[p5sagit/p5-mst-13.2.git] / lib / Math / BigFloat.pm

package Math::BigFloat;

use Math::BigInt;

use Exporter;  # just for use to be happy
@ISA = (Exporter);
$VERSION = '0.03';

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])},
'%'	=>	sub {new Math::BigFloat
		       $_[2]? scalar fmod($_[1],${$_[0]}) :
			 scalar fmod(${$_[0]},$_[1])},
'neg'	=>	sub {new Math::BigFloat &fneg},
'abs'	=>	sub {new Math::BigFloat &fabs},
'int'	=>	sub {new Math::BigInt &f2int},

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 ( defined $e )
    {
        if ($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;
}

sub import {
  shift;
  return unless @_;
  die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
  overload::constant float => sub {Math::BigFloat->new(shift)};
}

$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) = @_;
	$exp = 0 unless defined $exp;
    if ($_ 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);
    }
}

# modular division
#   args are dividend, divisor
sub fmod #(fnum_str, fnum_str) return fnum_str
{
    local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
    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);
	if ( $xe < $ye )
	{
		$ym .= ('0' x ($ye-$xe));
	}
	else
	{
		$xm .= ('0' x ($xe-$ye));
	}
	&norm(Math::BigInt::bmod($xm,$ym));
    }
}
# 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($xm,$[+$scale+1),"+1"."0" x length(substr($xm,$[+$scale+1))),
		  $xe+length($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"."0" x length(substr($xm,$[+1))), $scale);
	    } else {
		&norm(&round(substr($xm,$[,$xe),
		      "+0".substr($xm,$[+$xe),
		      "+1"."0" x length(substr($xm,$[+$xe))), $scale);
	    }
	}
    }
}

# Calculate the integer part of $x
sub f2int { #(fnum_str) return inum_str
    local($x) = ${$_[$[]};
    if ($x eq 'NaN') {
	die "Attempt to take int(NaN)";
    } else {
	local($xm,$xe) = split('E',$x);
	if ($xe >= 0) {
	    $xm . '0' x $xe;
	} else {
	    $xe = length($xm)+$xe;
	    if ($xe <= 1) {
		'+0';
	    } else {
	        substr($xm,$[,$xe);
	    }
	}
    }
}

