| 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($_[1])); |
| 141 | if ($x eq 'NaN') { |
| 142 | 'NaN'; |
| 143 | } |
| 144 | elsif ($y eq 'NaN') { |
| 145 | 'NaN'; |
| 146 | } |
| 147 | else { |
| 148 | ($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0'; |
| 149 | $x; |
| 150 | } |
| 151 | } |
| 152 | \f |
| 153 | # routine to add two base 100000 numbers |
| 154 | # stolen from Knuth Vol 2 Algorithm A pg 231 |
| 155 | # there are separate routines to add and sub as per Kunth pg 233 |
| 156 | sub add { #(int_num_array, int_num_array) return int_num_array |
| 157 | local(*x, *y) = @_; |
| 158 | $car = 0; |
| 159 | for $x (@x) { |
| 160 | last unless @y || $car; |
| 161 | $x -= 100000 if $car = (($x += shift @y + $car) >= 100000); |
| 162 | } |
| 163 | for $y (@y) { |
| 164 | last unless $car; |
| 165 | $y -= 100000 if $car = (($y += $car) >= 100000); |
| 166 | } |
| 167 | (@x, @y, $car); |
| 168 | } |
| 169 | |
| 170 | # subtract base 100000 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y |
| 171 | sub sub { #(int_num_array, int_num_array) return int_num_array |
| 172 | local(*sx, *sy) = @_; |
| 173 | $bar = 0; |
| 174 | for $sx (@sx) { |
| 175 | last unless @y || $bar; |
| 176 | $sx += 100000 if $bar = (($sx -= shift @sy + $bar) < 0); |
| 177 | } |
| 178 | @sx; |
| 179 | } |
| 180 | |
| 181 | # multiply two numbers -- stolen from Knuth Vol 2 pg 233 |
| 182 | sub main'bmul { #(num_str, num_str) return num_str |
| 183 | local(*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); |
| 184 | if ($x eq 'NaN') { |
| 185 | 'NaN'; |
| 186 | } elsif ($y eq 'NaN') { |
| 187 | 'NaN'; |
| 188 | } else { |
| 189 | @x = &internal($x); |
| 190 | @y = &internal($y); |
| 191 | local($signr) = (shift @x ne shift @y) ? '-' : '+'; |
| 192 | @prod = (); |
| 193 | for $x (@x) { |
| 194 | ($car, $cty) = (0, 0); |
| 195 | for $y (@y) { |
| 196 | $prod = $x * $y + $prod[$cty] + $car; |
| 197 | $prod[$cty++] = |
| 198 | $prod - ($car = int($prod * (1/100000))) * 100000; |
| 199 | } |
| 200 | $prod[$cty] += $car if $car; |
| 201 | $x = shift @prod; |
| 202 | } |
| 203 | &external($signr, @x, @prod); |
| 204 | } |
| 205 | } |
| 206 | |
| 207 | # modulus |
| 208 | sub main'bmod { #(num_str, num_str) return num_str |
| 209 | (&'bdiv(@_))[1]; |
| 210 | } |
| 211 | \f |
| 212 | sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str |
| 213 | local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1])); |
| 214 | return wantarray ? ('NaN','NaN') : 'NaN' |
| 215 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0'); |
| 216 | return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0); |
| 217 | @x = &internal($x); @y = &internal($y); |
| 218 | $srem = $y[0]; |
| 219 | $sr = (shift @x ne shift @y) ? '-' : '+'; |
| 220 | $car = $bar = $prd = 0; |
| 221 | if (($dd = int(100000/($y[$#y]+1))) != 1) { |
| 222 | for $x (@x) { |
| 223 | $x = $x * $dd + $car; |
| 224 | $x -= ($car = int($x * (1/100000))) * 100000; |
| 225 | } |
| 226 | push(@x, $car); $car = 0; |
| 227 | for $y (@y) { |
| 228 | $y = $y * $dd + $car; |
| 229 | $y -= ($car = int($y * (1/100000))) * 100000; |
| 230 | } |
| 231 | } |
| 232 | else { |
| 233 | push(@x, 0); |
| 234 | } |
| 235 | @q = (); ($v2,$v1) = @y[$#y-1,$#y]; |
| 236 | while ($#x > $#y) { |
| 237 | ($u2,$u1,$u0) = @x[($#x-2)..$#x]; |
| 238 | $q = (($u0 == $v1) ? 99999 : int(($u0*100000+$u1)/$v1)); |
| 239 | --$q while ($v2*$q > ($u0*100000+$u1-$q*$v1)*100000+$u2); |
| 240 | if ($q) { |
| 241 | ($car, $bar) = (0,0); |
| 242 | for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { |
| 243 | $prd = $q * $y[$y] + $car; |
| 244 | $prd -= ($car = int($prd * (1/100000))) * 100000; |
| 245 | $x[$x] += 100000 if ($bar = (($x[$x] -= $prd + $bar) < 0)); |
| 246 | } |
| 247 | if ($x[$#x] < $car + $bar) { |
| 248 | $car = 0; --$q; |
| 249 | for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) { |
| 250 | $x[$x] -= 100000 |
| 251 | if ($car = (($x[$x] += $y[$y] + $car) > 100000)); |
| 252 | } |
| 253 | } |
| 254 | } |
| 255 | pop(@x); unshift(@q, $q); |
| 256 | } |
| 257 | if (wantarray) { |
| 258 | @d = (); |
| 259 | if ($dd != 1) { |
| 260 | $car = 0; |
| 261 | for $x (reverse @x) { |
| 262 | $prd = $car * 100000 + $x; |
| 263 | $car = $prd - ($tmp = int($prd / $dd)) * $dd; |
| 264 | unshift(@d, $tmp); |
| 265 | } |
| 266 | } |
| 267 | else { |
| 268 | @d = @x; |
| 269 | } |
| 270 | (&external($sr, @q), &external($srem, @d, 0)); |
| 271 | } else { |
| 272 | &external($sr, @q); |
| 273 | } |
| 274 | } |
| 275 | 1; |
projects / p5sagit/p5-mst-13.2.git / blame