From 5303340c1eb77f5b18e12347ed4a7fa2eb6cd9f7 Mon Sep 17 00:00:00 2001
From: Larry Wall <lwall@jpl-devvax.jpl.nasa.gov>
Date: Fri, 9 Nov 1990 13:39:17 +0000
Subject: perl 3.0 patch #38 (combined patch)

Forget the description, it's too late at night...
---
 lib/bigrat.pl | 146 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 146 insertions(+)
 create mode 100644 lib/bigrat.pl

(limited to 'lib/bigrat.pl')

diff --git a/lib/bigrat.pl b/lib/bigrat.pl
new file mode 100644
index 0000000000..3157cf8244
--- /dev/null
+++ b/lib/bigrat.pl
@@ -0,0 +1,146 @@
+package bigrat;
+require "bigint.pl";
+
+# Arbitrary size rational math package
+#
+# Input values to these routines consist of strings of the form 
+#   m|^\s*[+-]?[\d\s]+(/[\d\s]+)?$|.
+# Examples:
+#   "+0/1"                          canonical zero value
+#   "3"                             canonical value "+3/1"
+#   "   -123/123 123"               canonical value "-1/1001"
+#   "123 456/7890"                  canonical value "+20576/1315"
+# Output values always include a sign and no leading zeros or
+#   white space.
+# This package makes use of the bigint package.
+# The string 'NaN' is used to represent the result when input arguments 
+#   that are not numbers, as well as the result of dividing by zero and
+#       the sqrt of a negative number.
+# Extreamly naive algorthims are used.
+#
+# Routines provided are:
+#
+#   rneg(RAT) return RAT                negation
+#   rabs(RAT) return RAT                absolute value
+#   rcmp(RAT,RAT) return CODE           compare numbers (undef,<0,=0,>0)
+#   radd(RAT,RAT) return RAT            addition
+#   rsub(RAT,RAT) return RAT            subtraction
+#   rmul(RAT,RAT) return RAT            multiplication
+#   rdiv(RAT,RAT) return RAT            division
+#   rmod(RAT) return (RAT,RAT)          integer and fractional parts
+#   rnorm(RAT) return RAT               normalization
+#   rsqrt(RAT, cycles) return RAT       square root
+
+# Convert a number to the canonical string form m|^[+-]\d+/\d+|.
+sub main'rnorm { #(string) return rat_num
+    local($_) = @_;
+    s/\s+//g;
+    if (m#^([+-]?\d+)(/(\d*[1-9]0*))?$#) {
+	&norm($1, $3 ? $3 : '+1');
+    } else {
+	'NaN';
+    }
+}
+
+# Normalize by reducing to lowest terms
+sub norm { #(bint, bint) return rat_num
+    local($num,$dom) = @_;
+    if ($num eq 'NaN') {
+	'NaN';
+    } elsif ($dom eq 'NaN') {
+	'NaN';
+    } elsif ($dom =~ /^[+-]?0+$/) {
+	'NaN';
+    } else {
+	local($gcd) = &'bgcd($num,$dom);
+	if ($gcd ne '+1') { 
+	    $num = &'bdiv($num,$gcd);
+	    $dom = &'bdiv($dom,$gcd);
+	} else {
+	    $num = &'bnorm($num);
+	    $dom = &'bnorm($dom);
+	}
+	substr($dom,0,1) = '';
+	"$num/$dom";
+    }
+}
+
+# negation
+sub main'rneg { #(rat_num) return rat_num
+    local($_) = &'rnorm($_[0]);
+    tr/-+/+-/ if ($_ ne '+0/1');
+    $_;
+}
+
+# absolute value
+sub main'rabs { #(rat_num) return $rat_num
+    local($_) = &'rnorm($_[0]);
+    substr($_,0,1) = '+';
+    $_;
+}
+
+# multipication
+sub main'rmul { #(rat_num, rat_num) return rat_num
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($yn,$yd) = split('/',&'rnorm($_[1]));
+    &norm(&'bmul($xn,$yn),&'bmul($xd,$yd));
+}
+
+# division
+sub main'rdiv { #(rat_num, rat_num) return rat_num
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($yn,$yd) = split('/',&'rnorm($_[1]));
+    &norm(&'bmul($xn,$yd),&'bmul($xd,$yn));
+}
+
+# addition
+sub main'radd { #(rat_num, rat_num) return rat_num
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($yn,$yd) = split('/',&'rnorm($_[1]));
+    &norm(&'badd(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
+}
+
+# subtraction
+sub main'rsub { #(rat_num, rat_num) return rat_num
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($yn,$yd) = split('/',&'rnorm($_[1]));
+    &norm(&'bsub(&'bmul($xn,$yd),&'bmul($yn,$xd)),&'bmul($xd,$yd));
+}
+
+# comparison
+sub main'rcmp { #(rat_num, rat_num) return cond_code
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($yn,$yd) = split('/',&'rnorm($_[1]));
+    &bigint'cmp(&'bmul($xn,$yd),&'bmul($yn,$xd));
+}
+
+# int and frac parts
+sub main'rmod { #(rat_num) return (rat_num,rat_num)
+    local($xn,$xd) = split('/',&'rnorm($_[0]));
+    local($i,$f) = &'bdiv($xn,$xd);
+    if (wantarray) {
+	("$i/1", "$f/$xd");
+    } else {
+	"$i/1";
+    }   
+}
+
+# square root by Newtons method.
+#   cycles specifies the number of iterations default: 5
+sub main'rsqrt { #(fnum_str[, cycles]) return fnum_str
+    local($x, $scale) = (&'rnorm($_[0]), $_[1]);
+    if ($x eq 'NaN') {
+	'NaN';
+    } elsif ($x =~ /^-/) {
+	'NaN';
+    } else {
+	local($gscale, $guess) = (0, '+1/1');
+	$scale = 5 if (!$scale);
+	while ($gscale++ < $scale) {
+	    $guess = &'rmul(&'radd($guess,&'rdiv($x,$guess)),"+1/2");
+	}
+	"$guess";          # quotes necessary due to perl bug
+    }
+}
+
+1;
-- 
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