# 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;
	}
	if ( $xe < $ye )	# adjust the exponents to be equal
	{
		$ym .= '0' x ($ye - $xe);
		$ye = $xe;
	}
	elsif ( $ye < $xe )	# same here
	{
		$xm .= '0' x ($xe - $ye);
		$xe = $ye;
	}
	return Math::BigInt::cmp($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->fmod(NSTR) returns NSTR           modular remainder
  $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
Patches by John Peacock Apr 2001
=cut
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);
288d023a	7	$VERSION = '0.03';
a0d0e21e	8
a5f75d66	9	use overload
	10	'+' => sub {new Math::BigFloat &fadd},
	11	'-' => sub {new Math::BigFloat
a0d0e21e	12	$_[2]? fsub($_[1],${$_[0]}) : fsub(${$_[0]},$_[1])},
5d7098d5	13	'<=>' => sub {$_[2]? fcmp($_[1],${$_[0]}) : fcmp(${$_[0]},$_[1])},
5d7098d5	14	'cmp' => sub {$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
a5f75d66	15	'*' => sub {new Math::BigFloat &fmul},
288d023a	16	'/' => sub {new Math::BigFloat
a0d0e21e	17	$_[2]? scalar fdiv($_[1],${$_[0]}) :
a0d0e21e	18	scalar fdiv(${$_[0]},$_[1])},
288d023a	19	'%' => sub {new Math::BigFloat
	20	$_[2]? scalar fmod($_[1],${$_[0]}) :
	21	scalar fmod(${$_[0]},$_[1])},
a5f75d66	22	'neg' => sub {new Math::BigFloat &fneg},
a5f75d66	23	'abs' => sub {new Math::BigFloat &fabs},
f216259d	24	'int' => sub {new Math::BigInt &f2int},
a0d0e21e	25
	26	qw(
	27	"" stringify
	28	0+ numify) # Order of arguments unsignificant
a5f75d66	29	;
a0d0e21e	30
a0d0e21e	31	sub new {
a5f75d66	32	my ($class) = shift;
a5f75d66	33	my ($foo) = fnorm(shift);
a5f75d66	34	bless \$foo, $class;
a0d0e21e	35	}
0e8b9368	36
a0d0e21e	37	sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
	38	# comparing to direct compilation based on
	39	# stringify
	40	sub stringify {
	41	my $n = ${$_[0]};
	42
9b599b2a	43	my $minus = ($n =~ s/^([+-])// && $1 eq '-');
a0d0e21e	44	$n =~ s/E//;
	45
	46	$n =~ s/([-+]\d+)$//;
	47
	48	my $e = $1;
	49	my $ln = length($n);
	50
288d023a	51	if ( defined $e )
	52	{
	53	if ($e > 0) {
	54	$n .= "0" x $e . '.';
	55	} elsif (abs($e) < $ln) {
	56	substr($n, $ln + $e, 0) = '.';
	57	} else {
	58	$n = '.' . ("0" x (abs($e) - $ln)) . $n;
	59	}
a0d0e21e	60	}
9b599b2a	61	$n = "-$n" if $minus;
a0d0e21e	62
	63	# 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/;
	64
	65	return $n;
	66	}
	67
f216259d	68	sub import {
	69	shift;
	70	return unless @_;
	71	die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
	72	overload::constant float => sub {Math::BigFloat->new(shift)};
	73	}
	74
a0d0e21e	75	$div_scale = 40;
	76
	77	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	78
	79	$rnd_mode = 'even';
	80
	81	sub fadd; sub fsub; sub fmul; sub fdiv;
	82	sub fneg; sub fabs; sub fcmp;
	83	sub fround; sub ffround;
	84	sub fnorm; sub fsqrt;
	85
a0d0e21e	86	# Convert a number to canonical string form.
	87	# Takes something that looks like a number and converts it to
	88	# the form /^[+-]\d+E[+-]\d+$/.
	89	sub fnorm { #(string) return fnum_str
	90	local($_) = @_;
	91	s/\s+//g; # strip white space
db376a24	92	no warnings; # $4 and $5 below might legitimately be undefined
a0d0e21e	93	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
	94	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
	95	} else {
	96	'NaN';
	97	}
	98	}
	99
	100	# normalize number -- for internal use
	101	sub norm { #(mantissa, exponent) return fnum_str
	102	local($_, $exp) = @_;
3deb277d	103	$exp = 0 unless defined $exp;
a0d0e21e	104	if ($_ eq 'NaN') {
	105	'NaN';
	106	} else {
	107	s/^([+-])0+/$1/; # strip leading zeros
	108	if (length($_) == 1) {
	109	'+0E+0';
	110	} else {
	111	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	112	sprintf("%sE%+ld", $_, $exp);
	113	}
	114	}
	115	}
	116
	117	# negation
	118	sub fneg { #(fnum_str) return fnum_str
	119	local($_) = fnorm($_[$[]);
	120	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
	121	s/^H/N/;
	122	$_;
	123	}
	124
	125	# absolute value
	126	sub fabs { #(fnum_str) return fnum_str
	127	local($_) = fnorm($_[$[]);
	128	s/^-/+/; # mash sign
	129	$_;
	130	}
	131
	132	# multiplication
	133	sub fmul { #(fnum_str, fnum_str) return fnum_str
	134	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	135	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	136	'NaN';
	137	} else {
	138	local($xm,$xe) = split('E',$x);
	139	local($ym,$ye) = split('E',$y);
	140	&norm(Math::BigInt::bmul($xm,$ym),$xe+$ye);
	141	}
