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authorlloyd <[email protected]>2009-11-18 03:53:33 +0000
committerlloyd <[email protected]>2009-11-18 03:53:33 +0000
commit09c2c8502ee8ea3c9eb39041c07953bb0afec4ea (patch)
tree50ea67252cd57f2749ef55be96e9a9a09c1cf036 /src/math
parent32d8a82ab0785e55b00b82d029f50d13e00418ce (diff)
Clean up BigInt doxygen comments
Diffstat (limited to 'src/math')
-rw-r--r--src/math/bigint/bigint.h929
1 files changed, 458 insertions, 471 deletions
diff --git a/src/math/bigint/bigint.h b/src/math/bigint/bigint.h
index 16a1bba96..83986e0f1 100644
--- a/src/math/bigint/bigint.h
+++ b/src/math/bigint/bigint.h
@@ -17,472 +17,459 @@
namespace Botan {
/**
- * Big Integer representation. This class defines an integer type,
- * that can be very big. Additionally some helper functions are
- * defined to work more comfortably.
-
- */
+* Arbitrary precision integer
+*/
class BOTAN_DLL BigInt
{
public:
- /**
- * Base-Enumerator (currently 8,10,16 and 256 are defined)
- */
- enum Base { Octal = 8, Decimal = 10, Hexadecimal = 16, Binary = 256 };
-
- /**
- * Sign symbol definitions for positive and negative numbers
- */
- enum Sign { Negative = 0, Positive = 1 };
-
- /**
- * Number types (Powers of 2)
- */
- enum NumberType { Power2 };
-
- /**
- * DivideByZero Exception
- */
- struct DivideByZero : public Exception
- { DivideByZero() : Exception("BigInt divide by zero") {} };
-
- /*************
- * operators
- *************/
-
- /**
- * += Operator
- * @param y the BigInt to add to the local value
- */
- BigInt& operator+=(const BigInt& y);
-
- /**
- * -= Operator
- * @param y the BigInt to subtract from the local value
- */
- BigInt& operator-=(const BigInt& y);
-
- /**
- * *= Operator
- * @param y the BigInt to multiply with the local value
- */
- BigInt& operator*=(const BigInt& y);
-
- /**
- * /= Operator
- * @param y the BigInt to divide the local value by
- */
- BigInt& operator/=(const BigInt& y);
-
- /**
- * %= Operator, modulo operator.
- * @param y the modulus to reduce the local value by
- */
- BigInt& operator%=(const BigInt& y);
-
- /**
- * %= Operator
- * @param y the modulus (word) to reduce the local value by
- */
- word operator%=(word y);
-
- /**
- * <<= Operator
- * @param y the amount of bits to shift the local value left
- */
- BigInt& operator<<=(u32bit y);
-
- /**
- * >>= Operator
- * @param y the amount of bits to shift the local value right
- */
- BigInt& operator>>=(u32bit y);
-
- /**
- * ++ Operator
- */
- BigInt& operator++() { return (*this += 1); }
-
- /**
- * -- Operator
- */
- BigInt& operator--() { return (*this -= 1); }
-
- /**
- * ++ Operator (postfix)
- */
- BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; }
-
- /**
- * -- Operator (postfix)
- */
- BigInt operator--(int) { BigInt x = (*this); --(*this); return x; }
-
- /**
- * - Operator
- */
- BigInt operator-() const;
-
- /**
- * ! Operator
- */
- bool operator !() const { return (!is_nonzero()); }
-
- /**
- * [] Operator (array access)
- */
- word& operator[](u32bit i) { return reg[i]; }
-
- /**
- * [] Operator (array access)
- */
- word operator[](u32bit i) const { return reg[i]; }
-
- /**
- * Zeroize the BigInt
- */
- void clear() { get_reg().clear(); }
-
- /*************
- * functions
- ************/
-
- /**
- * Compare *this to another BigInt.
- * @param n the BigInt value to compare to the local value.
- * @param check_signs Include sign in comparison?
- * @result if (this<n) return -1, if (this>n) return 1, if both
- * values are identical return 0.
