perl 3.0 patch #38 (combined patch)

Forget the description, it's too late at night...

1 files changed, 236 insertions, 0 deletions

diff --git a/lib/bigfloat.pl b/lib/bigfloat.pl
new file mode 100644
index 0000000000..feaaa6e494
--- /dev/null
+++ b/lib/bigfloat.pl
@@ -0,0 +1,236 @@
+package bigfloat;
+require "bigint.pl";
+
+# Arbitrary length float math package
+#
+# 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'.
+
+$rnd_mode = 'even';
+
+#   bigfloat routines
+#
+#   fadd(NSTR, NSTR) return NSTR            addition
+#   fsub(NSTR, NSTR) return NSTR            subtraction
+#   fmul(NSTR, NSTR) return NSTR            multiplication
+#   fdiv(NSTR, NSTR[,SCALE]) returns NSTR   division to SCALE places
+#   fneg(NSTR) return NSTR                  negation
+#   fabs(NSTR) return NSTR                  absolute value
+#   fcmp(NSTR,NSTR) return CODE             compare undef,<0,=0,>0
+#   fround(NSTR, SCALE) return NSTR         round to SCALE digits
+#   ffround(NSTR, SCALE) return NSTR        round at SCALEth place
+#   fnorm(NSTR) return (NSTR)               normalize
+#   fsqrt(NSTR[, SCALE]) return NSTR        sqrt to SCALE places
+
+# Convert a number to canonical string form.
+#   Takes something that looks like a number and converts it to
+#   the form /^[+-]\d+E[+-]\d+$/.
+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($_[0]);
+    substr($_,0,1) =~ tr/+-/-+/ if ($_ ne '+0E+0'); # flip sign
+    $_;
+}
+
+# absolute value
+sub main'fabs { #(fnum_str) return fnum_str
+    local($_) = &'fnorm($_[0]);
+    substr($_,0,1) = '+';                       # 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+$ye);
+    }
+}
+
+# addition
+sub main'fadd { #(fnum_str, fnum_str) return fnum_str
+    local($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);
+    }
+}
+
+# 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);
+	}
+    }
+}
+
+# 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" || $y eq "NaN") {
+	undef;
+    } elsif ($x eq $y) {
+	0;
+    } elsif (ord($x) != ord($y)) {
+	(ord($y) - ord($x));                # based on signs
+    } else {
+	local($xm,$xe) = split('E',$x);
+	local($ym,$ye) = split('E',$y);
+	if ($xe ne $ye) {
+	    ($xe - $ye) * (substr($x,0,1).'1');
+	} else {
+	    &bigint'cmp($xm,$ym);           # based on value
+	}
+    }
+}
+
+# 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;