lib/perl5/5.10/bigint.pl - chromium/deps/cygwin - Git at Google

 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;
     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) = '+' 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,$[,1),length($d)-2);
     substr($d,$[,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($_[$[]),&'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, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
     if ($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($_[$[],&'bneg($_[$[+1]));
 }

 # GCD -- Euclids algorithm Knuth Vol 2 pg 296
 sub main'bgcd { #(num_str, num_str) return num_str
     local($x,$y) = (&'bnorm($_[$[]),&'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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
     if ($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, $[);
 	    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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
     return wantarray ? ('NaN','NaN') : 'NaN'
 	if ($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 = $y[$[];
     $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 = $[, $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 = $[, $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;
	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;
	my $use_mult = int($x1e-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) = '+' 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,$[,1),length($d)-2);
	substr($d,$[,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($_[$[]),&'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, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
	if ($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($_[$[],&'bneg($_[$[+1]));
	}

	# GCD -- Euclids algorithm Knuth Vol 2 pg 296
	sub main'bgcd { #(num_str, num_str) return num_str
	local($x,$y) = (&'bnorm($_[$[]),&'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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
	if ($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, $[);
	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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
	return wantarray ? ('NaN','NaN') : 'NaN'
	if ($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 = $y[$[];
	$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$q > ($u01e5+$u1-$q$v1)1e5+$u2);
	if ($q) {
	($car, $bar) = (0,0);
	for ($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 = $[, $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;