	142	}
a5f75d66	143
a0d0e21e	144	# addition
	145	sub fadd { #(fnum_str, fnum_str) return fnum_str
	146	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	147	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	148	'NaN';
	149	} else {
	150	local($xm,$xe) = split('E',$x);
	151	local($ym,$ye) = split('E',$y);
	152	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	153	&norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	154	}
	155	}
	156
	157	# subtraction
	158	sub fsub { #(fnum_str, fnum_str) return fnum_str
288d023a	159	fadd($_[$[],fneg($_[$[+1]));
a0d0e21e	160	}
	161
	162	# division
	163	# args are dividend, divisor, scale (optional)
	164	# result has at most max(scale, length(dividend), length(divisor)) digits
	165	sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	166	{
	167	local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]);
	168	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	169	'NaN';
	170	} else {
	171	local($xm,$xe) = split('E',$x);
	172	local($ym,$ye) = split('E',$y);
	173	$scale = $div_scale if (!$scale);
	174	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	175	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	176	$scale = $scale + length($ym) - length($xm);
5d7098d5	177	&norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),
5d7098d5	178	Math::BigInt::babs($ym)),
a0d0e21e	179	$xe-$ye-$scale);
	180	}
	181	}
a5f75d66	182
288d023a	183	# modular division
	184	# args are dividend, divisor
	185	sub fmod #(fnum_str, fnum_str) return fnum_str
	186	{
	187	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	188	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	189	'NaN';
	190	} else {
	191	local($xm,$xe) = split('E',$x);
	192	local($ym,$ye) = split('E',$y);
	193	if ( $xe < $ye )
	194	{
	195	$ym .= ('0' x ($ye-$xe));
	196	}
	197	else
	198	{
	199	$xm .= ('0' x ($xe-$ye));
	200	}
	201	&norm(Math::BigInt::bmod($xm,$ym));
	202	}
	203	}
a0d0e21e	204	# round int $q based on fraction $r/$base using $rnd_mode
	205	sub round { #(int_str, int_str, int_str) return int_str
	206	local($q,$r,$base) = @_;
	207	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	208	'NaN';
	209	} elsif ($rnd_mode eq 'trunc') {
	210	$q; # just truncate
	211	} else {
	212	local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base);
	213	if ( $cmp < 0 \|\|
3deb277d	214	($cmp == 0 && (
3deb277d	215	($rnd_mode eq 'zero' ) \|\|
a0d0e21e	216	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
a0d0e21e	217	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
288d023a	218	($rnd_mode eq 'even' && $q =~ /[24680]$/ ) \|\|
	219	($rnd_mode eq 'odd' && $q =~ /[13579]$/ ) )
	220	)
3deb277d	221	) {
a0d0e21e	222	$q; # round down
	223	} else {
	224	Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
	225	# round up
	226	}
	227	}
	228	}
	229
	230	# round the mantissa of $x to $scale digits
	231	sub fround { #(fnum_str, scale) return fnum_str
	232	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	233	if ($x eq 'NaN' \|\| $scale <= 0) {
	234	$x;
	235	} else {
	236	local($xm,$xe) = split('E',$x);
	237	if (length($xm)-1 <= $scale) {
	238	$x;
	239	} else {
288d023a	240	&norm(&round(substr($xm,$[,$scale+1),
288d023a	241	"+0".substr($xm,$[+$scale+1),"+1"."0" x length(substr($xm,$[+$scale+1))),
a0d0e21e	242	$xe+length($xm)-$scale-1);
	243	}
	244	}
	245	}
a5f75d66	246
a0d0e21e	247	# round $x at the 10 to the $scale digit place
	248	sub ffround { #(fnum_str, scale) return fnum_str
	249	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	250	if ($x eq 'NaN') {
	251	'NaN';
	252	} else {
	253	local($xm,$xe) = split('E',$x);
	254	if ($xe >= $scale) {
	255	$x;
	256	} else {
	257	$xe = length($xm)+$xe-$scale;
	258	if ($xe < 1) {
	259	'+0E+0';
	260	} elsif ($xe == 1) {
5d7098d5	261	# The first substr preserves the sign, passing a non-
	262	# normalized "-0" to &round when rounding -0.006 (for
	263	# example), purely so &round won't lose the sign.
	264	&norm(&round(substr($xm,$[,1).'0',
288d023a	265	"+0".substr($xm,$[+1),
288d023a	266	"+1"."0" x length(substr($xm,$[+1))), $scale);
a0d0e21e	267	} else {
a0d0e21e	268	&norm(&round(substr($xm,$[,$xe),
288d023a	269	"+0".substr($xm,$[+$xe),
288d023a	270	"+1"."0" x length(substr($xm,$[+$xe))), $scale);
a0d0e21e	271	}
	272	}
	273	}
	274	}
f216259d	275
	276	# Calculate the integer part of $x
	277	sub f2int { #(fnum_str) return inum_str
	278	local($x) = ${$_[$[]};
