diff options
Diffstat (limited to 'lib/bigint.pl')
| -rw-r--r-- | lib/bigint.pl | 324 |
1 files changed, 0 insertions, 324 deletions
diff --git a/lib/bigint.pl b/lib/bigint.pl deleted file mode 100644 index 6de1c53fcf..0000000000 --- a/lib/bigint.pl +++ /dev/null @@ -1,324 +0,0 @@ -warn "Legacy library @{[(caller(0))[6]]} will be removed from the Perl core distribution in the next major release. Please install it from the CPAN distribution Perl4::CoreLibs. It is being used at @{[(caller)[1]]}, line @{[(caller)[2]]}.\n"; - -package bigint; -# -# This library is no longer being maintained, and is included for backward -# compatibility with Perl 4 programs which may require it. -# -# In particular, this should not be used as an example of modern Perl -# programming techniques. -# This legacy library is deprecated and will be removed in a future -# release of perl. -# -# Suggested alternative: Math::BigInt - -# arbitrary size integer math package -# -# by Mark Biggar -# -# Canonical Big integer value are strings of the form -# /^[+-]\d+$/ with leading zeros suppressed -# Input values to these routines may be strings of the form -# /^\s*[+-]?[\d\s]+$/. -# Examples: -# '+0' canonical zero value -# ' -123 123 123' canonical value '-123123123' -# '1 23 456 7890' canonical value '+1234567890' -# Output values always in canonical form -# -# Actual math is done in an internal format consisting of an array -# whose first element is the sign (/^[+-]$/) and whose remaining -# elements are base 100000 digits with the least significant digit first. -# The string 'NaN' is used to represent the result when input arguments -# are not numbers, as well as the result of dividing by zero -# -# routines provided are: -# -# bneg(BINT) return BINT negation -# babs(BINT) return BINT absolute value -# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0) -# badd(BINT,BINT) return BINT addition -# bsub(BINT,BINT) return BINT subtraction -# bmul(BINT,BINT) return BINT multiplication -# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar -# bmod(BINT,BINT) return BINT modulus -# bgcd(BINT,BINT) return BINT greatest common divisor -# bnorm(BINT) return BINT normalization -# - -# overcome a floating point problem on certain osnames (posix-bc, os390) -BEGIN { - my $x = 100000.0; - my $use_mult = int($x*1e-5)*1e5 == $x ? 1 : 0; -} - -$zero = 0; - - -# normalize string form of number. Strip leading zeros. Strip any -# white space and add a sign, if missing. -# Strings that are not numbers result the value 'NaN'. - -sub main'bnorm { #(num_str) return num_str - local($_) = @_; - s/\s+//g; # strip white space - if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number - substr($_,0,0) = '+' unless $1; # Add missing sign - s/^-0/+0/; - $_; - } else { - 'NaN'; - } -} - -# Convert a number from string format to internal base 100000 format. -# Assumes normalized value as input. -sub internal { #(num_str) return int_num_array - local($d) = @_; - ($is,$il) = (substr($d,0,1),length($d)-2); - substr($d,0,1) = ''; - ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d))); -} - -# Convert a number from internal base 100000 format to string format. -# This routine scribbles all over input array. -sub external { #(int_num_array) return num_str - $es = shift; - grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad - &'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize -} - -# Negate input value. -sub main'bneg { #(num_str) return num_str - local($_) = &'bnorm(@_); - vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0'; - s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC - $_; -} - -# Returns the absolute value of the input. -sub main'babs { #(num_str) return num_str - &abs(&'bnorm(@_)); -} - -sub abs { # post-normalized abs for internal use - local($_) = @_; - s/^-/+/; - $_; -} - -# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) -sub main'bcmp { #(num_str, num_str) return cond_code - local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1])); - if ($x eq 'NaN') { - undef; - } elsif ($y eq 'NaN') { - undef; - } else { - &cmp($x,$y); - } -} - -sub cmp { # post-normalized compare for internal use - local($cx, $cy) = @_; - return 0 if ($cx eq $cy); - - local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1)); - local($ld); - - if ($sx eq '+') { - return 1 if ($sy eq '-' || $cy eq '+0'); - $ld = length($cx) - length($cy); - return $ld if ($ld); - return $cx cmp $cy; - } else { # $sx eq '-' - return -1 if ($sy eq '+'); - $ld = length($cy) - length($cx); - return $ld if ($ld); - return $cy cmp $cx; - } - -} - -sub main'badd { #(num_str, num_str) return num_str - local(*x, *y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1])); - if ($x eq 'NaN') { - 'NaN'; - } elsif ($y eq 'NaN') { - 'NaN'; - } else { - @x = &internal($x); # convert to internal form - @y = &internal($y); - local($sx, $sy) = (shift @x, shift @y); # get signs - if ($sx eq $sy) { - &external($sx, &add(*x, *y)); # if same sign add - } else { - ($x, $y) = (&abs($x),&abs($y)); # make abs - if (&cmp($y,$x) > 0) { - &external($sy, &sub(*y, *x)); - } else { - &external($sx, &sub(*x, *y)); - } - } - } -} - -sub main'bsub { #(num_str, num_str) return num_str - &'badd($_[0],&'bneg($_[1])); -} - -# GCD -- Euclid's algorithm Knuth Vol 2 pg 296 -sub main'bgcd { #(num_str, num_str) return num_str - local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1])); - if ($x eq 'NaN' || $y eq 'NaN') { - 'NaN'; - } else { - ($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0'; - $x; - } -} - -# routine to add two base 1e5 numbers -# stolen from Knuth Vol 2 Algorithm A pg 231 -# there are separate routines to add and sub as per Kunth pg 233 -sub add { #(int_num_array, int_num_array) return int_num_array - local(*x, *y) = @_; - $car = 0; - for $x (@x) { - last unless @y || $car; - $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0; - } - for $y (@y) { - last unless $car; - $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0; - } - (@x, @y, $car); -} - -# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y -sub sub { #(int_num_array, int_num_array) return int_num_array - local(*sx, *sy) = @_; - $bar = 0; - for $sx (@sx) { - last unless @y || $bar; - $sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0); - } - @sx; -} - -# multiply two numbers -- stolen from Knuth Vol 2 pg 233 -sub main'bmul { #(num_str, num_str) return num_str - local(*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); - if ($x eq 'NaN') { - 'NaN'; - } elsif ($y eq 'NaN') { - 'NaN'; - } else { - @x = &internal($x); - @y = &internal($y); - local($signr) = (shift @x ne shift @y) ? '-' : '+'; - @prod = (); - for $x (@x) { - ($car, $cty) = (0, 0); - for $y (@y) { - $prod = $x * $y + $prod[$cty] + $car; - if ($use_mult) { - $prod[$cty++] = - $prod - ($car = int($prod * 1e-5)) * 1e5; - } - else { - $prod[$cty++] = - $prod - ($car = int($prod / 1e5)) * 1e5; - } - } - $prod[$cty] += $car if $car; - $x = shift @prod; - } - &external($signr, @x, @prod); - } -} - -# modulus -sub main'bmod { #(num_str, num_str) return num_str - (&'bdiv(@_))[1]; -} - -sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str - local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); - return wantarray ? ('NaN','NaN') : 'NaN' - if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); - return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); - @x = &internal($x); @y = &internal($y); - $srem = $y[0]; - $sr = (shift @x ne shift @y) ? '-' : '+'; - $car = $bar = $prd = 0; - if (($dd = int(1e5/($y[$#y]+1))) != 1) { - for $x (@x) { - $x = $x * $dd + $car; - if ($use_mult) { - $x -= ($car = int($x * 1e-5)) * 1e5; - } - else { - $x -= ($car = int($x / 1e5)) * 1e5; - } - } - push(@x, $car); $car = 0; - for $y (@y) { - $y = $y * $dd + $car; - if ($use_mult) { - $y -= ($car = int($y * 1e-5)) * 1e5; - } - else { - $y -= ($car = int($y / 1e5)) * 1e5; - } - } - } - else { - push(@x, 0); - } - @q = (); ($v2,$v1) = @y[-2,-1]; - while ($#x > $#y) { - ($u2,$u1,$u0) = @x[-3..-1]; - $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1)); - --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2); - if ($q) { - ($car, $bar) = (0,0); - for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { - $prd = $q * $y[$y] + $car; - if ($use_mult) { - $prd -= ($car = int($prd * 1e-5)) * 1e5; - } - else { - $prd -= ($car = int($prd / 1e5)) * 1e5; - } - $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0)); - } - if ($x[$#x] < $car + $bar) { - $car = 0; --$q; - for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { - $x[$x] -= 1e5 - if ($car = (($x[$x] += $y[$y] + $car) > 1e5)); - } - } - } - pop(@x); unshift(@q, $q); - } - if (wantarray) { - @d = (); - if ($dd != 1) { - $car = 0; - for $x (reverse @x) { - $prd = $car * 1e5 + $x; - $car = $prd - ($tmp = int($prd / $dd)) * $dd; - unshift(@d, $tmp); - } - } - else { - @d = @x; - } - (&external($sr, @q), &external($srem, @d, $zero)); - } else { - &external($sr, @q); - } -} -1; |