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
# '+0' canonical zero value
# ' -123 123 123' canonical value '-123123123'
# '1 23 456 7890' canonical value '+1234567890'
-# Output values always always in canonical form
+# 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
# 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;
+
\f
# 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 $1; # Add missing sign
+ substr($_,$[,0) = '+' unless $1; # Add missing sign
s/^-0/+0/;
$_;
} else {
# Assumes normalized value as input.
sub internal { #(num_str) return int_num_array
local($d) = @_;
- ($is,$il) = (substr($d,0,1),length($d)-2);
- substr($d,0,1) = '';
+ ($is,$il) = (substr($d,$[,1),length($d)-2);
+ substr($d,$[,1) = '';
($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
}
sub main'bneg { #(num_str) return num_str
local($_) = &'bnorm(@_);
vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
- s/^H/N/;
+ s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
$_;
}
\f
# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
- local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
+ local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
if ($x eq 'NaN') {
undef;
} elsif ($y eq 'NaN') {
sub cmp { # post-normalized compare for internal use
local($cx, $cy) = @_;
- $cx cmp $cy
- &&
- (
- ord($cy) <=> ord($cx)
- ||
- ($cx cmp ',') * (length($cy) <=> length($cx) || $cy cmp $cx)
- );
+ return 0 if ($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($_[1]));
+ local(*x, *y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
if ($x eq 'NaN') {
'NaN';
} elsif ($y eq 'NaN') {
}
sub main'bsub { #(num_str, num_str) return num_str
- &'badd($_[0],&'bneg($_[1]));
+ &'badd($_[$[],&'bneg($_[$[+1]));
}
# GCD -- Euclids algorithm Knuth Vol 2 pg 296
sub main'bgcd { #(num_str, num_str) return num_str
- local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
+ local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
if ($x eq 'NaN' || $y eq 'NaN') {
'NaN';
} else {
$car = 0;
for $x (@x) {
last unless @y || $car;
- $x -= 1e5 if $car = (($x += shift @y + $car) >= 1e5);
+ $x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
}
for $y (@y) {
last unless $car;
- $y -= 1e5 if $car = (($y += $car) >= 1e5);
+ $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
}
(@x, @y, $car);
}
$bar = 0;
for $sx (@sx) {
last unless @y || $bar;
- $sx += 1e5 if $bar = (($sx -= shift @sy + $bar) < 0);
+ $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($_[1]));
+ local(*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
if ($x eq 'NaN') {
'NaN';
} elsif ($y eq 'NaN') {
local($signr) = (shift @x ne shift @y) ? '-' : '+';
@prod = ();
for $x (@x) {
- ($car, $cty) = (0, 0);
+ ($car, $cty) = (0, $[);
for $y (@y) {
$prod = $x * $y + $prod[$cty] + $car;
- $prod[$cty++] =
- $prod - ($car = int($prod * 1e-5)) * 1e5;
+ if ($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;
$x = shift @prod;
# modulus
sub main'bmod { #(num_str, num_str) return num_str
- (&'bdiv(@_))[1];
+ (&'bdiv(@_))[$[+1];
}
\f
sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
- local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
+ local (*x, *y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
return wantarray ? ('NaN','NaN') : 'NaN'
if ($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];
+ $srem = $y[$[];
$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,$v1) = @y[$#y-1,$#y];
+ @q = (); ($v2,$v1) = @y[-2,-1];
while ($#x > $#y) {
- ($u2,$u1,$u0) = @x[($#x-2)..$#x];
+ ($u2,$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,++$x) {
+ for ($y = $[, $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,++$x) {
+ for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
$x[$x] -= 1e5
if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
}
else {
@d = @x;
}
- (&external($sr, @q), &external($srem, @d, 0));
+ (&external($sr, @q), &external($srem, @d, $zero));
} else {
&external($sr, @q);
}
https://perl5.git.perl.org / perl5.git / blobdiff