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1 | package Math::BigFloat; |
| 2 | |
| 3 | use Math::BigInt; |
| 4 | |
| 5 | use Exporter; # just for use to be happy |
| 6 | @ISA = (Exporter); |
| 7 | |
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8 | use overload |
| 9 | '+' => sub {new Math::BigFloat &fadd}, |
| 10 | '-' => sub {new Math::BigFloat |
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11 | $_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])}, |
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12 | '<=>' => sub {new Math::BigFloat |
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13 | $_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])}, |
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14 | 'cmp' => sub {new Math::BigFloat |
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15 | $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
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16 | '*' => sub {new Math::BigFloat &fmul}, |
| 17 | '/' => sub {new Math::BigFloat |
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18 | $_[2]? scalar fdiv($_[1],${$_[0]}) : |
| 19 | scalar fdiv(${$_[0]},$_[1])}, |
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20 | 'neg' => sub {new Math::BigFloat &fneg}, |
| 21 | 'abs' => sub {new Math::BigFloat &fabs}, |
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22 | |
| 23 | qw( |
| 24 | "" stringify |
| 25 | 0+ numify) # Order of arguments unsignificant |
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26 | ; |
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27 | |
| 28 | sub new { |
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29 | my ($class) = shift; |
| 30 | my ($foo) = fnorm(shift); |
| 31 | panic("Not a number initialized to Math::BigFloat") if $foo eq "NaN"; |
| 32 | bless \$foo, $class; |
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33 | } |
| 34 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
| 35 | # comparing to direct compilation based on |
| 36 | # stringify |
| 37 | sub stringify { |
| 38 | my $n = ${$_[0]}; |
| 39 | |
| 40 | $n =~ s/^\+//; |
| 41 | $n =~ s/E//; |
| 42 | |
| 43 | $n =~ s/([-+]\d+)$//; |
| 44 | |
| 45 | my $e = $1; |
| 46 | my $ln = length($n); |
| 47 | |
| 48 | if ($e > 0) { |
| 49 | $n .= "0" x $e . '.'; |
| 50 | } elsif (abs($e) < $ln) { |
| 51 | substr($n, $ln + $e, 0) = '.'; |
| 52 | } else { |
| 53 | $n = '.' . ("0" x (abs($e) - $ln)) . $n; |
| 54 | } |
| 55 | |
| 56 | # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/; |
| 57 | |
| 58 | return $n; |
| 59 | } |
| 60 | |
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61 | $div_scale = 40; |
| 62 | |
| 63 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
| 64 | |
| 65 | $rnd_mode = 'even'; |
| 66 | |
| 67 | sub fadd; sub fsub; sub fmul; sub fdiv; |
| 68 | sub fneg; sub fabs; sub fcmp; |
| 69 | sub fround; sub ffround; |
| 70 | sub fnorm; sub fsqrt; |
| 71 | |
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72 | # Convert a number to canonical string form. |
| 73 | # Takes something that looks like a number and converts it to |
| 74 | # the form /^[+-]\d+E[+-]\d+$/. |
| 75 | sub fnorm { #(string) return fnum_str |
| 76 | local($_) = @_; |
| 77 | s/\s+//g; # strip white space |
| 78 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
| 79 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
| 80 | } else { |
| 81 | 'NaN'; |
| 82 | } |
| 83 | } |
| 84 | |
| 85 | # normalize number -- for internal use |
| 86 | sub norm { #(mantissa, exponent) return fnum_str |
| 87 | local($_, $exp) = @_; |
| 88 | if ($_ eq 'NaN') { |
| 89 | 'NaN'; |
| 90 | } else { |
| 91 | s/^([+-])0+/$1/; # strip leading zeros |
| 92 | if (length($_) == 1) { |
| 93 | '+0E+0'; |
| 94 | } else { |
| 95 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
| 96 | sprintf("%sE%+ld", $_, $exp); |
| 97 | } |
| 98 | } |
| 99 | } |
| 100 | |
| 101 | # negation |
| 102 | sub fneg { #(fnum_str) return fnum_str |
| 103 | local($_) = fnorm($_[$[]); |
