LibCrypto: Added static non-allocating UnsignedBigInteger operators

This changes the plus, minus, etc... operators from UnsignedBigInteger to use a
static helper method. The static methods do not allocate any variables, instead
all the required BigInteger output and temporary variables are required on call
as parameters.

This change already optimizes the number of allocations in complex operations
such as multiply or divide, by having a single allocation per call (instead of
one per loop).

This new API also provides a way to limit the number of allocations for complex
computations in other parts of the code. This is done by using these helpers in
any place that currently makes use of the standard operators.

Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp

@@ -96,6 +96,21 @@ String UnsignedBigInteger::to_base10() const
     return builder.to_string();
 }
 
+void UnsignedBigInteger::set_to_0()
+{
+    m_words.clear_with_capacity();
+    m_is_invalid = false;
+}
+
+void UnsignedBigInteger::set_to(const UnsignedBigInteger& other)
+{
+    m_is_invalid = other.m_is_invalid;
+    m_words.clear_with_capacity();
+    m_words.ensure_capacity(other.m_words.size());
+    for (size_t i = 0; i < other.m_words.size(); ++i)
+        m_words.unchecked_append(other.m_words[i]);
+}
+
 size_t UnsignedBigInteger::trimmed_length() const
 {
     size_t num_leading_zeroes = 0;
@@ -106,18 +121,135 @@ size_t UnsignedBigInteger::trimmed_length() const
     return length() - num_leading_zeroes;
 }
 
+FLATTEN UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    add_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+
+    subtract_without_allocation(*this, other, result);
+
+    return result;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
+{
+    UnsignedBigInteger output;
+    UnsignedBigInteger temp_result;
+    UnsignedBigInteger temp_plus;
+
+    shift_left_without_allocation(*this, num_bits, temp_result, temp_plus, output);
+
+    return output;
+}
+
+FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
+{
+    UnsignedBigInteger result;
+    UnsignedBigInteger temp_shift_result;
+    UnsignedBigInteger temp_shift_plus;
+    UnsignedBigInteger temp_shift;
+    UnsignedBigInteger temp_plus;
+
+    multiply_without_allocation(*this, other, temp_shift_result, temp_shift_plus, temp_shift, temp_plus, result);
+
+    return result;
+}
+
+FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
+{
+    UnsignedBigInteger quotient;
+    UnsignedBigInteger remainder;
+
+    UnsignedBigInteger temp_shift_result;
+    UnsignedBigInteger temp_shift_plus;
+    UnsignedBigInteger temp_shift;
+    UnsignedBigInteger temp_minus;
+
+    divide_without_allocation(*this, divisor, temp_shift_result, temp_shift_plus, temp_shift, temp_minus, quotient, remainder);
+
+    return UnsignedDivisionResult { quotient, remainder };
+}
+
+void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
+{
+    const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
+    const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
+
+    m_words.ensure_capacity(word_index);
+
+    for (size_t i = length(); i <= word_index; ++i) {
+        m_words.unchecked_append(0);
+    }
+    m_words[word_index] |= (1 << inner_word_index);
+}
+
+bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
+{
+    auto length = trimmed_length();
+
+    if (length != other.trimmed_length()) {
+        return false;
+    }
+
+    if (is_invalid() != other.is_invalid()) {
+        return false;
+    }
+
+    return !__builtin_memcmp(m_words.data(), other.words().data(), length);
+}
+
+bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
+{
+    return !(*this == other);
+}
+
+bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
+{
+    auto length = trimmed_length();
+    auto other_length = other.trimmed_length();
+
+    if (length < other_length) {
+        return true;
+    }
+
+    if (length > other_length) {
+        return false;
+    }
+
+    if (length == 0) {
+        return false;
+    }
+    for (int i = length - 1; i >= 0; --i) {
+        if (m_words[i] == other.m_words[i])
+            continue;
+        return m_words[i] < other.m_words[i];
+    }
+    return false;
+}
+
 /**
  * Complexity: O(N) where N is the number of words in the larger number
  */
-UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) const
+void UnsignedBigInteger::add_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
 {
-    const UnsignedBigInteger* const longer = (length() > other.length()) ? this : &other;
-    const UnsignedBigInteger* const shorter = (longer == &other) ? this : &other;
-    UnsignedBigInteger result;
+    const UnsignedBigInteger* const longer = (left.length() > right.length()) ? &left : &right;
+    const UnsignedBigInteger* const shorter = (longer == &right) ? &left : &right;
 
     u8 carry = 0;
 
