--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/decimal/decint.d	Thu Mar 25 21:43:40 2010 -0700
@@ -0,0 +1,1763 @@
+/** 
+ * A D programming language implementation of the 
+ * General Decimal Arithmetic Specification, 
+ * Version 1.70, (25 March 2009).
+ *
+ * by Paul D. Anderson
+ *
+ * Boost Software License - Version 1.0 - August 17th, 2003
+ *
+ * Permission is hereby granted, free of charge, to any person or organization
+ * obtaining a copy of the software and accompanying documentation covered by
+ * this license (the "Software") to use, reproduce, display, distribute,
+ * execute, and transmit the Software, and to prepare derivative works of the
+ * Software, and to permit third-parties to whom the Software is furnished to
+ * do so, all subject to the following:
+ *
+ * The copyright notices in the Software and this entire statement, including
+ * the above license grant, this restriction and the following disclaimer,
+ * must be included in all copies of the Software, in whole or in part, and
+ * all derivative works of the Software, unless such copies or derivative
+ * works are solely in the form of machine-executable object code generated by
+ * a source language processor.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+ * SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+ * FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
+ * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+**/
+
+module decimal.decint;
+
+import std.algorithm: max;
+import std.conv: ConvError;
+import std.math;
+import std.stdio: write, writeln;
+import std.string: strip;
+
+alias ubyte Digit;
+alias DecInt decint;
+
+public immutable DecInt ZERO = { digits:[0] };
+public immutable DecInt ONE  = { digits:[1] };
+public immutable DecInt NEG_ONE = { sign:true, digits:[1] };
+
+/+static this() {
+	immutable(DecInt) MAX_LONG = cast(immutable) DecInt(long.max);
+//	MAX_LONG = cast(immutable) DecInt(long.max);
+	}+/
+
+/**
+ * Enumeration of available rounding modes.
+ */
+public enum Rounding {
+	HALF_EVEN,
+	HALF_DOWN,
+	HALF_UP,
+	DOWN,
+	UP,
+	FLOOR,
+	CEILING,
+}
+
+/**
+ * Provides BCD-encoded integral values of arbitrary length.
+ *
+ * Advantages of BCD:
+ * To/from string is easy.
+ * Easy to pull values of individual digits.
+ * Easy to multiply and divide by powers of 10.
+ * 
+ * Disadvantages of BCD:
+ * Significantly less compact representation.
+ * Operations are carried out bytewise, requiring more iterations.
+ * Extra steps required for addition.
+ *
+ */
+public struct DecInt {
+
+//--------------------------------
+// members
+//-------------------------------- 
+
+	/**
+	 * The sign of the BCD integer. Sign is kept explicitly
+	 * and not encoded in the number.
+	 **/
+	private bool sign = false;
+	
+	/**
+	 * An array of decimal digits in reverse (right-to-left) order
+	 * representing an integral value. 
+	 * Trailing zeros have no effect on the value of the number;
+	 * they correspond to leading zeros in a left-to-right representation.
+	**/
+	private Digit[] digits = [ 0 ];
+	
+//--------------------------------
+// construction
+//-------------------------------- 
+
+	//--------------------------------
+	// copy construction
+	//-------------------------------- 
+
+
+	/**
+	 * Copy constructor. Returns a (non-const) copy of the argument.
+	 */
+	public this(const DecInt bcd) {
+		sign = bcd.sign;
+		digits = bcd.digits.dup;
+	}
+	
+	/**
+	 * Copies a BCD integer and adjusts the number of digits,
+	 * padding or turncating, if necessary.
+	 */
+	public this(const DecInt bcd, uint numDigits) {
+		this(bcd);
+		setNumDigits(numDigits);
+	}
+	
+	//--------------------------------
+	// construction from integer types.
+	//-------------------------------- 
+
+	/**
+	 * Constructs a BCD integer from a (signed) byte, short, int or long value.
+	 */
+	public this(const long n) {
+		ulong m;	
+		if (n < 0) {
+			sign = true;
+			m = std.math.abs(n);
+		}
+		else {
+			sign = false;
+			m = n;
+		}
+		Digit[20] dig;
+		int i = 0;
+		do {
+			ulong q = m/10;
+			ulong r = m%10;
+			dig[i] = cast(Digit) r;
+			m = q;
+			i++;
+		} while (m > 0);
+		digits = dig[0..i].dup;
+	}
+		
+	/**
+	 * Constructs a BCD integer from a (signed) byte, short,
+	 * int or long value, and then adjusts the number of digits,
+	 * padding or truncating as needed.
+	 */
+	public this(const long n, uint numDigits) {
+		this = n;
+		setNumDigits(numDigits);
+	}
+		
+	unittest {
+		write("this(long)..");
+		DecInt p;
+		p = -1234;
+		assert(p == DecInt("-1234"));
+		p = 12345678L;
+		assert(p == DecInt("12345678"));
+		p = DecInt(-19166586400L);
+		assert(p == DecInt("-19166586400"));
+		p = DecInt(139676498390L);
+		assert(p == DecInt("139676498390"));
+		writeln("passed");
+	}
+
+	//--------------------------------
+	// construction from a string.
+	//-------------------------------- 
+
+	/**
+	 * Constructs a BCD integer from a string representation.
+	 * If the string has leading zeros they are retained internally.
+	 */
+	public this(const string str) {
+		this = parse(str);
+	}
+	
+//--------------------------------
+// member access functions
+//-------------------------------- 
+
+	//--------------------------------
+	// access to the sign of the number
+	//-------------------------------- 
+
+	const bool isSigned() {
+		return sign;
+	}
+	
+	void setSign(bool sign) {
+		this.sign = sign;
+	}
+	
+	//--------------------------------
+	// access to the digits
+	//-------------------------------- 
+
+	/**
+	 * Returns the number of digits in this BCD integer.
+	 * Includes leading zero digits.
+	 */
+	const uint numDigits() {
+		return digits.length;
+	}
+	
+	/**
+	 * Adjusts the number of digits in this BCD integer,
+	 * padding or truncating if necessary. 
