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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); |
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7 | $VERSION = '0.01'; # never had version before |
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8 | |
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9 | use overload |
10 | '+' => sub {new Math::BigFloat &fadd}, |
11 | '-' => sub {new Math::BigFloat |
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12 | $_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])}, |
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13 | '<=>' => sub {$_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])}, |
14 | 'cmp' => sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
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15 | '*' => sub {new Math::BigFloat &fmul}, |
16 | '/' => sub {new Math::BigFloat |
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17 | $_[2]? scalar fdiv($_[1],${$_[0]}) : |
18 | scalar fdiv(${$_[0]},$_[1])}, |
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19 | 'neg' => sub {new Math::BigFloat &fneg}, |
20 | 'abs' => sub {new Math::BigFloat &fabs}, |
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21 | 'int' => sub {new Math::BigInt &f2int}, |
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22 | |
23 | qw( |
24 | "" stringify |
25 | 0+ numify) # Order of arguments unsignificant |
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26 | ; |
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27 | |
28 | sub new { |
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29 | my ($class) = shift; |
30 | my ($foo) = fnorm(shift); |
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31 | bless \$foo, $class; |
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32 | } |
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33 | |
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34 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
35 | # comparing to direct compilation based on |
36 | # stringify |
37 | sub stringify { |
38 | my $n = ${$_[0]}; |
39 | |
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40 | my $minus = ($n =~ s/^([+-])// && $1 eq '-'); |
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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 | } |
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55 | $n = "-$n" if $minus; |
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56 | |
57 | # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/; |
58 | |
59 | return $n; |
60 | } |
61 | |
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62 | sub import { |
63 | shift; |
64 | return unless @_; |
65 | die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant'; |
66 | overload::constant float => sub {Math::BigFloat->new(shift)}; |
67 | } |
68 | |
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69 | $div_scale = 40; |
70 | |
71 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
72 | |
73 | $rnd_mode = 'even'; |
74 | |
75 | sub fadd; sub fsub; sub fmul; sub fdiv; |
76 | sub fneg; sub fabs; sub fcmp; |
77 | sub fround; sub ffround; |
78 | sub fnorm; sub fsqrt; |
79 | |
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80 | # Convert a number to canonical string form. |
81 | # Takes something that looks like a number and converts it to |
82 | # the form /^[+-]\d+E[+-]\d+$/. |
83 | sub fnorm { #(string) return fnum_str |
84 | local($_) = @_; |
85 | s/\s+//g; # strip white space |
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86 | no warnings; # $4 and $5 below might legitimately be undefined |
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87 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
88 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
89 | } else { |
90 | 'NaN'; |
91 | } |
92 | } |
93 | |
94 | # normalize number -- for internal use |
95 | sub norm { #(mantissa, exponent) return fnum_str |
96 | local($_, $exp) = @_; |
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97 | $exp = 0 unless defined $exp; |
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98 | if ($_ eq 'NaN') { |
99 | 'NaN'; |
100 | } else { |
101 | s/^([+-])0+/$1/; # strip leading zeros |
102 | if (length($_) == 1) { |
103 | '+0E+0'; |
104 | } else { |
105 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
106 | sprintf("%sE%+ld", $_, $exp); |
107 | } |
108 | } |
109 | } |
110 | |
111 | # negation |
112 | sub fneg { #(fnum_str) return fnum_str |
113 | local($_) = fnorm($_[$[]); |
114 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
115 | s/^H/N/; |
116 | $_; |
117 | } |
118 | |
119 | # absolute value |
120 | sub fabs { #(fnum_str) return fnum_str |
121 | local($_) = fnorm($_[$[]); |
122 | s/^-/+/; # mash sign |
123 | $_; |
124 | } |
125 | |
126 | # multiplication |
127 | sub fmul { #(fnum_str, fnum_str) return fnum_str |
128 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
129 | if ($x eq 'NaN' || $y eq 'NaN') { |
130 | 'NaN'; |
131 | } else { |
132 | local($xm,$xe) = split('E',$x); |
133 | local($ym,$ye) = split('E',$y); |
