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Merge branch 'int64-fix'
* int64-fix: BigInteger: update comments and add test case BigInteger: fix some int64 issues
This commit is contained in:
Andreas Fischer
commit
431e3a04c7
@ -19,10 +19,6 @@
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* which only supports integers. Although this fact will slow this library down, the fact that such a high
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* base is being used should more than compensate.
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*
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* When PHP version 6 is officially released, we'll be able to use 64-bit integers. This should, once again,
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* allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition /
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* subtraction).
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*
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* Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian} format. ie.
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* (new Math_BigInteger(pow(2, 26)))->value = array(0, 1)
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*
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@ -924,7 +920,7 @@ class Math_BigInteger
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$carry = $sum >= MATH_BIGINTEGER_MAX_DIGIT2; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
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$sum = $carry ? $sum - MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
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$temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
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$temp = $this->_carry($sum);
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$value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000)
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$value[$j] = $temp;
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@ -1060,7 +1056,7 @@ class Math_BigInteger
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$carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
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$sum = $carry ? $sum + MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
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$temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
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$temp = $this->_carry($sum);
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$x_value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp);
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$x_value[$j] = $temp;
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@ -1208,7 +1204,7 @@ class Math_BigInteger
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for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0
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$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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}
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@ -1221,7 +1217,7 @@ class Math_BigInteger
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for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) {
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$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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}
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@ -1309,13 +1305,13 @@ class Math_BigInteger
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$i2 = $i << 1;
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$temp = $square_value[$i2] + $value[$i] * $value[$i];
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$square_value[$i2] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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// note how we start from $i+1 instead of 0 as we do in multiplication.
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for ($j = $i + 1, $k = $i2 + 1; $j <= $max_index; ++$j, ++$k) {
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$temp = $square_value[$k] + 2 * $value[$j] * $value[$i] + $carry;
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$square_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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}
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@ -1513,9 +1509,8 @@ class Math_BigInteger
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if ($x_window[0] == $y_window[0]) {
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$quotient_value[$q_index] = MATH_BIGINTEGER_MAX_DIGIT;
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} else {
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$quotient_value[$q_index] = (int) (
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($x_window[0] * MATH_BIGINTEGER_BASE_FULL + $x_window[1])
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/
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$quotient_value[$q_index] = $this->_safe_divide(
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$x_window[0] * MATH_BIGINTEGER_BASE_FULL + $x_window[1],
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$y_window[0]
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);
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}
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@ -1583,7 +1578,7 @@ class Math_BigInteger
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for ($i = count($dividend) - 1; $i >= 0; --$i) {
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$temp = MATH_BIGINTEGER_BASE_FULL * $carry + $dividend[$i];
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$result[$i] = (int) ($temp / $divisor);
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$result[$i] = $this->_safe_divide($temp, $divisor);
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$carry = (int) ($temp - $divisor * $result[$i]);
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}
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@ -2200,7 +2195,7 @@ class Math_BigInteger
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for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0, $k = $i
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$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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}
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@ -2216,7 +2211,7 @@ class Math_BigInteger
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for ($j = 0, $k = $i; $j < $x_length && $k < $stop; ++$j, ++$k) {
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$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
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}
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@ -2265,7 +2260,7 @@ class Math_BigInteger
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for ($i = 0; $i < $k; ++$i) {
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$temp = $result[MATH_BIGINTEGER_VALUE][$i] * $cache[MATH_BIGINTEGER_DATA][$key];
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$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
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$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
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$temp = $this->_regularMultiply(array($temp), $n);
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$temp = array_merge($this->_array_repeat(0, $i), $temp);
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$result = $this->_add($result[MATH_BIGINTEGER_VALUE], false, $temp, false);
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@ -2322,9 +2317,9 @@ class Math_BigInteger
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$a = array(MATH_BIGINTEGER_VALUE => $this->_array_repeat(0, $n + 1));
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for ($i = 0; $i < $n; ++$i) {
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$temp = $a[MATH_BIGINTEGER_VALUE][0] + $x[$i] * $y[0];
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$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
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$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
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$temp = $temp * $cache[MATH_BIGINTEGER_DATA][$key];
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$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
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$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
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$temp = $this->_add($this->_regularMultiply(array($x[$i]), $y), false, $this->_regularMultiply(array($temp), $m), false);
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$a = $this->_add($a[MATH_BIGINTEGER_VALUE], false, $temp[MATH_BIGINTEGER_VALUE], false);
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$a[MATH_BIGINTEGER_VALUE] = array_slice($a[MATH_BIGINTEGER_VALUE], 1);
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@ -3464,7 +3459,7 @@ class Math_BigInteger
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for ($i = 0; $i < count($this->value); ++$i) {
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$temp = $this->value[$i] * $shift + $carry;
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$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
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$carry = $this->_carry($temp);
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$this->value[$i] = (int) ($temp - $carry * MATH_BIGINTEGER_BASE_FULL);
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}
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@ -3712,4 +3707,58 @@ class Math_BigInteger
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$temp = ltrim(pack('N', $length), chr(0));
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return pack('Ca*', 0x80 | strlen($temp), $temp);
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}
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/**
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* Calculate the carry
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*
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* when PHP uses int32, phpseclib uses float64 / base-26. at that point the largest intermediary
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* value numbers can have is 2**52. you can't left shift to get the top (most significant) 26 bits
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* because left shift takes in ints, which have 31-bits of usable precision, since PHP does
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* signed int32. as a consequence of the above, division takes place
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*
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* when PHP uses int64, phpseclib uses int64 / base-31. at that point the largest intermediary
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* value numbers can have is 2**62. you can't divide because PHP's division operator returns
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* a float64 (which doesn't have sufficient precision) unless the two operands are evenly
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* divisible. but we can left shift.
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*
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* here are some examples.
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*
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* intval(0x7FFFFFFFFFFFFFFF / 0x80000000) returns 4294967296 when in fact it should
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* return 4294967295. actually, the answer is 4294967295.999999 but float64 is rounding
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* up when in fact we want it to round down.
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*
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* pow(2, 52) >> 31 returns 0 on int32 when the answer with int64 is 2097152.
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*
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* @access private
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* @param Integer $x
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* @return Integer
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*/
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function _carry($x)
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{
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if (MATH_BIGINTEGER_BASE === 26) {
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return (int) ($x / 0x4000000);
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}
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// MATH_BIGINTEGER_BASE === 31
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return $x >> 31;
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}
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/**
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* Single digit division
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*
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* @see _carry()
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* @access private
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* @param Integer $x
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* @param Integer $y
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* @return Integer
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*/
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function _safe_divide($x, $y)
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{
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if (MATH_BIGINTEGER_BASE === 26) {
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return (int) ($x / $y);
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}
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// MATH_BIGINTEGER_BASE === 31
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return ($x - ($x % $y)) / $y;
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}
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}
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@ -14,4 +14,11 @@ class Math_BigInteger_InternalTest extends Math_BigInteger_TestCase
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self::ensureConstant('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_INTERNAL);
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self::ensureConstant('MATH_BIGINTEGER_OPENSSL_DISABLE', true);
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}
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public function testInternalRepresentation()
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{
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$x = new Math_BigInteger('FFFFFFFFFFFFFFFFC90FDA', 16);
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$y = new Math_BigInteger("$x");
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$this->assertSame($x->value, $y->value);
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}
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}
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