X-Git-Url: https://mattmccutchen.net/bigint/bigint.git/blobdiff_plain/05780f4b578d6ae054be0b19b8498d32a4f16c60..ef2b7c5922c36f93923dd3482c5bfd41b14d82ce:/BigUnsigned.cc diff --git a/BigUnsigned.cc b/BigUnsigned.cc index f70560a..3c9a1d7 100644 --- a/BigUnsigned.cc +++ b/BigUnsigned.cc @@ -1,11 +1,10 @@ /* * Matt McCutchen's Big Integer Library -* http://mysite.verizon.net/mccutchen/bigint/ */ #include "BigUnsigned.hh" -// The "management" routines that used to be here are now in NumberlikeArray.cpp. +// The "management" routines that used to be here are now in NumberlikeArray.hh. /* * The steps for construction of a BigUnsigned @@ -16,14 +15,19 @@ * 4. If x is of a signed type, convert x to the unsigned * type of the same length. * 5. Expand x to a Blk, and store it in the number array. +* +* Since 2005.01.06, NumberlikeArray uses `NULL' rather +* than a real array if one of zero length is needed. +* These constructors implicitly call NumberlikeArray's +* default constructor, which sets `blk = NULL, cap = len = 0'. +* So if the input number is zero, they can just return. +* See remarks in `NumberlikeArray.hh'. */ BigUnsigned::BigUnsigned(unsigned long x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else { + if (x == 0) + ; // NumberlikeArray already did all the work + else { cap = 1; blk = new Blk[1]; len = 1; @@ -32,25 +36,21 @@ BigUnsigned::BigUnsigned(unsigned long x) { } BigUnsigned::BigUnsigned(long x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else if (x > 0) { + if (x == 0) + ; + else if (x > 0) { cap = 1; blk = new Blk[1]; len = 1; blk[0] = Blk(x); } else - throw "BigUnsigned::BigUnsigned(long): Cannot construct a BigUnsigned from a negative number"; + throw "BigUnsigned::BigUnsigned(long): Cannot construct a BigUnsigned from a negative number"; } BigUnsigned::BigUnsigned(unsigned int x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else { + if (x == 0) + ; + else { cap = 1; blk = new Blk[1]; len = 1; @@ -59,25 +59,21 @@ BigUnsigned::BigUnsigned(unsigned int x) { } BigUnsigned::BigUnsigned(int x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else if (x > 0) { + if (x == 0) + ; + else if (x > 0) { cap = 1; blk = new Blk[1]; len = 1; blk[0] = Blk(x); } else - throw "BigUnsigned::BigUnsigned(int): Cannot construct a BigUnsigned from a negative number"; + throw "BigUnsigned::BigUnsigned(int): Cannot construct a BigUnsigned from a negative number"; } BigUnsigned::BigUnsigned(unsigned short x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else { + if (x == 0) + ; + else { cap = 1; blk = new Blk[1]; len = 1; @@ -86,17 +82,15 @@ BigUnsigned::BigUnsigned(unsigned short x) { } BigUnsigned::BigUnsigned(short x) { - if (x == 0) { - cap = 0; - blk = new Blk[0]; - len = 0; - } else if (x > 0) { + if (x == 0) + ; + else if (x > 0) { cap = 1; blk = new Blk[1]; len = 1; blk[0] = Blk(x); } else - throw "BigUnsigned::BigUnsigned(short): Cannot construct a BigUnsigned from a negative number"; + throw "BigUnsigned::BigUnsigned(short): Cannot construct a BigUnsigned from a negative number"; } // CONVERTERS @@ -202,11 +196,59 @@ BigUnsigned::CmpRes BigUnsigned::compareTo(const BigUnsigned &x) const { // PUT-HERE OPERATIONS +/* +* Below are implementations of the four basic arithmetic operations +* for `BigUnsigned's. Their purpose is to use a mechanism that can +* calculate the sum, difference, product, and quotient/remainder of +* two individual blocks in order to calculate the sum, difference, +* product, and quotient/remainder of two multi-block BigUnsigned +* numbers. +* +* As alluded to in the comment before class `BigUnsigned', +* these algorithms bear a remarkable similarity (in purpose, if +* not