[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.
# 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
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.
8e1a0ca7 S	6	# This legacy library is deprecated and will be removed in a future
8e1a0ca7 S	7	# release of perl.
a6d71656 GS	8	#
	9	# In particular, this should not be used as an example of modern Perl
	10	# programming techniques.
	11	#
	12	# Suggested alternative: Math::BigFloat
8e1a0ca7	13
5303340c LW	14	# Arbitrary length float math package
5303340c LW	15	#
68decaef LW	16	# by Mark Biggar
68decaef LW	17	#
5303340c LW	18	# number format
5303340c LW	19	# canonical strings have the form /[+-]\d+E[+-]\d+/
5d7098d5	20	# Input values can have embedded whitespace
5303340c LW	21	# Error returns
	22	# 'NaN' An input parameter was "Not a Number" or
	23	# divide by zero or sqrt of negative number
	24	# Division is computed to
79072805	25	# max($div_scale,length(dividend)+length(divisor))
5303340c LW	26	# digits by default.
	27	# Also used for default sqrt scale
	28
	29	$div_scale = 40;
	30
	31	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	32
	33	$rnd_mode = 'even';
	34
	35	# bigfloat routines
	36	#
	37	# fadd(NSTR, NSTR) return NSTR addition
	38	# fsub(NSTR, NSTR) return NSTR subtraction
	39	# fmul(NSTR, NSTR) return NSTR multiplication
	40	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	41	# fneg(NSTR) return NSTR negation
	42	# fabs(NSTR) return NSTR absolute value
	43	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	44	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	45	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	46	# fnorm(NSTR) return (NSTR) normalize
	47	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	48	\f
	49	# Convert a number to canonical string form.
	50	# Takes something that looks like a number and converts it to
	51	# the form /^[+-]\d+E[+-]\d+$/.
	52	sub main'fnorm { #(string) return fnum_str
	53	local($_) = @_;
	54	s/\s+//g; # strip white space
afea815c CS	55	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/
	56	&& ($2 ne '' \|\| defined($4))) {
	57	my $x = defined($4) ? $4 : '';
	58	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
5303340c LW	59	} else {
	60	'NaN';
	61	}
	62	}
	63
	64	# normalize number -- for internal use
	65	sub norm { #(mantissa, exponent) return fnum_str
	66	local($_, $exp) = @_;
	67	if ($_ eq 'NaN') {
	68	'NaN';
	69	} else {
	70	s/^([+-])0+/$1/; # strip leading zeros
	71	if (length($_) == 1) {
	72	'+0E+0';
	73	} else {
	74	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	75	sprintf("%sE%+ld", $_, $exp);
	76	}
	77	}
	78	}
	79
	80	# negation
	81	sub main'fneg { #(fnum_str) return fnum_str
859172fe	82	local($_) = &'fnorm($_[0]);
e334a159	83	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
f70c35af GS	84	if ( ord("\t") == 9 ) { # ascii
	85	s/^H/N/;
	86	}
	87	else { # ebcdic character set
	88	s/\373/N/;
	89	}
5303340c LW	90	$_;
	91	}
	92
	93	# absolute value
	94	sub main'fabs { #(fnum_str) return fnum_str
859172fe	95	local($_) = &'fnorm($_[0]);
68decaef	96	s/^-/+/; # mash sign
5303340c LW	97	$_;
	98	}
	99
	100	# multiplication
	101	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
859172fe	102	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	103	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	104	'NaN';
	105	} else {
	106	local($xm,$xe) = split('E',$x);
	107	local($ym,$ye) = split('E',$y);
	108	&norm(&'bmul($xm,$ym),$xe+$ye);
	109	}
	110	}
	111	\f
	112	# addition
	113	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
859172fe	114	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	115	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	116	'NaN';
	117	} else {
	118	local($xm,$xe) = split('E',$x);
	119	local($ym,$ye) = split('E',$y);
	120	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	121	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	122	}
	123	}
	124
	125	# subtraction
	126	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
859172fe	127	&'fadd($_[0],&'fneg($_[1]));
5303340c LW	128	}
	129
	130	# division
	131	# args are dividend, divisor, scale (optional)
	132	# result has at most max(scale, length(dividend), length(divisor)) digits