+	 * If truncating, first leading zeros are stripped away, then
+	 * the remainder is clipped.
+	 */
+	void setNumDigits(uint n) {
+		if (n == 0) n++;
+		digits.length = n;
+	}
+
+/+	/**
+	 * Adjusts the number of digits in this BCD integer,
+	 * padding or truncating if necessary. 
+	 * If truncating, first leading zeros are stripped away, then
+	 * the remainder is clipped.
+	 */
+	void setNumDigits(uint n) {
+		stripl(this);
+		if (n > digits.length) {
+			digits.length = n;
+		}
+		else {
+			this = truncate(this, n);
+		}
+	}+/
+	
+/+unittest {
+	write("setWidth...");
+	DecInt a;
+	a = 1234567;
+	a.setNumDigits(5);
+	assert(a == DecInt(12345));
+	a.setNumDigits(9);
+	assert(a.toString == "000012345");
+	writeln("passed");
+}+/
+
+	/**
+	 * Returns the first digit of this BCD integer. If the
+	 * integer has leading zeros this function will return 
+	 * zero, but the value of the number is not necessarily zero.
+	 */
+	const uint firstDigit() {
+		return digits[$-1];
+	}
+	
+	/**
+	 * Returns the last digit of this BCD integer.
+	 */
+	const uint lastDigit() {
+		return digits[0];
+	}
+	
+	/**
+	 * Returns the specified digit of this BCD integer. The index is 
+	 * zero based, i.e., getDigit(0) returns the first digit.
+	 */
+	const int getDigit(int n) {
+		return digits[$-n-1];
+	}
+	
+	/**
+	 * Sets the specified digit of this BCD integer to the specified value.
+	 * The index is zero based, i.e., getDigit(0) returns the first digit.
+	 */
+	void setDigit(uint n, Digit value) {
+		assert(value < 10);
+		digits[$-n-1] = value;
+	}
+	
+/+	unittest {
+		write("digits...");
+		DecInt bcd;
+		bcd = 12345678;
+		assert(bcd.numDigits() == 8);
+		assert(bcd.firstDigit() == 1);
+		assert(bcd.lastDigit() == 8);
+		assert(bcd.getDigit(3) == 4);
+		bcd.setDigit(3, 7);
+		assert(bcd.getDigit(3) == 7);
+		bcd.setNumDigits(10);
+		assert(bcd.numDigits == 10);
+		assert(bcd.firstDigit() == 0);
+		assert(bcd.getDigit(5) == 7);
+		bcd.setNumDigits(5);
+		assert(bcd.getDigit(2) == 3);
+		writeln("passed");
+	}+/
+	
+//--------------------------------
+// Common object functions.
+//-------------------------------- 
+
+	/**
+	 * Returns a string representation of this BCD integer.
+	 * Leading zeros are displayed. The sign is displayed if
+	 * the number is negative.
+	 */
+	const string toString() {
+		return format(this);
+	}
+	
+	unittest {
+		write("toString...");
+		writeln("passed");
+	}
+	
+	/**
+	 * Returns a hash code for this BCD integer.
+	 */
+	const hash_t toHash() {
+		hash_t hash = 0;
+		foreach(Digit digit; digits) {
+			hash += digit;
+		}
+		return hash;
+	}
+	
+	unittest {
+		write("toHash...");
+		writeln("passed");
+	}
+	
+	/**
+	 * Returns a mutable copy of this BCD integer.
+	 */
+	const DecInt dup() {
+		DecInt bcd;
+		bcd.sign = this.sign;
+		bcd.digits = digits.dup;
+		return bcd;
+	}
+	
+//--------------------------------
+// Utility functions.
+//-------------------------------- 
+
+	/**
+	 * Returns true if the internal representation of
+	 * this BCD integer has leading zeros.
+	 */
+	const bool hasLeadingZeros() {
+		return numDigits > 1 && firstDigit == 0;
+	}
+	
+	unittest {
+	write("hasLeadingZeros...");
+	assert(!ZERO.hasLeadingZeros);
+	DecInt b = DecInt(0);
+	assert(!b.hasLeadingZeros);
+	b = "-00000001";
+	assert(b.hasLeadingZeros);
+	b = "-00000000";
+	assert(b.hasLeadingZeros);
+	writeln("passed");
+	}
+	
+	/**
+	 * Returns true if the value of this BCD integer is zero.
+	 * Ignores leading zeros and sign.
+	 */
+	const bool isZero() {
+		DecInt b = canonical(this);
+		if (b.numDigits > 1) return false;
+		return b.lastDigit == 0;
+	}
+	
+	unittest {
+	write("isZero.........");
+	assert(ZERO.isZero);
+	DecInt b = DecInt(0);
+	assert(b.isZero);
+	b = "-00000001";
+	assert(!b.isZero);
+	b = "-00000000";
+	assert(b.isZero);
+	writeln("passed");
+	}
+	
+//--------------------------------
+// casting operators.
+//-------------------------------- 
+
+	const long opCast() {
+		DecInt MAX_LONG = DecInt(long.max);
+		DecInt MIN_LONG = DecInt(long.min);
+
+		if (this > MAX_LONG || this < MIN_LONG)
+			throw new Exception("Can't cast -- out of range");
+		
+		long n = 0;
+		foreach_reverse(Digit digit; digits) {
+			n = 10*n + digit;
+		}
+		return this.sign ? -n : n;
+	}
+	
+	unittest {
+	write("cast(long)...");
+	DecInt a;
+	a = "12345678901234567890123456";
+//	long n = cast(long) a;
+	a = 12345678L;
+	long n = cast(long) a;
+	assert(n == 12345678L);
+	int m = cast(int) a;
+	assert(m == 12345678L);
+	a = -a;
+	m = cast(int) a;
+	assert(m == -12345678L);
+	
+	writeln("passed");
+}
+
+
+//--------------------------------
+// Assignment operators.
+//-------------------------------- 
+
+	/**
+	 * Assignment operator for BCD integer to BCD integer operations.
+	 */
+	DecInt opAssign(const DecInt that) {
+		this.sign = that.sign;
+		this.digits = that.digits.dup;
+		return this;
+	}
+	
+	/**
+	 * Converts the string argument into a BCD integer and assigns it 
+	 * to this BCD integer.
