[perl5.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
#

$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) = '+' 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/^-/+/;
    $_;
}
\f
# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
sub main'bcmp { #(num_str, num_str) return cond_code
    local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
    if ($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;
    }
}
\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) ? 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;
		$prod[$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, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
    return wantarray ? ('NaN','NaN') : 'NaN'
	if ($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;
	    $x -= ($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,$v1) = @y[-2,-1];
    while ($#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;
		$prd -= ($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 = $[, $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;
Commit	Line	Data
5303340c LW	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	#
8990e307 LW	36
	37	$zero = 0;
	38
5303340c LW	39	\f
	40	# normalize string form of number. Strip leading zeros. Strip any
	41	# white space and add a sign, if missing.
	42	# Strings that are not numbers result the value 'NaN'.
8990e307	43
5303340c LW	44	sub main'bnorm { #(num_str) return num_str
	45	local($_) = @_;
	46	s/\s+//g; # strip white space
	47	if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
79072805	48	substr($_,$[,0) = '+' unless $1; # Add missing sign
5303340c LW	49	s/^-0/+0/;
	50	$_;
	51	} else {
	52	'NaN';
	53	}
	54	}
	55
	56	# Convert a number from string format to internal base 100000 format.
	57	# Assumes normalized value as input.
	58	sub internal { #(num_str) return int_num_array
	59	local($d) = @_;
79072805 LW	60	($is,$il) = (substr($d,$[,1),length($d)-2);
79072805 LW	61	substr($d,$[,1) = '';
5303340c LW	62	($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
	63	}
	64
	65	# Convert a number from internal base 100000 format to string format.
	66	# This routine scribbles all over input array.
	67	sub external { #(int_num_array) return num_str
	68	$es = shift;
	69	grep($_ > 9999 \|\| ($_ = substr('0000'.$_,-5)), @_); # zero pad
	70	&'bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
	71	}
	72
	73	# Negate input value.
	74	sub main'bneg { #(num_str) return num_str
	75	local($_) = &'bnorm(@_);
	76	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
9d116dd7	77	s/^./N/ unless /^[-+]/; # works both in ASCII and EBCDIC
5303340c LW	78	$_;
	79	}
	80
	81	# Returns the absolute value of the input.
	82	sub main'babs { #(num_str) return num_str
	83	&abs(&'bnorm(@_));
	84	}
	85
	86	sub abs { # post-normalized abs for internal use
	87	local($_) = @_;
	88	s/^-/+/;
	89	$_;
	90	}
	91	\f
	92	# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
	93	sub main'bcmp { #(num_str, num_str) return cond_code
79072805	94	local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
5303340c LW	95	if ($x eq 'NaN') {
	96	undef;
	97	} elsif ($y eq 'NaN') {
	98	undef;
	99	} else {
	100	&cmp($x,$y);
	101	}
	102	}
	103
	104	sub cmp { # post-normalized compare for internal use
	105	local($cx, $cy) = @_;
1e2e1ae8 JH	106	return 0 if ($cx eq $cy);
	107
	108	local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
	109	local($ld);
	110
	111	if ($sx eq '+') {
	112	return 1 if ($sy eq '-' \|\| $cy eq '+0');
	113	$ld = length($cx) - length($cy);
	114	return $ld if ($ld);
	115	return $cx cmp $cy;
	116	} else { # $sx eq '-'
	117	return -1 if ($sy eq '+');
	118	$ld = length($cy) - length($cx);
	119	return $ld if ($ld);
	120	return $cy cmp $cx;
	121	}
	122
5303340c LW	123	}
	124
	125	sub main'badd { #(num_str, num_str) return num_str
79072805	126	local(x, y); ($x, $y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
5303340c LW	127	if ($x eq 'NaN') {
	128	'NaN';
	129	} elsif ($y eq 'NaN') {
	130	'NaN';
	131	} else {
	132	@x = &internal($x); # convert to internal form
	133	@y = &internal($y);
	134	local($sx, $sy) = (shift @x, shift @y); # get signs
	135	if ($sx eq $sy) {
	136	&external($sx, &add(x, y)); # if same sign add
	137	} else {
	138	($x, $y) = (&abs($x),&abs($y)); # make abs
	139	if (&cmp($y,$x) > 0) {
	140	&external($sy, &sub(y, x));
	141	} else {
	142	&external($sx, &sub(x, y));
	143	}
	144	}
	145	}
	146	}
	147
