[perl5.git] / lib / bigfloat.pl

package bigfloat;
require "bigint.pl";
# Arbitrary length float math package
#
# by Mark Biggar
#
# number format
#   canonical strings have the form /[+-]\d+E[+-]\d+/
#   Input values can have inbedded 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),$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) {
		&norm(&round('+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";
5303340c LW	3	# Arbitrary length float math package
5303340c LW	4	#
68decaef LW	5	# by Mark Biggar
68decaef LW	6	#
5303340c LW	7	# number format
	8	# canonical strings have the form /[+-]\d+E[+-]\d+/
	9	# Input values can have inbedded whitespace
	10	# Error returns
	11	# 'NaN' An input parameter was "Not a Number" or
	12	# divide by zero or sqrt of negative number
	13	# Division is computed to
79072805	14	# max($div_scale,length(dividend)+length(divisor))
5303340c LW	15	# digits by default.
	16	# Also used for default sqrt scale
	17
	18	$div_scale = 40;
	19
	20	# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
	21
	22	$rnd_mode = 'even';
	23
	24	# bigfloat routines
	25	#
	26	# fadd(NSTR, NSTR) return NSTR addition
	27	# fsub(NSTR, NSTR) return NSTR subtraction
	28	# fmul(NSTR, NSTR) return NSTR multiplication
	29	# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
	30	# fneg(NSTR) return NSTR negation
	31	# fabs(NSTR) return NSTR absolute value
	32	# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
	33	# fround(NSTR, SCALE) return NSTR round to SCALE digits
	34	# ffround(NSTR, SCALE) return NSTR round at SCALEth place
	35	# fnorm(NSTR) return (NSTR) normalize
	36	# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
	37	\f
	38	# Convert a number to canonical string form.
	39	# Takes something that looks like a number and converts it to
	40	# the form /^[+-]\d+E[+-]\d+$/.
	41	sub main'fnorm { #(string) return fnum_str
	42	local($_) = @_;
	43	s/\s+//g; # strip white space
afea815c CS	44	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/
	45	&& ($2 ne '' \|\| defined($4))) {
	46	my $x = defined($4) ? $4 : '';
	47	&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
5303340c LW	48	} else {
	49	'NaN';
	50	}
	51	}
	52
	53	# normalize number -- for internal use
	54	sub norm { #(mantissa, exponent) return fnum_str
	55	local($_, $exp) = @_;
	56	if ($_ eq 'NaN') {
	57	'NaN';
	58	} else {
	59	s/^([+-])0+/$1/; # strip leading zeros
	60	if (length($_) == 1) {
	61	'+0E+0';
	62	} else {
	63	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	64	sprintf("%sE%+ld", $_, $exp);
	65	}
	66	}
	67	}
	68
	69	# negation
	70	sub main'fneg { #(fnum_str) return fnum_str
79072805	71	local($_) = &'fnorm($_[$[]);
e334a159	72	vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
68decaef	73	s/^H/N/;
5303340c LW	74	$_;
	75	}
	76
	77	# absolute value
	78	sub main'fabs { #(fnum_str) return fnum_str
79072805	79	local($_) = &'fnorm($_[$[]);
68decaef	80	s/^-/+/; # mash sign
5303340c LW	81	$_;
	82	}
	83
	84	# multiplication
	85	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
79072805	86	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	87	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	88	'NaN';
	89	} else {
	90	local($xm,$xe) = split('E',$x);
	91	local($ym,$ye) = split('E',$y);
	92	&norm(&'bmul($xm,$ym),$xe+$ye);
	93	}
	94	}
	95	\f
	96	# addition
	97	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
79072805	98	local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	99	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	100	'NaN';
	101	} else {
	102	local($xm,$xe) = split('E',$x);
	103	local($ym,$ye) = split('E',$y);
	104	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	105	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	106	}
	107	}
	108
	109	# subtraction
	110	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
79072805	111	&'fadd($_[$[],&'fneg($_[$[+1]));
5303340c LW	112	}
	113
	114	# division
	115	# args are dividend, divisor, scale (optional)
	116	# result has at most max(scale, length(dividend), length(divisor)) digits
