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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); |
29 | panic("Not a number initialized to Math::BigFloat") if $foo eq "NaN"; |
30 | bless \$foo, $class; |
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31 | } |
32 | sub numify { 0 + "${$_[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($_) = @_; |
76 | s/\s+//g; # strip white space |
77 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
78 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
79 | } else { |
80 | 'NaN'; |
81 | } |
82 | } |
83 | |
84 | # normalize number -- for internal use |
85 | sub norm { #(mantissa, exponent) return fnum_str |
86 | local($_, $exp) = @_; |
87 | if ($_ eq 'NaN') { |
88 | 'NaN'; |
89 | } else { |
90 | s/^([+-])0+/$1/; # strip leading zeros |
91 | if (length($_) == 1) { |
92 | '+0E+0'; |
93 | } else { |
94 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
95 | sprintf("%sE%+ld", $_, $exp); |
96 | } |
97 | } |
98 | } |
99 | |
100 | # negation |
101 | sub fneg { #(fnum_str) return fnum_str |
102 | local($_) = fnorm($_[$[]); |
103 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
104 | s/^H/N/; |
105 | $_; |
106 | } |
107 | |
108 | # absolute value |
109 | sub fabs { #(fnum_str) return fnum_str |
110 | local($_) = fnorm($_[$[]); |
111 | s/^-/+/; # mash sign |
112 | $_; |
113 | } |
114 | |
115 | # multiplication |
116 | sub fmul { #(fnum_str, fnum_str) return fnum_str |
117 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
118 | if ($x eq 'NaN' || $y eq 'NaN') { |
119 | 'NaN'; |
120 | } else { |
121 | local($xm,$xe) = split('E',$x); |
122 | local($ym,$ye) = split('E',$y); |
123 | &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); |
124 | } |
125 | } |
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126 | |
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127 | # addition |
128 | sub fadd { #(fnum_str, fnum_str) return fnum_str |
129 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
130 | if ($x eq 'NaN' || $y eq 'NaN') { |
131 | 'NaN'; |
132 | } else { |
133 | local($xm,$xe) = split('E',$x); |
134 | local($ym,$ye) = split('E',$y); |
135 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
136 | &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
137 | } |
138 | } |
139 | |
140 | # subtraction |
141 | sub fsub { #(fnum_str, fnum_str) return fnum_str |
142 | fadd($_[$[],fneg($_[$[+1])); |
143 | } |
144 | |
145 | # division |
146 | # args are dividend, divisor, scale (optional) |
147 | # result has at most max(scale, length(dividend), length(divisor)) digits |
148 | sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
149 | { |
150 | local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); |
151 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
152 | 'NaN'; |
153 | } else { |
154 | local($xm,$xe) = split('E',$x); |
155 | local($ym,$ye) = split('E',$y); |
156 | $scale = $div_scale if (!$scale); |
157 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
158 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
159 | $scale = $scale + length($ym) - length($xm); |
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160 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym), |
161 | Math::BigInt::babs($ym)), |
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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) { |
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221 | # The first substr preserves the sign, passing a non- |
222 | # normalized "-0" to &round when rounding -0.006 (for |
223 | # example), purely so &round won't lose the sign. |
224 | &norm(&round(substr($xm,$[,1).'0', |
225 | "+0".substr($xm,$[+1,1),"+10"), $scale); |
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226 | } else { |
227 | &norm(&round(substr($xm,$[,$xe), |
228 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
229 | } |
230 | } |
231 | } |
232 | } |
233 | |
234 | # compare 2 values returns one of undef, <0, =0, >0 |
235 | # returns undef if either or both input value are not numbers |
236 | sub fcmp #(fnum_str, fnum_str) return cond_code |
237 | { |
238 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
239 | if ($x eq "NaN" || $y eq "NaN") { |
240 | undef; |
241 | } else { |
242 | ord($y) <=> ord($x) |
243 | || |
244 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), |
245 | (($xe <=> $ye) * (substr($x,$[,1).'1') |
246 | || Math::BigInt::cmp($xm,$ym)) |
247 | ); |
248 | } |
249 | } |
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250 | |
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251 | # square root by Newtons method. |
252 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
253 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
254 | if ($x eq 'NaN' || $x =~ /^-/) { |
255 | 'NaN'; |
256 | } elsif ($x eq '+0E+0') { |
257 | '+0E+0'; |
258 | } else { |
259 | local($xm, $xe) = split('E',$x); |
260 | $scale = $div_scale if (!$scale); |
261 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
262 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
263 | while ($gs < 2*$scale) { |
264 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
265 | $gs *= 2; |
266 | } |
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267 | new Math::BigFloat &fround($guess, $scale); |
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268 | } |
269 | } |
270 | |
271 | 1; |
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272 | __END__ |
273 | |
274 | =head1 NAME |
275 | |
276 | Math::BigFloat - Arbitrary length float math package |
277 | |
278 | =head1 SYNOPSIS |
279 | |
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280 | use Math::BigFloat; |
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281 | $f = Math::BigFloat->new($string); |
282 | |
283 | $f->fadd(NSTR) return NSTR addition |
284 | $f->fsub(NSTR) return NSTR subtraction |
285 | $f->fmul(NSTR) return NSTR multiplication |
286 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
287 | $f->fneg() return NSTR negation |
288 | $f->fabs() return NSTR absolute value |
289 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
290 | $f->fround(SCALE) return NSTR round to SCALE digits |
291 | $f->ffround(SCALE) return NSTR round at SCALEth place |
292 | $f->fnorm() return (NSTR) normalize |
293 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
294 | |
295 | =head1 DESCRIPTION |
296 | |
297 | All basic math operations are overloaded if you declare your big |
298 | floats as |
299 | |
300 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
301 | |
302 | =over 2 |
303 | |
304 | =item number format |
305 | |
306 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
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307 | have embedded whitespace. |
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308 | |
309 | =item Error returns 'NaN' |
310 | |
311 | An input parameter was "Not a Number" or divide by zero or sqrt of |
312 | negative number. |
313 | |
314 | =item Division is computed to |
315 | |
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316 | C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))> |
317 | digits by default. |
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318 | Also used for default sqrt scale. |
319 | |
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320 | =item Rounding is performed |
321 | |
322 | according to the value of |
323 | C<$Math::BigFloat::rnd_mode>: |
324 | |
325 | trunc truncate the value |
326 | zero round towards 0 |
327 | +inf round towards +infinity (round up) |
328 | -inf round towards -infinity (round down) |
329 | even round to the nearest, .5 to the even digit |
330 | odd round to the nearest, .5 to the odd digit |
331 | |
332 | The default is C<even> rounding. |
333 | |
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334 | =back |
335 | |
336 | =head1 BUGS |
337 | |
338 | The current version of this module is a preliminary version of the |
339 | real thing that is currently (as of perl5.002) under development. |
340 | |
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341 | The printf subroutine does not use the value of |
342 | C<$Math::BigFloat::rnd_mode> when rounding values for printing. |
343 | Consequently, the way to print rounded values is |
344 | to specify the number of digits both as an |
345 | argument to C<ffround> and in the C<%f> printf string, |
346 | as follows: |
347 | |
348 | printf "%.3f\n", $bigfloat->ffround(-3); |
349 | |
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350 | =head1 AUTHOR |
351 | |
352 | Mark Biggar |
353 | |
354 | =cut |