236 lines
6.6 KiB
Perl
236 lines
6.6 KiB
Perl
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package bigfloat;
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require "bigint.pl";
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# Arbitrary length float math package
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#
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# by Mark Biggar
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#
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# number format
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# canonical strings have the form /[+-]\d+E[+-]\d+/
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# Input values can have inbedded whitespace
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# Error returns
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# 'NaN' An input parameter was "Not a Number" or
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# divide by zero or sqrt of negative number
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# Division is computed to
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# max($div_scale,length(dividend)+length(divisor))
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# digits by default.
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# Also used for default sqrt scale
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$div_scale = 40;
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# Rounding modes one of 'even', 'odd', '+inf', '-inf', 'zero' or 'trunc'.
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$rnd_mode = 'even';
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# bigfloat routines
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#
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# fadd(NSTR, NSTR) return NSTR addition
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# fsub(NSTR, NSTR) return NSTR subtraction
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# fmul(NSTR, NSTR) return NSTR multiplication
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# fdiv(NSTR, NSTR[,SCALE]) returns NSTR division to SCALE places
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# fneg(NSTR) return NSTR negation
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# fabs(NSTR) return NSTR absolute value
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# fcmp(NSTR,NSTR) return CODE compare undef,<0,=0,>0
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# fround(NSTR, SCALE) return NSTR round to SCALE digits
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# ffround(NSTR, SCALE) return NSTR round at SCALEth place
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# fnorm(NSTR) return (NSTR) normalize
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# fsqrt(NSTR[, SCALE]) return NSTR sqrt to SCALE places
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# Convert a number to canonical string form.
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# Takes something that looks like a number and converts it to
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# the form /^[+-]\d+E[+-]\d+$/.
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sub main'fnorm { #(string) return fnum_str
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local($_) = @_;
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s/\s+//g; # strip white space
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if (/^([+-]?)(\d*)(\.(\d*))?([Ee]([+-]?\d+))?$/
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&& ($2 ne '' || defined($4))) {
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my $x = defined($4) ? $4 : '';
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&norm(($1 ? "$1$2$x" : "+$2$x"), (($x ne '') ? $6-length($x) : $6));
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} else {
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'NaN';
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}
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}
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# normalize number -- for internal use
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sub norm { #(mantissa, exponent) return fnum_str
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local($_, $exp) = @_;
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if ($_ eq 'NaN') {
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'NaN';
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} else {
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s/^([+-])0+/$1/; # strip leading zeros
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if (length($_) == 1) {
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'+0E+0';
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} else {
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$exp += length($1) if (s/(0+)$//); # strip trailing zeros
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sprintf("%sE%+ld", $_, $exp);
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}
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}
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}
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# negation
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sub main'fneg { #(fnum_str) return fnum_str
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local($_) = &'fnorm($_[$[]);
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vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0E+0'; # flip sign
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s/^H/N/;
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$_;
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}
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# absolute value
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sub main'fabs { #(fnum_str) return fnum_str
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local($_) = &'fnorm($_[$[]);
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s/^-/+/; # mash sign
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$_;
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}
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# multiplication
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sub main'fmul { #(fnum_str, fnum_str) return fnum_str
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local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
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if ($x eq 'NaN' || $y eq 'NaN') {
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'NaN';
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} else {
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local($xm,$xe) = split('E',$x);
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local($ym,$ye) = split('E',$y);
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&norm(&'bmul($xm,$ym),$xe+$ye);
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}
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}
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# addition
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sub main'fadd { #(fnum_str, fnum_str) return fnum_str
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local($x,$y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
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if ($x eq 'NaN' || $y eq 'NaN') {
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'NaN';
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} else {
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local($xm,$xe) = split('E',$x);
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local($ym,$ye) = split('E',$y);
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($xm,$xe,$ym,$ye) = ($ym,$ye,$xm,$xe) if ($xe < $ye);
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&norm(&'badd($ym,$xm.('0' x ($xe-$ye))),$ye);
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}
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}
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# subtraction
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sub main'fsub { #(fnum_str, fnum_str) return fnum_str
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&'fadd($_[$[],&'fneg($_[$[+1]));
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}
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# division
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# args are dividend, divisor, scale (optional)
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# result has at most max(scale, length(dividend), length(divisor)) digits
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sub main'fdiv #(fnum_str, fnum_str[,scale]) return fnum_str
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{
