[p5sagit/p5-mst-13.2.git] / lib / bigint.pl

package 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 always in canonical form
#
# Actual math is done in an internal format consisting of an array
#   whose first element is the sign (/^[+-]$/) and whose remaining 
#   elements are base 100000 digits with the least significant digit first.
# The string 'NaN' is used to represent the result when input arguments 
#   are not numbers, as well as the result of dividing by zero
#
# routines provided are:
#
#   bneg(BINT) return BINT              negation
#   babs(BINT) return BINT              absolute value
#   bcmp(BINT,BINT) return CODE         compare numbers (undef,<0,=0,>0)
#   badd(BINT,BINT) return BINT         addition
#   bsub(BINT,BINT) return BINT         subtraction
#   bmul(BINT,BINT) return BINT         multiplication
#   bdiv(BINT,BINT) return (BINT,BINT)  division (quo,rem) just quo if scalar
#   bmod(BINT,BINT) return BINT         modulus
#   bgcd(BINT,BINT) return BINT         greatest common divisor
#   bnorm(BINT) return BINT             normalization
#
\f
# normalize string form of number.   Strip leading zeros.  Strip any
#   white space and add a sign, if missing.
# Strings that are not numbers result the value 'NaN'.
sub main'bnorm { #(num_str) return num_str
    local($_) = @_;
    s/\s+//g;                           # strip white space
    if (s/^([+-]?)0*(\d+)$/$1$2/) {     # test if number
	substr($_,0,0) = '+' unless $1; # Add missing sign
	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/^H/N/;
    $_;
}

# 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/^-/+/;
    $_;
}
\f
# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
    if ($x eq 'NaN') {
	undef;
    } elsif ($y eq 'NaN') {
	undef;
    } else {
	&cmp($x,$y);
    }
}

sub cmp { # post-normalized compare for internal use
    local($cx, $cy) = @_;
    $cx cmp $cy
    &&
    (
	ord($cy) <=> ord($cx)
	||
	($cx cmp ',') * (length($cy) <=> length($cx) || $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 -- Euclids 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;
    }
}
\f
# 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);
    }
    for $y (@y) {
	last unless $car;
	$y -= 1e5 if $car = (($y += $car) >= 1e5);
    }
    (@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;
		$prod[$cty++] =
		    $prod - ($car = int($prod * 1e-5)) * 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];
}
\f
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;
	    $x -= ($car = int($x * 1e-5)) * 1e5;
	}
	push(@x, $car); $car = 0;
	for $y (@y) {
	    $y = $y * $dd + $car;
	    $y -= ($car = int($y * 1e-5)) * 1e5;
	}
    }
    else {
	push(@x, 0);
    }
    @q = (); ($v2,$v1) = @y[$#y-1,$#y];
    while ($#x > $#y) {
	($u2,$u1,$u0) = @x[($#x-2)..$#x];
	$q = (($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;
		$prd -= ($car = int($prd * 1e-5)) * 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($srem, @d, 0));
    } else {
	&external($sr, @q);
    }
}
1;
Commit	Line	Data
5303340c	1	package bigint;
	2
	3	# arbitrary size integer math package
	4	#
	5	# by Mark Biggar
	6	#
	7	# Canonical Big integer value are strings of the form
	8	# /^[+-]\d+$/ with leading zeros suppressed
	9	# Input values to these routines may be strings of the form
	10	# /^\s*[+-]?[\d\s]+$/.
	11	# Examples:
	12	# '+0' canonical zero value
	13	# ' -123 123 123' canonical value '-123123123'
	14	# '1 23 456 7890' canonical value '+1234567890'
	15	# Output values always always in canonical form
	16	#
	17	# Actual math is done in an internal format consisting of an array
	18	# whose first element is the sign (/^[+-]$/) and whose remaining
	19	# elements are base 100000 digits with the least significant digit first.
