[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

warn( "The 'bigfloat.pl' legacy library is deprecated and will be"
      . " removed in the next major release of perl. Please use the"
      . " Math::BigFloat module instead." );

# 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.
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 S	13
	14	warn( "The 'bigfloat.pl' legacy library is deprecated and will be"
	15	. " removed in the next major release of perl. Please use the"
	16	. " Math::BigFloat module instead." );
	17
5303340c LW	18	# Arbitrary length float math package
5303340c LW	19	#
68decaef LW	20	# by Mark Biggar
68decaef LW	21	#
5303340c LW	22	# number format
5303340c LW	23	# canonical strings have the form /[+-]\d+E[+-]\d+/
5d7098d5	24	# Input values can have embedded whitespace
5303340c LW	25	# Error returns
	26	# 'NaN' An input parameter was "Not a Number" or
	27	# divide by zero or sqrt of negative number
	28	# Division is computed to
79072805	29	# max($div_scale,length(dividend)+length(divisor))
5303340c LW	30	# digits by default.
	31	# Also used for default sqrt scale
	32
	33	$div_scale = 40;
	34
	35	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	36
	37	$rnd_mode = 'even';
	38
	39	# bigfloat routines
	40	#
	41	# fadd(NSTR, NSTR) return NSTR addition
	42	# fsub(NSTR, NSTR) return NSTR subtraction
	43	# fmul(NSTR, NSTR) return NSTR multiplication
	44	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	45	# fneg(NSTR) return NSTR negation
	46	# fabs(NSTR) return NSTR absolute value
	47	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	48	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	49	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	50	# fnorm(NSTR) return (NSTR) normalize
	51	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	52	\f
	53	# Convert a number to canonical string form.
	54	# Takes something that looks like a number and converts it to
	55	# the form /^[+-]\d+E[+-]\d+$/.
	56	sub main'fnorm { #(string) return fnum_str
	57	local($_) = @_;
	58	s/\s+//g; # strip white space
afea815c CS	59	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/
	60	&& ($2 ne '' \|\| defined($4))) {
	61	my $x = defined($4) ? $4 : '';
	62	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
5303340c LW	63	} else {
	64	'NaN';
	65	}
	66	}
	67
	68	# normalize number -- for internal use
	69	sub norm { #(mantissa, exponent) return fnum_str
	70	local($_, $exp) = @_;
	71	if ($_ eq 'NaN') {
	72	'NaN';
	73	} else {
	74	s/^([+-])0+/$1/; # strip leading zeros
	75	if (length($_) == 1) {
	76	'+0E+0';
	77	} else {
	78	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	79	sprintf("%sE%+ld", $_, $exp);
	80	}
	81	}
	82	}
	83
	84	# negation
	85	sub main'fneg { #(fnum_str) return fnum_str
79072805	86	local($_) = &'fnorm($_[$[]);
e334a159	87	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
f70c35af GS	88	if ( ord("\t") == 9 ) { # ascii
	89	s/^H/N/;
	90	}
	91	else { # ebcdic character set
	92	s/\373/N/;
	93	}
5303340c LW	94	$_;
	95	}
	96
	97	# absolute value
	98	sub main'fabs { #(fnum_str) return fnum_str
79072805	99	local($_) = &'fnorm($_[$[]);
68decaef	100	s/^-/+/; # mash sign
5303340c LW	101	$_;
	102	}
	103
	104	# multiplication
	105	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
79072805	106	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	107	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	108	'NaN';
	109	} else {
	110	local($xm,$xe) = split('E',$x);
	111	local($ym,$ye) = split('E',$y);
	112	&norm(&'bmul($xm,$ym),$xe+$ye);
	113	}
	114	}
	115	\f
	116	# addition
	117	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
79072805	118	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	119	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	120	'NaN';
	121	} else {
	122	local($xm,$xe) = split('E',$x);
	123	local($ym,$ye) = split('E',$y);
	124	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	125	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	126	}
	127	}
	128
	129	# subtraction
	130	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
79072805	131	&'fadd($_[$[],&'fneg($_[$[+1]));
5303340c LW	132	}
	133
	134	# division
	135	# args are dividend, divisor, scale (optional)