+	 */
+	void opAssign(const string str) {
+		this = DecInt(str);
+	}
+	
+	/**
+	 * Converts the integer argument into a BCD integer and assigns it 
+	 * to this BCD integer.
+	 */
+	void opAssign(const long n) {
+		this = DecInt(n);
+	}
+	
+	
+	// index operator
+	Digit opIndex(uint index) {
+		return this.digits[index];
+	}
+	
+	// index assign operator
+	void opIndexAssign(Digit value, uint index) {
+		this.digits[index] = value;
+	}
+	
+//--------------------------------
+// unary operators
+//-------------------------------- 
+	
+	const DecInt opPos() {
+		return this.dup;
+	}
+	
+	const DecInt opNeg() {
+		return negate(this);
+	}
+	
+	const DecInt opCom() {
+		return twosComp(this);
+	}
+	
+	const DecInt opNot() {
+		return not(this);
+	}
+	
+	DecInt opPostInc() {
+		this = this + ONE;
+		return this;
+	}
+	
+	DecInt opPostDec() {
+		this = this - ONE;
+		return this;
+	}
+	
+	const DecInt opShl(int n) {
+		return shift(this, n);
+	}
+	
+	DecInt opShlAssign(int n) {
+		this = this << n;
+		return this;
+	}
+	
+	const DecInt opShr(int n) {
+		return shift(this, -n);
+	}
+	
+	DecInt opShrAssign(int n) {
+		this = this >> n;
+		return this;
+	}
+	
+//--------------------------------
+// binary operators
+//-------------------------------- 
+	
+	const DecInt opAdd(T:DecInt)(const T addend) {
+		return add(this, addend);
+	}
+	
+	const DecInt opAdd(T)(const T addend) {
+		return add(this, DecInt(addend));
+	}
+	
+	DecInt opAddAssign(T)(const T addend) {
+		this = this + addend;
+		return this;
+	}
+
+	const DecInt opSub(T:DecInt)(const T addend) {
+		return subtract(this, addend);
+	}
+	
+	const DecInt opSub(T)(const T addend) {
+		return subtract(this, DecInt(addend));
+	}
+	
+	DecInt opSubAssign(T)(const T addend) {
+		this = this - addend;
+		return this;
+	}
+
+	const DecInt opMul(T:DecInt)(const T b) {
+		return multiply(this, b);
+	}
+	
+	const DecInt opMul(T)(const T b) {
+		return multiply(this, DecInt(b));
+	}
+	
+	DecInt opMulAssign(T)(const T b) {
+		this = this * b;
+		return this;
+	}
+
+	unittest {
+		write("multiply...");
+		DecInt a, b, c;
+		a = 105, b = -22;
+		c = a * b;
+		assert(c == -2310);
+		c = 45;
+		c *= 1205;
+	//	writeln("c = ", c);
+		assert(c == 54225);
+		writeln("passed");
+	}
+
+	const DecInt opDiv(T:DecInt)(const T b) {
+		DecInt rem;
+		return divide(this, b, rem);
+	}
+	
+	unittest {
+		write("opDiv...");
+		DecInt a, b;
+		a = 7;
+		b = 3;
+		assert(a/b == 2);
+		writeln("passed");
+	}
+	
+	const DecInt opDiv(T)(const T b) {
+		DecInt rem;
+		return divide(this, DecInt(b), rem);
+	}
+	
+	DecInt opDivAssign(T)(const T b) {
+		this = this / b;
+		return this;
+	}
+
+	const DecInt opMod(T:DecInt)(const T b) {
+		DecInt rem;
+		divide(this, b, rem);
+		return rem;
+	}
+	
+	unittest {
+		write("opMod...");
+		DecInt a, b;
+		a = 7;
+		b = 3;
+		assert(a % b == 1);
+		writeln("passed");
+	}
+	
+	const DecInt opMod(T)(const T b) {
+		DecInt rem;
+		divide(this, DecInt(b), rem);
+		return rem;
+	}
+	
+	DecInt opModAssign(T)(const T b) {
+		this = this % b;
+		return this;
+	}
+
+	const DecInt opAnd(const DecInt a) {
+		return and(this, a);
+	}
+	
+	DecInt opAndAssign(const DecInt a) {
+		this = this & a;
+		return this;
+	}
+
+	const DecInt opOr(const DecInt a) {
+		return or(this, a);
+	}
+	
+	DecInt opOrAssign(const DecInt a) {
+		this = this | a;
+		return this;
+	}
+
+	const DecInt opXor(const DecInt a) {
+		return xor(this, a);
+	}
+	
+	DecInt opXorAssign(const DecInt a) {
+		this = this ^ a;
+		return this;
+	}
+
+//--------------------------------
+// comparison, equality operators
+//-------------------------------- 
+	
+	const int opCmp(T:DecInt)(const T that) {
+		return compare(this, that);
+	}
+	
+	unittest {
+		write("compare...");
+		DecInt a,b;
+		a = 100;
+		b = 5;
+		assert(a > b);
+		a = -100;
+		b = 5;
+		assert(a < b);
+		a = -100;
+		b = -5;
+		assert(a < b);
