[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 = '0.01';	# never had version before

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},
'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 ($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);
    }
}

# 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' && $q =~ /[13579]$/        ) ||
		   ($rnd_mode eq 'odd'  && $q =~ /[24680]$/        )    )
		  ) 
		) {
	    $q;                     # round down
	} else {
	    Math::BigInt::badd($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);
	    }
	}
    }
}

# 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->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
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);
3deb277d	7	$VERSION = '0.01'; # never had version before
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},
a5f75d66	16	'/' => sub {new Math::BigFloat
a0d0e21e	17	$_[2]? scalar fdiv($_[1],${$_[0]}) :
a0d0e21e	18	scalar fdiv(${$_[0]},$_[1])},
a5f75d66	19	'neg' => sub {new Math::BigFloat &fneg},
a5f75d66	20	'abs' => sub {new Math::BigFloat &fabs},
f216259d	21	'int' => sub {new Math::BigInt &f2int},
a0d0e21e	22
	23	qw(
	24	"" stringify
	25	0+ numify) # Order of arguments unsignificant
a5f75d66	26	;
a0d0e21e	27
a0d0e21e	28	sub new {
a5f75d66	29	my ($class) = shift;
a5f75d66	30	my ($foo) = fnorm(shift);
a5f75d66	31	bless \$foo, $class;
a0d0e21e	32	}
0e8b9368	33
a0d0e21e	34	sub numify { 0 + "${$_[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
f216259d	62	sub import {
	63	shift;
	64	return unless @_;
	65	die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
	66	overload::constant float => sub {Math::BigFloat->new(shift)};
	67	}
	68
a0d0e21e	69	$div_scale = 40;
	70
	71	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	72
	73	$rnd_mode = 'even';
	74
	75	sub fadd; sub fsub; sub fmul; sub fdiv;
	76	sub fneg; sub fabs; sub fcmp;
	77	sub fround; sub ffround;
	78	sub fnorm; sub fsqrt;
	79
a0d0e21e	80	# Convert a number to canonical string form.
	81	# Takes something that looks like a number and converts it to
	82	# the form /^[+-]\d+E[+-]\d+$/.
	83	sub fnorm { #(string) return fnum_str
	84	local($_) = @_;
	85	s/\s+//g; # strip white space
db376a24	86	no warnings; # $4 and $5 below might legitimately be undefined
a0d0e21e	87	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
	88	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
	89	} else {
	90	'NaN';
	91	}
	92	}
	93
	94	# normalize number -- for internal use
	95	sub norm { #(mantissa, exponent) return fnum_str
	96	local($_, $exp) = @_;
3deb277d	97	$exp = 0 unless defined $exp;
a0d0e21e	98	if ($_ eq 'NaN') {
	99	'NaN';
	100	} else {
	101	s/^([+-])0+/$1/; # strip leading zeros
	102	if (length($_) == 1) {
	103	'+0E+0';
	104	} else {
	105	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	106	sprintf("%sE%+ld", $_, $exp);
	107	}
	108	}
	109	}
	110
	111	# negation
	112	sub fneg { #(fnum_str) return fnum_str
	113	local($_) = fnorm($_[$[]);
	114	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
	115	s/^H/N/;
	116	$_;
	117	}
	118
	119	# absolute value
	120	sub fabs { #(fnum_str) return fnum_str
	121	local($_) = fnorm($_[$[]);
	122	s/^-/+/; # mash sign
	123	$_;
	124	}
	125
	126	# multiplication
	127	sub fmul { #(fnum_str, fnum_str) return fnum_str
	128	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	129	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	130	'NaN';
	131	} else {
	132	local($xm,$xe) = split('E',$x);
	133	local($ym,$ye) = split('E',$y);
	134	&norm(Math::BigInt::bmul($xm,$ym),$xe+$ye);
	135	}
	136	}
a5f75d66	137
a0d0e21e	138	# addition
	139	sub fadd { #(fnum_str, fnum_str) return fnum_str
	140	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	141	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	142	'NaN';
	143	} else {
	144	local($xm,$xe) = split('E',$x);
	145	local($ym,$ye) = split('E',$y);
	146	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	147	&norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	148	}
	149	}
	150
	151	# subtraction
	152	sub fsub { #(fnum_str, fnum_str) return fnum_str
	153	fadd($_[$[],fneg($_[$[+1]));
	154	}
	155
	156	# division
