[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},

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) = @_;
	$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);
	    }
	}
    }
}
    
# 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);
22d4bb9c	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]},$_[1])},
a5f75d66	19	'neg' => sub {new Math::BigFloat &fneg},
a5f75d66	20	'abs' => sub {new Math::BigFloat &fabs},
a0d0e21e	21
	22	qw(
	23	"" stringify
	24	0+ numify) # Order of arguments unsignificant
a5f75d66	25	;
a0d0e21e	26
a0d0e21e	27	sub new {
a5f75d66	28	my ($class) = shift;
a5f75d66	29	my ($foo) = fnorm(shift);
a5f75d66	30	bless \$foo, $class;
a0d0e21e	31	}
0e8b9368	32
a0d0e21e	33	sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
	34	# comparing to direct compilation based on
	35	# stringify
	36	sub stringify {
	37	my $n = ${$_[0]};
	38
9b599b2a	39	my $minus = ($n =~ s/^([+-])// && $1 eq '-');
a0d0e21e	40	$n =~ s/E//;
	41
	42	$n =~ s/([-+]\d+)$//;
	43
	44	my $e = $1;
	45	my $ln = length($n);
	46
	47	if ($e > 0) {
	48	$n .= "0" x $e . '.';
	49	} elsif (abs($e) < $ln) {
	50	substr($n, $ln + $e, 0) = '.';
	51	} else {
	52	$n = '.' . ("0" x (abs($e) - $ln)) . $n;
	53	}
9b599b2a	54	$n = "-$n" if $minus;
a0d0e21e	55
	56	# 1 while $n =~ s/(.*\d)(\d\d\d)/$1,$2/;
	57
	58	return $n;
	59	}
	60
a0d0e21e	61	$div_scale = 40;
	62
	63	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	64
	65	$rnd_mode = 'even';
	66
	67	sub fadd; sub fsub; sub fmul; sub fdiv;
	68	sub fneg; sub fabs; sub fcmp;
	69	sub fround; sub ffround;
	70	sub fnorm; sub fsqrt;
	71
a0d0e21e	72	# Convert a number to canonical string form.
	73	# Takes something that looks like a number and converts it to
	74	# the form /^[+-]\d+E[+-]\d+$/.
	75	sub fnorm { #(string) return fnum_str
	76	local($_) = @_;
	77	s/\s+//g; # strip white space
cb50131a	78	no warnings; # $4 and $5 below might legitimately be undefined
a0d0e21e	79	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
	80	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
	81	} else {
	82	'NaN';
	83	}
	84	}
	85
	86	# normalize number -- for internal use
	87	sub norm { #(mantissa, exponent) return fnum_str
	88	local($_, $exp) = @_;
22d4bb9c	89	$exp = 0 unless defined $exp;
a0d0e21e	90	if ($_ eq 'NaN') {
	91	'NaN';
	92	} else {
	93	s/^([+-])0+/$1/; # strip leading zeros
	94	if (length($_) == 1) {
	95	'+0E+0';
	96	} else {
	97	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	98	sprintf("%sE%+ld", $_, $exp);
	99	}
	100	}
	101	}
	102
	103	# negation
	104	sub fneg { #(fnum_str) return fnum_str
	105	local($_) = fnorm($_[$[]);
	106	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
	107	s/^H/N/;
	108	$_;
	109	}
	110
	111	# absolute value
	112	sub fabs { #(fnum_str) return fnum_str
	113	local($_) = fnorm($_[$[]);
	114	s/^-/+/; # mash sign
	115	$_;
	116	}
	117
	118	# multiplication
	119	sub fmul { #(fnum_str, fnum_str) return fnum_str
	120	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	121	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	122	'NaN';
	123	} else {
	124	local($xm,$xe) = split('E',$x);
	125	local($ym,$ye) = split('E',$y);
	126	&norm(Math::BigInt::bmul($xm,$ym),$xe+$ye);
	127	}
	128	}
a5f75d66	129
a0d0e21e	130	# addition
	131	sub fadd { #(fnum_str, fnum_str) return fnum_str
	132	local($x,$y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	133	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	134	'NaN';
	135	} else {
	136	local($xm,$xe) = split('E',$x);
	137	local($ym,$ye) = split('E',$y);
	138	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	139	&norm(Math::BigInt::badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	140	}
	141	}
	142
	143	# subtraction
	144	sub fsub { #(fnum_str, fnum_str) return fnum_str
	145	fadd($_[$[],fneg($_[$[+1]));
	146	}
