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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]},$_[1])}, |
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12 | '<=>' => sub {$_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])}, |
13 | 'cmp' => sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
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14 | '*' => sub {new Math::BigFloat &fmul}, |
15 | '/' => sub {new Math::BigFloat |
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16 | $_[2]? scalar fdiv($_[1],${$_[0]}) : |
17 | scalar fdiv(${$_[0]},$_[1])}, |
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18 | 'neg' => sub {new Math::BigFloat &fneg}, |
19 | 'abs' => sub {new Math::BigFloat &fabs}, |
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20 | |
21 | qw( |
22 | "" stringify |
23 | 0+ numify) # Order of arguments unsignificant |
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24 | ; |
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25 | |
26 | sub new { |
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27 | my ($class) = shift; |
28 | my ($foo) = fnorm(shift); |
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29 | bless \$foo, $class; |
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30 | } |
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31 | |
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32 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
33 | # comparing to direct compilation based on |
34 | # stringify |
35 | sub stringify { |
36 | my $n = ${$_[0]}; |
37 | |
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38 | my $minus = ($n =~ s/^([+-])// && $1 eq '-'); |
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39 | $n =~ s/E//; |
40 | |
41 | $n =~ s/([-+]\d+)$//; |
42 | |
43 | my $e = $1; |
44 | my $ln = length($n); |
45 | |
46 | if ($e > 0) { |
47 | $n .= "0" x $e . '.'; |
48 | } elsif (abs($e) < $ln) { |
49 | substr($n, $ln + $e, 0) = '.'; |
50 | } else { |
51 | $n = '.' . ("0" x (abs($e) - $ln)) . $n; |
52 | } |
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53 | $n = "-$n" if $minus; |
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54 | |
55 | # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/; |
56 | |
57 | return $n; |
58 | } |
59 | |
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60 | $div_scale = 40; |
61 | |
62 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
63 | |
64 | $rnd_mode = 'even'; |
65 | |
66 | sub fadd; sub fsub; sub fmul; sub fdiv; |
67 | sub fneg; sub fabs; sub fcmp; |
68 | sub fround; sub ffround; |
69 | sub fnorm; sub fsqrt; |
70 | |
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71 | # Convert a number to canonical string form. |
72 | # Takes something that looks like a number and converts it to |
73 | # the form /^[+-]\d+E[+-]\d+$/. |
74 | sub fnorm { #(string) return fnum_str |
75 | local($_) = @_; |
76 | s/\s+//g; # strip white space |
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77 | local $^W = 0; # $4 and $5 below might legitimately be undefined |
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78 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$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($xm); |
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161 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym), |
162 | Math::BigInt::babs($ym)), |
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163 | $xe-$ye-$scale); |
164 | } |
165 | } |
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166 | |
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167 | # round int $q based on fraction $r/$base using $rnd_mode |
168 | sub round { #(int_str, int_str, int_str) return int_str |
169 | local($q,$r,$base) = @_; |
170 | if ($q eq 'NaN' || $r eq 'NaN') { |
171 | 'NaN'; |
172 | } elsif ($rnd_mode eq 'trunc') { |
173 | $q; # just truncate |
174 | } else { |
175 | local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base); |
176 | if ( $cmp < 0 || |
177 | ($cmp == 0 && |
178 | ( $rnd_mode eq 'zero' || |
179 | ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || |
180 | ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || |
181 | ($rnd_mode eq 'even' && $q =~ /[24680]$/) || |
182 | ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { |
183 | $q; # round down |
184 | } else { |
185 | Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); |
186 | # round up |
187 | } |
188 | } |
189 | } |
190 | |
191 | # round the mantissa of $x to $scale digits |
192 | sub fround { #(fnum_str, scale) return fnum_str |
193 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
194 | if ($x eq 'NaN' || $scale <= 0) { |
195 | $x; |
196 | } else { |
197 | local($xm,$xe) = split('E',$x); |
198 | if (length($xm)-1 <= $scale) { |
199 | $x; |
200 | } else { |
201 | &norm(&round(substr($xm,$[,$scale+1), |
202 | "+0".substr($xm,$[+$scale+1,1),"+10"), |
203 | $xe+length($xm)-$scale-1); |
204 | } |
205 | } |
206 | } |
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207 | |
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208 | # round $x at the 10 to the $scale digit place |
209 | sub ffround { #(fnum_str, scale) return fnum_str |
210 | local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); |
211 | if ($x eq 'NaN') { |
212 | 'NaN'; |
213 | } else { |
214 | local($xm,$xe) = split('E',$x); |
