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BigInteger: speedup internal mode slightly

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Changes should yield a slight speedup per the analysis at https://github.com/phpseclib/phpseclib/pull/317#issuecomment-42122335
This commit is contained in:
terrafrost 2014-05-05 11:34:45 -05:00
parent 431e3a04c7
commit 309c8fd555
1 changed files with 17 additions and 48 deletions
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65
phpseclib/Math/BigInteger.php
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@ -920,7 +920,7 @@ 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 = $this->_carry($sum);
$temp = MATH_BIGINTEGER_BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31);
$value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000)
$value[$j] = $temp;
@ -1056,7 +1056,7 @@ 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 = $this->_carry($sum);
$temp = MATH_BIGINTEGER_BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31);
$x_value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp);
$x_value[$j] = $temp;
@ -1204,7 +1204,7 @@ class Math_BigInteger
for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0
$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -1217,7 +1217,7 @@ class Math_BigInteger
for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) {
$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -1305,13 +1305,13 @@ class Math_BigInteger
$i2 = $i << 1;
$temp = $square_value[$i2] + $value[$i] * $value[$i];
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$square_value[$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 = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$square_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -2195,7 +2195,7 @@ class Math_BigInteger
for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0, $k = $i
$temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -2211,7 +2211,7 @@ class Math_BigInteger
for ($j = 0, $k = $i; $j < $x_length && $k < $stop; ++$j, ++$k) {
$temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
}
@ -2260,7 +2260,7 @@ class Math_BigInteger
for ($i = 0; $i < $k; ++$i) {
$temp = $result[MATH_BIGINTEGER_VALUE][$i] * $cache[MATH_BIGINTEGER_DATA][$key];
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
$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);
@ -2317,9 +2317,9 @@ 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 = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
$temp = $temp * $cache[MATH_BIGINTEGER_DATA][$key];
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * $this->_carry($temp);
$temp = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
$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);
@ -3459,7 +3459,7 @@ class Math_BigInteger
for ($i = 0; $i < count($this->value); ++$i) {
$temp = $this->value[$i] * $shift + $carry;
$carry = $this->_carry($temp);
$carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
$this->value[$i] = (int) ($temp - $carry * MATH_BIGINTEGER_BASE_FULL);
}
@ -3708,45 +3708,14 @@ class Math_BigInteger
return pack('Ca*', 0x80 | strlen($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 (most significant) 26 bits
* because left shift takes in ints, which have 31-bits of usable precision, since PHP does
* signed int32. as a consequence of the above, division takes place
*
* 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()
* Even if int64 is being used the division operator will return a float64 value
* if the dividend is not evenly divisible by the divisor. Since a float64 doesn't
* have the precision of int64 this is a problem so, when int64 is being used,
* we'll guarantee that the dividend is divisible by first subtracting the remainder.
*
* @access private
* @param Integer $x
* @param Integer $y