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root |
1.1 |
package bigint; |
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# |
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# This library is no longer being maintained, and is included for backward |
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# compatibility with Perl 4 programs which may require it. |
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# |
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# In particular, this should not be used as an example of modern Perl |
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# programming techniques. |
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# |
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# Suggested alternative: Math::BigInt |
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# |
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# arbitrary size integer math package |
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# |
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# by Mark Biggar |
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# |
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# Canonical Big integer value are strings of the form |
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# /^[+-]\d+$/ with leading zeros suppressed |
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# Input values to these routines may be strings of the form |
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# /^\s*[+-]?[\d\s]+$/. |
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# Examples: |
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# '+0' canonical zero value |
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# ' -123 123 123' canonical value '-123123123' |
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# '1 23 456 7890' canonical value '+1234567890' |
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# Output values always in canonical form |
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# |
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# Actual math is done in an internal format consisting of an array |
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# whose first element is the sign (/^[+-]$/) and whose remaining |
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# elements are base 100000 digits with the least significant digit first. |
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# The string 'NaN' is used to represent the result when input arguments |
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# are not numbers, as well as the result of dividing by zero |
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# |
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# routines provided are: |
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# |
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# bneg(BINT) return BINT negation |
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# babs(BINT) return BINT absolute value |
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# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0) |
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# badd(BINT,BINT) return BINT addition |
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# bsub(BINT,BINT) return BINT subtraction |
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# bmul(BINT,BINT) return BINT multiplication |
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# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar |
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# bmod(BINT,BINT) return BINT modulus |
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# bgcd(BINT,BINT) return BINT greatest common divisor |
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# bnorm(BINT) return BINT normalization |
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# |
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# overcome a floating point problem on certain osnames (posix-bc, os390) |
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BEGIN { |
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my $x = 100000.0; |
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my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0; |
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} |
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$zero = 0; |
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# normalize string form of number. Strip leading zeros. Strip any |
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# white space and add a sign, if missing. |
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# Strings that are not numbers result the value 'NaN'. |
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sub main'bnorm { #(num_str) return num_str |
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local($_) = @_; |
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s/\s+//g; # strip white space |
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if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number |
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substr($_,$[,0) = '+' unless $1; # Add missing sign |
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s/^-0/+0/; |
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$_; |
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} else { |
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'NaN'; |
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} |
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} |
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# Convert a number from string format to internal base 100000 format. |
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# Assumes normalized value as input. |
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sub internal { #(num_str) return int_num_array |
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local($d) = @_; |
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($is,$il) = (substr($d,$[,1),length($d)-2); |
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substr($d,$[,1) = ''; |
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($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d))); |
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} |
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# Convert a number from internal base 100000 format to string format. |
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# This routine scribbles all over input array. |
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sub external { #(int_num_array) return num_str |
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$es = shift; |
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grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad |
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&'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize |
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} |
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# Negate input value. |
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sub main'bneg { #(num_str) return num_str |
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local($_) = &'bnorm(@_); |
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vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0'; |
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s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC |
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$_; |
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} |
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# Returns the absolute value of the input. |
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sub main'babs { #(num_str) return num_str |
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&abs(&'bnorm(@_)); |
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} |
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sub abs { # post-normalized abs for internal use |
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local($_) = @_; |
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s/^-/+/; |
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$_; |
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} |
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# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) |
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sub main'bcmp { #(num_str, num_str) return cond_code |
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local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); |
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if ($x eq 'NaN') { |
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undef; |
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} elsif ($y eq 'NaN') { |
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undef; |
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} else { |
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&cmp($x,$y); |
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} |
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} |
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sub cmp { # post-normalized compare for internal use |
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local($cx, $cy) = @_; |
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return 0 if ($cx eq $cy); |
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local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1)); |
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local($ld); |
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if ($sx eq '+') { |
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return 1 if ($sy eq '-' || $cy eq '+0'); |
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$ld = length($cx) - length($cy); |
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return $ld if ($ld); |
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return $cx cmp $cy; |
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} else { # $sx eq '-' |
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return -1 if ($sy eq '+'); |
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$ld = length($cy) - length($cx); |
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return $ld if ($ld); |
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return $cy cmp $cx; |
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} |
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} |
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sub main'badd { #(num_str, num_str) return num_str |
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local(*x, *y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); |
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if ($x eq 'NaN') { |
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'NaN'; |
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} elsif ($y eq 'NaN') { |
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'NaN'; |
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} else { |
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@x = &internal($x); # convert to internal form |
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@y = &internal($y); |
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local($sx, $sy) = (shift @x, shift @y); # get signs |
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if ($sx eq $sy) { |
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&external($sx, &add(*x, *y)); # if same sign add |
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} else { |
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($x, $y) = (&abs($x),&abs($y)); # make abs |
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if (&cmp($y,$x) > 0) { |
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&external($sy, &sub(*y, *x)); |
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} else { |
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&external($sx, &sub(*x, *y)); |
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} |
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} |
