[perl5.git] / lib / bigfloat.pl

warn "Legacy library @{[(caller(0))[6]]} will be removed from the Perl core distribution in the next major release. Please install it from the CPAN distribution Perl4::CoreLibs. It is being used at @{[(caller)[1]]}, line @{[(caller)[2]]}.\n";

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.
# This legacy library is deprecated and will be removed in a future
# release of perl.
#
# 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($_) = &'fnorm($_[0]);
    vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
    if ( ord("\t") == 9 ) { # ascii
        s/^H/N/;
    }
    else { # ebcdic character set
        s/\373/N/;
    }
    $_;
}

# absolute value
sub main'fabs { #(fnum_str) return fnum_str
    local($_) = &'fnorm($_[0]);
    s/^-/+/;		                       # mash sign
    $_;
}

# multiplication
sub main'fmul { #(fnum_str, fnum_str) return fnum_str
    local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[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,$y) = (&'fnorm($_[0]),&'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($_[0],&'fneg($_[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,$scale) = (&'fnorm($_[0]),&'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($q,0,1) eq '+')) ||
		   ($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) ||
		   ($rnd_mode eq 'even' && $q =~ /[24680]$/)        ||
		   ($rnd_mode eq 'odd'  && $q =~ /[13579]$/)        )) ) {
	    $q;                     # round down
	} else {
	    &'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
				    # round up
	}
    }
}

