[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
    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($_) = &'fnorm($_[$[]);
    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
f70c35af GS	82	if ( ord("\t") == 9 ) { # ascii
	83	s/^H/N/;
	84	}
	85	else { # ebcdic character set
	86	s/\373/N/;
	87	}
5303340c LW	88	$_;
	89	}
	90
	91	# absolute value
	92	sub main'fabs { #(fnum_str) return fnum_str
79072805	93	local($_) = &'fnorm($_[$[]);
68decaef	94	s/^-/+/; # mash sign
5303340c LW	95	$_;
	96	}
	97
	98	# multiplication
	99	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
79072805	100	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	101	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	102	'NaN';
	103	} else {
	104	local($xm,$xe) = split('E',$x);
	105	local($ym,$ye) = split('E',$y);
	106	&norm(&'bmul($xm,$ym),$xe+$ye);
	107	}
	108	}
	109	\f
	110	# addition
	111	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
79072805	112	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	113	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	114	'NaN';
	115	} else {
	116	local($xm,$xe) = split('E',$x);
	117	local($ym,$ye) = split('E',$y);
	118	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	119	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	120	}
	121	}
	122
	123	# subtraction
	124	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
79072805	125	&'fadd($_[$[],&'fneg($_[$[+1]));
5303340c LW	126	}
	127
	128	# division
	129	# args are dividend, divisor, scale (optional)
	130	# result has at most max(scale, length(dividend), length(divisor)) digits
	131	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	132	{
79072805	133	local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
5303340c LW	134	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	135	'NaN';
	136	} else {
	137	local($xm,$xe) = split('E',$x);
	138	local($ym,$ye) = split('E',$y);
	139	$scale = $div_scale if (!$scale);
	140	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	141	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	142	$scale = $scale + length($ym) - length($xm);
5d7098d5	143	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
5303340c LW	144	$xe-$ye-$scale);
	145	}
	146	}
	147	\f
	148	# round int $q based on fraction $r/$base using $rnd_mode
	149	sub round { #(int_str, int_str, int_str) return int_str
	150	local($q,$r,$base) = @_;
	151	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	152	'NaN';
	153	} elsif ($rnd_mode eq 'trunc') {
	154	$q; # just truncate
	155	} else {
	156	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	157	if ( $cmp < 0 \|\|
	158	($cmp == 0 &&
	159	( $rnd_mode eq 'zero' \|\|
79072805 LW	160	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
79072805 LW	161	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
5303340c LW	162	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	163	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	164	$q; # round down
	165	} else {
79072805	166	&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
5303340c LW	167	# round up
	168	}
	169	}
	170	}
	171
	172	# round the mantissa of $x to $scale digits
	173	sub main'fround { #(fnum_str, scale) return fnum_str
79072805	174	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	175	if ($x eq 'NaN' \|\| $scale <= 0) {
	176	$x;
	177	} else {
	178	local($xm,$xe) = split('E',$x);
	179	if (length($xm)-1 <= $scale) {
	180	$x;
	181	} else {
79072805 LW	182	&norm(&round(substr($xm,$[,$scale+1),
79072805 LW	183	"+0".substr($xm,$[+$scale+1,1),"+10"),
5303340c LW	184	$xe+length($xm)-$scale-1);
	185	}
	186	}
	187	}
	188	\f
	189	# round $x at the 10 to the $scale digit place
	190	sub main'ffround { #(fnum_str, scale) return fnum_str
79072805	191	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	192	if ($x eq 'NaN') {
	193	'NaN';
	194	} else {
	195	local($xm,$xe) = split('E',$x);
	196	if ($xe >= $scale) {
	197	$x;
	198	} else {
	199	$xe = length($xm)+$xe-$scale;
	200	if ($xe < 1) {
	201	'+0E+0';
	202	} elsif ($xe == 1) {
5d7098d5 SK	203	# The first substr preserves the sign, which means that
	204	# we'll pass a non-normalized "-0" to &round when rounding
	205	# -0.006 (for example), purely so that &round won't lose
	206	# the sign.
	207	&norm(&round(substr($xm,$[,1).'0',
	208	"+0".substr($xm,$[+1,1),"+10"), $scale);
5303340c	209	} else {
79072805 LW	210	&norm(&round(substr($xm,$[,$xe),
79072805 LW	211	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
5303340c LW	212	}
	213	}
	214	}
	215	}
	216
	217	# compare 2 values returns one of undef, <0, =0, >0
	218	# returns undef if either or both input value are not numbers
	219	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	220	{
79072805	221	local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	222	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	223	undef;
5303340c	224	} else {
68decaef LW	225	ord($y) <=> ord($x)
	226	\|\|
	227	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
79072805	228	(($xe <=> $ye) * (substr($x,$[,1).'1')
68decaef LW	229	\|\| &bigint'cmp($xm,$ym))
68decaef LW	230	);
5303340c LW	231	}
	232	}
	233	\f
	234	# square root by Newtons method.
	235	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
79072805	236	local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
5303340c LW	237	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	238	'NaN';
	239	} elsif ($x eq '+0E+0') {
	240	'+0E+0';
	241	} else {
	242	local($xm, $xe) = split('E',$x);
	243	$scale = $div_scale if (!$scale);
	244	$scale = length($xm)-1 if ($scale < length($xm)-1);
	245	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	246	while ($gs < 2*$scale) {
	247	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	248	$gs *= 2;
	249	}
	250	&'fround($guess, $scale);
	251	}
	252	}
	253
	254	1;