bigint.pl revision 7c478bd95313f5f23a4c958a745db2134aa03244
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.
#
# 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;
}
$zero = 0;
# normalize string form of number. Strip leading zeros. Strip any
# white space and add a sign, if missing.
# Strings that are not numbers result the value 'NaN'.
sub main'bnorm { #(num_str) return num_str
local($_) = @_;
s/\s+//g; # strip white space
if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
substr($_,$[,0) = '+' 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) = @_;
substr($d,$[,1) = '';
}
# 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/^-/+/;
$_;
}
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
if ($x eq 'NaN') {
undef;
} elsif ($y eq 'NaN') {
undef;
} else {
&cmp($x,$y);
}
}
sub cmp { # post-normalized compare for internal use
local($ld);
if ($sx eq '+') {
} else { # $sx eq '-'
}
}
sub main'badd { #(num_str, num_str) return num_str
if ($x eq 'NaN') {
'NaN';
} elsif ($y eq 'NaN') {
'NaN';
} else {
@x = &internal($x); # convert to internal form
@y = &internal($y);
} else {
if (&cmp($y,$x) > 0) {
} else {
}
}
}
}
sub main'bsub { #(num_str, num_str) return num_str
}
# GCD -- Euclids algorithm Knuth Vol 2 pg 296
sub main'bgcd { #(num_str, num_str) return num_str
if ($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;
}
for $y (@y) {
last unless $car;
}
(@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
$bar = 0;
last unless @y || $bar;
}
@sx;
}
# multiply two numbers -- stolen from Knuth Vol 2 pg 233
sub main'bmul { #(num_str, num_str) return num_str
if ($x eq 'NaN') {
'NaN';
} elsif ($y eq 'NaN') {
'NaN';
} else {
@x = &internal($x);
@y = &internal($y);
@prod = ();
for $x (@x) {
for $y (@y) {
if ($use_mult) {
}
else {
}
}
$x = shift @prod;
}
}
}
# modulus
sub main'bmod { #(num_str, num_str) return num_str
(&'bdiv(@_))[$[+1];
}
sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
return wantarray ? ('NaN','NaN') : 'NaN'
if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
$srem = $y[$[];
for $x (@x) {
if ($use_mult) {
}
else {
}
}
for $y (@y) {
if ($use_mult) {
}
else {
}
}
}
else {
push(@x, 0);
}
while ($#x > $#y) {
if ($q) {
for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
if ($use_mult) {
}
else {
}
}
if ($x[$#x] < $car + $bar) {
$car = 0; --$q;
for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
$x[$x] -= 1e5
}
}
}
pop(@x); unshift(@q, $q);
}
if (wantarray) {
@d = ();
if ($dd != 1) {
$car = 0;
for $x (reverse @x) {
unshift(@d, $tmp);
}
}
else {
@d = @x;
}
} else {
}
}
1;