| 104 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
| 105 | s/^H/N/; |
| 106 | $_; |
| 107 | } |
| 108 | |
| 109 | # absolute value |
| 110 | sub fabs { #(fnum_str) return fnum_str |
| 111 | local($_) = fnorm($_[$[]); |
| 112 | s/^-/+/; # mash sign |
| 113 | $_; |
| 114 | } |
| 115 | |
| 116 | # multiplication |
| 117 | sub fmul { #(fnum_str, fnum_str) return fnum_str |
| 118 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
| 119 | if ($x eq 'NaN' || $y eq 'NaN') { |
| 120 | 'NaN'; |
| 121 | } else { |
| 122 | local($xm,$xe) = split('E',$x); |
| 123 | local($ym,$ye) = split('E',$y); |
| 124 | &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); |
| 125 | } |
| 126 | } |
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127 | |
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128 | # addition |
| 129 | sub fadd { #(fnum_str, fnum_str) return fnum_str |
| 130 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
| 131 | if ($x eq 'NaN' || $y eq 'NaN') { |
| 132 | 'NaN'; |
| 133 | } else { |
| 134 | local($xm,$xe) = split('E',$x); |
| 135 | local($ym,$ye) = split('E',$y); |
| 136 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
| 137 | &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
| 138 | } |
| 139 | } |
| 140 | |
| 141 | # subtraction |
| 142 | sub fsub { #(fnum_str, fnum_str) return fnum_str |
| 143 | fadd($_[$[],fneg($_[$[+1])); |
| 144 | } |
| 145 | |
| 146 | # division |
| 147 | # args are dividend, divisor, scale (optional) |
| 148 | # result has at most max(scale, length(dividend), length(divisor)) digits |
| 149 | sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
| 150 | { |
| 151 | local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); |
| 152 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
| 153 | 'NaN'; |
| 154 | } else { |
| 155 | local($xm,$xe) = split('E',$x); |
| 156 | local($ym,$ye) = split('E',$y); |
| 157 | $scale = $div_scale if (!$scale); |
| 158 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
| 159 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
| 160 | $scale = $scale + length($ym) - length($xm); |
| 161 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),$ym), |
| 162 | $xe-$ye-$scale); |
| 163 | } |
| 164 | } |
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165 | |
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166 | # round int $q based on fraction $r/$base using $rnd_mode |
| 167 | sub round { #(int_str, int_str, int_str) return int_str |
| 168 | local($q,$r,$base) = @_; |
| 169 | if ($q eq 'NaN' || $r eq 'NaN') { |
| 170 | 'NaN'; |
| 171 | } elsif ($rnd_mode eq 'trunc') { |
| 172 | $q; # just truncate |
| 173 | } else { |
| 174 | local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base); |
| 175 | if ( $cmp < 0 || |
| 176 | ($cmp == 0 && |
| 177 | ( $rnd_mode eq 'zero' || |
| 178 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
| 179 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || |
| 180 | ($rnd_mode eq 'even' && $q =~ /[24680]$/) || |
| 181 | ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { |
| 182 | $q; # round down |
| 183 | } else { |
| 184 | Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
| 185 | # round up |
| 186 | } |
| 187 | } |
| 188 | } |
| 189 | |
| 190 | # round the mantissa of $x to $scale digits |
| 191 | sub fround { #(fnum_str, scale) return fnum_str |
| 192 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
| 193 | if ($x eq 'NaN' || $scale <= 0) { |
| 194 | $x; |
| 195 | } else { |
| 196 | local($xm,$xe) = split('E',$x); |
| 197 | if (length($xm)-1 <= $scale) { |
| 198 | $x; |
| 199 | } else { |
| 200 | &norm(&round(substr($xm,$[,$scale+1), |
| 201 | "+0".substr($xm,$[+$scale+1,1),"+10"), |
| 202 | $xe+length($xm)-$scale-1); |
| 203 | } |
| 204 | } |
| 205 | } |
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206 | |
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207 | # round $x at the 10 to the $scale digit place |
| 208 | sub ffround { #(fnum_str, scale) return fnum_str |
| 209 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
