Commit | Line | Data |
a0d0e21e |
1 | package Math::BigFloat; |
2 | |
3 | use Math::BigInt; |
4 | |
5 | use Exporter; # just for use to be happy |
6 | @ISA = (Exporter); |
7 | |
a5f75d66 |
8 | use overload |
9 | '+' => sub {new Math::BigFloat &fadd}, |
10 | '-' => sub {new Math::BigFloat |
a0d0e21e |
11 | $_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])}, |
a5f75d66 |
12 | '<=>' => sub {new Math::BigFloat |
a0d0e21e |
13 | $_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])}, |
a5f75d66 |
14 | 'cmp' => sub {new Math::BigFloat |
a0d0e21e |
15 | $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, |
a5f75d66 |
16 | '*' => sub {new Math::BigFloat &fmul}, |
17 | '/' => sub {new Math::BigFloat |
a0d0e21e |
18 | $_[2]? scalar fdiv($_[1],${$_[0]}) : |
19 | scalar fdiv(${$_[0]},$_[1])}, |
a5f75d66 |
20 | 'neg' => sub {new Math::BigFloat &fneg}, |
21 | 'abs' => sub {new Math::BigFloat &fabs}, |
a0d0e21e |
22 | |
23 | qw( |
24 | "" stringify |
25 | 0+ numify) # Order of arguments unsignificant |
a5f75d66 |
26 | ; |
a0d0e21e |
27 | |
28 | sub new { |
a5f75d66 |
29 | my ($class) = shift; |
30 | my ($foo) = fnorm(shift); |
31 | panic("Not a number initialized to Math::BigFloat") if $foo eq "NaN"; |
32 | bless \$foo, $class; |
a0d0e21e |
33 | } |
34 | sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead |
35 | # comparing to direct compilation based on |
36 | # stringify |
37 | sub stringify { |
38 | my $n = ${$_[0]}; |
39 | |
9b599b2a |
40 | my $minus = ($n =~ s/^([+-])// && $1 eq '-'); |
a0d0e21e |
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 | } |
9b599b2a |
55 | $n = "-$n" if $minus; |
a0d0e21e |
56 | |
57 | # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/; |
58 | |
59 | return $n; |
60 | } |
61 | |
a0d0e21e |
62 | $div_scale = 40; |
63 | |
64 | # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. |
65 | |
66 | $rnd_mode = 'even'; |
67 | |
68 | sub fadd; sub fsub; sub fmul; sub fdiv; |
69 | sub fneg; sub fabs; sub fcmp; |
70 | sub fround; sub ffround; |
71 | sub fnorm; sub fsqrt; |
72 | |
a0d0e21e |
73 | # Convert a number to canonical string form. |
74 | # Takes something that looks like a number and converts it to |
75 | # the form /^[+-]\d+E[+-]\d+$/. |
76 | sub fnorm { #(string) return fnum_str |
77 | local($_) = @_; |
78 | s/\s+//g; # strip white space |
79 | if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { |
80 | &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); |
81 | } else { |
82 | 'NaN'; |
83 | } |
84 | } |
85 | |
86 | # normalize number -- for internal use |
87 | sub norm { #(mantissa, exponent) return fnum_str |
88 | local($_, $exp) = @_; |
89 | if ($_ eq 'NaN') { |
90 | 'NaN'; |
91 | } else { |
92 | s/^([+-])0+/$1/; # strip leading zeros |
93 | if (length($_) == 1) { |
94 | '+0E+0'; |
95 | } else { |
96 | $exp += length($1) if (s/(0+)$//); # strip trailing zeros |
97 | sprintf("%sE%+ld", $_, $exp); |
98 | } |
99 | } |
100 | } |
101 | |
102 | # negation |
103 | sub fneg { #(fnum_str) return fnum_str |
104 | local($_) = fnorm($_[$[]); |
105 | vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign |
106 | s/^H/N/; |
107 | $_; |
108 | } |
109 | |
110 | # absolute value |
111 | sub fabs { #(fnum_str) return fnum_str |
112 | local($_) = fnorm($_[$[]); |
113 | s/^-/+/; # mash sign |
114 | $_; |
115 | } |
116 | |
117 | # multiplication |
118 | sub fmul { #(fnum_str, fnum_str) return fnum_str |
119 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
120 | if ($x eq 'NaN' || $y eq 'NaN') { |
121 | 'NaN'; |
122 | } else { |
123 | local($xm,$xe) = split('E',$x); |
124 | local($ym,$ye) = split('E',$y); |
125 | &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); |
126 | } |
127 | } |
a5f75d66 |
128 | |
a0d0e21e |
129 | # addition |
130 | sub fadd { #(fnum_str, fnum_str) return fnum_str |
131 | local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
132 | if ($x eq 'NaN' || $y eq 'NaN') { |
133 | 'NaN'; |
134 | } else { |
135 | local($xm,$xe) = split('E',$x); |
136 | local($ym,$ye) = split('E',$y); |
137 | ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); |
138 | &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); |
139 | } |
140 | } |
141 | |
142 | # subtraction |
143 | sub fsub { #(fnum_str, fnum_str) return fnum_str |
144 | fadd($_[$[],fneg($_[$[+1])); |
145 | } |
146 | |
147 | # division |
148 | # args are dividend, divisor, scale (optional) |