	157	# args are dividend, divisor, scale (optional)
	158	# result has at most max(scale, length(dividend), length(divisor)) digits
	159	sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	160	{
	161	local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]);
	162	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	163	'NaN';
	164	} else {
	165	local($xm,$xe) = split('E',$x);
	166	local($ym,$ye) = split('E',$y);
	167	$scale = $div_scale if (!$scale);
	168	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	169	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	170	$scale = $scale + length($ym) - length($xm);
5d7098d5	171	&norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),
5d7098d5	172	Math::BigInt::babs($ym)),
a0d0e21e	173	$xe-$ye-$scale);
	174	}
	175	}
a5f75d66	176
a0d0e21e	177	# round int $q based on fraction $r/$base using $rnd_mode
	178	sub round { #(int_str, int_str, int_str) return int_str
	179	local($q,$r,$base) = @_;
	180	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	181	'NaN';
	182	} elsif ($rnd_mode eq 'trunc') {
	183	$q; # just truncate
	184	} else {
	185	local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base);
	186	if ( $cmp < 0 \|\|
3deb277d	187	($cmp == 0 && (
3deb277d	188	($rnd_mode eq 'zero' ) \|\|
a0d0e21e	189	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
a0d0e21e	190	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
3deb277d	191	($rnd_mode eq 'even' && $q =~ /[13579]$/ ) \|\|
	192	($rnd_mode eq 'odd' && $q =~ /[24680]$/ ) )
	193	)
	194	) {
a0d0e21e	195	$q; # round down
	196	} else {
	197	Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
	198	# round up
	199	}
	200	}
	201	}
	202
	203	# round the mantissa of $x to $scale digits
	204	sub fround { #(fnum_str, scale) return fnum_str
	205	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	206	if ($x eq 'NaN' \|\| $scale <= 0) {
	207	$x;
	208	} else {
	209	local($xm,$xe) = split('E',$x);
	210	if (length($xm)-1 <= $scale) {
	211	$x;
	212	} else {
	213	&norm(&round(substr($xm,$[,$scale+1),
	214	"+0".substr($xm,$[+$scale+1,1),"+10"),
	215	$xe+length($xm)-$scale-1);
	216	}
	217	}
	218	}
a5f75d66	219
a0d0e21e	220	# round $x at the 10 to the $scale digit place
	221	sub ffround { #(fnum_str, scale) return fnum_str
	222	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	223	if ($x eq 'NaN') {
	224	'NaN';
	225	} else {
	226	local($xm,$xe) = split('E',$x);
	227	if ($xe >= $scale) {
	228	$x;
	229	} else {
	230	$xe = length($xm)+$xe-$scale;
	231	if ($xe < 1) {
	232	'+0E+0';
	233	} elsif ($xe == 1) {
5d7098d5	234	# The first substr preserves the sign, passing a non-
	235	# normalized "-0" to &round when rounding -0.006 (for
	236	# example), purely so &round won't lose the sign.
	237	&norm(&round(substr($xm,$[,1).'0',
	238	"+0".substr($xm,$[+1,1),"+10"), $scale);
a0d0e21e	239	} else {
	240	&norm(&round(substr($xm,$[,$xe),
	241	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
	242	}
	243	}
	244	}
	245	}
f216259d	246
	247	# Calculate the integer part of $x
	248	sub f2int { #(fnum_str) return inum_str
	249	local($x) = ${$_[$[]};
	250	if ($x eq 'NaN') {
	251	die "Attempt to take int(NaN)";
	252	} else {
	253	local($xm,$xe) = split('E',$x);
	254	if ($xe >= 0) {
	255	$xm . '0' x $xe;
	256	} else {
	257	$xe = length($xm)+$xe;
	258	if ($xe <= 1) {
	259	'+0';
	260	} else {
	261	substr($xm,$[,$xe);
	262	}
	263	}
	264	}
	265	}
a0d0e21e	266
	267	# compare 2 values returns one of undef, <0, =0, >0
	268	# returns undef if either or both input value are not numbers
	269	sub fcmp #(fnum_str, fnum_str) return cond_code
	270	{
	271	local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	272	if ($x eq "NaN" \|\| $y eq "NaN") {
	273	undef;
	274	} else {
5dce09b1	275	local($xm,$xe,$ym,$ye) = split('E', $x."E$y");
	276	if ($xm eq '+0' \|\| $ym eq '+0') {
	277	return $xm <=> $ym;
	278	}
3deb277d	279	if ( $xe < $ye ) # adjust the exponents to be equal
	280	{
	281	$ym .= '0' x ($ye - $xe);
	282	$ye = $xe;
	283	}
	284	elsif ( $ye < $xe ) # same here
	285	{
	286	$xm .= '0' x ($xe - $ye);
	287	$xe = $ye;
	288	}
	289	return Math::BigInt::cmp($xm,$ym);
a0d0e21e	290	}
a0d0e21e	291	}
a5f75d66	292
a0d0e21e	293	# square root by Newtons method.