- */
- s32bit cmp(const BigInt& n, bool check_signs = true) const;
-
- /**
- * Test if the integer has an even value
- * @result true, if the integer an even value, false otherwise
- */
- bool is_even() const { return (get_bit(0) == 0); }
-
- /**
- * Test if the integer has an odd value
- * @result true, if the integer an odd value, false otherwise
- */
- bool is_odd() const { return (get_bit(0) == 1); }
-
- /**
- * Test if the integer is not zero.
- * @result true, if the integer has a non-zero value, false otherwise
- */
- bool is_nonzero() const { return (!is_zero()); }
-
- /**
- * Test if the integer is zero.
- * @result true, if the integer has the value zero, false otherwise
- */
- bool is_zero() const
- {
- const u32bit sw = sig_words();
-
- for(u32bit i = 0; i != sw; ++i)
- if(reg[i])
- return false;
- return true;
- }
-
- /**
- * Set bit at specified position
- * @param n bit position to set
- */
- void set_bit(u32bit n);
-
- /**
- * Clear bit at specified position
- * @param n bit position to clear
- */
- void clear_bit(u32bit n);
-
- /**
- * Clear all but the lowest n bits
- * @param n amount of bits to keep
- */
- void mask_bits(u32bit n);
-
- /**
- * Return bit value at specified position
- * @param n the bit offset to test
- * @result true, if the bit at position n is set, false otherwise
- */
- bool get_bit(u32bit n) const;
-
- /**
- * Return (a maximum of) 32 bits of the complete value
- * @param offset the offset to start extracting
- * @param length amount of bits to extract (starting at offset)
- * @result the integer extracted from the register starting at
- * offset with specified length
- */
- u32bit get_substring(u32bit offset, u32bit length) const;
-
- byte byte_at(u32bit) const;
-
- /**
- * Return the word at a specified position of the internal register
- * @param n position in the register
- * @return the value at position n
- */
- word word_at(u32bit n) const
- { return ((n < size()) ? reg[n] : 0); }
-
- /**
- * Return the integer as an unsigned 32bit-integer-value. If the
- * value is negative OR to big to be stored in 32bits, this
- * function will throw an exception.
- * @result a 32bit-integer
- */
- u32bit to_u32bit() const;
-
- /**
- * Tests if the sign of the integer is negative.
- * @result true, if the integer has a negative sign,
- */
- bool is_negative() const { return (sign() == Negative); }
-
- /**
- * Tests if the sign of the integer is positive.
- * @result true, if the integer has a positive sign,
- */
- bool is_positive() const { return (sign() == Positive); }
-
- /**
- * Return the sign of the integer
- * @result the sign of the integer
- */
- Sign sign() const { return (signedness); }
-
- /**
- * Return the opposite sign of the represented integer value
- * @result the opposite sign of the represented integer value
- */
- Sign reverse_sign() const;
-
- /**
- * Flip (change!) the sign of the integer to its opposite value
- */
- void flip_sign();
-
- /**
- * Set sign of the integer
- * @param sign new Sign to set
- */
- void set_sign(Sign sign);
-
- /**
- * Give absolute (positive) value of the integer
- * @result absolute (positive) value of the integer
- */
- BigInt abs() const;
-
- /**
- * Give size of internal register
- * @result size of internal register in words
- */
- u32bit size() const { return get_reg().size(); }
-
- /**
- * Give significant words of the represented integer value
- * @result significant words of the represented integer value
- */
- u32bit sig_words() const
- {
- const word* x = reg.begin();
- u32bit sig = reg.size();
-
- while(sig && (x[sig-1] == 0))
- sig--;
- return sig;
- }
-
- /**
- * Give byte-length of the integer
- * @result byte-length of the represented integer value
- */
- u32bit bytes() const;
-
- /**
- * Get the bit-length of the integer.
- * @result bit-length of the represented integer value
- */
- u32bit bits() const;
-
- /**
- * Return a pointer to the big integer word register.
