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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]},$_[1])}, |
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19 | 'neg' => sub {new Math::BigFloat &fneg}, |
20 | 'abs' => sub {new Math::BigFloat &fabs}, |
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21 | |
22 | qw( |
23 | "" stringify |
24 | 0+ numify) # Order of arguments unsignificant |
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25 | ; |
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26 | |
27 | sub new { |
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28 | my ($class) = shift; |
29 | my ($foo) = fnorm(shift); |
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30 | bless \$foo, $class; |
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31 | } |
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32 | |
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33 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
34 | # comparing to direct compilation based on |
35 | # stringify |
36 | sub stringify { |
37 | my $n = ${$_[0]}; |
38 | |
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39 | my $minus = ($n =~ s/^([+-])// && $1 eq '-'); |
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40 | $n =~ s/E//; |
41 | |
42 | $n =~ s/([-+]\d+)$//; |
43 | |
44 | my $e = $1; |
45 | my $ln = length($n); |
46 | |
47 | if ($e > 0) { |
48 | $n .= "0" x $e . '.'; |
49 | } elsif (abs($e) < $ln) { |
50 | substr($n, $ln + $e, 0) = '.'; |
51 | } else { |
52 | $n = '.' . ("0" x (abs($e) - $ln)) . $n; |
53 | } |
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54 | $n = "-$n" if $minus; |
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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 |
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78 | no warnings; # $4 and $5 below might legitimately be undefined |
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79 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
80 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
81 | } else { |
82 | 'NaN'; |
83 | } |
84 | } |
85 | |
86 | # normalize number -- for internal use |
87 | sub norm { #(mantissa, exponent) return fnum_str |
88 | local($_, $exp) = @_; |
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89 | $exp = 0 unless defined $exp; |
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90 | if ($_ eq 'NaN') { |
91 | 'NaN'; |
92 | } else { |
93 | s/^([+-])0+/$1/; # strip leading zeros |
94 | if (length($_) == 1) { |
95 | '+0E+0'; |
96 | } else { |
97 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
98 | sprintf("%sE%+ld", $_, $exp); |
99 | } |
100 | } |
101 | } |
102 | |
103 | # negation |
104 | sub fneg { #(fnum_str) return fnum_str |
105 | local($_) = fnorm($_[$[]); |
106 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
107 | s/^H/N/; |
108 | $_; |
109 | } |
110 | |
111 | # absolute value |
112 | sub fabs { #(fnum_str) return fnum_str |
113 | local($_) = fnorm($_[$[]); |
114 | s/^-/+/; # mash sign |
115 | $_; |
116 | } |
117 | |
118 | # multiplication |
119 | sub fmul { #(fnum_str, fnum_str) return fnum_str |
120 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
121 | if ($x eq 'NaN' || $y eq 'NaN') { |
122 | 'NaN'; |
123 | } else { |
124 | local($xm,$xe) = split('E',$x); |
125 | local($ym,$ye) = split('E',$y); |
126 | &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); |
127 | } |
128 | } |
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129 | |
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130 | # addition |
131 | sub fadd { #(fnum_str, fnum_str) return fnum_str |
132 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
133 | if ($x eq 'NaN' || $y eq 'NaN') { |
134 | 'NaN'; |
135 | } else { |
136 | local($xm,$xe) = split('E',$x); |
137 | local($ym,$ye) = split('E',$y); |
138 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
139 | &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
140 | } |
141 | } |
142 | |
143 | # subtraction |
144 | sub fsub { #(fnum_str, fnum_str) return fnum_str |
145 | fadd($_[$[],fneg($_[$[+1])); |
146 | } |
147 | |
148 | # division |
149 | # args are dividend, divisor, scale (optional) |
150 | # result has at most max(scale, length(dividend), length(divisor)) digits |
151 | sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
152 | { |
153 | local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); |
154 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
155 | 'NaN'; |
156 | } else { |
157 | local($xm,$xe) = split('E',$x); |
158 | local($ym,$ye) = split('E',$y); |
159 | $scale = $div_scale if (!$scale); |
160 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
161 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
162 | $scale = $scale + length($ym) - length($xm); |
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163 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym), |
164 | Math::BigInt::babs($ym)), |
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165 | $xe-$ye-$scale); |
166 | } |
167 | } |
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168 | |
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169 | # round int $q based on fraction $r/$base using $rnd_mode |
170 | sub round { #(int_str, int_str, int_str) return int_str |
171 | local($q,$r,$base) = @_; |
172 | if ($q eq 'NaN' || $r eq 'NaN') { |
173 | 'NaN'; |
174 | } elsif ($rnd_mode eq 'trunc') { |
175 | $q; # just truncate |
176 | } else { |
177 | local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base); |
178 | if ( $cmp < 0 || |
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179 | ($cmp == 0 && ( |
180 | ($rnd_mode eq 'zero' ) || |
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181 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
182 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || |
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183 | ($rnd_mode eq 'even' && $q =~ /[13579]$/ ) || |
184 | ($rnd_mode eq 'odd' && $q =~ /[24680]$/ ) ) |
185 | ) |
186 | ) { |
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187 | $q; # round down |
188 | } else { |
189 | Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
190 | # round up |
191 | } |
192 | } |
193 | } |
194 | |
195 | # round the mantissa of $x to $scale digits |
196 | sub fround { #(fnum_str, scale) return fnum_str |
197 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
198 | if ($x eq 'NaN' || $scale <= 0) { |