	133	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	134	{
859172fe	135	local($x,$y,$scale) = (&'fnorm($_[0]),&'fnorm($_[1]),$_[2]);
5303340c LW	136	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	137	'NaN';
	138	} else {
	139	local($xm,$xe) = split('E',$x);
	140	local($ym,$ye) = split('E',$y);
	141	$scale = $div_scale if (!$scale);
	142	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	143	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	144	$scale = $scale + length($ym) - length($xm);
5d7098d5	145	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
5303340c LW	146	$xe-$ye-$scale);
	147	}
	148	}
	149	\f
	150	# round int $q based on fraction $r/$base using $rnd_mode
	151	sub round { #(int_str, int_str, int_str) return int_str
	152	local($q,$r,$base) = @_;
	153	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	154	'NaN';
	155	} elsif ($rnd_mode eq 'trunc') {
	156	$q; # just truncate
	157	} else {
	158	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	159	if ( $cmp < 0 \|\|
	160	($cmp == 0 &&
	161	( $rnd_mode eq 'zero' \|\|
859172fe Z	162	($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) \|\|
859172fe Z	163	($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) \|\|
5303340c LW	164	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	165	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	166	$q; # round down
	167	} else {
859172fe	168	&'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
5303340c LW	169	# round up
	170	}
	171	}
	172	}
	173
	174	# round the mantissa of $x to $scale digits
	175	sub main'fround { #(fnum_str, scale) return fnum_str
859172fe	176	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
5303340c LW	177	if ($x eq 'NaN' \|\| $scale <= 0) {
	178	$x;
	179	} else {
	180	local($xm,$xe) = split('E',$x);
	181	if (length($xm)-1 <= $scale) {
	182	$x;
	183	} else {
859172fe Z	184	&norm(&round(substr($xm,0,$scale+1),
859172fe Z	185	"+0".substr($xm,$scale+1,1),"+10"),
5303340c LW	186	$xe+length($xm)-$scale-1);
	187	}
	188	}
	189	}
	190	\f
	191	# round $x at the 10 to the $scale digit place
	192	sub main'ffround { #(fnum_str, scale) return fnum_str
859172fe	193	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
5303340c LW	194	if ($x eq 'NaN') {
	195	'NaN';
	196	} else {
	197	local($xm,$xe) = split('E',$x);
	198	if ($xe >= $scale) {
	199	$x;
	200	} else {
	201	$xe = length($xm)+$xe-$scale;
	202	if ($xe < 1) {
	203	'+0E+0';
	204	} elsif ($xe == 1) {
5d7098d5 SK	205	# The first substr preserves the sign, which means that
	206	# we'll pass a non-normalized "-0" to &round when rounding
	207	# -0.006 (for example), purely so that &round won't lose
	208	# the sign.
859172fe Z	209	&norm(&round(substr($xm,0,1).'0',
859172fe Z	210	"+0".substr($xm,1,1),"+10"), $scale);
5303340c	211	} else {
859172fe Z	212	&norm(&round(substr($xm,0,$xe),
859172fe Z	213	"+0".substr($xm,$xe,1),"+10"), $scale);
5303340c LW	214	}
	215	}
	216	}
	217	}
	218
	219	# compare 2 values returns one of undef, <0, =0, >0
	220	# returns undef if either or both input value are not numbers
	221	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	222	{
859172fe	223	local($x, $y) = (&'fnorm($_[0]),&'fnorm($_[1]));
5303340c LW	224	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	225	undef;
5303340c	226	} else {
68decaef LW	227	ord($y) <=> ord($x)
	228	\|\|
	229	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
859172fe	230	(($xe <=> $ye) * (substr($x,0,1).'1')
68decaef LW	231	\|\| &bigint'cmp($xm,$ym))
68decaef LW	232	);
5303340c LW	233	}
	234	}
	235	\f
	236	# square root by Newtons method.
	237	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
859172fe	238	local($x, $scale) = (&'fnorm($_[0]), $_[1]);
5303340c LW	239	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	240	'NaN';
	241	} elsif ($x eq '+0E+0') {
	242	'+0E+0';
	243	} else {
	244	local($xm, $xe) = split('E',$x);
	245	$scale = $div_scale if (!$scale);
	246	$scale = length($xm)-1 if ($scale < length($xm)-1);
	247	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	248	while ($gs < 2*$scale) {
	249	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	250	$gs *= 2;
	251	}
	252	&'fround($guess, $scale);
	253	}
	254	}
	255
	256	1;