- * @result a pointer to the start of the internal register of
- * the integer value
- */
- const word* data() const { return reg.begin(); }
-
- /**
- * return a reference to the internal register containing the value
- * @result a reference to the word-array (SecureVector<word>)
- * with the internal register value (containing the integer
- * value)
- */
- SecureVector<word>& get_reg() { return reg; }
-
- /**
- * return a const reference to the internal register containing the value
- * @result a const reference to the word-array (SecureVector<word>)
- * with the internal register value (containing the integer
- * value)
- */
- const SecureVector<word>& get_reg() const { return reg; }
-
- /**
- * Increase internal register buffer by n words
- * @param n increase by n words
- */
- void grow_reg(u32bit n);
-
- void grow_to(u32bit n);
-
- /**
- * Fill BigInt with a random number with size of bitsize
- * @param rng the random number generator to use
- * @param bitsize number of bits the created random value should have
- */
- void randomize(RandomNumberGenerator& rng, u32bit bitsize = 0);
-
- /**
- * Store BigInt-value in a given byte array
- * @param buf destination byte array for the integer value
- */
- void binary_encode(byte buf[]) const;
-
- /**
- * Read integer value from a byte array with given size
- * @param buf byte array buffer containing the integer
- * @param length size of buf
- */
- void binary_decode(const byte buf[], u32bit length);
-
- /**
- * Read integer value from a byte array (MemoryRegion<byte>)
- * @param buf the BigInt value to compare to the local value.
- */
- void binary_decode(const MemoryRegion<byte>& buf);
-
- u32bit encoded_size(Base = Binary) const;
-
- /**
- @param rng a random number generator
- @result a random integer between min and max
- */
- static BigInt random_integer(RandomNumberGenerator& rng,
- const BigInt& min, const BigInt& max);
-
- /**
- * Encode the integer value from a BigInt to a SecureVector of bytes
- * @param n the BigInt to use as integer source
- * @param base number-base of resulting byte array representation
- * @result SecureVector of bytes containing the integer with given base
- */
- static SecureVector<byte> encode(const BigInt& n, Base base = Binary);
-
- /**
- * Encode the integer value from a BigInt to a byte array
- * @param buf destination byte array for the encoded integer
- * value with given base
- * @param n the BigInt to use as integer source
- * @param base number-base of resulting byte array representation
- */
- static void encode(byte buf[], const BigInt& n, Base base = Binary);
-
- /**
- * Create a BigInt from an integer in a byte array
- * @param buf the BigInt value to compare to the local value.
- * @param length size of buf
- * @param base number-base of the integer in buf
- * @result BigInt-representing the given integer read from the byte array
- */
- static BigInt decode(const byte buf[], u32bit length,
- Base base = Binary);
-
- static BigInt decode(const MemoryRegion<byte>&, Base = Binary);
-
- /**
- * Encode a Big Integer to a byte array according to IEEE1363.
- * @param n the Big Integer to encode
- * @param bytes the length of the resulting SecureVector<byte>
- * @result a SecureVector<byte> containing the encoded Big Integer
- */
- static SecureVector<byte> encode_1363(const BigInt& n, u32bit bytes);
-
- /**
- * Swap BigInt-value with given BigInt.
- * @param bigint the BigInt to swap values with
- */
- void swap(BigInt& bigint);
-
- /**
- * constructors
- */
-
- /**
- * Create empty BigInt
- */
- BigInt() { signedness = Positive; }
-
- /**
- * Create BigInt from 64bit-Integer value
- * @param n 64bit-integer
- */
- BigInt(u64bit n);
-
- /**
- * Copy-Constructor: clone given BigInt
- * @param bigint the BigInt to clone
- */
- BigInt(const BigInt& bigint);
-
- /**
- * Create BigInt from a string.
- * If the string starts with 0x the rest of the string will be
- * interpreted as hexadecimal digits.
- * If the string starts with 0 and the second character is NOT
- * an 'x' the string will be interpreted as octal digits.
- * If the string starts with non-zero digit, it will be
- * interpreted as a decimal number.
- * @param str the string to parse for an integer value
- */
- BigInt(const std::string& str);
-
- /**
- * Create a BigInt from an integer in a byte array
- * @param buf the BigInt value to compare to the local value.