-    result.m_words.ensure_capacity(longer->length() + 1);
+    output.set_to_0();
+    output.m_words.ensure_capacity(longer->length() + 1);
 
     for (size_t i = 0; i < shorter->length(); ++i) {
         u32 word_addition_result = shorter->m_words[i] + longer->m_words[i];
@@ -130,7 +262,7 @@ UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) con
             word_addition_result++;
         }
         carry = carry_out;
-        result.m_words.unchecked_append(word_addition_result);
+        output.m_words.unchecked_append(word_addition_result);
     }
 
     for (size_t i = shorter->length(); i < longer->length(); ++i) {
@@ -140,97 +272,130 @@ UnsignedBigInteger UnsignedBigInteger::plus(const UnsignedBigInteger& other) con
         if (word_addition_result < longer->m_words[i]) {
             carry = 1;
         }
-        result.m_words.unchecked_append(word_addition_result);
+        output.m_words.unchecked_append(word_addition_result);
     }
     if (carry) {
-        result.m_words.unchecked_append(carry);
+        output.m_words.unchecked_append(carry);
     }
-    return result;
 }
 
 /**
  * Complexity: O(N) where N is the number of words in the larger number
  */
-UnsignedBigInteger UnsignedBigInteger::minus(const UnsignedBigInteger& other) const
+void UnsignedBigInteger::subtract_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& output)
 {
-    UnsignedBigInteger result;
-
-    if (*this < other) {
-        return UnsignedBigInteger::create_invalid();
+    if (left < right) {
+        output.invalidate();
+        return;
     }
 
     u8 borrow = 0;
-    auto own_length = length(), other_length = other.length();
+    auto own_length = left.length();
+    auto other_length = right.length();
 
-    result.m_words.ensure_capacity(own_length);
+    output.set_to_0();
+    output.m_words.ensure_capacity(own_length);
 
     for (size_t i = 0; i < own_length; ++i) {
-        u32 other_word = (i < other_length) ? other.m_words[i] : 0;
-        i64 temp = static_cast<i64>(m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
+        u32 other_word = (i < other_length) ? right.m_words[i] : 0;
+        i64 temp = static_cast<i64>(left.m_words[i]) - static_cast<i64>(other_word) - static_cast<i64>(borrow);
         // If temp < 0, we had an underflow
         borrow = (temp >= 0) ? 0 : 1;
         if (temp < 0) {
             temp += (UINT32_MAX + 1);
         }
-        result.m_words.append(temp);
+        output.m_words.append(temp);
     }
 
     // This assertion should not fail, because we verified that *this>=other at the beginning of the function
     ASSERT(borrow == 0);
-
-    return result;
 }
 
-UnsignedBigInteger UnsignedBigInteger::shift_left(size_t num_bits) const
+/**
+ * Complexity : O(N + num_bits % 8) where N is the number of words in the number
+ * Shift method :
+ * Start by shifting by whole words in num_bits (by putting missing words at the start),
+ * then shift the number's words two by two by the remaining amount of bits.
+ */
+FLATTEN void UnsignedBigInteger::shift_left_without_allocation(
+    const UnsignedBigInteger& number,
+    size_t num_bits,
+    UnsignedBigInteger& temp_result,
+    UnsignedBigInteger& temp_plus,
+    UnsignedBigInteger& output)
 {
     // We can only do shift operations on individual words
     // where the shift amount is <= size of word (32).
     // But we do know how to shift by a multiple of word size (e.g 64=32*2)
     // So we first shift the result by how many whole words fit in 'num_bits'
-    UnsignedBigInteger temp_result = shift_left_by_n_words(num_bits / UnsignedBigInteger::BITS_IN_WORD);
+    shift_left_by_n_words(number, num_bits / UnsignedBigInteger::BITS_IN_WORD, temp_result);
+
+    output.set_to(temp_result);
 