in implementation) to the way humans operate on big numbers. +* The built-in `+', `-', `*', `/' and `%' operators are analogous +* to elementary-school ``math facts'' and ``times tables''; the +* four routines below are analogous to ``long division'' and its +* relatives. (Only a computer can ``memorize'' a times table with +* 18446744073709551616 entries! (For 32-bit blocks.)) +* +* The discovery of these four algorithms, called the ``classical +* algorithms'', marked the beginning of the study of computer science. +* 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 DTRT_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 DTRT_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"; + DTRT_ALIASED(this == &a || this == &b, add(a, b)); // If one argument is zero, copy the other. if (a.len == 0) { operator =(b); @@ -215,6 +257,7 @@ void BigUnsigned::add(const BigUnsigned &a, const BigUnsigned &b) { operator =(a); return; } + // Some variables... // Carries in and out of an addition stage bool carryIn, carryOut; Blk temp; @@ -266,15 +309,14 @@ void BigUnsigned::add(const BigUnsigned &a, const BigUnsigned &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"; + DTRT_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); return; } else if (a.len < b.len) throw "BigUnsigned::subtract: Negative result in unsigned calculation"; + // Some variables... bool borrowIn, borrowOut; Blk temp; Index i; @@ -312,22 +354,90 @@ void BigUnsigned::subtract(const BigUnsigned &a, const BigUnsigned &b) { zapLeadingZeros(); } +/* +* About the multiplication and division algorithms: +* +* I searched unsucessfully for fast built-in operations like the `b_0' +* and `c_0' Knuth describes in Section 4.3.1 of ``The Art of Computer +* Programming'' (replace `place' by `Blk'): +* +* ``b_0[:] multiplication of a one-place integer by another one-place +* integer, giving a two-place answer; +* +* ``c_0[:] division of a two-place integer by a one-place integer, +* provided that the quotient is a one-place integer, and yielding +* also a one-place remainder.'' +* +* I also missed his note that ``[b]y adjusting the word size, if +* necessary, nearly all computers will have these three operations +* available'', so I gave up on trying to use algorithms similar to his. +* A future version of the library might include such algorithms; I +* would welcome contributions from others for this. +* +* I eventually decided to use bit-shifting algorithms. To multiply `a' +* and `b', we zero out the result. Then, for each `1' bit in `a', we +* shift `b' left the appropriate amount and add it to the result. +* Similarly, to divide `a' by `b', we shift `b' left varying amounts, +* repeatedly trying to subtract it from `a'. When we succeed, we note +* the fact by setting a bit in the quotient. While these algorithms +* have the same O(n^2) time complexity as Knuth's, the ``constant factor'' +* is likely to be larger. +* +* Because I used these algorithms, which require single-block addition +* and subtraction rather than single-block multiplication and division, +* the innermost loops of all four routines are very similar. Study one +* of them and all will become clear. +*/ + +/* +* This is a little inline function used by both the multiplication +* routine and the division routine. +* +* `getShiftedBlock' returns the `x'th block of `num << y'. +* `y' may be anything from 0 to N - 1, and `x' may be anything from +* 0 to `num.len'. +* +* Two things contribute to this block: +* +* (1) The `N - y' low bits of `num.blk[x]', shifted `y' bits left. +* +* (2) The `y' high bits of `num.blk[x-1]', shifted `N - y' bits right. +* +* But we must be careful if `x == 0' or `x == num.len', in +* which case we should use 0 instead of (2) or (1), respectively. +* +* If `y == 0', then (2) contributes 0, as it should. However, +* in some computer environments, for a reason I cannot understand, +* `a >> b' means `a >> (b % N)'. This means `num.blk[x-1] >> (N - y)' +* will return `num.blk[x-1]' instead of the desired 0 when `y == 0'; +* the test `y == 0' handles this case specially. +*/ +inline BigUnsigned::Blk getShiftedBlock(const BigUnsigned &num, + BigUnsigned::Index x, unsigned int y) { + BigUnsigned::Blk part1 = (x == 0 || y == 0) ? 0 : (num.blk[x - 1] >> (BigUnsigned::N - y)); + BigUnsigned::Blk part2 = (x == num.len) ? 0 : (num.blk[x] << y); + return part1 | part2; +} + // 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"; + DTRT_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; return; } - // Overall method: this = 0, then for each 1-bit of a, add b - // to this shifted the appropriate amount. + /* + * Overall method: + * + * Set this = 0. + * For each 1-bit of `a' (say the `i2'th bit of block `i'): + * Add `b << (i blocks and i2 bits)' to *this. + */ // Variables for the calculation Index i, j, k; unsigned int i2; - Blk aBlk, bHigh, temp; + Blk temp; bool carryIn, carryOut; // Set preliminary length and make room len = a.len + b.len; @@ -338,16 +448,28 @@ void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) { // For each block of the first number... for (i = 0; i < a.len; i++) { // For each 1-bit of that block... - for (i2 = 0, aBlk = a.blk[i]; aBlk != 0; i2++, aBlk >>= 1) { - if ((aBlk & 1) == 0) + for (i2 = 0; i2 < N; i2++) { + if ((a.blk[i] & (Blk(1) << i2)) == 0) continue; - /* Add b to this, shifted left i blocks and i2 bits. + /* + * Add b to this, shifted left i blocks and i2 bits. * j is the index in b, and k = i + j is the index in this. - * The low bits of b.blk[j] are shifted and added to blk[k]. - * bHigh is used to carry the high bits to the next addition. */ - bHigh = 0; - for (j = 0, k = i, carryIn = false; j < b.len; j++, k++) { - temp = blk[k] + ((b.blk[j] << i2) | bHigh); + * + * `getShiftedBlock', a short inline function defined above, + * is now used for the bit handling. It replaces the more + * complex `bHigh' code, in which each run of the loop dealt + * immediately with the low bits and saved the high bits to + * be picked up next time. The last run of the loop used to + * leave leftover high bits, which were handled separately. + * Instead, this loop runs an additional time with j == b.len. + * These changes were made on 2005.01.11. + */ + for (j = 0, k = i, carryIn = false; j <= b.len; j++, k++) { + /* + * The body of this loop is very similar to the body of the first loop + * in `add', except that this loop does a `+=' instead of a `+'. + */ + temp = blk[k] + getShiftedBlock(b, j, i2); carryOut = (temp < blk[k]); if (carryIn) { temp++; @@ -355,17 +477,9 @@ void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) { } blk[k] = temp; carryIn = carryOut; - bHigh = (i2 == 0) ? 0 : b.blk[j] >> (8 * sizeof(Blk) - i2); - } - temp = blk[k] + bHigh; - carryOut = (temp < blk[k]); - if (carryIn) { - temp++; - carryOut |= (temp == 0); } - blk[k] = temp; - carryIn = carryOut; - k++; // Added by Matt 2004.12.23: Move to the next block. It belongs here (and there was a corresponding line in the division routine), but I'm not certain whether it ever matters. + // No more extra iteration to deal with `bHigh'. + // Roll-over a carry as necessary. for (; carryIn; k++) { blk[k]++; carryIn = (blk[k] == 0); @@ -391,11 +505,28 @@ void BigUnsigned::multiply(const BigUnsigned &a, const BigUnsigned &b) { * 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 @@ -424,43 +555,62 @@ void BigUnsigned::divideWithRemainder(const BigUnsigned &b, BigUnsigned &q) { * At this point we know *this > b > 0. (Whew!) */ - /* DEBUG * - std::cout << "divideWithRemainder starting\n" - << "length of dividend: " << len - << "\nlast block of dividend: " << getBlock(0) - << "\nlength of divisor: " << b.len - << "\nlast block of divisor: " << b.getBlock(0) - << std::endl; */ - /* - * Overall method: Subtract b, shifted varying amounts to - * the left, from this, setting the bit in the quotient q - * whenever the subtraction succeeds. Eventually q will contain the entire - * quotient, and this will be left with the remainder. + * Overall method: + * + * For each appropriate i and i2, decreasing: + * Try to subtract (b << (i blocks and i2 bits)) from *this. + * (`work2' holds the result of this subtraction.) + * If the result is nonnegative: + * Turn on bit i2 of block i of the quotient q. + * Save the result of the subtraction back into *this. + * Otherwise: + * Bit i2 of block i remains off, and *this is unchanged. + * + * Eventually q will contain the entire quotient, and *this will + * be left with the remainder. * * We use work2 to temporarily store the result of a subtraction. - * But we don't even compute the i lowest blocks of the result, - * because they are unaffected (we shift left i places). - * */ + * work2[x] corresponds to blk[x], not blk[x+i], since 2005.01.11. + * If the subtraction is successful, we copy work2 back to blk. + * (There's no `work1'. In a previous version, when division was + * coded for a read-only dividend, `work1' played the role of + * the here-modifiable `*this' and got the remainder.) + * + * We never touch the i lowest blocks of either blk or work2 because + * they are unaffected by the subtraction: we are subtracting + * (b << (i blocks and i2 bits)), which ends in at least `i' zero blocks. + */ // Variables for the calculation Index i, j, k; unsigned int i2; - Blk bHigh, temp; + Blk temp; bool borrowIn, borrowOut; - // Make sure we have an extra zero block just past the value, - // but don't increase the logical length. A shifted subtraction - // (for example, subtracting 1 << 2 from 4) might stick into - // this block. - allocateAndCopy(len + 1); - blk[len] = 0; + /* + * Make sure we have an extra zero block just past the value. + * + * When we attempt a subtraction, we might shift `b' so + * its first block begins a few bits left of the dividend, + * and then we'll try to compare these extra bits with + * a nonexistent block to the left of the dividend. The + * extra zero block ensures sensible behavior; we need + * an extra block in `work2' for exactly the same reason. + * + * See below `divideWithRemainder' for the interesting and + * amusing story of this section of code. + */ + Index origLen = len; // Save real length. + // 2006.05.03: Copy the number and then change the length! + allocateAndCopy(len + 1); // Get the space. + len++; // Increase the length. + blk[origLen] = 0; // Zero the extra block. - // work2 holds part of the result of a subtraction. - // (There's no work1. The name work2 is from a previous version.) + // work2 holds part of the result of a subtraction; see above. Blk *work2 = new Blk[len]; // Set preliminary length for quotient and make room - q.len = len - b.len + 1; + q.len = origLen - b.len + 1; q.allocate(q.len); // Zero out the quotient for (i = 0; i < q.len; i++) @@ -471,52 +621,51 @@ void BigUnsigned::divideWithRemainder(const BigUnsigned &b, BigUnsigned &q) { while (i > 0) { i--; // For each possible left-shift of b in bits... + // (Remember, N is the number of bits in a Blk.) q.blk[i] = 0; - i2 = 8 * sizeof(Blk); + i2 = N; while (i2 > 0) { i2--; /* - * Subtract b, shifted left i blocks and i2 bits, from this. - * and store the answer in work2. + * Subtract b, shifted left i blocks and i2 bits, from *this, + * and store the answer in work2. In the for loop, `k == i + j'. * * Compare this to the middle section of `multiply'. They - * are in many ways analogous. + * are in many ways analogous. See especially the discussion + * of `getShiftedBlock'. */ - bHigh = 0; - for (j = 0, k = i, borrowIn = false; j < b.len; j++, k++) { - temp = blk[k] - ((b.blk[j] << i2) | bHigh); + for (j = 0, k = i, borrowIn = false; j <= b.len; j++, k++) { + temp = blk[k] - getShiftedBlock(b, j, i2); borrowOut = (temp > blk[k]); if (borrowIn) { borrowOut |= (temp == 0); temp--; } - work2[j] = temp; + // Since 2005.01.11, indices of `work2' directly match those of `blk', so use `k'. + work2[k] = temp; borrowIn = borrowOut; - bHigh = (i2 == 0) ? 0 : b.blk[j] >> (8 * sizeof(Blk) - i2); - } - temp = blk[k] - bHigh; - borrowOut = (temp > blk[k]); - if (borrowIn) { - borrowOut |= (temp == 0); - temp--; } - work2[j] = temp; - borrowIn = borrowOut; - j++; - k++; - for (; k < len && borrowIn; j++, k++) { + // No more extra iteration to deal with `bHigh'. + // Roll-over a borrow as necessary. + for (; k < origLen && borrowIn; k++) { borrowIn = (blk[k] == 0); - work2[j] = blk[k] - 1; + work2[k] = blk[k] - 1; } - /* If the subtraction was performed successfully (!borrowIn), set bit i2 - * in block i of the quotient, and copy the changed portion of - * work2 back to this. Otherwise, reset that bit and move on. */ + /* + * If the subtraction was performed successfully (!borrowIn), + * set bit i2 in block i of the quotient. + * + * Then, copy the portion of work2 filled by the subtraction + * back to *this. This portion starts with block i and ends-- + * where? Not necessarily at block `i + b.len'! Well, we + * increased k every time we saved a block into work2, so + * the region of work2 we copy is just [i, k). + */ if (!borrowIn) { - q.blk[i] |= (1 << i2); - while (j > 0) { - j--; + q.blk[i] |= (Blk(1) << i2); + while (k > i) { k--; - blk[k] = work2[j]; + blk[k] = work2[k]; } } } @@ -530,20 +679,51 @@ void BigUnsigned::divideWithRemainder(const BigUnsigned &b, BigUnsigned &q) { // (Thanks to Brad Spencer for noticing my accidental omission of this!) delete [] work2; - /* DEBUG * - std::cout << "divideWithRemainder complete\n" - << "length of quotient: " << q.len - << "\nlast block of quotient: " << q.getBlock(0) - << "\nlength of remainder: " << len - << "\nlast block of remainder: " << getBlock(0) - << std::endl; */ } +/* +* The out-of-bounds accesses story: +* +* On 2005.01.06 or 2005.01.07 (depending on your time zone), +* Milan Tomic reported out-of-bounds memory accesses in +* the Big Integer Library. To investigate the problem, I +* added code to bounds-check every access to the `blk' array +* of a `NumberlikeArray'. +* +* This gave me warnings that fell into two categories of false +* positives. The bounds checker was based on length, not +* capacity, and in two places I had accessed memory that I knew +* was inside the capacity but that wasn't inside the length: +* +* (1) The extra zero block at the left of `*this'. Earlier +* versions said `allocateAndCopy(len + 1); blk[len] = 0;' +* but did not increment `len'. +* +* (2) The entire digit array in the conversion constructor +* ``BigUnsignedInABase(BigUnsigned)''. It was allocated with +* a conservatively high capacity, but the length wasn't set +* until the end of the constructor. +* +* To simplify matters, I changed both sections of code so that +* all accesses occurred within the length. The messages went +* away, and I told