	136	# result has at most max(scale, length(dividend), length(divisor)) digits
	137	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	138	{
79072805	139	local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
5303340c LW	140	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	141	'NaN';
	142	} else {
	143	local($xm,$xe) = split('E',$x);
	144	local($ym,$ye) = split('E',$y);
	145	$scale = $div_scale if (!$scale);
	146	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	147	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	148	$scale = $scale + length($ym) - length($xm);
5d7098d5	149	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),&'babs($ym)),
5303340c LW	150	$xe-$ye-$scale);
	151	}
	152	}
	153	\f
	154	# round int $q based on fraction $r/$base using $rnd_mode
	155	sub round { #(int_str, int_str, int_str) return int_str
	156	local($q,$r,$base) = @_;
	157	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	158	'NaN';
	159	} elsif ($rnd_mode eq 'trunc') {
	160	$q; # just truncate
	161	} else {
	162	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	163	if ( $cmp < 0 \|\|
	164	($cmp == 0 &&
	165	( $rnd_mode eq 'zero' \|\|
79072805 LW	166	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
79072805 LW	167	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
5303340c LW	168	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	169	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	170	$q; # round down
	171	} else {
79072805	172	&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
5303340c LW	173	# round up
	174	}
	175	}
	176	}
	177
	178	# round the mantissa of $x to $scale digits
	179	sub main'fround { #(fnum_str, scale) return fnum_str
79072805	180	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	181	if ($x eq 'NaN' \|\| $scale <= 0) {
	182	$x;
	183	} else {
	184	local($xm,$xe) = split('E',$x);
	185	if (length($xm)-1 <= $scale) {
	186	$x;
	187	} else {
79072805 LW	188	&norm(&round(substr($xm,$[,$scale+1),
79072805 LW	189	"+0".substr($xm,$[+$scale+1,1),"+10"),
5303340c LW	190	$xe+length($xm)-$scale-1);
	191	}
	192	}
	193	}
	194	\f
	195	# round $x at the 10 to the $scale digit place
	196	sub main'ffround { #(fnum_str, scale) return fnum_str
79072805	197	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	198	if ($x eq 'NaN') {
	199	'NaN';
	200	} else {
	201	local($xm,$xe) = split('E',$x);
	202	if ($xe >= $scale) {
	203	$x;
	204	} else {
	205	$xe = length($xm)+$xe-$scale;
	206	if ($xe < 1) {
	207	'+0E+0';
	208	} elsif ($xe == 1) {
5d7098d5 SK	209	# The first substr preserves the sign, which means that
	210	# we'll pass a non-normalized "-0" to &round when rounding
	211	# -0.006 (for example), purely so that &round won't lose
	212	# the sign.
	213	&norm(&round(substr($xm,$[,1).'0',
	214	"+0".substr($xm,$[+1,1),"+10"), $scale);
5303340c	215	} else {
79072805 LW	216	&norm(&round(substr($xm,$[,$xe),
79072805 LW	217	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
5303340c LW	218	}
	219	}
	220	}
	221	}
	222
	223	# compare 2 values returns one of undef, <0, =0, >0
	224	# returns undef if either or both input value are not numbers
	225	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	226	{
79072805	227	local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	228	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	229	undef;
5303340c	230	} else {
68decaef LW	231	ord($y) <=> ord($x)
	232	\|\|
	233	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
79072805	234	(($xe <=> $ye) * (substr($x,$[,1).'1')
68decaef LW	235	\|\| &bigint'cmp($xm,$ym))
68decaef LW	236	);
5303340c LW	237	}
	238	}
	239	\f
	240	# square root by Newtons method.
	241	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
79072805	242	local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
5303340c LW	243	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	244	'NaN';
	245	} elsif ($x eq '+0E+0') {
	246	'+0E+0';
	247	} else {
	248	local($xm, $xe) = split('E',$x);
	249	$scale = $div_scale if (!$scale);
	250	$scale = length($xm)-1 if ($scale < length($xm)-1);
	251	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	252	while ($gs < 2*$scale) {
	253	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	254	$gs *= 2;
	255	}
	256	&'fround($guess, $scale);
	257	}
	258	}
	259
	260	1;