[perl5.git] / lib / bigfloat.pl

package bigfloat;
require "bigint.pl";
#
# This library is no longer being maintained, and is included for backward
# compatibility with Perl 4 programs which may require it.
#
# In particular, this should not be used as an example of modern Perl
# programming techniques.
#
# Suggested alternative: Math::BigFloat
#
# Arbitrary length float math package
#
# by Mark Biggar
#
# number format
#   canonical strings have the form /[+-]\d+E[+-]\d+/
#   Input values can have embedded whitespace
# Error returns
#   'NaN'           An input parameter was "Not a Number" or 
#                       divide by zero or sqrt of negative number
# Division is computed to 
#   max($div_scale,length(dividend)+length(divisor)) 
#   digits by default.
# Also used for default sqrt scale

$div_scale = 40;

# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.

$rnd_mode = 'even';

#   bigfloat routines
#
#   fadd(NSTR, NSTR) return NSTR            addition
#   fsub(NSTR, NSTR) return NSTR            subtraction
#   fmul(NSTR, NSTR) return NSTR            multiplication
#   fdiv(NSTR, NSTR[,SCALE]) returns NSTR   division to SCALE places
#   fneg(NSTR) return NSTR                  negation
#   fabs(NSTR) return NSTR                  absolute value
#   fcmp(NSTR,NSTR) return CODE             compare undef,<0,=0,>0
#   fround(NSTR, SCALE) return NSTR         round to SCALE digits
#   ffround(NSTR, SCALE) return NSTR        round at SCALEth place
#   fnorm(NSTR) return (NSTR)               normalize
#   fsqrt(NSTR[, SCALE]) return NSTR        sqrt to SCALE places
\f
# Convert a number to canonical string form.
#   Takes something that looks like a number and converts it to
#   the form /^[+-]\d+E[+-]\d+$/.
sub main'fnorm { #(string) return fnum_str
    local($_) = @_;
    s/\s+//g;                               # strip white space
    if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/
	  && ($2 ne '' || defined($4))) {
	my $x = defined($4) ? $4 : '';
	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $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 main'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 main'fabs { #(fnum_str) return fnum_str
    local($_) = &'fnorm($_[$[]);
    s/^-/+/;		                       # mash sign
    $_;
}

# multiplication
sub main'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',$y);
	&norm(&'bmul($xm,$ym),$xe+$ye);
    }
}
\f
# addition
sub main'fadd { #(fnum_str, fnum_str) return fnum_str
    local($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 < $ye);
	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
    }
}

# subtraction
sub main'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 main'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($xm);
	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
	    $xe-$ye-$scale);
    }
}
\f
# 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) = &'bcmp(&'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'  && $q =~ /[13579]$/)        )) ) {
	    $q;                     # round down
	} else {
	    &'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
				    # round up
	}
    }
}

# round the mantissa of $x to $scale digits
sub main'fround { #(fnum_str, scale) return fnum_str
    local($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);
	}
    }
}
\f
# round $x at the 10 to the $scale digit place
sub main'ffround { #(fnum_str, scale) return fnum_str
    local($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, which means that
		# we'll pass a non-normalized "-0" to &round when rounding
		# -0.006 (for example), purely so that &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 main'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,$[,1).'1')
             || &bigint'cmp($xm,$ym))
	);
    }
}
\f
# square root by Newtons method.
sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
    local($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");
	    $gs *= 2;
	}
	&'fround($guess, $scale);
    }
}