	117	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	118	{
79072805	119	local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
5303340c LW	120	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	121	'NaN';
	122	} else {
	123	local($xm,$xe) = split('E',$x);
	124	local($ym,$ye) = split('E',$y);
	125	$scale = $div_scale if (!$scale);
	126	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	127	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	128	$scale = $scale + length($ym) - length($xm);
	129	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),$ym),
	130	$xe-$ye-$scale);
	131	}
	132	}
	133	\f
	134	# round int $q based on fraction $r/$base using $rnd_mode
	135	sub round { #(int_str, int_str, int_str) return int_str
	136	local($q,$r,$base) = @_;
	137	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	138	'NaN';
	139	} elsif ($rnd_mode eq 'trunc') {
	140	$q; # just truncate
	141	} else {
	142	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	143	if ( $cmp < 0 \|\|
	144	($cmp == 0 &&
	145	( $rnd_mode eq 'zero' \|\|
79072805 LW	146	($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) \|\|
79072805 LW	147	($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) \|\|
5303340c LW	148	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
	149	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
	150	$q; # round down
	151	} else {
79072805	152	&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
5303340c LW	153	# round up
	154	}
	155	}
	156	}
	157
	158	# round the mantissa of $x to $scale digits
	159	sub main'fround { #(fnum_str, scale) return fnum_str
79072805	160	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	161	if ($x eq 'NaN' \|\| $scale <= 0) {
	162	$x;
	163	} else {
	164	local($xm,$xe) = split('E',$x);
	165	if (length($xm)-1 <= $scale) {
	166	$x;
	167	} else {
79072805 LW	168	&norm(&round(substr($xm,$[,$scale+1),
79072805 LW	169	"+0".substr($xm,$[+$scale+1,1),"+10"),
5303340c LW	170	$xe+length($xm)-$scale-1);
	171	}
	172	}
	173	}
	174	\f
	175	# round $x at the 10 to the $scale digit place
	176	sub main'ffround { #(fnum_str, scale) return fnum_str
79072805	177	local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
5303340c LW	178	if ($x eq 'NaN') {
	179	'NaN';
	180	} else {
	181	local($xm,$xe) = split('E',$x);
	182	if ($xe >= $scale) {
	183	$x;
	184	} else {
	185	$xe = length($xm)+$xe-$scale;
	186	if ($xe < 1) {
	187	'+0E+0';
	188	} elsif ($xe == 1) {
79072805	189	&norm(&round('+0',"+0".substr($xm,$[+1,1),"+10"), $scale);
5303340c	190	} else {
79072805 LW	191	&norm(&round(substr($xm,$[,$xe),
79072805 LW	192	"+0".substr($xm,$[+$xe,1),"+10"), $scale);
5303340c LW	193	}
	194	}
	195	}
	196	}
	197
	198	# compare 2 values returns one of undef, <0, =0, >0
	199	# returns undef if either or both input value are not numbers
	200	sub main'fcmp #(fnum_str, fnum_str) return cond_code
	201	{
79072805	202	local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
5303340c LW	203	if ($x eq "NaN" \|\| $y eq "NaN") {
5303340c LW	204	undef;
5303340c	205	} else {
68decaef LW	206	ord($y) <=> ord($x)
	207	\|\|
	208	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
79072805	209	(($xe <=> $ye) * (substr($x,$[,1).'1')
68decaef LW	210	\|\| &bigint'cmp($xm,$ym))
68decaef LW	211	);
5303340c LW	212	}
	213	}
	214	\f
	215	# square root by Newtons method.
	216	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
79072805	217	local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
5303340c LW	218	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	219	'NaN';
	220	} elsif ($x eq '+0E+0') {
	221	'+0E+0';
	222	} else {
	223	local($xm, $xe) = split('E',$x);
	224	$scale = $div_scale if (!$scale);
	225	$scale = length($xm)-1 if ($scale < length($xm)-1);
	226	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	227	while ($gs < 2*$scale) {
	228	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	229	$gs *= 2;
	230	}
	231	&'fround($guess, $scale);
	232	}
	233	}
	234
	235	1;