	279	if ($x eq 'NaN') {
	280	die "Attempt to take int(NaN)";
	281	} else {
	282	local($xm,$xe) = split('E',$x);
	283	if ($xe >= 0) {
	284	$xm . '0' x $xe;
	285	} else {
	286	$xe = length($xm)+$xe;
	287	if ($xe <= 1) {
	288	'+0';
	289	} else {
	290	substr($xm,$[,$xe);
	291	}
	292	}
	293	}
	294	}
288d023a	295
a0d0e21e	296	# compare 2 values returns one of undef, <0, =0, >0
	297	# returns undef if either or both input value are not numbers
	298	sub fcmp #(fnum_str, fnum_str) return cond_code
	299	{
	300	local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	301	if ($x eq "NaN" \|\| $y eq "NaN") {
	302	undef;
	303	} else {
5dce09b1	304	local($xm,$xe,$ym,$ye) = split('E', $x."E$y");
	305	if ($xm eq '+0' \|\| $ym eq '+0') {
	306	return $xm <=> $ym;
	307	}
3deb277d	308	if ( $xe < $ye ) # adjust the exponents to be equal
	309	{
	310	$ym .= '0' x ($ye - $xe);
	311	$ye = $xe;
	312	}
	313	elsif ( $ye < $xe ) # same here
	314	{
	315	$xm .= '0' x ($xe - $ye);
	316	$xe = $ye;
	317	}
	318	return Math::BigInt::cmp($xm,$ym);
a0d0e21e	319	}
a0d0e21e	320	}
a5f75d66	321
a0d0e21e	322	# square root by Newtons method.
	323	sub fsqrt { #(fnum_str[, scale]) return fnum_str
	324	local($x, $scale) = (fnorm($_[$[]), $_[$[+1]);
	325	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	326	'NaN';
	327	} elsif ($x eq '+0E+0') {
	328	'+0E+0';
	329	} else {
	330	local($xm, $xe) = split('E',$x);
	331	$scale = $div_scale if (!$scale);
	332	$scale = length($xm)-1 if ($scale < length($xm)-1);
	333	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	334	while ($gs < 2*$scale) {
	335	$guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5");
	336	$gs *= 2;
	337	}
a5f75d66	338	new Math::BigFloat &fround($guess, $scale);
a0d0e21e	339	}
	340	}
	341
	342	1;
a5f75d66	343	__END__
	344
	345	=head1 NAME
	346
	347	Math::BigFloat - Arbitrary length float math package
	348
	349	=head1 SYNOPSIS
	350
a2008d6d	351	use Math::BigFloat;
a5f75d66	352	$f = Math::BigFloat->new($string);
	353
	354	$f->fadd(NSTR) return NSTR addition
	355	$f->fsub(NSTR) return NSTR subtraction
	356	$f->fmul(NSTR) return NSTR multiplication
	357	$f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places
288d023a	358	$f->fmod(NSTR) returns NSTR modular remainder
a5f75d66	359	$f->fneg() return NSTR negation
	360	$f->fabs() return NSTR absolute value
	361	$f->fcmp(NSTR) return CODE compare undef,<0,=0,>0
	362	$f->fround(SCALE) return NSTR round to SCALE digits
	363	$f->ffround(SCALE) return NSTR round at SCALEth place
	364	$f->fnorm() return (NSTR) normalize
	365	$f->fsqrt([SCALE]) return NSTR sqrt to SCALE places
	366
	367	=head1 DESCRIPTION
	368
	369	All basic math operations are overloaded if you declare your big
	370	floats as
	371
	372	$float = new Math::BigFloat "2.123123123123123123123123123123123";
	373
	374	=over 2
	375
	376	=item number format
	377
	378	canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can
db696efe	379	have embedded whitespace.
a5f75d66	380
	381	=item Error returns 'NaN'
	382
	383	An input parameter was "Not a Number" or divide by zero or sqrt of
	384	negative number.
	385
288d023a	386	=item Division is computed to
a5f75d66	387
5d7098d5	388	C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))>
5d7098d5	389	digits by default.
a5f75d66	390	Also used for default sqrt scale.
a5f75d66	391
5d7098d5	392	=item Rounding is performed
	393
	394	according to the value of
	395	C<$Math::BigFloat::rnd_mode>:
	396
	397	trunc truncate the value
	398	zero round towards 0
	399	+inf round towards +infinity (round up)
	400	-inf round towards -infinity (round down)
	401	even round to the nearest, .5 to the even digit
	402	odd round to the nearest, .5 to the odd digit
	403
	404	The default is C<even> rounding.
	405
a5f75d66	406	=back
	407
	408	=head1 BUGS
	409
	410	The current version of this module is a preliminary version of the
	411	real thing that is currently (as of perl5.002) under development.
	412
5d7098d5	413	The printf subroutine does not use the value of
	414	C<$Math::BigFloat::rnd_mode> when rounding values for printing.
	415	Consequently, the way to print rounded values is
	416	to specify the number of digits both as an
	417	argument to C<ffround> and in the C<%f> printf string,
	418	as follows:
	419
	420	printf "%.3f\n", $bigfloat->ffround(-3);
	421
a5f75d66	422	=head1 AUTHOR
	423
	424	Mark Biggar
288d023a	425	Patches by John Peacock Apr 2001
a5f75d66	426	=cut