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]},$_[1])},
'<=>' => sub {$_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])},
'cmp' => sub {$_[2]? ($_[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);
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
no warnings; # $4 and $5 below might legitimately be undefined
if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/ && "$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),
Math::BigInt::babs($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) {
# The first substr preserves the sign, passing a non-
# normalized "-0" to &round when rounding -0.006 (for
# example), purely so &round won't lose the sign.
&norm(&round(substr($xm,$[,1).'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" || $y eq "NaN") {
undef;
} else {
local($xm,$xe,$ym,$ye) = split('E', $x."E$y");
if ($xm eq '+0' || $ym eq '+0') {
return $xm <=> $ym;
}
ord($y) <=> ord($x)
|| ($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
$float = new Math::BigFloat "2.123123123123123123123123123123123";
=over 2
=item number format
canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can
have embedded whitespace.
=item Error returns 'NaN'
An input parameter was "Not a Number" or divide by zero or sqrt of
negative number.
=item Division is computed to
C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))>
digits by default.
Also used for default sqrt scale.
=item Rounding is performed
according to the value of
C<$Math::BigFloat::rnd_mode>:
trunc truncate the value
zero round towards 0
+inf round towards +infinity (round up)
-inf round towards -infinity (round down)
even round to the nearest, .5 to the even digit
odd round to the nearest, .5 to the odd digit
The default is C<even> rounding.
=back
=head1 BUGS
The current version of this module is a preliminary version of the
real thing that is currently (as of perl5.002) under development.
The printf subroutine does not use the value of
C<$Math::BigFloat::rnd_mode> when rounding values for printing.
Consequently, the way to print rounded values is
to specify the number of digits both as an
argument to C<ffround> and in the C<%f> printf string,
as follows:
printf "%.3f\n", $bigfloat->ffround(-3);
=head1 AUTHOR
Mark Biggar
=cut