# round the mantissa of $x to $scale digits
sub main'fround { #(fnum_str, scale) return fnum_str
    local($x,$scale) = (&'fnorm($_[0]),$_[1]);
    if ($x eq 'NaN' || $scale <= 0) {
	$x;
    } else {
	local($xm,$xe) = split('E',$x);
	if (length($xm)-1 <= $scale) {
	    $x;
	} else {
	    &norm(&round(substr($xm,0,$scale+1),
			 "+0".substr($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,$scale) = (&'fnorm($_[0]),$_[1]);
    if ($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($xm,0,1).'0',
		      "+0".substr($xm,1,1),"+10"), $scale);
	    } else {
		&norm(&round(substr($xm,0,$xe),
		      "+0".substr($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, $y) = (&'fnorm($_[0]),&'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,0,1).'1')
             || &bigint'cmp($xm,$ym))
	);
    }
}
\f
# square root by Newtons method.
sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
    local($x, $scale) = (&'fnorm($_[0]), $_[1]);
    if ($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
0111154e Z	1	warn "Legacy library @{[(caller(0))[6]]} will be removed from the Perl core distribution in the next major release. Please install it from the CPAN distribution Perl4::CoreLibs. It is being used at @{[(caller)[1]]}, line @{[(caller)[2]]}.\n";
0111154e Z	2
5303340c LW	3	package bigfloat;
5303340c LW	4	require "bigint.pl";
a6d71656 GS	5	#
	6	# This library is no longer being maintained, and is included for backward
	7	# compatibility with Perl 4 programs which may require it.
8e1a0ca7 S	8	# This legacy library is deprecated and will be removed in a future
8e1a0ca7 S	9	# release of perl.
a6d71656 GS	10	#
	11	# In particular, this should not be used as an example of modern Perl
	12	# programming techniques.
	13	#
	14	# Suggested alternative: Math::BigFloat
8e1a0ca7	15
5303340c LW	16	# Arbitrary length float math package
5303340c LW	17	#
68decaef LW	18	# by Mark Biggar
68decaef LW	19	#
5303340c LW	20	# number format
5303340c LW	21	# canonical strings have the form /[+-]\d+E[+-]\d+/
5d7098d5	22	# Input values can have embedded whitespace
5303340c LW	23	# Error returns
	24	# 'NaN' An input parameter was "Not a Number" or
	25	# divide by zero or sqrt of negative number
	26	# Division is computed to
79072805	27	# max($div_scale,length(dividend)+length(divisor))
5303340c LW	28	# digits by default.
	29	# Also used for default sqrt scale
	30
	31	$div_scale = 40;
	32
	33	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	34
	35	$rnd_mode = 'even';
	36
	37	# bigfloat routines
	38	#
	39	# fadd(NSTR, NSTR) return NSTR addition
	40	# fsub(NSTR, NSTR) return NSTR subtraction
	41	# fmul(NSTR, NSTR) return NSTR multiplication
	42	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	43	# fneg(NSTR) return NSTR negation
	44	# fabs(NSTR) return NSTR absolute value
	45	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	46	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	47	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	48	# fnorm(NSTR) return (NSTR) normalize
	49	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	50	\f
	51	# Convert a number to canonical string form.
	52	# Takes something that looks like a number and converts it to
	53	# the form /^[+-]\d+E[+-]\d+$/.
	54	sub main'fnorm { #(string) return fnum_str
	55	local($_) = @_;
	56	s/\s+//g; # strip white space
afea815c CS	57	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/
	58	&& ($2 ne '' \|\| defined($4))) {
	59	my $x = defined($4) ? $4 : '';
	60	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
5303340c LW	61	} else {
	62	'NaN';
	63	}
	64	}
	65
	66	# normalize number -- for internal use
	67	sub norm { #(mantissa, exponent) return fnum_str
	68	local($_, $exp) = @_;
	69	if ($_ eq 'NaN') {
	70	'NaN';
	71	} else {
	72	s/^([+-])0+/$1/; # strip leading zeros
	73	if (length($_) == 1) {
	74	'+0E+0';
	75	} else {
	76	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	77	sprintf("%sE%+ld", $_, $exp);
	78	}
	79	}
	80	}
	81
	82	# negation
	83	sub main'fneg { #(fnum_str) return fnum_str
859172fe	84	local($_) = &'fnorm($_[0]);
e334a159	85	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
f70c35af GS	86	if ( ord("\t") == 9 ) { # ascii
	87	s/^H/N/;
	88	}
	89	else { # ebcdic character set
	90	s/\373/N/;
	91	}
5303340c LW	92	$_;
	93	}
	94
	95	# absolute value
	96	sub main'fabs { #(fnum_str) return fnum_str
859172fe	97	local($_) = &'fnorm($_[0]);
68decaef	98	s/^-/+/; # mash sign
5303340c LW	99	$_;
	100	}
	101
	102	# multiplication
	103	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
859172fe	104	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	105	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	106	'NaN';
	107	} else {
	108	local($xm,$xe) = split('E',$x);
	109	local($ym,$ye) = split('E',$y);
	110	&norm(&'bmul($xm,$ym),$xe+$ye);
	111	}
	112	}
	113	\f
	114	# addition
	115	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
859172fe	116	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	117	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	118	'NaN';
	119	} else {
	120	local($xm,$xe) = split('E',$x);
	121	local($ym,$ye) = split('E',$y);
	122	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	123	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	124	}
	125	}
	126
	127	# subtraction
	128	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
859172fe	129	&'fadd($_[0],&'fneg($_[1]));
5303340c LW	130	}
	131
	132	# division
	133	# args are dividend, divisor, scale (optional)
	134	# result has at most max(scale, length(dividend), length(divisor)) digits
	135	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	136	{
859172fe	137	local($x,$y,$scale) = (&'fnorm($_[0]),&'fnorm($_[1]),$_[2]);
5303340c LW	138	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	139	'NaN';
	140	} else {
	141	local($xm,$xe) = split('E',$x);
	142	local($ym,$ye) = split('E',$y);
	143	$scale = $div_scale if (!$scale);
	144	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	145	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	146	$scale = $scale + length($ym) - length($xm);
5d7098d5	147	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
5303340c LW	148	$xe-$ye-$scale);
	149	}
	150	}
	151	\f
	152	# round int $q based on fraction $r/$base using $rnd_mode
	153	sub round { #(int_str, int_str, int_str) return int_str
	154	local($q,$r,$base) = @_;
	155	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	156	'NaN';
	157	} elsif ($rnd_mode eq 'trunc') {
	158	$q; # just truncate
	159	} else {
	160	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	161	if ( $cmp < 0 \|\|
	162	($cmp == 0 &&
	163	( $rnd_mode eq 'zero' \|\|
859172fe Z	164	($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) \|\|
859172fe Z	165	($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) \|\|
5303340c LW	166	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	167	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	168	$q; # round down
	169	} else {
859172fe	170	&'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
5303340c LW	171	# round up
	172	}
	173	}
	174	}
	175
	176	# round the mantissa of $x to $scale digits
	177	sub main'fround { #(fnum_str, scale) return fnum_str
859172fe	178	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
5303340c LW	179	if ($x eq 'NaN' \|\| $scale <= 0) {
	180	$x;
	181	} else {
	182	local($xm,$xe) = split('E',$x);
	183	if (length($xm)-1 <= $scale) {
	184	$x;
	185	} else {
859172fe Z	186	&norm(&round(substr($xm,0,$scale+1),
859172fe Z	187	"+0".substr($xm,$scale+1,1),"+10"),
5303340c LW	188	$xe+length($xm)-$scale-1);
	189	}
	190	}
	191	}
	192	\f
	193	# round $x at the 10 to the $scale digit place
	194	sub main'ffround { #(fnum_str, scale) return fnum_str
859172fe	195	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
5303340c LW	196	if ($x eq 'NaN') {
	197	'NaN';
	198	} else {
	199	local($xm,$xe) = split('E',$x);
	200	if ($xe >= $scale) {
	201	$x;
	202	} else {
	203	$xe = length($xm)+$xe-$scale;
	204	if ($xe < 1) {
	205	'+0E+0';
	206	} elsif ($xe == 1) {
5d7098d5 SK	207	# The first substr preserves the sign, which means that
	208	# we'll pass a non-normalized "-0" to &round when rounding
	209	# -0.006 (for example), purely so that &round won't lose
	210	# the sign.
859172fe Z	211	&norm(&round(substr($xm,0,1).'0',
859172fe Z	212	"+0".substr($xm,1,1),"+10"), $scale);
5303340c	213	} else {
859172fe Z	214	&norm(&round(substr($xm,0,$xe),
859172fe Z	215	"+0".substr($xm,$xe,1),"+10"), $scale);
5303340c LW	216	}
	217	}
	218	}
	219	}
	220
	221	# compare 2 values returns one of undef, <0, =0, >0
	222	# returns undef if either or both input value are not numbers
	223	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	224	{
859172fe	225	local($x, $y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	226	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	227	undef;
5303340c	228	} else {
68decaef LW	229	ord($y) <=> ord($x)
	230	\|\|
	231	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
859172fe	232	(($xe <=> $ye) * (substr($x,0,1).'1')
68decaef LW	233	\|\| &bigint'cmp($xm,$ym))
68decaef LW	234	);
5303340c LW	235	}
	236	}
	237	\f
	238	# square root by Newtons method.
	239	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
859172fe	240	local($x, $scale) = (&'fnorm($_[0]), $_[1]);
5303340c LW	241	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	242	'NaN';
	243	} elsif ($x eq '+0E+0') {
	244	'+0E+0';
	245	} else {
	246	local($xm, $xe) = split('E',$x);
	247	$scale = $div_scale if (!$scale);
	248	$scale = length($xm)-1 if ($scale < length($xm)-1);
	249	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	250	while ($gs < 2*$scale) {
	251	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	252	$gs *= 2;
	253	}
	254	&'fround($guess, $scale);
	255	}
	256	}
	257
	258	1;