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local($x,$y,$scale) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]),$_[$[+2]);
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if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0E+0') {
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'NaN';
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} else {
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local($xm,$xe) = split('E',$x);
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local($ym,$ye) = split('E',$y);
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$scale = $div_scale if (!$scale);
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$scale = length($xm)-1 if (length($xm)-1 > $scale);
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$scale = length($ym)-1 if (length($ym)-1 > $scale);
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$scale = $scale + length($ym) - length($xm);
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&norm(&round(&'bdiv($xm.('0' x $scale),$ym),$ym),
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$xe-$ye-$scale);
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}
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}
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# round int $q based on fraction $r/$base using $rnd_mode
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sub round { #(int_str, int_str, int_str) return int_str
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local($q,$r,$base) = @_;
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if ($q eq 'NaN' || $r eq 'NaN') {
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'NaN';
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} elsif ($rnd_mode eq 'trunc') {
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$q; # just truncate
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} else {
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local($cmp) = &'bcmp(&'bmul($r,'+2'),$base);
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if ( $cmp < 0 ||
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($cmp == 0 &&
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( $rnd_mode eq 'zero' ||
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($rnd_mode eq '-inf' && (substr($q,$[,1) eq '+')) ||
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($rnd_mode eq '+inf' && (substr($q,$[,1) eq '-')) ||
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($rnd_mode eq 'even' && $q =~ /[24680]$/) ||
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($rnd_mode eq 'odd' && $q =~ /[13579]$/) )) ) {
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$q; # round down
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} else {
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&'badd($q, ((substr($q,$[,1) eq '-') ? '-1' : '+1'));
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# round up
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}
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}
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}
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# round the mantissa of $x to $scale digits
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sub main'fround { #(fnum_str, scale) return fnum_str
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local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
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if ($x eq 'NaN' || $scale <= 0) {
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$x;
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} else {
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local($xm,$xe) = split('E',$x);
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if (length($xm)-1 <= $scale) {
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$x;
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} else {
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&norm(&round(substr($xm,$[,$scale+1),
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"+0".substr($xm,$[+$scale+1,1),"+10"),
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$xe+length($xm)-$scale-1);
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}
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}
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}
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# round $x at the 10 to the $scale digit place
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sub main'ffround { #(fnum_str, scale) return fnum_str
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local($x,$scale) = (&'fnorm($_[$[]),$_[$[+1]);
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if ($x eq 'NaN') {
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'NaN';
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} else {
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local($xm,$xe) = split('E',$x);
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if ($xe >= $scale) {
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$x;
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} else {
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$xe = length($xm)+$xe-$scale;
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if ($xe < 1) {
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'+0E+0';
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} elsif ($xe == 1) {
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&norm(&round('+0',"+0".substr($xm,$[+1,1),"+10"), $scale);
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} else {
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&norm(&round(substr($xm,$[,$xe),
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"+0".substr($xm,$[+$xe,1),"+10"), $scale);
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}
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}
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}
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}
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# compare 2 values returns one of undef, <0, =0, >0
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# returns undef if either or both input value are not numbers
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sub main'fcmp #(fnum_str, fnum_str) return cond_code
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{
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local($x, $y) = (&'fnorm($_[$[]),&'fnorm($_[$[+1]));
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if ($x eq "NaN" || $y eq "NaN") {
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undef;
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} else {
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ord($y) <=> ord($x)
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( local($xm,$xe,$ym,$ye) = split('E', $x."E$y"),
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(($xe <=> $ye) * (substr($x,$[,1).'1')
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|| &bigint'cmp($xm,$ym))
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);
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}
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}
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# square root by Newtons method.
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sub main'fsqrt { #(fnum_str[, scale]) return fnum_str
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local($x, $scale) = (&'fnorm($_[$[]), $_[$[+1]);
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if ($x eq 'NaN' || $x =~ /^-/) {
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'NaN';
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} elsif ($x eq '+0E+0') {
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'+0E+0';
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} else {
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local($xm, $xe) = split('E',$x);
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$scale = $div_scale if (!$scale);
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$scale = length($xm)-1 if ($scale < length($xm)-1);
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local($gs, $guess) = (1, sprintf("1E%+d", (length($xm)+$xe-1)/2));
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while ($gs < 2*$scale) {
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$guess = &'fmul(&'fadd($guess,&'fdiv($x,$guess,$gs*2)),".5");
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$gs *= 2;
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}
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&'fround($guess, $scale);
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}
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}
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1;
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