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} |
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} |
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sub main'bsub { #(num_str, num_str) return num_str |
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&'badd($_[$[],&'bneg($_[$[+1])); |
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} |
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# GCD -- Euclids algorithm Knuth Vol 2 pg 296 |
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sub main'bgcd { #(num_str, num_str) return num_str |
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local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1])); |
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if ($x eq 'NaN' || $y eq 'NaN') { |
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'NaN'; |
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} else { |
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($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0'; |
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$x; |
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} |
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} |
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# routine to add two base 1e5 numbers |
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# stolen from Knuth Vol 2 Algorithm A pg 231 |
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# there are separate routines to add and sub as per Kunth pg 233 |
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sub add { #(int_num_array, int_num_array) return int_num_array |
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local(*x, *y) = @_; |
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$car = 0; |
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for $x (@x) { |
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last unless @y || $car; |
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$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0; |
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} |
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for $y (@y) { |
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last unless $car; |
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$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0; |
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} |
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(@x, @y, $car); |
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} |
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# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
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sub sub { #(int_num_array, int_num_array) return int_num_array |
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local(*sx, *sy) = @_; |
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$bar = 0; |
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for $sx (@sx) { |
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last unless @y || $bar; |
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$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0); |
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} |
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@sx; |
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} |
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# multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
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sub main'bmul { #(num_str, num_str) return num_str |
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local(*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1])); |
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if ($x eq 'NaN') { |
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'NaN'; |
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} elsif ($y eq 'NaN') { |
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'NaN'; |
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} else { |
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@x = &internal($x); |
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@y = &internal($y); |
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local($signr) = (shift @x ne shift @y) ? '-' : '+'; |
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@prod = (); |
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for $x (@x) { |
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($car, $cty) = (0, $[); |
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for $y (@y) { |
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$prod = $x * $y + $prod[$cty] + $car; |
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if ($use_mult) { |
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$prod[$cty++] = |
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$prod - ($car = int($prod * 1e-5)) * 1e5; |
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} |
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else { |
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$prod[$cty++] = |
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$prod - ($car = int($prod / 1e5)) * 1e5; |
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} |
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} |
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$prod[$cty] += $car if $car; |
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$x = shift @prod; |
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} |
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&external($signr, @x, @prod); |
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} |
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} |
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# modulus |
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sub main'bmod { #(num_str, num_str) return num_str |
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(&'bdiv(@_))[$[+1]; |
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} |
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sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str |
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local (*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1])); |
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return wantarray ? ('NaN','NaN') : 'NaN' |
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if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); |
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return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); |
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@x = &internal($x); @y = &internal($y); |
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$srem = $y[$[]; |
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$sr = (shift @x ne shift @y) ? '-' : '+'; |
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$car = $bar = $prd = 0; |
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if (($dd = int(1e5/($y[$#y]+1))) != 1) { |
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for $x (@x) { |
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$x = $x * $dd + $car; |
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if ($use_mult) { |
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$x -= ($car = int($x * 1e-5)) * 1e5; |
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} |
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else { |
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$x -= ($car = int($x / 1e5)) * 1e5; |
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} |
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} |
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push(@x, $car); $car = 0; |
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for $y (@y) { |
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$y = $y * $dd + $car; |
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if ($use_mult) { |
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$y -= ($car = int($y * 1e-5)) * 1e5; |
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} |
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else { |
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$y -= ($car = int($y / 1e5)) * 1e5; |
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} |
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} |
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} |
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else { |
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push(@x, 0); |
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} |
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@q = (); ($v2,$v1) = @y[-2,-1]; |
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while ($#x > $#y) { |
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($u2,$u1,$u0) = @x[-3..-1]; |
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$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1)); |
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--$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2); |
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if ($q) { |
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($car, $bar) = (0,0); |
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for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
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$prd = $q * $y[$y] + $car; |
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if ($use_mult) { |
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$prd -= ($car = int($prd * 1e-5)) * 1e5; |
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} |
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else { |
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$prd -= ($car = int($prd / 1e5)) * 1e5; |
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} |
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$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0)); |
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} |
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if ($x[$#x] < $car + $bar) { |
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$car = 0; --$q; |
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for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) { |
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$x[$x] -= 1e5 |
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if ($car = (($x[$x] += $y[$y] + $car) > 1e5)); |
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} |
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} |
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} |
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pop(@x); unshift(@q, $q); |
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} |
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if (wantarray) { |
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@d = (); |
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if ($dd != 1) { |
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$car = 0; |
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for $x (reverse @x) { |
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$prd = $car * 1e5 + $x; |
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$car = $prd - ($tmp = int($prd / $dd)) * $dd; |
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unshift(@d, $tmp); |
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} |
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} |
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else { |
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@d = @x; |
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} |
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(&external($sr, @q), &external($srem, @d, $zero)); |
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} else { |
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&external($sr, @q); |
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} |
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} |
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1; |