     // And now we shift by the leftover amount of bits
     num_bits %= UnsignedBigInteger::BITS_IN_WORD;
 
-    UnsignedBigInteger result(temp_result);
+    if (num_bits == 0) {
+        return;
+    }
 
     for (size_t i = 0; i < temp_result.length(); ++i) {
-        u32 current_word_of_temp_result = temp_result.shift_left_get_one_word(num_bits, i);
-        result.m_words[i] = current_word_of_temp_result;
+        u32 current_word_of_temp_result = shift_left_get_one_word(temp_result, num_bits, i);
+        output.m_words[i] = current_word_of_temp_result;
     }
 
     // Shifting the last word can produce a carry
-    u32 carry_word = temp_result.shift_left_get_one_word(num_bits, temp_result.length());
+    u32 carry_word = shift_left_get_one_word(temp_result, num_bits, temp_result.length());
     if (carry_word != 0) {
-        result = result.plus(UnsignedBigInteger(carry_word).shift_left_by_n_words(temp_result.length()));
+
+        // output += (carry_word << temp_result.length())
+        // FIXME : Using temp_plus this way to transform carry_word into a bigint is not
+        // efficient nor pretty. Maybe we should have an "add_with_shift" method ?
+        temp_plus.set_to_0();
+        temp_plus.m_words.append(carry_word);
+        shift_left_by_n_words(temp_plus, temp_result.length(), temp_result);
+        add_without_allocation(output, temp_result, temp_plus);
+        output.set_to(temp_plus);
     }
-    return result;
 }
 
 /**
  * Complexity: O(N^2) where N is the number of words in the larger number
- * Multiplcation method:
+ * Multiplication method:
  * An integer is equal to the sum of the powers of two
  * according to the indexes of its 'on' bits.
  * So to multiple x*y, we go over each '1' bit in x (say the i'th bit), 
  * and add y<<i to the result.
  */
-FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigInteger& other) const
+FLATTEN void UnsignedBigInteger::multiply_without_allocation(
+    const UnsignedBigInteger& left,
+    const UnsignedBigInteger& right,
+    UnsignedBigInteger& temp_shift_result,
+    UnsignedBigInteger& temp_shift_plus,
+    UnsignedBigInteger& temp_shift,
+    UnsignedBigInteger& temp_plus,
+    UnsignedBigInteger& output)
 {
-    UnsignedBigInteger result;
+    output.set_to_0();
+
     // iterate all bits
-    for (size_t word_index = 0; word_index < length(); ++word_index) {
+    for (size_t word_index = 0; word_index < left.length(); ++word_index) {
         for (size_t bit_index = 0; bit_index < UnsignedBigInteger::BITS_IN_WORD; ++bit_index) {
             // If the bit is off - skip over it
-            if (!(m_words[word_index] & (1 << bit_index)))
+            if (!(left.m_words[word_index] & (1 << bit_index)))
                 continue;
 
             const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
-            auto shift_result = other.shift_left(shift_amount);
-            result = result.plus(shift_result);
+
+            // output += (right << shift_amount);
+            shift_left_without_allocation(right, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
+            add_without_allocation(output, temp_shift, temp_plus);
+            output.set_to(temp_plus);
         }
     }
-    return result;
 }
 