	147
	148	# division
	149	# args are dividend, divisor, scale (optional)
	150	# result has at most max(scale, length(dividend), length(divisor)) digits
	151	sub fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	152	{
	153	local($x,$y,$scale) = (fnorm($_[$[]),fnorm($_[$[+1]),$_[$[+2]);
	154	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	155	'NaN';
	156	} else {
	157	local($xm,$xe) = split('E',$x);
	158	local($ym,$ye) = split('E',$y);
	159	$scale = $div_scale if (!$scale);
	160	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	161	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	162	$scale = $scale + length($ym) - length($xm);
5d7098d5	163	&norm(&round(Math::BigInt::bdiv($xm.('0' x $scale),$ym),
5d7098d5	164	Math::BigInt::babs($ym)),
a0d0e21e	165	$xe-$ye-$scale);
	166	}
	167	}
a5f75d66	168
a0d0e21e	169	# round int $q based on fraction $r/$base using $rnd_mode
	170	sub round { #(int_str, int_str, int_str) return int_str
	171	local($q,$r,$base) = @_;
	172	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	173	'NaN';
	174	} elsif ($rnd_mode eq 'trunc') {
	175	$q; # just truncate
	176	} else {
	177	local($cmp) = Math::BigInt::bcmp(Math::BigInt::bmul($r,'+2'),$base);
	178	if ( $cmp < 0 \|\|
22d4bb9c	179	($cmp == 0 && (
22d4bb9c	180	($rnd_mode eq 'zero' ) \|\|
a0d0e21e	181	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
a0d0e21e	182	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
22d4bb9c	183	($rnd_mode eq 'even' && $q =~ /[13579]$/ ) \|\|
	184	($rnd_mode eq 'odd' && $q =~ /[24680]$/ ) )
	185	)
	186	) {
a0d0e21e	187	$q; # round down
	188	} else {
	189	Math::BigInt::badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
	190	# round up
	191	}
	192	}
	193	}
	194
	195	# round the mantissa of $x to $scale digits
	196	sub fround { #(fnum_str, scale) return fnum_str
	197	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	198	if ($x eq 'NaN' \|\| $scale <= 0) {
	199	$x;
	200	} else {
	201	local($xm,$xe) = split('E',$x);
	202	if (length($xm)-1 <= $scale) {
	203	$x;
	204	} else {
	205	&norm(&round(substr($xm,$[,$scale+1),
	206	"+0".substr($xm,$[+$scale+1,1),"+10"),
	207	$xe+length($xm)-$scale-1);
	208	}
	209	}
	210	}
a5f75d66	211
a0d0e21e	212	# round $x at the 10 to the $scale digit place
	213	sub ffround { #(fnum_str, scale) return fnum_str
	214	local($x,$scale) = (fnorm($_[$[]),$_[$[+1]);
	215	if ($x eq 'NaN') {
	216	'NaN';
	217	} else {
	218	local($xm,$xe) = split('E',$x);
	219	if ($xe >= $scale) {
	220	$x;
	221	} else {
	222	$xe = length($xm)+$xe-$scale;
	223	if ($xe < 1) {
	224	'+0E+0';
	225	} elsif ($xe == 1) {
5d7098d5	226	# The first substr preserves the sign, passing a non-
	227	# normalized "-0" to &round when rounding -0.006 (for
	228	# example), purely so &round won't lose the sign.
	229	&norm(&round(substr($xm,$[,1).'0',
	230	"+0".substr($xm,$[+1,1),"+10"), $scale);
a0d0e21e	231	} else {
	232	&norm(&round(substr($xm,$[,$xe),
	233	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
	234	}
	235	}
	236	}
	237	}
	238
	239	# compare 2 values returns one of undef, <0, =0, >0
	240	# returns undef if either or both input value are not numbers
	241	sub fcmp #(fnum_str, fnum_str) return cond_code
	242	{
	243	local($x, $y) = (fnorm($_[$[]),fnorm($_[$[+1]));
	244	if ($x eq "NaN" \|\| $y eq "NaN") {
	245	undef;
	246	} else {
146174a9	247	local($xm,$xe,$ym,$ye) = split('E', $x."E$y");
	248	if ($xm eq '+0' \|\| $ym eq '+0') {
	249	return $xm <=> $ym;
	250	}
22d4bb9c	251	if ( $xe < $ye ) # adjust the exponents to be equal
	252	{
	253	$ym .= '0' x ($ye - $xe);
	254	$ye = $xe;
	255	}
	256	elsif ( $ye < $xe ) # same here
	257	{
	258	$xm .= '0' x ($xe - $ye);
	259	$xe = $ye;
	260	}
	261	return Math::BigInt::cmp($xm,$ym);
a0d0e21e	262	}
a0d0e21e	263	}
a5f75d66	264
a0d0e21e	265	# square root by Newtons method.