	20	# The string 'NaN' is used to represent the result when input arguments
	21	# are not numbers, as well as the result of dividing by zero
	22	#
	23	# routines provided are:
	24	#
	25	# bneg(BINT) return BINT negation
	26	# babs(BINT) return BINT absolute value
	27	# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0)
	28	# badd(BINT,BINT) return BINT addition
	29	# bsub(BINT,BINT) return BINT subtraction
	30	# bmul(BINT,BINT) return BINT multiplication
	31	# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
	32	# bmod(BINT,BINT) return BINT modulus
	33	# bgcd(BINT,BINT) return BINT greatest common divisor
	34	# bnorm(BINT) return BINT normalization
	35	#
	36	\f
	37	# normalize string form of number. Strip leading zeros. Strip any
	38	# white space and add a sign, if missing.
	39	# Strings that are not numbers result the value 'NaN'.
	40	sub main'bnorm { #(num_str) return num_str
	41	local($_) = @_;
	42	s/\s+//g; # strip white space
	43	if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
	44	substr($_,0,0) = '+' unless $1; # Add missing sign
	45	s/^-0/+0/;
	46	$_;
	47	} else {
	48	'NaN';
	49	}
	50	}
	51
	52	# Convert a number from string format to internal base 100000 format.
	53	# Assumes normalized value as input.
	54	sub internal { #(num_str) return int_num_array
	55	local($d) = @_;
	56	($is,$il) = (substr($d,0,1),length($d)-2);
	57	substr($d,0,1) = '';
	58	($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
	59	}
	60
	61	# Convert a number from internal base 100000 format to string format.
	62	# This routine scribbles all over input array.
	63	sub external { #(int_num_array) return num_str
	64	$es = shift;
65	grep($_ > 9999 \|\| ($_ = substr('0000'.$_,-5)), @_); # zero pad
66	&'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
67	}
68
69	# Negate input value.
70	sub main'bneg { #(num_str) return num_str
71	local($_) = &'bnorm(@_);
72	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
73	s/^H/N/;
74	$_;
75	}
76
77	# Returns the absolute value of the input.
78	sub main'babs { #(num_str) return num_str
79	&abs(&'bnorm(@_));
80	}
81
82	sub abs { # post-normalized abs for internal use
83	local($_) = @_;
84	s/^-/+/;
85	$_;
86	}
87	\f
88	# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
89	sub main'bcmp { #(num_str, num_str) return cond_code
90	local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
91	if ($x eq 'NaN') {
92	undef;
93	} elsif ($y eq 'NaN') {
94	undef;
95	} else {
96	&cmp($x,$y);
97	}
98	}
99
100	sub cmp { # post-normalized compare for internal use
101	local($cx, $cy) = @_;
102	$cx cmp $cy
103	&&
104	(
105	ord($cy) <=> ord($cx)
106	\|\|
107	($cx cmp ',') * (length($cy) <=> length($cx) \|\| $cy cmp $cx)
108	);
109	}
110
111	sub main'badd { #(num_str, num_str) return num_str
112	local(x, y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1]));
113	if ($x eq 'NaN') {
114	'NaN';
115	} elsif ($y eq 'NaN') {
116	'NaN';
117	} else {
118	@x = &internal($x); # convert to internal form
119	@y = &internal($y);
120	local($sx, $sy) = (shift @x, shift @y); # get signs
121	if ($sx eq $sy) {
122	&external($sx, &add(x, y)); # if same sign add
123	} else {
124	($x, $y) = (&abs($x),&abs($y)); # make abs
125	if (&cmp($y,$x) > 0) {
126	&external($sy, &sub(y, x));
127	} else {
128	&external($sx, &sub(x, y));
129	}
130	}
131	}
132	}
133
134	sub main'bsub { #(num_str, num_str) return num_str
135	&'badd($_[0],&'bneg($_[1]));
136	}
137
138	# GCD -- Euclids algorithm Knuth Vol 2 pg 296
139	sub main'bgcd { #(num_str, num_str) return num_str
140	local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
68decaef	141	if ($x eq 'NaN' \|\| $y eq 'NaN') {
5303340c	142	'NaN';
68decaef	143	} else {
5303340c	144	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
