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-rwxr-xr-xMaster/tlpkg/tlperl/lib/bigfloat.pl254
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diff --git a/Master/tlpkg/tlperl/lib/bigfloat.pl b/Master/tlpkg/tlperl/lib/bigfloat.pl
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+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.
+#
+# In particular, this should not be used as an example of modern Perl
+# programming techniques.
+#
+# Suggested alternative: Math::BigFloat
+#
+# 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
+ 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+$ye);
+ }
+}
+
+# addition
+sub main'fadd { #(fnum_str, fnum_str) return fnum_str
+ local($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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