+		a = 100;
+		b = -5;
+		assert(a > b);
+		a = 5;
+		b = 100;
+		assert(a < b);
+		assert(b > a);
+		writeln("passed");
+	}
+	
+	const int opCmp(T)(const T that) {
+		return opCmp(DecInt(that));
+	}
+	
+	const bool opEquals(T:DecInt)(const T that) {
+		DecInt a = comparable(this);
+		DecInt b = comparable(that);
+		if (this.sign != that.sign) return false;
+		if (a.digits.length != b.digits.length) return false;
+		foreach_reverse(int i, Digit digit; a.digits) {
+			if (digit != b.digits[i]) return false;
+		}
+		return true;
+	}
+	
+	const bool opEquals(T)(const T that) {
+		return opEquals(DecInt(that));
+	}
+
+	unittest {
+	write("equals...");	
+	assert(DecInt(0) == DecInt(0));
+	assert(DecInt(4) == DecInt(4));
+	assert(DecInt(40) == DecInt(40));
+	assert(DecInt(-400) == DecInt(-400));
+	assert(DecInt(12345678) == DecInt(+12345678));
+	assert(DecInt(40) != DecInt(53));
+	assert(DecInt(402) != DecInt(531));
+	assert(DecInt(402) != DecInt(-402));
+    assert(DecInt(65432) != DecInt(65431));
+	assert(DecInt(2) != DecInt(1));
+	assert(DecInt(1) != DecInt(2));
+	writeln("passed");
+	}
+	
+} // end struct DecInt
+
+
+public bool isCanonical(const DecInt a) {
+	// no leading zeros
+	return !a.hasLeadingZeros;
+}
+
+// Strips leading zeros
+public DecInt canonical(const DecInt a) {
+	DecInt d = a.dup;
+	if (isCanonical(a)) return d;
+	stripl(d);
+	return d;
+}
+
+// Strips leading zeros and changes sign if == -0
+private DecInt comparable(const DecInt a) {
+	DecInt d = canonical(a);
+	if (d.numDigits == 1 && d.firstDigit == 0) {
+		d.sign = false;
+	}
+	return d;
+}
+
+
+private void clipFirst(ref DecInt a, uint n = 1) {
+	if (n == 0) return;
+	if (n >= a.digits.length) a = ZERO;
+	else a.digits = a.digits[0..$-n];
+}
+
+private void clipLast(ref DecInt a, uint n = 1) {
+	if (n == 0) return;
+	if (n >= a.digits.length) a = ZERO;
+	else a.digits = a.digits[n..$];
+}
+
+unittest {
+	write("clipping....");
+	DecInt a;
+	a = 12345;
+	clipFirst(a);
+	assert(a == 2345);
+	clipLast(a);
+	assert(a == 234);
+	a = 1234567890;
+	clipFirst(a, 3);
+	assert(a == 4567890);
+	clipLast(a, 5);
+	assert(a == 45);
+	clipLast(a, 5);
+	assert(a == 0);
+	writeln("passed");
+}
+
+
+/**
+ * Strips leading zeros from the specified decint.
+ */
+private void stripl(ref DecInt a) {
+	if (a.hasLeadingZeros) {
+		foreach_reverse(int i, Digit digit; a.digits) {
+			if (i == 0 || digit != 0) {
+				a.digits.length = i+1;
+				break;
+			}
+		}
+	} 
+}
+
+unittest {
+	write("stripl......");
+	DecInt b = DecInt("+00023");
+	assert(b.toString == "00023");
+	stripl(b);
+	assert(b.toString == "23");
+	b = "-00050432";
+	stripl(b);
+	assert(b.toString == "-50432");
+	b = "-000";
+	stripl(b);
+	assert(b.toString == "-0");
+	writeln("passed");
+}
+
+/**
+ * Strips trailing zeros from the specified decint.
+ */
+private void stripr(ref DecInt a) {
+	int len = a.digits.length;
+	foreach(int i, Digit digit; a.digits) {
+		if (i == len-1 || digit != 0) {
+			a.digits = a.digits[i..$];
+			break;
+		}
+	}
+}
+
+unittest {
+	write("stripl......");
+	DecInt b;
+	b = 23;
+	stripr(b);
+	assert(b == 23);
+	b = "-5000";
+	stripr(b);
+	assert(b.toString == "-5");
+	b = "-000";
+	stripr(b);
+	assert(b.toString == "-0");
+	writeln("passed");
+}
+
+//public string format(const DecInt bcd, bool showPlus = false, bool showLeadingZeros = false) {
+public string format(const DecInt bcd) {
+	int len = bcd.digits.length;
+	if (bcd.isSigned) len++;
+//	if (bcd.isSigned || bcd.hasLeadingZeros) len++;
+	char[] str = new char[len];
+	
+	int index = 0;
+	if (bcd.sign) {
+		str[index] = '-';
+		index++;
+	}
+/+	if (bcd.hasLeadingZeros) {
+		str[index] = '+';
+		index++;
+	}+/
+	foreach_reverse(Digit digit; bcd.digits) {
+		str[index] = cast(char) digit + '0';
+		index++;
+	}
+	return str.idup;
+}
+
+public DecInt parse(string str) {
+	DecInt bcd;
+	// are leading zeros retained?