1;
Commit	Line	Data
5303340c LW	1	package bigfloat;
5303340c LW	2	require "bigint.pl";
a6d71656 GS	3	#
	4	# This library is no longer being maintained, and is included for backward
	5	# compatibility with Perl 4 programs which may require it.
	6	#
	7	# In particular, this should not be used as an example of modern Perl
	8	# programming techniques.
	9	#
	10	# Suggested alternative: Math::BigFloat
	11	#
5303340c LW	12	# Arbitrary length float math package
5303340c LW	13	#
68decaef LW	14	# by Mark Biggar
68decaef LW	15	#
5303340c LW	16	# number format
5303340c LW	17	# canonical strings have the form /[+-]\d+E[+-]\d+/
5d7098d5	18	# Input values can have embedded whitespace
5303340c LW	19	# Error returns
	20	# 'NaN' An input parameter was "Not a Number" or
	21	# divide by zero or sqrt of negative number
	22	# Division is computed to
79072805	23	# max($div_scale,length(dividend)+length(divisor))
5303340c LW	24	# digits by default.
	25	# Also used for default sqrt scale
	26
	27	$div_scale = 40;
	28
	29	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	30
	31	$rnd_mode = 'even';
	32
	33	# bigfloat routines
	34	#
	35	# fadd(NSTR, NSTR) return NSTR addition
	36	# fsub(NSTR, NSTR) return NSTR subtraction
	37	# fmul(NSTR, NSTR) return NSTR multiplication
	38	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	39	# fneg(NSTR) return NSTR negation
	40	# fabs(NSTR) return NSTR absolute value
	41	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	42	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	43	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	44	# fnorm(NSTR) return (NSTR) normalize
	45	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	46	\f
	47	# Convert a number to canonical string form.
	48	# Takes something that looks like a number and converts it to
	49	# the form /^[+-]\d+E[+-]\d+$/.
	50	sub main'fnorm { #(string) return fnum_str
	51	local($_) = @_;
	52	s/\s+//g; # strip white space
afea815c CS	53	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/
	54	&& ($2 ne '' \|\| defined($4))) {
	55	my $x = defined($4) ? $4 : '';
	56	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
5303340c LW	57	} else {
	58	'NaN';
	59	}
	60	}
	61
	62	# normalize number -- for internal use
	63	sub norm { #(mantissa, exponent) return fnum_str
	64	local($_, $exp) = @_;
	65	if ($_ eq 'NaN') {
	66	'NaN';
	67	} else {
	68	s/^([+-])0+/$1/; # strip leading zeros
	69	if (length($_) == 1) {
	70	'+0E+0';
	71	} else {
	72	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	73	sprintf("%sE%+ld", $_, $exp);
	74	}
	75	}
	76	}
	77
	78	# negation
	79	sub main'fneg { #(fnum_str) return fnum_str
79072805	80	local($_) = &'fnorm($_[$[]);
e334a159	81	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
68decaef	82	s/^H/N/;
5303340c LW	83	$_;
	84	}
	85
	86	# absolute value
	87	sub main'fabs { #(fnum_str) return fnum_str
79072805	88	local($_) = &'fnorm($_[$[]);
68decaef	89	s/^-/+/; # mash sign
5303340c LW	90	$_;
	91	}
	92
	93	# multiplication
	94	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
79072805	95	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	96	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	97	'NaN';
	98	} else {
	99	local($xm,$xe) = split('E',$x);
	100	local($ym,$ye) = split('E',$y);
	101	&norm(&'bmul($xm,$ym),$xe+$ye);
	102	}
	103	}
	104	\f
	105	# addition
	106	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
79072805	107	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	108	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	109	'NaN';
	110	} else {
	111	local($xm,$xe) = split('E',$x);
	112	local($ym,$ye) = split('E',$y);
	113	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	114	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	115	}
	116	}
	117
	118	# subtraction
	119	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
79072805	120	&'fadd($_[$[],&'fneg($_[$[+1]));
5303340c LW	121	}
	122
	123	# division
	124	# args are dividend, divisor, scale (optional)
	125	# result has at most max(scale, length(dividend), length(divisor)) digits
	126	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	127	{
