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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 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'.
$rnd_mode = 'even';
# bigfloat routines
#
# fadd(NSTR, NSTR) return NSTR addition
# fsub(NSTR, NSTR) return NSTR subtraction
# fmul(NSTR, NSTR) return NSTR multiplication
# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
# fneg(NSTR) return NSTR negation
# fabs(NSTR) return NSTR absolute value
# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
# fround(NSTR, SCALE) return NSTR round to SCALE digits
# ffround(NSTR, SCALE) return NSTR round at SCALEth place
# fnorm(NSTR) return (NSTR) normalize
# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
# Convert a number to canonical string form.
# Takes something that looks like a number and converts it to
# the form /^[+-]\d+E[+-]\d+$/.
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+$ye);
}
}
# addition
sub main'fadd { #(fnum_str, fnum_str) return fnum_str
local($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);
}
}
# 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);
}
}
}
# 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,$ym))
);
}
}
# square root by Newtons method.
sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
local($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;
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