	148	sub main'bsub { #(num_str, num_str) return num_str
79072805	149	&'badd($_[$[],&'bneg($_[$[+1]));
5303340c LW	150	}
	151
	152	# GCD -- Euclids algorithm Knuth Vol 2 pg 296
	153	sub main'bgcd { #(num_str, num_str) return num_str
79072805	154	local($x,$y) = (&'bnorm($_[$[]),&'bnorm($_[$[+1]));
68decaef	155	if ($x eq 'NaN' \|\| $y eq 'NaN') {
5303340c	156	'NaN';
68decaef	157	} else {
5303340c LW	158	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
	159	$x;
	160	}
	161	}
	162	\f
68decaef	163	# routine to add two base 1e5 numbers
5303340c LW	164	# stolen from Knuth Vol 2 Algorithm A pg 231
	165	# there are separate routines to add and sub as per Kunth pg 233
	166	sub add { #(int_num_array, int_num_array) return int_num_array
	167	local(x, y) = @_;
	168	$car = 0;
	169	for $x (@x) {
	170	last unless @y \|\| $car;
55497cff	171	$x -= 1e5 if $car = (($x += shift(@y) + $car) >= 1e5) ? 1 : 0;
5303340c LW	172	}
	173	for $y (@y) {
	174	last unless $car;
55497cff	175	$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
5303340c LW	176	}
	177	(@x, @y, $car);
	178	}
	179
68decaef	180	# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
5303340c LW	181	sub sub { #(int_num_array, int_num_array) return int_num_array
	182	local(sx, sy) = @_;
	183	$bar = 0;
	184	for $sx (@sx) {
	185	last unless @y \|\| $bar;
e334a159	186	$sx += 1e5 if $bar = (($sx -= shift(@sy) + $bar) < 0);
5303340c LW	187	}
	188	@sx;
	189	}
	190
	191	# multiply two numbers -- stolen from Knuth Vol 2 pg 233
	192	sub main'bmul { #(num_str, num_str) return num_str
79072805	193	local(x, y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
5303340c LW	194	if ($x eq 'NaN') {
	195	'NaN';
	196	} elsif ($y eq 'NaN') {
	197	'NaN';
	198	} else {
	199	@x = &internal($x);
	200	@y = &internal($y);
	201	local($signr) = (shift @x ne shift @y) ? '-' : '+';
	202	@prod = ();
	203	for $x (@x) {
79072805	204	($car, $cty) = (0, $[);
5303340c LW	205	for $y (@y) {
	206	$prod = $x * $y + $prod[$cty] + $car;
	207	$prod[$cty++] =
68decaef	208	$prod - ($car = int($prod * 1e-5)) * 1e5;
5303340c LW	209	}
	210	$prod[$cty] += $car if $car;
	211	$x = shift @prod;
	212	}
	213	&external($signr, @x, @prod);
	214	}
	215	}
	216
	217	# modulus
	218	sub main'bmod { #(num_str, num_str) return num_str
79072805	219	(&'bdiv(@_))[$[+1];
5303340c LW	220	}
	221	\f
	222	sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
79072805	223	local (x, y); ($x, $y) = (&'bnorm($_[$[]), &'bnorm($_[$[+1]));
5303340c LW	224	return wantarray ? ('NaN','NaN') : 'NaN'
	225	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0');
	226	return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
	227	@x = &internal($x); @y = &internal($y);
79072805	228	$srem = $y[$[];
5303340c LW	229	$sr = (shift @x ne shift @y) ? '-' : '+';
5303340c LW	230	$car = $bar = $prd = 0;
68decaef	231	if (($dd = int(1e5/($y[$#y]+1))) != 1) {
5303340c LW	232	for $x (@x) {
5303340c LW	233	$x = $x * $dd + $car;
68decaef	234	$x -= ($car = int($x * 1e-5)) * 1e5;
5303340c LW	235	}
	236	push(@x, $car); $car = 0;
	237	for $y (@y) {
	238	$y = $y * $dd + $car;
68decaef	239	$y -= ($car = int($y * 1e-5)) * 1e5;
5303340c LW	240	}
	241	}
	242	else {
	243	push(@x, 0);
	244	}
ed6116ce	245	@q = (); ($v2,$v1) = @y[-2,-1];
5303340c	246	while ($#x > $#y) {
ed6116ce	247	($u2,$u1,$u0) = @x[-3..-1];
68decaef LW	248	$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
68decaef LW	249	--$q while ($v2$q > ($u01e5+$u1-$q$v1)1e5+$u2);
5303340c LW	250	if ($q) {
5303340c LW	251	($car, $bar) = (0,0);
79072805	252	for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
5303340c	253	$prd = $q * $y[$y] + $car;
68decaef LW	254	$prd -= ($car = int($prd * 1e-5)) * 1e5;
68decaef LW	255	$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
5303340c LW	256	}
	257	if ($x[$#x] < $car + $bar) {
	258	$car = 0; --$q;
79072805	259	for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
68decaef LW	260	$x[$x] -= 1e5
68decaef LW	261	if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
5303340c LW	262	}
	263	}
	264	}
	265	pop(@x); unshift(@q, $q);
	266	}
	267	if (wantarray) {
	268	@d = ();
	269	if ($dd != 1) {
	270	$car = 0;
	271	for $x (reverse @x) {
68decaef	272	$prd = $car * 1e5 + $x;
5303340c LW	273	$car = $prd - ($tmp = int($prd / $dd)) * $dd;
	274	unshift(@d, $tmp);
	275	}
	276	}
	277	else {
	278	@d = @x;
	279	}
8990e307	280	(&external($sr, @q), &external($srem, @d, $zero));
5303340c LW	281	} else {
	282	&external($sr, @q);
	283	}
	284	}
	285	1;