199 | $x; |
200 | } else { |
201 | local($xm,$xe) = split('E',$x); |
202 | if (length($xm)-1 <= $scale) { |
203 | $x; |
204 | } else { |
205 | &norm(&round(substr($xm,$[,$scale+1), |
206 | "+0".substr($xm,$[+$scale+1,1),"+10"), |
207 | $xe+length($xm)-$scale-1); |
208 | } |
209 | } |
210 | } |
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211 | |
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212 | # round $x at the 10 to the $scale digit place |
213 | sub ffround { #(fnum_str, scale) return fnum_str |
214 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
215 | if ($x eq 'NaN') { |
216 | 'NaN'; |
217 | } else { |
218 | local($xm,$xe) = split('E',$x); |
219 | if ($xe >= $scale) { |
220 | $x; |
221 | } else { |
222 | $xe = length($xm)+$xe-$scale; |
223 | if ($xe < 1) { |
224 | '+0E+0'; |
225 | } elsif ($xe == 1) { |
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226 | # The first substr preserves the sign, passing a non- |
227 | # normalized "-0" to &round when rounding -0.006 (for |
228 | # example), purely so &round won't lose the sign. |
229 | &norm(&round(substr($xm,$[,1).'0', |
230 | "+0".substr($xm,$[+1,1),"+10"), $scale); |
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231 | } else { |
232 | &norm(&round(substr($xm,$[,$xe), |
233 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
234 | } |
235 | } |
236 | } |
237 | } |
238 | |
239 | # compare 2 values returns one of undef, <0, =0, >0 |
240 | # returns undef if either or both input value are not numbers |
241 | sub fcmp #(fnum_str, fnum_str) return cond_code |
242 | { |
243 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
244 | if ($x eq "NaN" || $y eq "NaN") { |
245 | undef; |
246 | } else { |
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247 | local($xm,$xe,$ym,$ye) = split('E', $x."E$y"); |
248 | if ($xm eq '+0' || $ym eq '+0') { |
249 | return $xm <=> $ym; |
250 | } |
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251 | if ( $xe < $ye ) # adjust the exponents to be equal |
252 | { |
253 | $ym .= '0' x ($ye - $xe); |
254 | $ye = $xe; |
255 | } |
256 | elsif ( $ye < $xe ) # same here |
257 | { |
258 | $xm .= '0' x ($xe - $ye); |
259 | $xe = $ye; |
260 | } |
261 | return Math::BigInt::cmp($xm,$ym); |
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262 | } |
263 | } |
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264 | |
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265 | # square root by Newtons method. |
266 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
267 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
268 | if ($x eq 'NaN' || $x =~ /^-/) { |
269 | 'NaN'; |
270 | } elsif ($x eq '+0E+0') { |
271 | '+0E+0'; |
272 | } else { |
273 | local($xm, $xe) = split('E',$x); |
274 | $scale = $div_scale if (!$scale); |
275 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
276 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
277 | while ($gs < 2*$scale) { |
278 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
279 | $gs *= 2; |
280 | } |
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281 | new Math::BigFloat &fround($guess, $scale); |
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282 | } |
283 | } |
284 | |
285 | 1; |
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286 | __END__ |
287 | |
288 | =head1 NAME |
289 | |
290 | Math::BigFloat - Arbitrary length float math package |
291 | |
292 | =head1 SYNOPSIS |
293 | |
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294 | use Math::BigFloat; |
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295 | $f = Math::BigFloat->new($string); |
296 | |
297 | $f->fadd(NSTR) return NSTR addition |
298 | $f->fsub(NSTR) return NSTR subtraction |
299 | $f->fmul(NSTR) return NSTR multiplication |
300 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
301 | $f->fneg() return NSTR negation |
302 | $f->fabs() return NSTR absolute value |
303 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
304 | $f->fround(SCALE) return NSTR round to SCALE digits |
305 | $f->ffround(SCALE) return NSTR round at SCALEth place |
306 | $f->fnorm() return (NSTR) normalize |
307 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
308 | |
309 | =head1 DESCRIPTION |
310 | |
311 | All basic math operations are overloaded if you declare your big |
312 | floats as |
313 | |
314 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
315 | |
316 | =over 2 |
317 | |
318 | =item number format |
319 | |
320 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
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321 | have embedded whitespace. |
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322 | |
323 | =item Error returns 'NaN' |
324 | |
325 | An input parameter was "Not a Number" or divide by zero or sqrt of |
326 | negative number. |
327 | |
328 | =item Division is computed to |
329 | |
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330 | C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))> |
331 | digits by default. |
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332 | Also used for default sqrt scale. |
333 | |
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334 | =item Rounding is performed |
335 | |
336 | according to the value of |
337 | C<$Math::BigFloat::rnd_mode>: |
338 | |
339 | trunc truncate the value |
340 | zero round towards 0 |
341 | +inf round towards +infinity (round up) |
342 | -inf round towards -infinity (round down) |
343 | even round to the nearest, .5 to the even digit |
344 | odd round to the nearest, .5 to the odd digit |
345 | |
346 | The default is C<even> rounding. |
347 | |
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348 | =back |
349 | |
350 | =head1 BUGS |
351 | |
352 | The current version of this module is a preliminary version of the |
353 | real thing that is currently (as of perl5.002) under development. |
354 | |
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355 | The printf subroutine does not use the value of |
356 | C<$Math::BigFloat::rnd_mode> when rounding values for printing. |
357 | Consequently, the way to print rounded values is |
358 | to specify the number of digits both as an |
359 | argument to C<ffround> and in the C<%f> printf string, |
360 | as follows: |
361 | |
362 | printf "%.3f\n", $bigfloat->ffround(-3); |
363 | |
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364 | =head1 AUTHOR |
365 | |
366 | Mark Biggar |
367 | |
368 | =cut |