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Diffstat (limited to 'gnu/usr.bin/perl/lib/bigint.pl')
| -rw-r--r-- | gnu/usr.bin/perl/lib/bigint.pl | 271 |
1 files changed, 271 insertions, 0 deletions
diff --git a/gnu/usr.bin/perl/lib/bigint.pl b/gnu/usr.bin/perl/lib/bigint.pl new file mode 100644 index 0000000..5c79da9 --- /dev/null +++ b/gnu/usr.bin/perl/lib/bigint.pl @@ -0,0 +1,271 @@ +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 (/^[+-]$/) and whose remaining +# elements are base 100000 digits with the least significant digit first. +# The string 'NaN' is used to represent the result when input arguments +# are not numbers, as well as the result of dividing by zero +# +# routines provided are: +# +# bneg(BINT) return BINT negation +# babs(BINT) return BINT absolute value +# bcmp(BINT,BINT) return CODE compare numbers (undef,<0,=0,>0) +# badd(BINT,BINT) return BINT addition +# bsub(BINT,BINT) return BINT subtraction +# bmul(BINT,BINT) return BINT multiplication +# bdiv(BINT,BINT) return (BINT,BINT) division (quo,rem) just quo if scalar +# bmod(BINT,BINT) return BINT modulus +# bgcd(BINT,BINT) return BINT greatest common divisor +# bnorm(BINT) return BINT normalization +# + +# normalize string form of number. Strip leading zeros. Strip any +# white space and add a sign, if missing. +# Strings that are not numbers result the value 'NaN'. +sub main'bnorm { #(num_str) return num_str + local($_) = @_; + 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/^-/+/; + $_; +} + +# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort) +sub main'bcmp { #(num_str, num_str) return cond_code + local($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; + } +} + +# 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]; +} + +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; |
