From e4ff01f05475e81a56681ebfdb5473a07099e5ea Mon Sep 17 00:00:00 2001 From: terrafrost Date: Wed, 23 Apr 2014 16:57:20 -0500 Subject: [PATCH 1/2] BigInteger: fix some int64 issues --- phpseclib/Math/BigInteger.php | 85 ++++++++++++++++++++++++++++------- 1 file changed, 69 insertions(+), 16 deletions(-) diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php index 51eac0de..0916ab76 100644 --- a/phpseclib/Math/BigInteger.php +++ b/phpseclib/Math/BigInteger.php @@ -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; + } } From 9eb6e1ed67a7a2988ed7d3cb914dc9bccc5b7c0d Mon Sep 17 00:00:00 2001 From: terrafrost Date: Wed, 23 Apr 2014 23:13:27 -0500 Subject: [PATCH 2/2] BigInteger: update comments and add test case --- phpseclib/Math/BigInteger.php | 14 +++++--------- tests/Math/BigInteger/InternalTest.php | 7 +++++++ 2 files changed, 12 insertions(+), 9 deletions(-) diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php index 0916ab76..345945d6 100644 --- a/phpseclib/Math/BigInteger.php +++ b/phpseclib/Math/BigInteger.php @@ -19,10 +19,6 @@ * which only supports integers. Although this fact will slow this library down, the fact that such a high * base is being used should more than compensate. * - * When PHP version 6 is officially released, we'll be able to use 64-bit integers. This should, once again, - * allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition / - * subtraction). - * * Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian} format. ie. * (new Math_BigInteger(pow(2, 26)))->value = array(0, 1) * @@ -3715,12 +3711,12 @@ class Math_BigInteger /** * 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 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 + * 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. diff --git a/tests/Math/BigInteger/InternalTest.php b/tests/Math/BigInteger/InternalTest.php index b0292319..744b2df1 100644 --- a/tests/Math/BigInteger/InternalTest.php +++ b/tests/Math/BigInteger/InternalTest.php @@ -14,4 +14,11 @@ class Math_BigInteger_InternalTest extends Math_BigInteger_TestCase self::ensureConstant('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_INTERNAL); self::ensureConstant('MATH_BIGINTEGER_OPENSSL_DISABLE', true); } + + public function testInternalRepresentation() + { + $x = new Math_BigInteger('FFFFFFFFFFFFFFFFC90FDA', 16); + $y = new Math_BigInteger("$x"); + $this->assertSame($x->value, $y->value); + } }