134 | &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); |
135 | } |
136 | } |
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137 | |
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138 | # addition |
139 | sub fadd { #(fnum_str, fnum_str) return fnum_str |
140 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
141 | if ($x eq 'NaN' || $y eq 'NaN') { |
142 | 'NaN'; |
143 | } else { |
144 | local($xm,$xe) = split('E',$x); |
145 | local($ym,$ye) = split('E',$y); |
146 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
147 | &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
148 | } |
149 | } |
150 | |
151 | # subtraction |
152 | sub fsub { #(fnum_str, fnum_str) return fnum_str |
153 | fadd($_[$[],fneg($_[$[+1])); |
154 | } |
155 | |
156 | # division |
157 | # args are dividend, divisor, scale (optional) |
158 | # result has at most max(scale, length(dividend), length(divisor)) digits |
159 | sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
160 | { |
161 | local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); |
162 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
163 | 'NaN'; |
164 | } else { |
165 | local($xm,$xe) = split('E',$x); |
166 | local($ym,$ye) = split('E',$y); |
167 | $scale = $div_scale if (!$scale); |
168 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
169 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
170 | $scale = $scale + length($ym) - length($xm); |
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171 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym), |
172 | Math::BigInt::babs($ym)), |
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173 | $xe-$ye-$scale); |
174 | } |
175 | } |
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176 | |
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177 | # round int $q based on fraction $r/$base using $rnd_mode |
178 | sub round { #(int_str, int_str, int_str) return int_str |
179 | local($q,$r,$base) = @_; |
180 | if ($q eq 'NaN' || $r eq 'NaN') { |
181 | 'NaN'; |
182 | } elsif ($rnd_mode eq 'trunc') { |
183 | $q; # just truncate |
184 | } else { |
185 | local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base); |
186 | if ( $cmp < 0 || |
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187 | ($cmp == 0 && ( |
188 | ($rnd_mode eq 'zero' ) || |
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189 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
190 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || |
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191 | ($rnd_mode eq 'even' && $q =~ /[13579]$/ ) || |
192 | ($rnd_mode eq 'odd' && $q =~ /[24680]$/ ) ) |
193 | ) |
194 | ) { |
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195 | $q; # round down |
196 | } else { |
197 | Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
198 | # round up |
199 | } |
200 | } |
201 | } |
202 | |
203 | # round the mantissa of $x to $scale digits |
204 | sub fround { #(fnum_str, scale) return fnum_str |
205 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
206 | if ($x eq 'NaN' || $scale <= 0) { |
207 | $x; |
208 | } else { |
209 | local($xm,$xe) = split('E',$x); |
210 | if (length($xm)-1 <= $scale) { |
211 | $x; |
212 | } else { |
213 | &norm(&round(substr($xm,$[,$scale+1), |
214 | "+0".substr($xm,$[+$scale+1,1),"+10"), |
215 | $xe+length($xm)-$scale-1); |
216 | } |
217 | } |
218 | } |
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219 | |
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220 | # round $x at the 10 to the $scale digit place |
221 | sub ffround { #(fnum_str, scale) return fnum_str |
222 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
223 | if ($x eq 'NaN') { |
224 | 'NaN'; |
225 | } else { |
226 | local($xm,$xe) = split('E',$x); |
227 | if ($xe >= $scale) { |
228 | $x; |
229 | } else { |
230 | $xe = length($xm)+$xe-$scale; |
231 | if ($xe < 1) { |
232 | '+0E+0'; |
233 | } elsif ($xe == 1) { |
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234 | # The first substr preserves the sign, passing a non- |
235 | # normalized "-0" to &round when rounding -0.006 (for |
236 | # example), purely so &round won't lose the sign. |
237 | &norm(&round(substr($xm,$[,1).'0', |
238 | "+0".substr($xm,$[+1,1),"+10"), $scale); |
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239 | } else { |
240 | &norm(&round(substr($xm,$[,$xe), |
241 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
242 | } |
243 | } |
244 | } |
245 | } |
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246 | |
247 | # Calculate the integer part of $x |
248 | sub f2int { #(fnum_str) return inum_str |
249 | local($x) = ${$_[$[]}; |
250 | if ($x eq 'NaN') { |
251 | die "Attempt to take int(NaN)"; |
252 | } else { |
253 | local($xm,$xe) = split('E',$x); |
254 | if ($xe >= 0) { |
255 | $xm . '0' x $xe; |
256 | } else { |
257 | $xe = length($xm)+$xe; |
258 | if ($xe <= 1) { |
259 | '+0'; |
260 | } else { |
261 | substr($xm,$[,$xe); |
262 | } |
263 | } |
264 | } |
265 | } |
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266 | |
