* See Section 4.3.1 of Knuth's ``The Art of Computer Programming''.
*/
+/*
+ * On most calls to put-here operations, it's safe to read the inputs little by
+ * little and write the outputs little by little. However, if one of the
+ * inputs is coming from the same variable into which the output is to be
+ * stored (an "aliased" call), we risk overwriting the input before we read it.
+ * In this case, we first compute the result into a temporary BigUnsigned
+ * variable and then copy it into the requested output variable *this.
+ * Each put-here operation uses the DOTR_ALIASED macro (Do The Right Thing on
+ * aliased calls) to generate code for this check.
+ *
+ * I adopted this approach on 2007.02.13 (see Assignment Operators in
+ * BigUnsigned.hh). Before then, put-here operations rejected aliased calls
+ * with an exception. I think doing the right thing is better.
+ *
+ * Some of the put-here operations can probably handle aliased calls safely
+ * without the extra copy because (for example) they process blocks strictly
+ * right-to-left. At some point I might determine which ones don't need the
+ * copy, but my reasoning would need to be verified very carefully. For now
+ * I'll leave in the copy.
+ */
+#define DOTR_ALIASED(cond, op) \
+ if (cond) { \
+ BigUnsigned tmpThis; \
+ tmpThis.op; \
+ *this = tmpThis; \
+ return; \
+ }
+
// Addition
void BigUnsigned::add(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::add: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, add(a, b));
// If one argument is zero, copy the other.
if (a.len == 0) {
operator =(b);
// Subtraction
void BigUnsigned::subtract(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::subtract: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, subtract(a, b));
// If b is zero, copy a. If a is shorter than b, the result is negative.
if (b.len == 0) {
operator =(a);
// Multiplication
void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::multiply: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, multiply(a, b));
// If either a or b is zero, set to zero.
if (a.len == 0 || b.len == 0) {
len = 0;
* and provide outputs in the most convenient places so that no value ever needs
* to be copied in its entirety. That way, the client can perform exactly the
* copying it needs depending on where the inputs are and where it wants the output.
+* A better name for this function might be "modWithQuotient", but I would rather
+* not change the name now.
*/
void BigUnsigned::divideWithRemainder(const BigUnsigned &b, BigUnsigned &q) {
- // Block unsafe calls
- if (this == &b || &q == &b || this == &q)
- throw "BigUnsigned::divideWithRemainder: Some two objects involved are the same";
+ /*
+ * Defending against aliased calls is a bit tricky because we are
+ * writing to both *this and q.
+ *
+ * It would be silly to try to write quotient and remainder to the
+ * same variable. Rule that out right away.
+ */
+ if (this == &q)
+ throw "BigUnsigned::divideWithRemainder: Cannot write quotient and remainder into the same variable";
+ /*
+ * Now *this and q are separate, so the only concern is that b might be
+ * aliased to one of them. If so, use a temporary copy of b.
+ */
+ if (this == &b || &q == &b) {
+ BigUnsigned tmpB(b);
+ divideWithRemainder(tmpB, q);
+ return;
+ }
/*
* Note that the mathematical definition of mod (I'm trusting Knuth) is somewhat
// Bitwise and
void BigUnsigned::bitAnd(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::bitAnd: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, bitAnd(a, b));
len = (a.len >= b.len) ? b.len : a.len;
allocate(len);
Index i;
// Bitwise or
void BigUnsigned::bitOr(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::bitOr: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, bitOr(a, b));
Index i;
const BigUnsigned *a2, *b2;
if (a.len >= b.len) {
// Bitwise xor
void BigUnsigned::bitXor(const BigUnsigned &a, const BigUnsigned &b) {
- // Block unsafe calls
- if (this == &a || this == &b)
- throw "BigUnsigned::bitXor: One of the arguments is the invoked object";
+ DOTR_ALIASED(this == &a || this == &b, bitXor(a, b));
Index i;
const BigUnsigned *a2, *b2;
if (a.len >= b.len) {
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