+	bool lz = false;
+
+	// strip whitespace, convert to char array
+	char[] str1 = str.strip.dup;
+	
+	// check for leading '-'
+	if (str1[0] == '-') {
+		bcd.sign = true;
+		str1 = str1[1..$];
+		lz = true;
+	}
+	
+	// check for leading '+'
+	if (str1[0] == '+') {
+		bcd.sign = false;
+		str1 = str1[1..$];
+		lz = true;
+	}
+	
+	// verify chars are digits, strip out underscores
+	int index = 0;
+	char[] str2 = new char[str1.length];
+	foreach_reverse(char ch; str1) {
+		if (isDigit(ch)) {
+			str2[index] = ch;
+			index++;
+			continue;
+	    }
+		if (ch == '_') {
+			continue;
+		}
+		throw (new ConvError("Invalid character: " ~ ch));
+	}
+	str2.length = index;
+	
+	bcd.digits.length = index;
+	foreach(int i, char ch; str2) {
+		bcd.digits[i] = cast(Digit)(ch - '0');
+	}
+
+	if (!lz) return canonical(bcd);	
+	return bcd;
+}
+
+private bool isDigit(const char ch) {
+	return (ch >= '0' && ch <= '9');
+}
+
+public DecInt negate(const DecInt a) {
+	DecInt b = a.dup;
+	b.sign = !a.sign;
+	return b;
+}
+
+public DecInt abs(const DecInt a) {
+	return a.isSigned ? -a: +a;
+}
+
+public int compare(const DecInt m, const DecInt n) {
+	DecInt a = comparable(m);
+	DecInt b = comparable(n);
+	if (!a.isSigned && b.isSigned) return 1;
+	if (a.isSigned && !b.isSigned) return -1;
+	if (!a.isSigned) {
+		if (a.digits.length > b.digits.length) return 1;
+		if (a.digits.length < b.digits.length) return -1;
+		foreach_reverse(int i, Digit digit; a.digits) {
+			if (digit > b.digits[i]) return 1;
+			if (digit < b.digits[i]) return -1;
+		}
+	}
+	else {
+		if (a.digits.length > b.digits.length) return -1;
+		if (a.digits.length < b.digits.length) return 11;
+		foreach_reverse(int i, Digit digit; a.digits) {
+			if (digit > b.digits[i]) return -1;
+			if (digit < b.digits[i]) return 1;
+		}
+	}
+	return 0;
+}
+	
+unittest {
+	write("strip...");
+	DecInt bcd;
+	bcd = "+00123";
+	assert(bcd.toString == "00123");
+	bcd = canonical(bcd);
+//	writeln("bcd = ", bcd);
+	assert(bcd.toString == "123");
+	bcd = "+000";
+//	writeln("bcd = ", bcd);
+	assert(bcd.toString == "000");
+	bcd = canonical(bcd);
+//	writeln("bcd = ", bcd);
+	writeln("passed");
+}
+	
+private bool sameLength(const DecInt a, const DecInt b) {
+	return a.numDigits == b.numDigits;
+}
+
+private int setSameLength(ref DecInt a, ref DecInt b) {
+	if (sameLength(a, b)) return a.numDigits;
+	uint alen = a.numDigits;
+	uint blen = b.numDigits;
+	if (alen > blen) {
+		b.setNumDigits(alen);
+	}
+	else {
+		a.setNumDigits(blen);
+	}
+	return a.numDigits();
+}
+
+// TODO: really? private?
+private DecInt twosComp(const DecInt a) {
+	DecInt b = DecInt(0, a.numDigits);
+	foreach(int i, Digit digit; a.digits) {
+		b.digits[i] = digit == 0 ? 1 : 0 ;
+	}
+	return b;
+}
+
+unittest {
+	write("com...");
+	DecInt bcd;
+	bcd = 123;
+	assert(twosComp(bcd).toString == "000");
+	bcd = 40509;
+	assert(twosComp(bcd).toString == "01010");
+//	writeln("bcd = ", bcd);
+//	writeln("~bcd = ", twosComp(bcd));
+	writeln("passed");
+}
+	
+public int sgn(const DecInt bcd) {
+	if (bcd.isZero) return 0;
+	return bcd.isSigned ? -1 : 1;
+}
+
+public DecInt not(const DecInt a) {
+	DecInt b = a.dup;
+	foreach(Digit digit; b.digits) {
+		digit = not(digit);
+	}
+	return b;
+}
+
+private Digit not(const Digit a) {
+	return a != 0;
+}
+
+public DecInt and(const DecInt x, const DecInt y) {
+	DecInt a = x.dup;
+	DecInt b = y.dup;
+	int len = setSameLength(a,b);
+	DecInt result = DecInt(0, len);
+	for (int i = 0; i < len; i++) {
+		result[i] = and(a[i], b[i]);
+	}
+	return result;
+}
+
+private Digit and(const Digit a, const Digit b) {
+	return a != 0 && b != 0;
+}
+
+unittest {
+	write("and...");
+	DecInt a;
+	DecInt b;
+	a = 123000;
+	b = 123000;
+	assert(and(a,b).toString == "111000");
+	b = 12300;
+	assert(and(a,b).toString == "011000");
+	a = 1234567;
+	b = 7654321;
+	assert(and(a,b).toString == "1111111");
+	a = 1010;
+	b = 101;
+//	writeln("a = ", a);
+//	writeln("b = ", b);
+//	writeln("and = ", and(a,b));
+	assert(and(a,b).isZero);
+	writeln("passed");
+}
+
+// TODO: looks like there's some room for templates or mixins here.
+public DecInt or(const DecInt x, const DecInt y) {
+	DecInt a = x.dup;
+	DecInt b = y.dup;
+	int len = setSameLength(a,b);
+	DecInt result = DecInt(0, len);
+	for (int i = 0; i < len; i++) {
+		result[i] = or(a[i], b[i]);
+	}
+	return result;
+}
+
+private Digit or(const Digit a, const Digit b) {
+	return a != 0 || b != 0;
+}
+
+public DecInt xor(const DecInt x, const DecInt y) {
+	DecInt a = x.dup;
+	DecInt b = y.dup;
+	int len = setSameLength(a,b);
+	DecInt result = DecInt(0, len);
+	for (int i = 0; i < len; i++) {
+		result[i] = xor(a[i], b[i]);
+	}
+	return result;
+}
+
+private Digit xor(const Digit a, const Digit b) {
+	return (a == 0 && b != 0) || (a != 0 && b == 0);
+}
+
+// TODO: watch the leading zeros
+public DecInt add(const DecInt x, const DecInt y) {
+	DecInt a = x.dup;
+	DecInt b = y.dup;
+	DecInt sum;
+	if (a.sign == b.sign) {
+		sum = simpleAdd(a, b);
+		stripl(sum);
+		sum.sign = a.sign;
+		return sum;
+	}
+	else { // signs differ
+		bool sign;
+		switch (compare(abs(a), abs(b))) {
+			case 0:
+				return ZERO.dup;
+			case 1:
+				sign = a.isSigned;
+				break;
+			case -1:
+				sign = b.isSigned;
+				break;
+		}
+		setSameLength(a, b);
+		sum = simpleAdd(a, tensComp(b));
+		if (sum.firstDigit == 1) {
+			sum.digits = sum.digits[0..$-1];
+		}
+		else {
+			sum = tensComp(sum);
+		}
+		stripl(sum);
+		sum.sign = sign;
+	}
+	return sum;
+}
+
+unittest {
+	write("add....");
+	DecInt a, b;
+	a = 1234;
+	b = 4321;
+	assert(a + b == 5555);
+	a = 2000;
+	b = 1;
+	assert(a + b == 2001);
+	a = -2000;
+	b = -1;
+	assert(a + b == -2001);
+	a = 2000;
+	b = -1;
+	assert(a + b == 1999);
+	a = -123;
+	b = 1;
+	assert(a + b == -122);
+	a = 123;
+	b = -1;
+	assert(a + b == 122);
+	a = -1;
+	b = 123;
+//	writeln();
+//	writeln("a + b = ", a + b);
+	assert(a + b == 122);
+	a = -123;
+	b = 1;
+	assert(a + b == -122);
+	a = 1;
+	b = -123;
+	assert(a + b == -122);
+	writeln("passed");
+}
+
+DecInt subtract(const DecInt a, const DecInt b) {
+	return add(a, negate(b));
+}
+
+/**
+ * Adds two BCD integers without regard to sign
+**/
+private DecInt simpleAdd(const DecInt a, const DecInt b) {
+	DecInt x = a.dup;
+	DecInt y = b.dup;
+	int len = setSameLength(x, y);
+	DecInt sum = DecInt(0, len+1);
+	Digit carry = 0;
+	uint i;
+	// TODO: this is the place to stop adding zeros and
+	// just copy the rest of the digits.