267 | # compare 2 values returns one of undef, <0, =0, >0 |
268 | # returns undef if either or both input value are not numbers |
269 | sub fcmp #(fnum_str, fnum_str) return cond_code |
270 | { |
271 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
272 | if ($x eq "NaN" || $y eq "NaN") { |
273 | undef; |
274 | } else { |
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275 | local($xm,$xe,$ym,$ye) = split('E', $x."E$y"); |
276 | if ($xm eq '+0' || $ym eq '+0') { |
277 | return $xm <=> $ym; |
278 | } |
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279 | if ( $xe < $ye ) # adjust the exponents to be equal |
280 | { |
281 | $ym .= '0' x ($ye - $xe); |
282 | $ye = $xe; |
283 | } |
284 | elsif ( $ye < $xe ) # same here |
285 | { |
286 | $xm .= '0' x ($xe - $ye); |
287 | $xe = $ye; |
288 | } |
289 | return Math::BigInt::cmp($xm,$ym); |
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290 | } |
291 | } |
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292 | |
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293 | # square root by Newtons method. |
294 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
295 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
296 | if ($x eq 'NaN' || $x =~ /^-/) { |
297 | 'NaN'; |
298 | } elsif ($x eq '+0E+0') { |
299 | '+0E+0'; |
300 | } else { |
301 | local($xm, $xe) = split('E',$x); |
302 | $scale = $div_scale if (!$scale); |
303 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
304 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
305 | while ($gs < 2*$scale) { |
306 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
307 | $gs *= 2; |
308 | } |
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309 | new Math::BigFloat &fround($guess, $scale); |
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310 | } |
311 | } |
312 | |
313 | 1; |
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314 | __END__ |
315 | |
316 | =head1 NAME |
317 | |
318 | Math::BigFloat - Arbitrary length float math package |
319 | |
320 | =head1 SYNOPSIS |
321 | |
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322 | use Math::BigFloat; |
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323 | $f = Math::BigFloat->new($string); |
324 | |
325 | $f->fadd(NSTR) return NSTR addition |
326 | $f->fsub(NSTR) return NSTR subtraction |
327 | $f->fmul(NSTR) return NSTR multiplication |
328 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
329 | $f->fneg() return NSTR negation |
330 | $f->fabs() return NSTR absolute value |
331 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
332 | $f->fround(SCALE) return NSTR round to SCALE digits |
333 | $f->ffround(SCALE) return NSTR round at SCALEth place |
334 | $f->fnorm() return (NSTR) normalize |
335 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
336 | |
337 | =head1 DESCRIPTION |
338 | |
339 | All basic math operations are overloaded if you declare your big |
340 | floats as |
341 | |
342 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
343 | |
344 | =over 2 |
345 | |
346 | =item number format |
347 | |
348 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
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349 | have embedded whitespace. |
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350 | |
351 | =item Error returns 'NaN' |
352 | |
353 | An input parameter was "Not a Number" or divide by zero or sqrt of |
354 | negative number. |
355 | |
356 | =item Division is computed to |
357 | |
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358 | C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))> |
359 | digits by default. |
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360 | Also used for default sqrt scale. |
361 | |
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362 | =item Rounding is performed |
363 | |
364 | according to the value of |
365 | C<$Math::BigFloat::rnd_mode>: |
366 | |
367 | trunc truncate the value |
368 | zero round towards 0 |
369 | +inf round towards +infinity (round up) |
370 | -inf round towards -infinity (round down) |
371 | even round to the nearest, .5 to the even digit |
372 | odd round to the nearest, .5 to the odd digit |
373 | |
374 | The default is C<even> rounding. |
375 | |
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376 | =back |
377 | |
378 | =head1 BUGS |
379 | |
380 | The current version of this module is a preliminary version of the |
381 | real thing that is currently (as of perl5.002) under development. |
382 | |
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383 | The printf subroutine does not use the value of |
384 | C<$Math::BigFloat::rnd_mode> when rounding values for printing. |
385 | Consequently, the way to print rounded values is |
386 | to specify the number of digits both as an |
387 | argument to C<ffround> and in the C<%f> printf string, |
388 | as follows: |
389 | |
390 | printf "%.3f\n", $bigfloat->ffround(-3); |
391 | |
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392 | =head1 AUTHOR |
393 | |
394 | Mark Biggar |
395 | |
396 | =cut |