Milan that I couldn't reproduce the problem, +* sending a development snapshot of the bounds-checked code. +* +* Then, on 2005.01.09-10, he told me his debugger still found +* problems, specifically at the line `delete [] work2'. +* It was `work2', not `blk', that was causing the problems; +* this possibility had not occurred to me at all. In fact, +* the problem was that `work2' needed an extra block just +* like `*this'. Go ahead and laugh at me for finding (1) +* without seeing what was actually causing the trouble. :-) +* +* The 2005.01.11 version fixes this problem. I hope this is +* the last of my memory-related bloopers. So this is what +* starts happening to your C++ code if you use Java too much! +*/ // 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"; + DTRT_ALIASED(this == &a || this == &b, bitAnd(a, b)); len = (a.len >= b.len) ? b.len : a.len; allocate(len); Index i; @@ -554,9 +734,7 @@ void BigUnsigned::bitAnd(const BigUnsigned &a, const BigUnsigned &b) { // 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"; + DTRT_ALIASED(this == &a || this == &b, bitOr(a, b)); Index i; const BigUnsigned *a2, *b2; if (a.len >= b.len) { @@ -576,9 +754,7 @@ void BigUnsigned::bitOr(const BigUnsigned &a, const BigUnsigned &b) { // 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"; + DTRT_ALIASED(this == &a || this == &b, bitXor(a, b)); Index i; const BigUnsigned *a2, *b2; if (a.len >= b.len) { @@ -588,7 +764,7 @@ void BigUnsigned::bitXor(const BigUnsigned &a, const BigUnsigned &b) { a2 = &b; b2 = &a; } - allocate(b2->len); + allocate(a2->len); for (i = 0; i < b2->len; i++) blk[i] = a2->blk[i] ^ b2->blk[i]; for (; i < a2->len; i++) @@ -597,6 +773,51 @@ void BigUnsigned::bitXor(const BigUnsigned &a, const BigUnsigned &b) { zapLeadingZeros(); } +// Bitwise shift left +void BigUnsigned::bitShiftLeft(const BigUnsigned &a, unsigned int b) { + DTRT_ALIASED(this == &a, bitShiftLeft(a, b)); + Index shiftBlocks = b / N; + unsigned int shiftBits = b % N; + // + 1: room for high bits nudged left into another block + len = a.len + shiftBlocks + 1; + allocate(len); + Index i, j; + for (i = 0; i < shiftBlocks; i++) + blk[i] = 0; + for (j = 0, i = shiftBlocks; j <= a.len; j++, i++) + blk[i] = getShiftedBlock(a, j, shiftBits); + // Zap possible leading zero + if (blk[len - 1] == 0) + len--; +} + +// Bitwise shift right +void BigUnsigned::bitShiftRight(const BigUnsigned &a, unsigned int b) { + DTRT_ALIASED(this == &a, bitShiftRight(a, b)); + // This calculation is wacky, but expressing the shift as a left bit shift + // within each block lets us use getShiftedBlock. + Index rightShiftBlocks = (b + N - 1) / N; + unsigned int leftShiftBits = N * rightShiftBlocks - b; + // Now (N * rightShiftBlocks - leftShiftBits) == b + // and 0 <= leftShiftBits < N. + if (rightShiftBlocks >= a.len + 1) { + // All of a is guaranteed to be shifted off, even considering the left + // bit shift. + len = 0; + return; + } + // Now we're allocating a positive amount. + // + 1: room for high bits nudged left into another block + len = a.len + 1 - rightShiftBlocks; + allocate(len); + Index i, j; + for (j = rightShiftBlocks, i = 0; j <= a.len; j++, i++) + blk[i] = getShiftedBlock(a, j, leftShiftBits); + // Zap possible leading zero + if (blk[len - 1] == 0) + len--; +} + // INCREMENT/DECREMENT OPERATORS // Prefix increment @@ -609,8 +830,10 @@ void BigUnsigned::operator ++() { } if (carry) { // Matt fixed a bug 2004.12.24: next 2 lines used to say allocateAndCopy(len + 1) + // Matt fixed another bug 2006.04.24: + // old number only has len blocks, so copy before increasing length + allocateAndCopy(len + 1); len++; - allocateAndCopy(len); blk[i] = 1; } }