+	for (i = 0; i < len; i++) {
+		sum[i] = add(x[i], y[i], carry);
+	}
+	if (carry) {
+		sum[i] = 1;
+	}
+	else {
+		stripl(sum);
+	}
+	return sum;
+}
+
+// TODO: need a clipFirst, clipLast method
+
+/**
+ * Adds two digits and a carry digit.
+ * Returns the (single-digit) sum and sets or resets the carry digit.
+**/
+private Digit add(const Digit a, const Digit b, ref Digit carry) {
+	Digit sum = a + b + carry;
+	carry = sum > 9;
+	if (carry) sum -= 10;
+	return sum;
+}
+
+unittest {
+	write("simpleAdd...");
+	DecInt a, b;
+	a = 123;
+	b = 222;
+	DecInt sum = simpleAdd(a,b);
+	assert(sum == 345);
+	a = 2;
+	b = 102000;
+	sum = simpleAdd(a,b);
+	assert(sum == 102002);
+	writeln("passed");
+}
+
+private DecInt tensComp(const DecInt a) {
+/+	foreach(Digit digit; a.digits) {
+		digit = 9 - digit;
+	}
+	a = simpleAdd(a, ONE);
+	return a;+/
+
+	DecInt x = DecInt(0, a.numDigits);
+	foreach (int i, digit; a.digits) {
+		x[i] = 9 - digit;
+	}
+	return simpleAdd(x, ONE);
+}
+
+unittest {
+	write("tensComp...");
+	DecInt a, b, c;
+	a = 123456;
+	b = tensComp(a);
+//	writeln("a = ", a);
+//	writeln("b = ", b);
+	c = 876544;
+	assert(b == c);
+	a = DecInt(0, 4);
+	b = tensComp(a);
+	c = 10000;
+	assert(b == c);
+	a = DecInt(1, 4);
+	b = tensComp(a);
+	c = 9999;
+	assert(b == c);
+	a = 9999;
+	b = tensComp(a);
+	c = 1;
+	assert(b == c);
+	a = 10000;
+	b = tensComp(a);
+	c = 90000;
+	assert(b == c);
+	a = 1;
+	b = tensComp(a);
+	c = 9;
+//	writeln("a = ", a);
+//	writeln("b = ", b);
+	assert(b == c);
+	writeln("passed");
+}
+
+// TODO: there are lots of ways to speed this up.
+public DecInt multiply(const DecInt a, const DecInt b) {
+	DecInt n, m;
+	DecInt p = DecInt(0, a.numDigits + b.numDigits);
+	if (a.numDigits > b.numDigits) {
+		n = canonical(a);
+		m = canonical(b);	
+	}
+	else {
+		n = canonical(b);
+		m = canonical(a);
+	}
+	foreach(uint i, Digit d; m.digits) {
+		if (d == 0) continue;
+//        writeln("mul(n, m[i]) = ", mul(n, m[i]));
+//		writeln("pow10(mul(n, m[i]), i) = ", pow10(mul(n, m[i]), i));
+		p = simpleAdd(p, pow10(mul(n, m[i]), i)); 
+	}
+	p.sign = a.sign ^ b.sign;
+	return p;	
+}
+
+unittest {
+	write("mul...");
+	DecInt a, b, p;
+	a = 2105, b = 301;
+	p = multiply(a, b);
+	assert(p == DecInt(633605));
+	b = 800, a = 23958233;
+	p = multiply(a, b);
+	assert(p == DecInt("19166586400"));
+	b = 5830, a = 23958233;
+	p = multiply(a, b);
+	assert(p == DecInt("139676498390"));
+	writeln("passed");
+}
+
+private DecInt mul(const DecInt a, Digit m) {
+	DecInt p = DecInt(0, a.numDigits+1);
+	Digit c = 0;
+	int i = 0;
+	foreach (Digit d; a.digits) {
+		p[i] = mul(m, d, c);
+		i++;
+	}
+	if (c) p[i] = c;
+	return p;
+}
+
+unittest {
+	write("mul...");
+	DecInt a, p;
+	Digit m;
+	a = 2105, m = 3;
+	p = mul(a, m);
+	assert(p == DecInt(6315));
+	writeln("passed");
+}
+
+private Digit mul(Digit a, Digit b, ref Digit c) {
+	Digit p = a * b + c;
+	c = p / 10;
+	return p % 10;
+}
+
+unittest {
+	write("mul...");
+	Digit a, b, c, d;
+	a = 2, b = 3, c = 0;
+	d = mul(a,b,c);
+	assert(d == 6);
+	assert(c == 0);
+	a = 9, b = 8, c = 0;
+	d = mul(a,b,c);
+	assert(d == 2);
+	assert(c == 7);
+	writeln("passed");
+}
+
+public DecInt divide(const DecInt a, const DecInt b, out DecInt r) {
+
+	if (b == ZERO) throw new Exception("Divide by zero");
+	if (a == ZERO) return ZERO.dup;
+	
+	DecInt d = canonical(abs(b));
+	r = canonical(abs(a));
+	DecInt q;
+	DecInt p = d;
+	DecInt m;
+	
+	// shift the divisor
+	do {
+		m = p;
+		p <<= 1;
+	} while (p <= r && p > m);
+	
+	while (m >= d) {
+		q <<= 1;
+		// subtract repeatedly
+		while (m <= r) {
+			r -= m;
+			q++;
+		}
+		m >>= 1;
+	}
+	
+	// adjust the sign
+	r.sign = a.sign;
+	q.sign = a.sign != b.sign;
+	return q;
+}
+
+unittest {
+	write("divide...");
+	DecInt a, b, q, r;
+	a = 144;
+	b = 12;
+	q = divide(a, b, r);
+	assert(q == 12);
+	assert(r == 0);
+	a = 144;
+	b = 14;
+	q = divide(a, b, r);
+	assert(q == 10);
+	assert(r == 4);
+	a = 142351;
+	b = 12;
+	q = divide(a, b, r);
