package Math::BigFloat; use Math::BigInt; use Exporter; # just for use to be happy @ISA = (Exporter); use overload '+' => sub {new Math::BigFloat &fadd}, '-' => sub {new Math::BigFloat $_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])}, '<=>' => sub {new Math::BigFloat $_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])}, 'cmp' => sub {new Math::BigFloat $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])}, '*' => sub {new Math::BigFloat &fmul}, '/' => sub {new Math::BigFloat $_[2]? scalar fdiv($_[1],${$_[0]}) : scalar fdiv(${$_[0]},$_[1])}, 'neg' => sub {new Math::BigFloat &fneg}, 'abs' => sub {new Math::BigFloat &fabs}, qw( "" stringify 0+ numify) # Order of arguments unsignificant ; sub new { my ($class) = shift; my ($foo) = fnorm(shift); panic("Not a number initialized to Math::BigFloat") if $foo eq "NaN"; bless \$foo, $class; } sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead # comparing to direct compilation based on # stringify sub stringify { my $n = ${$_[0]}; my $minus = ($n =~ s/^([+-])// && $1 eq '-'); $n =~ s/E//; $n =~ s/([-+]\d+)$//; my $e = $1; my $ln = length($n); if ($e > 0) { $n .= "0" x $e . '.'; } elsif (abs($e) < $ln) { substr($n, $ln + $e, 0) = '.'; } else { $n = '.' . ("0" x (abs($e) - $ln)) . $n; } $n = "-$n" if $minus; # 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/; return $n; } $div_scale = 40; # Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'. $rnd_mode = 'even'; sub fadd; sub fsub; sub fmul; sub fdiv; sub fneg; sub fabs; sub fcmp; sub fround; sub ffround; sub fnorm; sub fsqrt; # Convert a number to canonical string form. # Takes something that looks like a number and converts it to # the form /^[+-]\d+E[+-]\d+$/. sub fnorm { #(string) return fnum_str local($_) = @_; s/\s+//g; # strip white space if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') { &norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6)); } else { 'NaN'; } } # normalize number -- for internal use sub norm { #(mantissa, exponent) return fnum_str local($_, $exp) = @_; if ($_ eq 'NaN') { 'NaN'; } else { s/^([+-])0+/$1/; # strip leading zeros if (length($_) == 1) { '+0E+0'; } else { $exp += length($1) if (s/(0+)$//); # strip trailing zeros sprintf("%sE%+ld", $_, $exp); } } } # negation sub fneg { #(fnum_str) return fnum_str local($_) = fnorm($_[$[]); vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign s/^H/N/; $_; } # absolute value sub fabs { #(fnum_str) return fnum_str local($_) = fnorm($_[$[]); s/^-/+/; # mash sign $_; } # multiplication sub fmul { #(fnum_str, fnum_str) return fnum_str local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); if ($x eq 'NaN' || $y eq 'NaN') { 'NaN'; } else { local($xm,$xe) = split('E',$x); local($ym,$ye) = split('E',$y); &norm(Math::BigInt::bmul($xm,$ym),$xe+$ye); } } # addition sub fadd { #(fnum_str, fnum_str) return fnum_str local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1])); if ($x eq 'NaN' || $y eq 'NaN') { 'NaN'; } else { local($xm,$xe) = split('E',$x); local($ym,$ye) = split('E',$y); ($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye); &norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye); } } # subtraction sub fsub { #(fnum_str, fnum_str) return fnum_str fadd($_[$[],fneg($_[$[+1])); } # division # args are dividend, divisor, scale (optional) # result has at most max(scale, length(dividend), length(divisor)) digits sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str { local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]); if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') { 'NaN'; } else { local($xm,$xe) = split('E',$x); local($ym,$ye) = split('E',$y); $scale = $div_scale if (!