 /**
@@ -241,118 +406,71 @@ FLATTEN UnsignedBigInteger UnsignedBigInteger::multiplied_by(const UnsignedBigIn
  * so we set the ith bit in the quotient and reduce divisor<<i from the dividend.
  * When we're done, what's left from the dividend is the remainder.
  */
-FLATTEN UnsignedDivisionResult UnsignedBigInteger::divided_by(const UnsignedBigInteger& divisor) const
+FLATTEN void UnsignedBigInteger::divide_without_allocation(
+    const UnsignedBigInteger& numerator,
+    const UnsignedBigInteger& denominator,
+    UnsignedBigInteger& temp_shift_result,
+    UnsignedBigInteger& temp_shift_plus,
+    UnsignedBigInteger& temp_shift,
+    UnsignedBigInteger& temp_minus,
+    UnsignedBigInteger& quotient,
+    UnsignedBigInteger& remainder)
 {
-    UnsignedBigInteger leftover_dividend(*this);
-    UnsignedBigInteger quotient;
+    quotient.set_to_0();
+    remainder.set_to(numerator);
 
     // iterate all bits
-    for (int word_index = trimmed_length() - 1; word_index >= 0; --word_index) {
+    for (int word_index = numerator.trimmed_length() - 1; word_index >= 0; --word_index) {
         for (int bit_index = UnsignedBigInteger::BITS_IN_WORD - 1; bit_index >= 0; --bit_index) {
-
             const size_t shift_amount = word_index * UnsignedBigInteger::BITS_IN_WORD + bit_index;
-            UnsignedBigInteger divisor_shifted = divisor.shift_left(shift_amount);
+            shift_left_without_allocation(denominator, shift_amount, temp_shift_result, temp_shift_plus, temp_shift);
 
-            UnsignedBigInteger temp_subtraction_result = leftover_dividend.minus(divisor_shifted);
-            if (!temp_subtraction_result.is_invalid()) {
-                leftover_dividend = temp_subtraction_result;
+            subtract_without_allocation(remainder, temp_shift, temp_minus);
+            if (!temp_minus.is_invalid()) {
+                remainder.set_to(temp_minus);
                 quotient.set_bit_inplace(shift_amount);
             }
         }
     }
-    return UnsignedDivisionResult { quotient, leftover_dividend };
-}
-
-void UnsignedBigInteger::set_bit_inplace(size_t bit_index)
-{
-    const size_t word_index = bit_index / UnsignedBigInteger::BITS_IN_WORD;
-    const size_t inner_word_index = bit_index % UnsignedBigInteger::BITS_IN_WORD;
-
-    m_words.ensure_capacity(word_index);
-
-    for (size_t i = length(); i <= word_index; ++i) {
-        m_words.unchecked_append(0);
-    }
-    m_words[word_index] |= (1 << inner_word_index);
 }
 
-bool UnsignedBigInteger::operator==(const UnsignedBigInteger& other) const
-{
-    auto length = trimmed_length();
-
-    if (length != other.trimmed_length()) {
-        return false;
-    }
-
-    if (is_invalid() != other.is_invalid()) {
-        return false;
-    }
-
-    return !__builtin_memcmp(m_words.data(), other.words().data(), length);
-}
-
-bool UnsignedBigInteger::operator!=(const UnsignedBigInteger& other) const
-{
-    return !(*this == other);
-}
-
-bool UnsignedBigInteger::operator<(const UnsignedBigInteger& other) const
-{
-    auto length = trimmed_length();
-    auto other_length = other.trimmed_length();
-
-    if (length < other_length) {
-        return true;
-    }
-
-    if (length > other_length) {
-        return false;
-    }
-
-    if (length == 0) {
-        return false;
-    }
-    for (int i = length - 1; i >= 0; --i) {
-        if (m_words[i] == other.m_words[i])
-            continue;
-        return m_words[i] < other.m_words[i];
-    }
-    return false;
-}
-
-ALWAYS_INLINE UnsignedBigInteger UnsignedBigInteger::shift_left_by_n_words(const size_t number_of_words) const
+ALWAYS_INLINE void UnsignedBigInteger::shift_left_by_n_words(
+    const UnsignedBigInteger& number,
+    const size_t number_of_words,
+    UnsignedBigInteger& output)
 {
     // shifting left by N words means just inserting N zeroes to the beginning of the words vector
-    UnsignedBigInteger result;
-
-    result.m_words.ensure_capacity(number_of_words + length());
+    output.set_to_0();
+    output.m_words.ensure_capacity(number_of_words + number.length());
 
     for (size_t i = 0; i < number_of_words; ++i) {
-        result.m_words.unchecked_append(0);
+        output.m_words.unchecked_append(0);
     }
-    for (size_t i = 0; i < length(); ++i) {
-        result.m_words.unchecked_append(m_words[i]);
+    for (size_t i = 0; i < number.length(); ++i) {
+        output.m_words.unchecked_append(number.m_words[i]);
     }
-    return result;
 }
 
