LibCrypto: Add a simple SignedBigInteger

This patchset adds a simple SignedBigInteger that is entirely defined in
terms of UnsignedBigInteger.

It also adds a NumberTheory::Power function, which is terribly
inefficient, but since the use of exponentiation is very much
discouraged for large inputs, no particular attempts were made
to make it more performant.

Libraries/LibCrypto/BigInt/SignedBigInteger.h

@@ -0,0 +1,159 @@
+/*
+ * Copyright (c) 2020, the SerenityOS developers.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice, this
+ *    list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ *    this list of conditions and the following disclaimer in the documentation
+ *    and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+ * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+ * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#pragma once
+
+#include <LibCrypto/BigInt/UnsignedBigInteger.h>
+
+namespace Crypto {
+
+struct SignedDivisionResult;
+
+class SignedBigInteger {
+public:
+    SignedBigInteger(i32 x)
+        : m_sign(x < 0)
+        , m_unsigned_data(abs(x))
+    {
+    }
+
+    SignedBigInteger(UnsignedBigInteger&& unsigned_data, bool sign)
+        : m_sign(sign)
+        , m_unsigned_data(move(unsigned_data))
+    {
+    }
+
+    explicit SignedBigInteger(UnsignedBigInteger unsigned_data)
+        : m_sign(false)
+        , m_unsigned_data(move(unsigned_data))
+    {
+    }
+
+    SignedBigInteger()
+        : m_sign(false)
+        , m_unsigned_data()
+    {
+    }
+
+    static SignedBigInteger create_invalid()
+    {
+        return { UnsignedBigInteger::create_invalid(), false };
+    }
+
+    static SignedBigInteger import_data(const AK::StringView& data) { return import_data((const u8*)data.characters_without_null_termination(), data.length()); }
+    static SignedBigInteger import_data(const u8* ptr, size_t length);
+
+    size_t export_data(AK::ByteBuffer& data) const;
+    size_t export_data(const u8* ptr, size_t length) const
+    {
+        auto buffer = ByteBuffer::wrap(ptr, length);
+        return export_data(buffer);
+    }
+
+    static SignedBigInteger from_base10(StringView str);
+    String to_base10() const;
+
+    const UnsignedBigInteger& unsigned_value() const { return m_unsigned_data; }
+    const Vector<u32, STARTING_WORD_SIZE> words() const { return m_unsigned_data.words(); }
+    bool is_negative() const { return m_sign; }
+
+    void negate() { m_sign = !m_sign; }
+
+    void set_to_0() { m_unsigned_data.set_to_0(); }
+    void set_to(i32 other)
+    {
+        m_unsigned_data.set_to((u32)other);
+        m_sign = other < 0;
+    }
+    void set_to(const SignedBigInteger& other)
+    {
+        m_unsigned_data.set_to(other.m_unsigned_data);
+        m_sign = other.m_sign;
+    }
+
+    void invalidate()
+    {
+        m_unsigned_data.invalidate();
+    }
+
+    bool is_invalid() const { return m_unsigned_data.is_invalid(); }
+
+    // These get + 1 byte for the sign.
+    size_t length() const { return m_unsigned_data.length() + 1; }
+    size_t trimmed_length() const { return m_unsigned_data.trimmed_length() + 1; };
+
+    SignedBigInteger plus(const SignedBigInteger& other) const;
+    SignedBigInteger minus(const SignedBigInteger& other) const;
+    SignedBigInteger shift_left(size_t num_bits) const;
+    SignedBigInteger multiplied_by(const SignedBigInteger& other) const;
+    SignedDivisionResult divided_by(const SignedBigInteger& divisor) const;
+
+    SignedBigInteger plus(const UnsignedBigInteger& other) const;
+    SignedBigInteger minus(const UnsignedBigInteger& other) const;
+    SignedBigInteger multiplied_by(const UnsignedBigInteger& other) const;
+    SignedDivisionResult divided_by(const UnsignedBigInteger& divisor) const;
+
+    void set_bit_inplace(size_t bit_index);
+
+    bool operator==(const SignedBigInteger& other) const;
+    bool operator!=(const SignedBigInteger& other) const;
+    bool operator<(const SignedBigInteger& other) const;
+
+    bool operator==(const UnsignedBigInteger& other) const;
+    bool operator!=(const UnsignedBigInteger& other) const;
+    bool operator<(const UnsignedBigInteger& other) const;
+
+private:
+    bool m_sign { false };
+    UnsignedBigInteger m_unsigned_data;
+};
+
+struct SignedDivisionResult {
+    Crypto::SignedBigInteger quotient;
+    Crypto::SignedBigInteger remainder;
+};
+
+}
+
+inline const LogStream&
+operator<<(const LogStream& stream, const Crypto::SignedBigInteger value)
+{
+    if (value.is_invalid()) {
+        stream << "Invalid BigInt";
+        return stream;
+    }
+    if (value.is_negative())
+        stream << "-";
+
+    stream << value.unsigned_value();
+    return stream;
+}
+
+inline Crypto::SignedBigInteger
+operator""_sbigint(const char* string, size_t length)
+{
+    return Crypto::SignedBigInteger::from_base10({ string, length });
+}