+//	writeln("q = ", q);
+//	writeln("r = ", r);
+	assert(q == 11862);
+	assert(r == 7);
+	a = 2;
+	b = 12;
+	q = divide(a, b, r);
+	assert(q == 0);
+	assert(r == 2);
+	a = 7;
+	b = 3;
+	q = divide(a, b, r);
+	assert(q == 2);
+	assert(r == 1);
+	a = 7;
+	b = -3;
+	q = divide(a, b, r);
+	assert(q == -2);
+	assert(r == 1);
+	a = -7;
+	b = 3;
+	q = divide(a, b, r);
+	assert(q == -2);
+	assert(r == -1);
+	a = -7;
+	b = -3;
+	q = divide(a, b, r);
+	assert(q == 2);
+	assert(r == -1);
+	writeln("passed");
+}
+
+
+public DecInt truncate(const DecInt a, int n) {
+	return truncate(a, n, DecInt());
+}
+
+unittest {
+	write("truncate....");
+	DecInt a;
+	a = 1234567;
+	assert(truncate(a,3) == 123);
+	a = 10256;
+	assert(truncate(a,5) == 10256);
+	a = 8500;
+	assert(truncate(a,1) == 8);
+	a = -8500;
+	assert(truncate(a,1) == -8);
+	a = -8500;
+	assert(truncate(a,-1) == 0);
+	writeln("passed");
+}
+
+/** 
+ * Truncate to the specified number of digits
+ */
+public DecInt truncate(const DecInt a, int n, out DecInt r) {
+	if (n <= 0) {
+		r = canonical(a);
+		return ZERO.dup;
+	}
+	if (n >= a.numDigits) {
+		r = ZERO.dup;
+		return canonical(a);
+	}
+	DecInt b;
+	b.digits = a.digits[$-n..$].dup;
+	b.sign = a.sign;
+	r.digits = a.digits[0..$-n].dup;
+	return b;
+}
+
+unittest {
+	write("truncRem...");
+	DecInt a;
+	DecInt r;
+	a = 1234567;
+	assert(truncate(a, 3, r) == 123);
+	assert(r == 4567);
+	a = 10256;
+	assert(truncate(a,5,r) == 10256);
+	assert(r == 0);
+	a = 8500;
+	assert(truncate(a,1,r) == 8);
+	assert(r == 500);
+	a = -8500;
+	assert(truncate(a,1,r) == -8);
+	assert(r == 500);
+	a = -8500;
+//	writeln("truncate(a, 6, r) = ", truncate(a, 6, r));
+//	writeln("r = ", r);
+	assert(truncate(a,6,r) == -8500);
+	assert(r == 0);
+	writeln("passed");
+}
+
+public DecInt pad(DecInt a, int n) {
+	if (n <= a.numDigits) return a.dup;
+	return DecInt(a,n);
+}
+
+unittest {
+	write("pad.........");
+	DecInt a;
+	a = 1234567;
+	assert(pad(a,3) == 1234567);
+	a = 10256;
+//	writeln("pad(a,9) = ", pad(a,9));
+	assert(pad(a,9).toString == "000010256");
+	a = 8500;
+	assert(pad(a,6).toString == "008500");
+	a = -8500;
+	assert(pad(a,6).toString == "-008500");
+	writeln("passed");
+}
+
+public DecInt pow10(const DecInt a, uint n) {
+	DecInt b = canonical(a);
+	if (n == 0 || b == 0) return b;
+	Digit[] zeros = new Digit[n];
+	b.digits = zeros ~ b.digits;
+	return b;
+}
+
+public DecInt pow10(uint n) {
+	return pow10(ONE, n);
+}
+
+unittest {
+	write("pow10...");
+	DecInt a, b;
+	a = 21345;
+	a = pow10(a, 12);
+	assert(a == DecInt("21345000000000000"));
+	a = pow10(a, 0);
+	assert(a == "21345000000000000"); 
+	a = pow10(9);
+	assert(a == DecInt("1000000000"));
+	writeln("passed");
+}
+
+public DecInt power(const DecInt a, uint n) {
+	DecInt b = canonical(a);
+	DecInt p = ONE.dup;
+	while (n > 0) {
+		if (n & 1) {
+			p *= b;
+			if (n == 1) return p;
+		}
+		b *= b;
+		n /= 2;
+	}
+	return p;
+}
+
+unittest {
+	write("power.......");
+	DecInt a;
+	a = 2;
+	int n = 3;
+	assert(power(a,n) == 8);
+	writeln("passed");
+}
+
+
+public DecInt shift(const DecInt a, int n) {
+	if (n == 0) return canonical(a);
+	if (n > 0) {	// shift left
+		return pow10(a, n);
+	}
+	else {			// shift right
+		if (-n >= a.numDigits) return ZERO.dup;
+		return truncate(a, a.numDigits + n);
+	}
+}
+
+unittest {
+	write("shift.......");
+	DecInt a, b;
+	a = 1234;
+	b = shift(a, 1);
+	assert(b.toString == "12340");
+	b = shift(a, 2);
+	assert(b.toString == "123400");
+	b = shift(a, -1);
+//	writeln("b = ", b);
+	assert(b.toString == "123");
+	b = shift(a, 0);
+	assert(b.toString == "1234");
+	b = shift(a, -12);
+/+	writeln("b = ", b);+/
+	assert(b.toString == "0");
+	b = shift(a, -4);
+	assert(b.toString == "0");
+	writeln("passed");
+}
+
+public DecInt shiftFixed(const DecInt a, int n) {
+	if (n == 0) return a.dup;
+	DecInt b = DecInt(0, a.numDigits);
+	if (std.math.abs(n) >= a.numDigits) return b; 
+	if (n > 0) {	// shiftFixed left
+		b.digits[0..$-n] = a.digits[n..$];