	294	sub fsqrt { #(fnum_str[, scale]) return fnum_str
	295	local($x, $scale) = (fnorm($_[$[]), $_[$[+1]);
	296	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	297	'NaN';
	298	} elsif ($x eq '+0E+0') {
	299	'+0E+0';
	300	} else {
	301	local($xm, $xe) = split('E',$x);
	302	$scale = $div_scale if (!$scale);
	303	$scale = length($xm)-1 if ($scale < length($xm)-1);
	304	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	305	while ($gs < 2*$scale) {
	306	$guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5");
	307	$gs *= 2;
	308	}
a5f75d66	309	new Math::BigFloat &fround($guess, $scale);
a0d0e21e	310	}
	311	}
	312
	313	1;
a5f75d66	314	__END__
	315
	316	=head1 NAME
	317
	318	Math::BigFloat - Arbitrary length float math package
	319
	320	=head1 SYNOPSIS
	321
a2008d6d	322	use Math::BigFloat;
a5f75d66	323	$f = Math::BigFloat->new($string);
	324
	325	$f->fadd(NSTR) return NSTR addition
	326	$f->fsub(NSTR) return NSTR subtraction
	327	$f->fmul(NSTR) return NSTR multiplication
	328	$f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places
	329	$f->fneg() return NSTR negation
	330	$f->fabs() return NSTR absolute value
	331	$f->fcmp(NSTR) return CODE compare undef,<0,=0,>0
	332	$f->fround(SCALE) return NSTR round to SCALE digits
	333	$f->ffround(SCALE) return NSTR round at SCALEth place
	334	$f->fnorm() return (NSTR) normalize
	335	$f->fsqrt([SCALE]) return NSTR sqrt to SCALE places
	336
	337	=head1 DESCRIPTION
	338
	339	All basic math operations are overloaded if you declare your big
	340	floats as
	341
	342	$float = new Math::BigFloat "2.123123123123123123123123123123123";
	343
	344	=over 2
	345
	346	=item number format
	347
	348	canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can
db696efe	349	have embedded whitespace.
a5f75d66	350
	351	=item Error returns 'NaN'
	352
	353	An input parameter was "Not a Number" or divide by zero or sqrt of
	354	negative number.
	355
	356	=item Division is computed to
	357
5d7098d5	358	C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))>
5d7098d5	359	digits by default.
a5f75d66	360	Also used for default sqrt scale.
a5f75d66	361
5d7098d5	362	=item Rounding is performed
	363
	364	according to the value of
	365	C<$Math::BigFloat::rnd_mode>:
	366
	367	trunc truncate the value
	368	zero round towards 0
	369	+inf round towards +infinity (round up)
	370	-inf round towards -infinity (round down)
	371	even round to the nearest, .5 to the even digit
	372	odd round to the nearest, .5 to the odd digit
	373
	374	The default is C<even> rounding.
	375
a5f75d66	376	=back
	377
	378	=head1 BUGS
	379
	380	The current version of this module is a preliminary version of the
	381	real thing that is currently (as of perl5.002) under development.
	382
5d7098d5	383	The printf subroutine does not use the value of
	384	C<$Math::BigFloat::rnd_mode> when rounding values for printing.
	385	Consequently, the way to print rounded values is
	386	to specify the number of digits both as an
	387	argument to C<ffround> and in the C<%f> printf string,
	388	as follows:
	389
	390	printf "%.3f\n", $bigfloat->ffround(-3);
	391
a5f75d66	392	=head1 AUTHOR
	393
	394	Mark Biggar
	395
	396	=cut