 $i->babs return BINT absolute value
345 $i->bcmp(BINT) return CODE compare numbers (undef,<0,=0,>0)
346 $i->badd(BINT) return BINT addition
347 $i->bsub(BINT) return BINT subtraction
348 $i->bmul(BINT) return BINT multiplication
349 $i->bdiv(BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
350 $i->bmod(BINT) return BINT modulus
351 $i->bgcd(BINT) return BINT greatest common divisor
352 $i->bnorm return BINT normalization
356 All basic math operations are overloaded if you declare your big
359 $i = new Math::BigInt '123 456 789 123 456 789';
364 =item Canonical notation
366 Big integer value are strings of the form C</^[+-]\d+$/> with leading
371 Input values to these routines may be strings of the form
372 C</^\s*[+-]?[\d\s]+$/>.
376 Output values always always in canonical form
380 Actual math is done in an internal format consisting of an array
381 whose first element is the sign (/^[+-]$/) and whose remaining
382 elements are base 100000 digits with the least significant digit first.
383 The string 'NaN' is used to represent the result when input arguments
384 are not numbers, as well as the result of dividing by zero.
388 '+0' canonical zero value
389 ' -123 123 123' canonical value '-123123123'
390 '1 23 456 7890' canonical value '+1234567890'
393 =head1 Autocreating constants
395 After C<use Math::BigInt ':constant'> all the integer decimal constants
396 in the given scope are converted to C<Math::BigInt>. This conversion
397 happens at compile time.
401 perl -MMath::BigInt=:constant -e 'print 2**100'
403 print the integer value of C<2**100>. Note that without conversion of
404 constants the expression 2**100 will be calculated as floating point number.
408 The current version of this module is a preliminary version of the
409 real thing that is currently (as of perl5.002) under development.
413 Mark Biggar, overloaded interface by Ilya Zakharevich.