149 | # result has at most max(scale, length(dividend), length(divisor)) digits |
150 | sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str |
151 | { |
152 | local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); |
153 | if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { |
154 | 'NaN'; |
155 | } else { |
156 | local($xm,$xe) = split('E',$x); |
157 | local($ym,$ye) = split('E',$y); |
158 | $scale = $div_scale if (!$scale); |
159 | $scale = length($xm)-1 if (length($xm)-1 > $scale); |
160 | $scale = length($ym)-1 if (length($ym)-1 > $scale); |
161 | $scale = $scale + length($ym) - length($xm); |
162 | &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),$ym), |
163 | $xe-$ye-$scale); |
164 | } |
165 | } |
a5f75d66 |
166 | |
a0d0e21e |
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 | } |
a5f75d66 |
207 | |
a0d0e21e |
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) { |
222 | &norm(&round('+0',"+0".substr($xm,$[+1,1),"+10"), $scale); |
223 | } else { |
224 | &norm(&round(substr($xm,$[,$xe), |
225 | "+0".substr($xm,$[+$xe,1),"+10"), $scale); |
226 | } |
227 | } |
228 | } |
229 | } |
230 | |
231 | # compare 2 values returns one of undef, <0, =0, >0 |
232 | # returns undef if either or both input value are not numbers |
233 | sub fcmp #(fnum_str, fnum_str) return cond_code |
234 | { |
235 | local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); |
236 | if ($x eq "NaN" || $y eq "NaN") { |
237 | undef; |
238 | } else { |
239 | ord($y) <=> ord($x) |
240 | || |
241 | ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), |
242 | (($xe <=> $ye) * (substr($x,$[,1).'1') |
243 | || Math::BigInt::cmp($xm,$ym)) |
244 | ); |
245 | } |
246 | } |
a5f75d66 |
247 | |
a0d0e21e |
248 | # square root by Newtons method. |
249 | sub fsqrt { #(fnum_str[, scale]) return fnum_str |
250 | local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); |
251 | if ($x eq 'NaN' || $x =~ /^-/) { |
252 | 'NaN'; |
253 | } elsif ($x eq '+0E+0') { |
254 | '+0E+0'; |
255 | } else { |
256 | local($xm, $xe) = split('E',$x); |
257 | $scale = $div_scale if (!$scale); |
258 | $scale = length($xm)-1 if ($scale < length($xm)-1); |
259 | local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); |
260 | while ($gs < 2*$scale) { |
261 | $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); |
262 | $gs *= 2; |
263 | } |
a5f75d66 |
264 | new Math::BigFloat &fround($guess, $scale); |
a0d0e21e |
265 | } |
266 | } |
267 | |
268 | 1; |
a5f75d66 |
269 | __END__ |
270 | |
271 | =head1 NAME |
272 | |
273 | Math::BigFloat - Arbitrary length float math package |
274 | |
275 | =head1 SYNOPSIS |
276 | |
a2008d6d |
277 | use Math::BigFloat; |
a5f75d66 |
278 | $f = Math::BigFloat->new($string); |
279 | |
280 | $f->fadd(NSTR) return NSTR addition |
281 | $f->fsub(NSTR) return NSTR subtraction |
282 | $f->fmul(NSTR) return NSTR multiplication |
283 | $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places |
284 | $f->fneg() return NSTR negation |
285 | $f->fabs() return NSTR absolute value |
286 | $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 |
287 | $f->fround(SCALE) return NSTR round to SCALE digits |
288 | $f->ffround(SCALE) return NSTR round at SCALEth place |
289 | $f->fnorm() return (NSTR) normalize |
290 | $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places |
291 | |
292 | =head1 DESCRIPTION |
293 | |
294 | All basic math operations are overloaded if you declare your big |
295 | floats as |
296 | |
297 | $float = new Math::BigFloat "2.123123123123123123123123123123123"; |
298 | |
299 | =over 2 |
300 | |
301 | =item number format |
302 | |
303 | canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can |
db696efe |
304 | have embedded whitespace. |
a5f75d66 |
305 | |
306 | =item Error returns 'NaN' |
307 | |
308 | An input parameter was "Not a Number" or divide by zero or sqrt of |
309 | negative number. |
310 | |
311 | =item Division is computed to |
312 | |
313 | C<max($div_scale,length(dividend)+length(divisor))> digits by default. |
314 | Also used for default sqrt scale. |
315 | |
316 | =back |
317 | |
318 | =head1 BUGS |
319 | |
320 | The current version of this module is a preliminary version of the |
321 | real thing that is currently (as of perl5.002) under development. |
322 | |
323 | =head1 AUTHOR |
324 | |
325 | Mark Biggar |
326 | |
327 | =cut |