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root |
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package bigrat; |
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require "bigint.pl"; |
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# |
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# This library is no longer being maintained, and is included for backward |
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# compatibility with Perl 4 programs which may require it. |
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# |
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# In particular, this should not be used as an example of modern Perl |
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# programming techniques. |
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# |
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# Arbitrary size rational math package |
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# |
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# by Mark Biggar |
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# |
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# Input values to these routines consist of strings of the form |
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# m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|. |
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# Examples: |
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# "+0/1" canonical zero value |
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# "3" canonical value "+3/1" |
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# " -123/123 123" canonical value "-1/1001" |
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# "123 456/7890" canonical value "+20576/1315" |
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# Output values always include a sign and no leading zeros or |
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# white space. |
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# This package makes use of the bigint package. |
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# The string 'NaN' is used to represent the result when input arguments |
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# that are not numbers, as well as the result of dividing by zero and |
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# the sqrt of a negative number. |
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# Extreamly naive algorthims are used. |
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# |
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# Routines provided are: |
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# |
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# rneg(RAT) return RAT negation |
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# rabs(RAT) return RAT absolute value |
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# rcmp(RAT,RAT) return CODE compare numbers (undef,<0,=0,>0) |
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# radd(RAT,RAT) return RAT addition |
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# rsub(RAT,RAT) return RAT subtraction |
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# rmul(RAT,RAT) return RAT multiplication |
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# rdiv(RAT,RAT) return RAT division |
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# rmod(RAT) return (RAT,RAT) integer and fractional parts |
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# rnorm(RAT) return RAT normalization |
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# rsqrt(RAT, cycles) return RAT square root |
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# Convert a number to the canonical string form m|^[+-]\d+/\d+|. |
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sub main'rnorm { #(string) return rat_num |
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local($_) = @_; |
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s/\s+//g; |
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if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) { |
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&norm($1, $3 ? $3 : '+1'); |
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} else { |
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'NaN'; |
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} |
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} |
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# Normalize by reducing to lowest terms |
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sub norm { #(bint, bint) return rat_num |
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local($num,$dom) = @_; |
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if ($num eq 'NaN') { |
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'NaN'; |
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} elsif ($dom eq 'NaN') { |
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'NaN'; |
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} elsif ($dom =~ /^[+-]?0+$/) { |
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'NaN'; |
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} else { |
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local($gcd) = &'bgcd($num,$dom); |
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$gcd =~ s/^-/+/; |
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if ($gcd ne '+1') { |
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$num = &'bdiv($num,$gcd); |
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$dom = &'bdiv($dom,$gcd); |
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} else { |
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$num = &'bnorm($num); |
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$dom = &'bnorm($dom); |
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} |
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substr($dom,$[,1) = ''; |
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"$num/$dom"; |
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} |
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} |
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# negation |
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sub main'rneg { #(rat_num) return rat_num |
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local($_) = &'rnorm(@_); |
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tr/-+/+-/ if ($_ ne '+0/1'); |
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$_; |
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} |
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# absolute value |
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sub main'rabs { #(rat_num) return $rat_num |
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local($_) = &'rnorm(@_); |
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substr($_,$[,1) = '+' unless $_ eq 'NaN'; |
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$_; |
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} |
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# multipication |
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sub main'rmul { #(rat_num, rat_num) return rat_num |
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local($xn,$xd) = split('/',&'rnorm($_[$[])); |
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local($yn,$yd) = split('/',&'rnorm($_[$[+1])); |
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&norm(&'bmul($xn,$yn),&'bmul($xd,$yd)); |
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} |
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# division |
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sub main'rdiv { #(rat_num, rat_num) return rat_num |
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local($xn,$xd) = split('/',&'rnorm($_[$[])); |
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local($yn,$yd) = split('/',&'rnorm($_[$[+1])); |
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&norm(&'bmul($xn,$yd),&'bmul($xd,$yn)); |
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} |
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# addition |
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sub main'radd { #(rat_num, rat_num) return rat_num |
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local($xn,$xd) = split('/',&'rnorm($_[$[])); |
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local($yn,$yd) = split('/',&'rnorm($_[$[+1])); |
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&norm(&'badd(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd)); |
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} |
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# subtraction |
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sub main'rsub { #(rat_num, rat_num) return rat_num |
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local($xn,$xd) = split('/',&'rnorm($_[$[])); |
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local($yn,$yd) = split('/',&'rnorm($_[$[+1])); |
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&norm(&'bsub(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd)); |
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} |
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# comparison |
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sub main'rcmp { #(rat_num, rat_num) return cond_code |
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local($xn,$xd) = split('/',&'rnorm($_[$[])); |
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local($yn,$yd) = split('/',&'rnorm($_[$[+1])); |
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&bigint'cmp(&'bmul($xn,$yd),&'bmul($yn,$xd)); |
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} |
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# int and frac parts |
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sub main'rmod { #(rat_num) return (rat_num,rat_num) |
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local($xn,$xd) = split('/',&'rnorm(@_)); |
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local($i,$f) = &'bdiv($xn,$xd); |
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if (wantarray) { |
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("$i/1", "$f/$xd"); |
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} else { |
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"$i/1"; |
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} |
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} |
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# square root by Newtons method. |
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# cycles specifies the number of iterations default: 5 |
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sub main'rsqrt { #(fnum_str[, cycles]) return fnum_str |
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local($x, $scale) = (&'rnorm($_[$[]), $_[$[+1]); |
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if ($x eq 'NaN') { |
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'NaN'; |
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} elsif ($x =~ /^-/) { |
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'NaN'; |
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} else { |
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local($gscale, $guess) = (0, '+1/1'); |
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$scale = 5 if (!$scale); |
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while ($gscale++ < $scale) { |
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$guess = &'rmul(&'radd($guess,&'rdiv($x,$guess)),"+1/2"); |
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} |
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"$guess"; # quotes necessary due to perl bug |
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} |
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} |
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1; |