$scale); $scale = length($xm)-1 if (length($xm)-1 > $scale); $scale = length($ym)-1 if (length($ym)-1 > $scale); $scale = $scale + length($ym) - length($xm); &norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),$ym), $xe-$ye-$scale); } } # round int $q based on fraction $r/$base using $rnd_mode sub round { #(int_str, int_str, int_str) return int_str local($q,$r,$base) = @_; if ($q eq 'NaN' || $r eq 'NaN') { 'NaN'; } elsif ($rnd_mode eq 'trunc') { $q; # just truncate } else { local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base); if ( $cmp < 0 || ($cmp == 0 && ( $rnd_mode eq 'zero' || ($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) || ($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) || ($rnd_mode eq 'even' && $q =~ /[24680]$/) || ($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) { $q; # round down } else { Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1')); # round up } } } # round the mantissa of $x to $scale digits sub fround { #(fnum_str, scale) return fnum_str local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); if ($x eq 'NaN' || $scale <= 0) { $x; } else { local($xm,$xe) = split('E',$x); if (length($xm)-1 <= $scale) { $x; } else { &norm(&round(substr($xm,$[,$scale+1), "+0".substr($xm,$[+$scale+1,1),"+10"), $xe+length($xm)-$scale-1); } } } # round $x at the 10 to the $scale digit place sub ffround { #(fnum_str, scale) return fnum_str local($x,$scale) = (fnorm($_[$[]),$_[$[+1]); if ($x eq 'NaN') { 'NaN'; } else { local($xm,$xe) = split('E',$x); if ($xe >= $scale) { $x; } else { $xe = length($xm)+$xe-$scale; if ($xe < 1) { '+0E+0'; } elsif ($xe == 1) { &norm(&round('+0',"+0".substr($xm,$[+1,1),"+10"), $scale); } else { &norm(&round(substr($xm,$[,$xe), "+0".substr($xm,$[+$xe,1),"+10"), $scale); } } } } # compare 2 values returns one of undef, <0, =0, >0 # returns undef if either or both input value are not numbers sub fcmp #(fnum_str, fnum_str) return cond_code { local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1])); if ($x eq "NaN" || $y eq "NaN") { undef; } else { ord($y) <=> ord($x) || ( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"), (($xe <=> $ye) * (substr($x,$[,1).'1') || Math::BigInt::cmp($xm,$ym)) ); } } # square root by Newtons method. sub fsqrt { #(fnum_str[, scale]) return fnum_str local($x, $scale) = (fnorm($_[$[]), $_[$[+1]); if ($x eq 'NaN' || $x =~ /^-/) { 'NaN'; } elsif ($x eq '+0E+0') { '+0E+0'; } else { local($xm, $xe) = split('E',$x); $scale = $div_scale if (!$scale); $scale = length($xm)-1 if ($scale < length($xm)-1); local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2)); while ($gs < 2*$scale) { $guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5"); $gs *= 2; } new Math::BigFloat &fround($guess, $scale); } } 1; __END__ =head1 NAME Math::BigFloat - Arbitrary length float math package =head1 SYNOPSIS use Math::BigFloat; $f = Math::BigFloat->new($string); $f->fadd(NSTR) return NSTR addition $f->fsub(NSTR) return NSTR subtraction $f->fmul(NSTR) return NSTR multiplication $f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places $f->fneg() return NSTR negation $f->fabs() return NSTR absolute value $f->fcmp(NSTR) return CODE compare undef,<0,=0,>0 $f->fround(SCALE) return NSTR round to SCALE digits $f->ffround(SCALE) return NSTR round at SCALEth place $f->fnorm() return (NSTR) normalize $f->fsqrt([SCALE]) return NSTR sqrt to SCALE places =head1 DESCRIPTION All basic math operations are overloaded if you declare your big floats as $float = new Math::BigFloat "2.123123123123123123123123123123123"; =over 2 =item number format canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can have imbedded whitespace. =item Error returns 'NaN' An input parameter was "Not a Number" or divide by zero or sqrt of negative number. =item Division is computed to C digits by default. Also used for default sqrt scale. =back =head1 BUGS The current version of this module is a preliminary version of the real thing that is currently (as of perl5.002) under development. =head1 AUTHOR Mark Biggar =cut