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BigInteger: fix some int64 issues

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terrafrost 2014-04-23 16:57:20 -05:00 committed by Andreas Fischer
parent b90deb5e83
commit e4ff01f054
1 changed files with 69 additions and 16 deletions
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85
phpseclib/Math/BigInteger.php
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@ -924,7 +924,7 @@ class Math_BigInteger
$carry = $sum >= MATH_BIGINTEGER_MAX_DIGIT2; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
$sum = $carry ? $sum - MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
$temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
$temp = $this->_carry($sum);
$value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000)
$value[$j] = $temp;
@ -1060,7 +1060,7 @@ class Math_BigInteger
$carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
$sum = $carry ? $sum + MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
$temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
$temp = $this->_carry($sum);
$x_value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp);
$x_value[$j] = $temp;
@ -1208,7 +1208,7 @@ class Math_BigInteger
for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0
$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -1221,7 +1221,7 @@ class Math_BigInteger
for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) {
$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -1309,13 +1309,13 @@ class Math_BigInteger
$i2 = $i << 1;
$temp = $square_value[$i2] + $value[$i] * $value[$i];
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$square_value[$i2] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
// note how we start from $i+1 instead of 0 as we do in multiplication.
for ($j = $i + 1, $k = $i2 + 1; $j <= $max_index; ++$j, ++$k) {
$temp = $square_value[$k] + 2 * $value[$j] * $value[$i] + $carry;
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$square_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -1513,9 +1513,8 @@ class Math_BigInteger
if ($x_window[0] == $y_window[0]) {
$quotient_value[$q_index] = MATH_BIGINTEGER_MAX_DIGIT;
} else {
$quotient_value[$q_index] = (int) (
($x_window[0] * MATH_BIGINTEGER_BASE_FULL + $x_window[1])
/
$quotient_value[$q_index] = $this->_safe_divide(
$x_window[0] * MATH_BIGINTEGER_BASE_FULL + $x_window[1],
$y_window[0]
);
}
@ -1583,7 +1582,7 @@ class Math_BigInteger
for ($i = count($dividend) - 1; $i >= 0; --$i) {
$temp = MATH_BIGINTEGER_BASE_FULL * $carry + $dividend[$i];
$result[$i] = (int) ($temp / $divisor);
$result[$i] = $this->_safe_divide($temp, $divisor);
$carry = (int) ($temp - $divisor * $result[$i]);
}
@ -2200,7 +2199,7 @@ class Math_BigInteger
for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0, $k = $i
$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -2216,7 +2215,7 @@ class Math_BigInteger
for ($j = 0, $k = $i; $j < $x_length && $k < $stop; ++$j, ++$k) {
$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -2265,7 +2264,7 @@ class Math_BigInteger
for ($i = 0; $i < $k; ++$i) {
$temp = $result[MATH_BIGINTEGER_VALUE][$i] * $cache[MATH_BIGINTEGER_DATA][$key];
$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $this->_regularMultiply(array($temp), $n);
$temp = array_merge($this->_array_repeat(0, $i), $temp);
$result = $this->_add($result[MATH_BIGINTEGER_VALUE], false, $temp, false);
@ -2322,9 +2321,9 @@ class Math_BigInteger
$a = array(MATH_BIGINTEGER_VALUE => $this->_array_repeat(0, $n + 1));
for ($i = 0; $i < $n; ++$i) {
$temp = $a[MATH_BIGINTEGER_VALUE][0] + $x[$i] * $y[0];
$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $temp * $cache[MATH_BIGINTEGER_DATA][$key];
$temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $this->_add($this->_regularMultiply(array($x[$i]), $y), false, $this->_regularMultiply(array($temp), $m), false);
$a = $this->_add($a[MATH_BIGINTEGER_VALUE], false, $temp[MATH_BIGINTEGER_VALUE], false);
$a[MATH_BIGINTEGER_VALUE] = array_slice($a[MATH_BIGINTEGER_VALUE], 1);
@ -3464,7 +3463,7 @@ class Math_BigInteger
for ($i = 0; $i < count($this->value); ++$i) {
$temp = $this->value[$i] * $shift + $carry;
$carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
$carry = $this->_carry($temp);
$this->value[$i] = (int) ($temp - $carry * MATH_BIGINTEGER_BASE_FULL);
}
@ -3712,4 +3711,58 @@ class Math_BigInteger
$temp = ltrim(pack('N', $length), chr(0));
return pack('Ca*', 0x80 | strlen($temp), $temp);
}
/**
* Calculate the carry
*
* when PHP uses int32 phpseclib uses float64 / base-26. at that point the largest intermediary
* value numbers can have is 2**52. you can't left shift to get the top 26 bits because left
* shift takes in ints, which have 31-bits of usuable precision, since PHP does signed int32.
* so we divide.
*
* when PHP uses int64 phpseclib uses int64 / base-31. at that point the largest intermediary
* value numbers can have is 2**62. you can't divide because PHP's division operator returns
* a float64 (which doesn't have sufficient precision) unless the two operands are evenly
* divisible. but we can left shift.
*
* here are some examples.
*
* intval(0x7FFFFFFFFFFFFFFF / 0x80000000) returns 4294967296 when in fact it should
* return 4294967295. actually, the answer is 4294967295.999999 but float64 is rounding
* up when in fact we want it to round down.
*
* pow(2, 52) >> 31 returns 0 on int32 when the answer with int64 is 2097152.
*
* @access private
* @param Integer $x
* @return Integer
*/
function _carry($x)
{
if (MATH_BIGINTEGER_BASE === 26) {
return (int) ($x / 0x4000000);
}
// MATH_BIGINTEGER_BASE === 31
return $x >> 31;
}
/**
* Single digit division
*
* @see _carry()
* @access private
* @param Integer $x
* @param Integer $y
* @return Integer
*/
function _safe_divide($x, $y)
{
if (MATH_BIGINTEGER_BASE === 26) {
return (int) ($x / $y);
}
// MATH_BIGINTEGER_BASE === 31
return ($x - ($x % $y)) / $y;
}
}