[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$4" ne '') {
	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $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
    s/^H/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),$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) {
		&norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale);
	    } else {
		&norm(&round(substr($xm,0,$trunc),
		      "+0".substr($xm,$trunc,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";
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
	14	# max($div_scale,length(dividend).length(divisor))
	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($_) = @_;
	43	s/\s+//g; # strip white space
	44	if (/^([+-]?)(\d)(\.(\d))?([Ee]([+-]?\d+))?$/ && "$2$4" ne '') {
	45	&norm(($1 ? "$1$2$4" : "+$2$4"),(($4 ne '') ? $6-length($4) : $6));
	46	} else {
	47	'NaN';
	48	}
	49	}
	50
	51	# normalize number -- for internal use
	52	sub norm { #(mantissa, exponent) return fnum_str
	53	local($_, $exp) = @_;
	54	if ($_ eq 'NaN') {
	55	'NaN';
	56	} else {
	57	s/^([+-])0+/$1/; # strip leading zeros
	58	if (length($_) == 1) {
	59	'+0E+0';
	60	} else {
	61	$exp += length($1) if (s/(0+)$//); # strip trailing zeros
	62	sprintf("%sE%+ld", $_, $exp);
	63	}
	64	}
	65	}
	66
	67	# negation
	68	sub main'fneg { #(fnum_str) return fnum_str
	69	local($_) = &'fnorm($_[0]);
68decaef LW	70	vec($_,0,8) =^ ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
68decaef LW	71	s/^H/N/;
5303340c LW	72	$_;
	73	}
	74
	75	# absolute value
	76	sub main'fabs { #(fnum_str) return fnum_str
	77	local($_) = &'fnorm($_[0]);
68decaef	78	s/^-/+/; # mash sign
5303340c LW	79	$_;
	80	}
	81
	82	# multiplication
	83	sub main'fmul { #(fnum_str, fnum_str) return fnum_str
	84	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
	85	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	86	'NaN';
	87	} else {
	88	local($xm,$xe) = split('E',$x);
	89	local($ym,$ye) = split('E',$y);
	90	&norm(&'bmul($xm,$ym),$xe+$ye);
	91	}
	92	}
	93	\f
	94	# addition
	95	sub main'fadd { #(fnum_str, fnum_str) return fnum_str
	96	local($x,$y) = (&'fnorm($_[0]),&'fnorm($_[1]));
	97	if ($x eq 'NaN' \|\| $y eq 'NaN') {
	98	'NaN';
	99	} else {
	100	local($xm,$xe) = split('E',$x);
	101	local($ym,$ye) = split('E',$y);
	102	($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
	103	&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
	104	}
	105	}
	106
	107	# subtraction
	108	sub main'fsub { #(fnum_str, fnum_str) return fnum_str
	109	&'fadd($_[0],&'fneg($_[1]));
	110	}
	111
	112	# division
	113	# args are dividend, divisor, scale (optional)
	114	# result has at most max(scale, length(dividend), length(divisor)) digits
	115	sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
	116	{
	117	local($x,$y,$scale) = (&'fnorm($_[0]),&'fnorm($_[1]),$_[2]);
	118	if ($x eq 'NaN' \|\| $y eq 'NaN' \|\| $y eq '+0E+0') {
	119	'NaN';
	120	} else {
	121	local($xm,$xe) = split('E',$x);
	122	local($ym,$ye) = split('E',$y);
	123	$scale = $div_scale if (!$scale);
	124	$scale = length($xm)-1 if (length($xm)-1 > $scale);
	125	$scale = length($ym)-1 if (length($ym)-1 > $scale);
	126	$scale = $scale + length($ym) - length($xm);
	127	&norm(&round(&'bdiv($xm.('0' x $scale),$ym),$ym),
	128	$xe-$ye-$scale);
	129	}
	130	}
	131	\f
	132	# round int $q based on fraction $r/$base using $rnd_mode
	133	sub round { #(int_str, int_str, int_str) return int_str
	134	local($q,$r,$base) = @_;
	135	if ($q eq 'NaN' \|\| $r eq 'NaN') {
	136	'NaN';
	137	} elsif ($rnd_mode eq 'trunc') {
	138	$q; # just truncate
	139	} else {
	140	local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
	141	if ( $cmp < 0 \|\|
	142	($cmp == 0 &&
143	( $rnd_mode eq 'zero' \|\|
144	($rnd_mode eq '-inf' && (substr($q,0,1) eq '+')) \|\|
145	($rnd_mode eq '+inf' && (substr($q,0,1) eq '-')) \|\|
146	($rnd_mode eq 'even' && $q =~ /[24680]$/) \|\|
147	($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
148	$q; # round down
149	} else {
150	&'badd($q, ((substr($q,0,1) eq '-') ? '-1' : '+1'));
151	# round up
152	}
153	}
154	}
155
156	# round the mantissa of $x to $scale digits
157	sub main'fround { #(fnum_str, scale) return fnum_str
158	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
159	if ($x eq 'NaN' \|\| $scale <= 0) {
160	$x;
161	} else {
162	local($xm,$xe) = split('E',$x);
163	if (length($xm)-1 <= $scale) {
164	$x;
165	} else {
166	&norm(&round(substr($xm,0,$scale+1),
167	"+0".substr($xm,$scale+1,1),"+10"),
168	$xe+length($xm)-$scale-1);
169	}
170	}
171	}
172	\f
173	# round $x at the 10 to the $scale digit place
174	sub main'ffround { #(fnum_str, scale) return fnum_str
175	local($x,$scale) = (&'fnorm($_[0]),$_[1]);
176	if ($x eq 'NaN') {
177	'NaN';
178	} else {
179	local($xm,$xe) = split('E',$x);
180	if ($xe >= $scale) {
181	$x;
182	} else {
183	$xe = length($xm)+$xe-$scale;
184	if ($xe < 1) {
185	'+0E+0';
186	} elsif ($xe == 1) {
187	&norm(&round('+0',"+0".substr($xm,1,1),"+10"), $scale);
188	} else {
189	&norm(&round(substr($xm,0,$trunc),
190	"+0".substr($xm,$trunc,1),"+10"), $scale);
191	}
192	}
193	}
194	}
195
196	# compare 2 values returns one of undef, <0, =0, >0
197	# returns undef if either or both input value are not numbers
198	sub main'fcmp #(fnum_str, fnum_str) return cond_code
199	{
200	local($x, $y) = (&'fnorm($_[0]),&'fnorm($_[1]));
201	if ($x eq "NaN" \|\| $y eq "NaN") {
202	undef;
5303340c	203	} else {
68decaef LW	204	ord($y) <=> ord($x)
	205	\|\|
	206	( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
	207	(($xe <=> $ye) * (substr($x,0,1).'1')
	208	\|\| &bigint'cmp($xm,$ym))
	209	);
5303340c LW	210	}
	211	}
	212	\f
	213	# square root by Newtons method.
	214	sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
	215	local($x, $scale) = (&'fnorm($_[0]), $_[1]);
	216	if ($x eq 'NaN' \|\| $x =~ /^-/) {
	217	'NaN';
	218	} elsif ($x eq '+0E+0') {
	219	'+0E+0';
	220	} else {
	221	local($xm, $xe) = split('E',$x);
	222	$scale = $div_scale if (!$scale);
	223	$scale = length($xm)-1 if ($scale < length($xm)-1);
	224	local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
	225	while ($gs < 2*$scale) {
	226	$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
	227	$gs *= 2;
	228	}
	229	&'fround($guess, $scale);
	230	}
	231	}
	232
	233	1;