	266	sub fsqrt { #(fnum_str[, scale]) return fnum_str
	267	local($x, $scale) = (fnorm($_[$[]), $_[$[+1]);
	268	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	269	'NaN';
	270	} elsif ($x eq '+0E+0') {
	271	'+0E+0';
	272	} else {
	273	local($xm, $xe) = split('E',$x);
	274	$scale = $div_scale if (!$scale);
	275	$scale = length($xm)-1 if ($scale < length($xm)-1);
	276	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	277	while ($gs < 2*$scale) {
	278	$guess = fmul(fadd($guess,fdiv($x,$guess,$gs*2)),".5");
	279	$gs *= 2;
	280	}
a5f75d66	281	new Math::BigFloat &fround($guess, $scale);
a0d0e21e	282	}
	283	}
	284
	285	1;
a5f75d66	286	__END__
	287
	288	=head1 NAME
	289
	290	Math::BigFloat - Arbitrary length float math package
	291
	292	=head1 SYNOPSIS
	293
a2008d6d	294	use Math::BigFloat;
a5f75d66	295	$f = Math::BigFloat->new($string);
	296
	297	$f->fadd(NSTR) return NSTR addition
	298	$f->fsub(NSTR) return NSTR subtraction
	299	$f->fmul(NSTR) return NSTR multiplication
	300	$f->fdiv(NSTR[,SCALE]) returns NSTR division to SCALE places
	301	$f->fneg() return NSTR negation
	302	$f->fabs() return NSTR absolute value
	303	$f->fcmp(NSTR) return CODE compare undef,<0,=0,>0
	304	$f->fround(SCALE) return NSTR round to SCALE digits
	305	$f->ffround(SCALE) return NSTR round at SCALEth place
	306	$f->fnorm() return (NSTR) normalize
	307	$f->fsqrt([SCALE]) return NSTR sqrt to SCALE places
	308
	309	=head1 DESCRIPTION
	310
	311	All basic math operations are overloaded if you declare your big
	312	floats as
	313
	314	$float = new Math::BigFloat "2.123123123123123123123123123123123";
	315
	316	=over 2
	317
	318	=item number format
	319
	320	canonical strings have the form /[+-]\d+E[+-]\d+/ . Input values can
db696efe	321	have embedded whitespace.
a5f75d66	322
	323	=item Error returns 'NaN'
	324
	325	An input parameter was "Not a Number" or divide by zero or sqrt of
	326	negative number.
	327
	328	=item Division is computed to
	329
5d7098d5	330	C<max($Math::BigFloat::div_scale,length(dividend)+length(divisor))>
5d7098d5	331	digits by default.
a5f75d66	332	Also used for default sqrt scale.
a5f75d66	333
5d7098d5	334	=item Rounding is performed
	335
	336	according to the value of
	337	C<$Math::BigFloat::rnd_mode>:
	338
	339	trunc truncate the value
	340	zero round towards 0
	341	+inf round towards +infinity (round up)
	342	-inf round towards -infinity (round down)
	343	even round to the nearest, .5 to the even digit
	344	odd round to the nearest, .5 to the odd digit
	345
	346	The default is C<even> rounding.
	347
a5f75d66	348	=back
	349
	350	=head1 BUGS
	351
	352	The current version of this module is a preliminary version of the
	353	real thing that is currently (as of perl5.002) under development.
	354
5d7098d5	355	The printf subroutine does not use the value of
	356	C<$Math::BigFloat::rnd_mode> when rounding values for printing.
	357	Consequently, the way to print rounded values is
	358	to specify the number of digits both as an
	359	argument to C<ffround> and in the C<%f> printf string,
	360	as follows:
	361
	362	printf "%.3f\n", $bigfloat->ffround(-3);
	363
a5f75d66	364	=head1 AUTHOR
	365
	366	Mark Biggar
	367
	368	=cut