| 210 | if ($x eq 'NaN') { |
| 211 | 'NaN'; |
| 212 | } else { |
| 213 | local($xm,$xe) = split('E',$x); |
| 214 | if ($xe >= $scale) { |
| 215 | $x; |
| 216 | } else { |
| 217 | $xe = length($xm)+$xe-$scale; |
| 218 | if ($xe < 1) { |
| 219 | '+0E+0'; |
| 220 | } elsif ($xe == 1) { |
| 221 | &norm(&round('+0',"+0".substr($xm,$[+1,1),"+10"), $scale); |
| 222 | } else { |
| 223 | &norm(&round(substr($xm,$[,$xe), |
| 224 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
| 225 | } |
| 226 | } |
| 227 | } |
| 228 | } |
| 229 | |
| 230 | # compare 2 values returns one of undef, <0, =0, >0 |
| 231 | # returns undef if either or both input value are not numbers |
| 232 | sub fcmp #(fnum_str, fnum_str) return cond_code |
| 233 | { |
| 234 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
| 235 | if ($x eq "NaN" || $y eq "NaN") { |
| 236 | undef; |
| 237 | } else { |
| 238 | ord($y) <=> ord($x) |
| 239 | || |
| 240 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), |
| 241 | (($xe <=> $ye) * (substr($x,$[,1).'1') |
| 242 | || Math::BigInt::cmp($xm,$ym)) |
| 243 | ); |
| 244 | } |
| 245 | } |
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246 | |
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247 | # square root by Newtons method. |
| 248 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
| 249 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
| 250 | if ($x eq 'NaN' || $x =~ /^-/) { |
| 251 | 'NaN'; |
| 252 | } elsif ($x eq '+0E+0') { |
| 253 | '+0E+0'; |
| 254 | } else { |
| 255 | local($xm, $xe) = split('E',$x); |
| 256 | $scale = $div_scale if (!$scale); |
| 257 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
| 258 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
| 259 | while ($gs < 2*$scale) { |
| 260 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
| 261 | $gs *= 2; |
| 262 | } |
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263 | new Math::BigFloat &fround($guess, $scale); |
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264 | } |
| 265 | } |
| 266 | |
| 267 | 1; |
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268 | __END__ |
| 269 | |
| 270 | =head1 NAME |
| 271 | |
| 272 | Math::BigFloat - Arbitrary length float math package |
| 273 | |
| 274 | =head1 SYNOPSIS |
| 275 | |
| 276 | use Math::BogFloat; |
| 277 | $f = Math::BigFloat->new($string); |
| 278 | |
| 279 | $f->fadd(NSTR) return NSTR addition |
| 280 | $f->fsub(NSTR) return NSTR subtraction |
| 281 | $f->fmul(NSTR) return NSTR multiplication |
| 282 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
| 283 | $f->fneg() return NSTR negation |
| 284 | $f->fabs() return NSTR absolute value |
| 285 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
| 286 | $f->fround(SCALE) return NSTR round to SCALE digits |
| 287 | $f->ffround(SCALE) return NSTR round at SCALEth place |
| 288 | $f->fnorm() return (NSTR) normalize |
| 289 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
| 290 | |
| 291 | =head1 DESCRIPTION |
| 292 | |
| 293 | All basic math operations are overloaded if you declare your big |
| 294 | floats as |
| 295 | |
| 296 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
| 297 | |
| 298 | =over 2 |
| 299 | |
| 300 | =item number format |
| 301 | |
| 302 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
| 303 | have inbedded whitespace. |
| 304 | |
| 305 | =item Error returns 'NaN' |
| 306 | |
| 307 | An input parameter was "Not a Number" or divide by zero or sqrt of |
| 308 | negative number. |
| 309 | |
| 310 | =item Division is computed to |
| 311 | |
| 312 | C<max($div_scale,length(dividend)+length(divisor))> digits by default. |
| 313 | Also used for default sqrt scale. |
| 314 | |
| 315 | =back |
| 316 | |
| 317 | =head1 BUGS |
| 318 | |
| 319 | The current version of this module is a preliminary version of the |
| 320 | real thing that is currently (as of perl5.002) under development. |
| 321 | |
| 322 | =head1 AUTHOR |
| 323 | |
| 324 | Mark Biggar |
| 325 | |
| 326 | =cut |
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