 /**
  * Returns the word at a requested index in the result of a shift operation
  */
-ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(const size_t num_bits, const size_t result_word_index) const
+ALWAYS_INLINE u32 UnsignedBigInteger::shift_left_get_one_word(
+    const UnsignedBigInteger& number,
+    const size_t num_bits,
+    const size_t result_word_index)
 {
     // "<= length()" (rather than length() - 1) is intentional,
     // The result inedx of length() is used when calculating the carry word
-    ASSERT(result_word_index <= length());
+    ASSERT(result_word_index <= number.length());
     ASSERT(num_bits <= UnsignedBigInteger::BITS_IN_WORD);
     u32 result = 0;
 
     // we need to check for "num_bits != 0" since shifting right by 32 is apparently undefined behaviour!
     if (result_word_index > 0 && num_bits != 0) {
-        result += m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
+        result += number.m_words[result_word_index - 1] >> (UnsignedBigInteger::BITS_IN_WORD - num_bits);
     }
-    if (result_word_index < length() && num_bits < 32) {
-        result += m_words[result_word_index] << num_bits;
+    if (result_word_index < number.length() && num_bits < 32) {
+        result += number.m_words[result_word_index] << num_bits;
     }
     return result;
 }

Libraries/LibCrypto/BigInt/UnsignedBigInteger.h

@@ -64,6 +64,8 @@ public:
 
     const AK::Vector<u32, STARTING_WORD_SIZE>& words() const { return m_words; }
 
+    void set_to_0();
+    void set_to(const UnsignedBigInteger& other);
     void invalidate() { m_is_invalid = true; }
 
     bool is_invalid() const { return m_is_invalid; }
@@ -80,13 +82,19 @@ public:
 
     void set_bit_inplace(size_t bit_index);
 
+    static void add_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void subtract_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& output);
+    static void shift_left_without_allocation(const UnsignedBigInteger& number, size_t bits_to_shift_by, UnsignedBigInteger& temp_result, UnsignedBigInteger& temp_plus, UnsignedBigInteger& output);
+    static void multiply_without_allocation(const UnsignedBigInteger& left, const UnsignedBigInteger& right, UnsignedBigInteger& temp_shift_result, UnsignedBigInteger& temp_shift_plus, UnsignedBigInteger& temp_shift, UnsignedBigInteger& temp_plus, UnsignedBigInteger& output);
+    static void divide_without_allocation(const UnsignedBigInteger& numerator, const UnsignedBigInteger& denominator, UnsignedBigInteger& temp_shift_result, UnsignedBigInteger& temp_shift_plus, UnsignedBigInteger& temp_shift, UnsignedBigInteger& temp_minus, UnsignedBigInteger& quotient, UnsignedBigInteger& remainder);
+
     bool operator==(const UnsignedBigInteger& other) const;
     bool operator!=(const UnsignedBigInteger& other) const;
     bool operator<(const UnsignedBigInteger& other) const;
 
 private:
-    ALWAYS_INLINE UnsignedBigInteger shift_left_by_n_words(const size_t number_of_words) const;
-    ALWAYS_INLINE u32 shift_left_get_one_word(const size_t num_bits, const size_t result_word_index) const;
+    ALWAYS_INLINE static void shift_left_by_n_words(const UnsignedBigInteger& number, size_t number_of_words, UnsignedBigInteger& output);
+    ALWAYS_INLINE static u32 shift_left_get_one_word(const UnsignedBigInteger& number, size_t num_bits, size_t result_word_index);
 
     static constexpr size_t BITS_IN_WORD = 32;
     AK::Vector<u32, STARTING_WORD_SIZE> m_words;