215 | if ($xe >= $scale) { |
216 | $x; |
217 | } else { |
218 | $xe = length($xm)+$xe-$scale; |
219 | if ($xe < 1) { |
220 | '+0E+0'; |
221 | } elsif ($xe == 1) { |
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222 | # The first substr preserves the sign, passing a non- |
223 | # normalized "-0" to &round when rounding -0.006 (for |
224 | # example), purely so &round won't lose the sign. |
225 | &norm(&round(substr($xm,$[,1).'0', |
226 | "+0".substr($xm,$[+1,1),"+10"), $scale); |
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227 | } else { |
228 | &norm(&round(substr($xm,$[,$xe), |
229 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
230 | } |
231 | } |
232 | } |
233 | } |
234 | |
235 | # compare 2 values returns one of undef, <0, =0, >0 |
236 | # returns undef if either or both input value are not numbers |
237 | sub fcmp #(fnum_str, fnum_str) return cond_code |
238 | { |
239 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
240 | if ($x eq "NaN" || $y eq "NaN") { |
241 | undef; |
242 | } else { |
243 | ord($y) <=> ord($x) |
244 | || |
245 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), |
246 | (($xe <=> $ye) * (substr($x,$[,1).'1') |
247 | || Math::BigInt::cmp($xm,$ym)) |
248 | ); |
249 | } |
250 | } |
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251 | |
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252 | # square root by Newtons method. |
253 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
254 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
255 | if ($x eq 'NaN' || $x =~ /^-/) { |
256 | 'NaN'; |
257 | } elsif ($x eq '+0E+0') { |
258 | '+0E+0'; |
259 | } else { |
260 | local($xm, $xe) = split('E',$x); |
261 | $scale = $div_scale if (!$scale); |
262 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
263 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
264 | while ($gs < 2*$scale) { |
265 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
266 | $gs *= 2; |
267 | } |
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268 | new Math::BigFloat &fround($guess, $scale); |
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269 | } |
270 | } |
271 | |
272 | 1; |
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273 | __END__ |
274 | |
275 | =head1 NAME |
276 | |
277 | Math::BigFloat - Arbitrary length float math package |
278 | |
279 | =head1 SYNOPSIS |
280 | |
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281 | use Math::BigFloat; |
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282 | $f = Math::BigFloat->new($string); |
283 | |
284 | $f->fadd(NSTR) return NSTR addition |
285 | $f->fsub(NSTR) return NSTR subtraction |
286 | $f->fmul(NSTR) return NSTR multiplication |
287 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
288 | $f->fneg() return NSTR negation |
289 | $f->fabs() return NSTR absolute value |
290 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
291 | $f->fround(SCALE) return NSTR round to SCALE digits |
292 | $f->ffround(SCALE) return NSTR round at SCALEth place |
293 | $f->fnorm() return (NSTR) normalize |
294 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
295 | |
296 | =head1 DESCRIPTION |
297 | |
298 | All basic math operations are overloaded if you declare your big |
299 | floats as |
300 | |
301 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
302 | |
303 | =over 2 |
304 | |
305 | =item number format |
306 | |
307 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
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308 | have embedded whitespace. |
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309 | |
310 | =item Error returns 'NaN' |
311 | |
312 | An input parameter was "Not a Number" or divide by zero or sqrt of |
313 | negative number. |
314 | |
315 | =item Division is computed to |
316 | |
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317 | C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))> |
318 | digits by default. |
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319 | Also used for default sqrt scale. |
320 | |
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321 | =item Rounding is performed |
322 | |
323 | according to the value of |
324 | C<$Math::BigFloat::rnd_mode>: |
325 | |
326 | trunc truncate the value |
327 | zero round towards 0 |
328 | +inf round towards +infinity (round up) |
329 | -inf round towards -infinity (round down) |
330 | even round to the nearest, .5 to the even digit |
331 | odd round to the nearest, .5 to the odd digit |
332 | |
333 | The default is C<even> rounding. |
334 | |
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335 | =back |
336 | |
337 | =head1 BUGS |
338 | |
339 | The current version of this module is a preliminary version of the |
340 | real thing that is currently (as of perl5.002) under development. |
341 | |
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342 | The printf subroutine does not use the value of |
343 | C<$Math::BigFloat::rnd_mode> when rounding values for printing. |
344 | Consequently, the way to print rounded values is |
345 | to specify the number of digits both as an |
346 | argument to C<ffround> and in the C<%f> printf string, |
347 | as follows: |
348 | |
349 | printf "%.3f\n", $bigfloat->ffround(-3); |
350 | |
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351 | =head1 AUTHOR |
352 | |
353 | Mark Biggar |
354 | |
355 | =cut |