+	}
+	else {			// shiftFixed right
+		n = -n;
+		b.digits[n..$] = a.digits[0..$-n];
+	}
+	return b;
+}
+
+unittest {
+	write("shiftFixed...");
+	DecInt a, b;
+	a = 1234;
+	b = shiftFixed(a, 1);
+	assert(b.toString == "0123");
+	b = shiftFixed(a, 2);
+	assert(b.toString == "0012");
+	b = shiftFixed(a, -1);
+	assert(b.toString == "2340");
+	b = shiftFixed(a, 0);
+	assert(b.toString == "1234");
+	b = shiftFixed(a, 12);
+	assert(b.toString == "0000");
+	b = shiftFixed(a, -4);
+	assert(b.toString == "0000");
+	writeln("passed");
+}
+
+public DecInt rotate(const DecInt a, int n) {
+	if (n == 0) return a.dup;
+	DecInt b = DecInt(0, a.numDigits);
+	if (std.math.abs(n) >= a.numDigits) {
+		bool sign = n < 0;
+		n = std.math.abs(n) % a.numDigits;
+		if (sign) n = -n;
+	}
+	if (n > 0) {	// rotate left
+		b.digits[0..$-n] = a.digits[n..$];
+		b.digits[$-n..$] = a.digits[0..n];
+	}
+	else {			// rotate right
+		n = -n;
+		b.digits[n..$] = a.digits[0..$-n];
+		b.digits[0..n] = a.digits[$-n..$];
+	}
+	return b;
+}
+
+unittest {
+	write("rotate...");
+	DecInt a, b;
+	a = 1234;
+	b = rotate(a, 1);
+	assert(b.toString == "4123");
+	b = rotate(a, 2);
+	assert(b.toString == "3412");
+	b = rotate(a, -1);
+	assert(b.toString == "2341");
+	b = rotate(a, 0);
+	assert(b.toString == "1234");
+	b = rotate(a, 12);
+	assert(b.toString == "1234");
+	b = rotate(a, -4);
+	assert(b.toString == "1234");
+	writeln("passed");
+}
+
+/**
+ * Rounds the specified integer to the specified number of digits.
+ * The rounding mode governs the method of rounding.
+ */
+public DecInt round(const DecInt a, int n, Rounding mode) {
+	DecInt r;
+	DecInt b = truncate(a, n, r);
+	return round(b, r, mode);
+//	return b;
+}
+
+/**
+ * Rounds the (truncated) integer based on its remainder and the rounding
+ * mode.
+ */
+public DecInt round(const DecInt a, const DecInt r, const Rounding mode) {
+	DecInt b = canonical(a);
+	ubyte rfd = r.firstDigit;
+	switch (mode) {
+		case Rounding.DOWN:
+			return b;
+
+		case Rounding.HALF_UP:
+			if (rfd >= 5) b++;
+			return b;
+
+		case Rounding.HALF_EVEN:
+			if (rfd < 5) return b;
+			if (rfd > 5) return ++b;
+            DecInt p = r.dup;
+			stripr(p);
+			if (p.numDigits > 1) return ++b;
+			// to reach this point the remainder must be exactly 5
+			// if odd, increment
+			if (b.lastDigit & 1 != 0) b++;
+			return b;
+			
+		case Rounding.CEILING:
+			if (!b.isSigned && !r.isZero) b++;
+			return b;
+			
+		case Rounding.FLOOR:
+			if (b.isSigned && !r.isZero) b++;
+			return b;
+			
+		case Rounding.HALF_DOWN:
+			if (rfd < 5) return b;
+			if (rfd > 5) return ++b;
+            DecInt p = r.dup;
+			stripr(p);
+			if (p.numDigits > 1) return ++b;
+			// to reach this point the remainder must be exactly 5
+			return b;
+			
+		case Rounding.UP:
+			if (!r.isZero) b++;
+			return b;
+	}
+	return b;
+}
+
+unittest {
+	write("rounding....");
+	DecInt a, b;
+	a = 12345;
+	b = round(a, 4, Rounding.DOWN);
+	assert(b == 1234);
+	b = round(a, 4, Rounding.HALF_UP);
+	assert(b == 1235);
+	b = round(a, 4, Rounding.CEILING);
+	assert(b == 1235);
+	b = round(a, 4, Rounding.HALF_EVEN);
+	assert(b == 1234);
+	b = round(a, 4, Rounding.FLOOR);
+	assert(b == 1234);
+	b = round(a, 4, Rounding.HALF_DOWN);
+	assert(b == 1234);
+	b = round(a, 4, Rounding.UP);
+	assert(b == 1235);
+	writeln("passed");
+}
+
+
+//==========================================
+
+public void main() {
+	writeln();
+	writeln("If you got this far all the unit tests were successful.");
+	writeln();
+	writeln("      Congratulations!");
+	DecInt bcd;
+	writeln("bcd = ", format(bcd));
+	bcd = parse("12");
+	writeln("bcd = ", format(bcd));
+	bcd = parse("012");
+	writeln("bcd = ", format(bcd));
+	bcd = parse("-012");
+	writeln("bcd = ", format(bcd));
+	bcd = parse("+012");
+	writeln("bcd = ", format(bcd));
+	bcd = parse("-0");
+	writeln("bcd = ", format(bcd));
+	bcd = parse("012_345_678");
+	writeln("bcd = ", format(bcd));
+
+/+	
+	writeln("OK!");+/
+}
+
+
+