79072805	128	local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
5303340c LW	129	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	130	'NaN';
	131	} else {
	132	local($xm,$xe) = split('E',$x);
	133	local($ym,$ye) = split('E',$y);
	134	$scale = $div_scale if (!$scale);
	135	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	136	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	137	$scale = $scale + length($ym) - length($xm);
5d7098d5	138	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
5303340c LW	139	$xe-$ye-$scale);
	140	}
	141	}
	142	\f
	143	# round int $q based on fraction $r/$base using $rnd_mode
	144	sub round { #(int_str, int_str, int_str) return int_str
	145	local($q,$r,$base) = @_;
	146	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	147	'NaN';
	148	} elsif ($rnd_mode eq 'trunc') {
	149	$q; # just truncate
	150	} else {
	151	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	152	if ( $cmp < 0 \|\|
	153	($cmp == 0 &&
	154	( $rnd_mode eq 'zero' \|\|
79072805 LW	155	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
79072805 LW	156	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
5303340c LW	157	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	158	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	159	$q; # round down
	160	} else {
79072805	161	&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
5303340c LW	162	# round up
	163	}
	164	}
	165	}
	166
	167	# round the mantissa of $x to $scale digits
	168	sub main'fround { #(fnum_str, scale) return fnum_str
79072805	169	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	170	if ($x eq 'NaN' \|\| $scale <= 0) {
	171	$x;
	172	} else {
	173	local($xm,$xe) = split('E',$x);
	174	if (length($xm)-1 <= $scale) {
	175	$x;
	176	} else {
79072805 LW	177	&norm(&round(substr($xm,$[,$scale+1),
79072805 LW	178	"+0".substr($xm,$[+$scale+1,1),"+10"),
5303340c LW	179	$xe+length($xm)-$scale-1);
	180	}
	181	}
	182	}
	183	\f
	184	# round $x at the 10 to the $scale digit place
	185	sub main'ffround { #(fnum_str, scale) return fnum_str
79072805	186	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	187	if ($x eq 'NaN') {
	188	'NaN';
	189	} else {
	190	local($xm,$xe) = split('E',$x);
	191	if ($xe >= $scale) {
	192	$x;
	193	} else {
	194	$xe = length($xm)+$xe-$scale;
	195	if ($xe < 1) {
	196	'+0E+0';
	197	} elsif ($xe == 1) {
5d7098d5 SK	198	# The first substr preserves the sign, which means that
	199	# we'll pass a non-normalized "-0" to &round when rounding
	200	# -0.006 (for example), purely so that &round won't lose
	201	# the sign.
	202	&norm(&round(substr($xm,$[,1).'0',
	203	"+0".substr($xm,$[+1,1),"+10"), $scale);
5303340c	204	} else {
79072805 LW	205	&norm(&round(substr($xm,$[,$xe),
79072805 LW	206	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
5303340c LW	207	}
	208	}
	209	}
	210	}
	211
	212	# compare 2 values returns one of undef, <0, =0, >0
	213	# returns undef if either or both input value are not numbers
	214	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	215	{
79072805	216	local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	217	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	218	undef;
5303340c	219	} else {
68decaef LW	220	ord($y) <=> ord($x)
	221	\|\|
	222	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
79072805	223	(($xe <=> $ye) * (substr($x,$[,1).'1')
68decaef LW	224	\|\| &bigint'cmp($xm,$ym))
68decaef LW	225	);
5303340c LW	226	}
	227	}
	228	\f
	229	# square root by Newtons method.
	230	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
79072805	231	local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
5303340c LW	232	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	233	'NaN';
	234	} elsif ($x eq '+0E+0') {
	235	'+0E+0';
	236	} else {
	237	local($xm, $xe) = split('E',$x);
	238	$scale = $div_scale if (!$scale);
	239	$scale = length($xm)-1 if ($scale < length($xm)-1);
	240	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	241	while ($gs < 2*$scale) {
	242	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	243	$gs *= 2;
	244	}
	245	&'fround($guess, $scale);
	246	}
	247	}
	248
	249	1;