	145	$x;
	146	}
	147	}
	148	\f
68decaef	149	# routine to add two base 1e5 numbers
5303340c	150	# stolen from Knuth Vol 2 Algorithm A pg 231
	151	# there are separate routines to add and sub as per Kunth pg 233
	152	sub add { #(int_num_array, int_num_array) return int_num_array
	153	local(x, y) = @_;
	154	$car = 0;
	155	for $x (@x) {
	156	last unless @y \|\| $car;
e334a159	157	$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5);
5303340c	158	}
	159	for $y (@y) {
	160	last unless $car;
68decaef	161	$y -= 1e5 if $car = (($y += $car) >= 1e5);
5303340c	162	}
	163	(@x, @y, $car);
	164	}
	165
68decaef	166	# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
5303340c	167	sub sub { #(int_num_array, int_num_array) return int_num_array
	168	local(sx, sy) = @_;
	169	$bar = 0;
	170	for $sx (@sx) {
	171	last unless @y \|\| $bar;
e334a159	172	$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
5303340c	173	}
	174	@sx;
	175	}
	176
	177	# multiply two numbers -- stolen from Knuth Vol 2 pg 233
	178	sub main'bmul { #(num_str, num_str) return num_str
	179	local(x, y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
	180	if ($x eq 'NaN') {
	181	'NaN';
	182	} elsif ($y eq 'NaN') {
	183	'NaN';
	184	} else {
	185	@x = &internal($x);
	186	@y = &internal($y);
	187	local($signr) = (shift @x ne shift @y) ? '-' : '+';
	188	@prod = ();
	189	for $x (@x) {
	190	($car, $cty) = (0, 0);
	191	for $y (@y) {
	192	$prod = $x * $y + $prod[$cty] + $car;
	193	$prod[$cty++] =
68decaef	194	$prod - ($car = int($prod * 1e-5)) * 1e5;
5303340c	195	}
	196	$prod[$cty] += $car if $car;
	197	$x = shift @prod;
	198	}
	199	&external($signr, @x, @prod);
	200	}
	201	}
	202
	203	# modulus
	204	sub main'bmod { #(num_str, num_str) return num_str
	205	(&'bdiv(@_))[1];
	206	}
	207	\f
	208	sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
	209	local (x, y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
	210	return wantarray ? ('NaN','NaN') : 'NaN'
	211	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0');
	212	return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
	213	@x = &internal($x); @y = &internal($y);
	214	$srem = $y[0];
	215	$sr = (shift @x ne shift @y) ? '-' : '+';
	216	$car = $bar = $prd = 0;
68decaef	217	if (($dd = int(1e5/($y[$#y]+1))) != 1) {
5303340c	218	for $x (@x) {
5303340c	219	$x = $x * $dd + $car;
68decaef	220	$x -= ($car = int($x * 1e-5)) * 1e5;
5303340c	221	}
	222	push(@x, $car); $car = 0;
	223	for $y (@y) {
	224	$y = $y * $dd + $car;
68decaef	225	$y -= ($car = int($y * 1e-5)) * 1e5;
5303340c	226	}
	227	}
	228	else {
	229	push(@x, 0);
	230	}
	231	@q = (); ($v2,$v1) = @y[$#y-1,$#y];
	232	while ($#x > $#y) {
	233	($u2,$u1,$u0) = @x[($#x-2)..$#x];
68decaef	234	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
68decaef	235	--$q while ($v2$q > ($u01e5+$u1-$q$v1)1e5+$u2);
5303340c	236	if ($q) {
	237	($car, $bar) = (0,0);
	238	for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
	239	$prd = $q * $y[$y] + $car;
68decaef	240	$prd -= ($car = int($prd * 1e-5)) * 1e5;
68decaef	241	$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
5303340c	242	}
	243	if ($x[$#x] < $car + $bar) {
	244	$car = 0; --$q;
	245	for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
68decaef	246	$x[$x] -= 1e5
68decaef	247	if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
5303340c	248	}
	249	}
	250	}
	251	pop(@x); unshift(@q, $q);
	252	}
	253	if (wantarray) {
	254	@d = ();
	255	if ($dd != 1) {
	256	$car = 0;
	257	for $x (reverse @x) {
68decaef	258	$prd = $car * 1e5 + $x;
5303340c	259	$car = $prd - ($tmp = int($prd / $dd)) * $dd;
	260	unshift(@d, $tmp);
	261	}
	262	}
	263	else {
	264	@d = @x;
	265	}
	266	(&external($sr, @q), &external($srem, @d, 0));
	267	} else {
	268	&external($sr, @q);
	269	}
	270	}
	271	1;