- * @param length size of buf
- * @param base number-base of the integer in buf
- */
- BigInt(const byte buf[], u32bit length, Base base = Binary);
-
- /**
- * Create a random BigInt of the specified size
- * @param rng random number generator
- * @param bits size in bits
- */
- BigInt(RandomNumberGenerator& rng, u32bit bits);
-
- /**
- * Create BigInt from unsigned 32 bit integer value and an
- * also specify the sign of the value
- * @param n integer value
- */
- BigInt(Sign, u32bit n);
-
- /**
- * Create a number of the specified type and size
- * @param type the type of number to create
- * @param n the size
- */
- BigInt(NumberType type, u32bit n);
+ /**
+ * Base enumerator for encoding and decoding
+ */
+ enum Base { Octal = 8, Decimal = 10, Hexadecimal = 16, Binary = 256 };
+
+ /**
+ * Sign symbol definitions for positive and negative numbers
+ */
+ enum Sign { Negative = 0, Positive = 1 };
+
+ /**
+ * Number types (currently only power-of-2 supported)
+ */
+ enum NumberType { Power2 };
+
+ /**
+ * DivideByZero Exception
+ */
+ struct DivideByZero : public Exception
+ { DivideByZero() : Exception("BigInt divide by zero") {} };
+
+ /**
+ * += Operator
+ * @param y the BigInt to add to this
+ */
+ BigInt& operator+=(const BigInt& y);
+
+ /**
+ * -= Operator
+ * @param y the BigInt to subtract from this
+ */
+ BigInt& operator-=(const BigInt& y);
+
+ /**
+ * *= Operator
+ * @param y the BigInt to multiply with this
+ */
+ BigInt& operator*=(const BigInt& y);
+
+ /**
+ * /= Operator
+ * @param y the BigInt to divide this by
+ */
+ BigInt& operator/=(const BigInt& y);
+
+ /**
+ * %= Operator, modulo operator.
+ * @param y the modulus to reduce this by
+ */
+ BigInt& operator%=(const BigInt& y);
+
+ /**
+ * %= Operator
+ * @param y the modulus (word) to reduce this by
+ */
+ word operator%=(word y);
+
+ /**
+ * <<= Operator
+ * @param y the amount of bits to shift this left
+ */
+ BigInt& operator<<=(u32bit y);
+
+ /**
+ * >>= Operator
+ * @param y the amount of bits to shift this right
+ */
+ BigInt& operator>>=(u32bit y);
+
+ /**
+ * ++ Operator
+ */
+ BigInt& operator++() { return (*this += 1); }
+
+ /**
+ * -- Operator
+ */
+ BigInt& operator--() { return (*this -= 1); }
+
+ /**
+ * ++ Operator (postfix)
+ */
+ BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; }
+
+ /**
+ * -- Operator (postfix)
+ */
+ BigInt operator--(int) { BigInt x = (*this); --(*this); return x; }
+
+ /**
+ * Unary - Operator
+ */
+ BigInt operator-() const;
+
+ /**
+ * ! Operator
+ */
+ bool operator !() const { return (!is_nonzero()); }
+
+ /**
+ * [] Operator (array access)
+ */
+ word& operator[](u32bit i) { return reg[i]; }
+
+ /**
+ * [] Operator (array access)
+ */
+ word operator[](u32bit i) const { return reg[i]; }
+
+ /**
+ * Zeroize the BigInt
+ */
+ void clear() { get_reg().clear(); }
+
+ /**
+ * Compare *this to another BigInt.
+ * @param n the BigInt value to compare to this.
+ * @param check_signs include sign in comparison?
+ * @result if (this<n) return -1, if (this>n) return 1, if both
+ * values are identical return 0 [like Perl's <=> operator]
+ */
+ s32bit cmp(const BigInt& n, bool check_signs = true) const;
+
+ /**
+ * Test if the integer has an even value
+ * @result true if the integer is even, false otherwise
+ */
+ bool is_even() const { return (get_bit(0) == 0); }
+
+ /**
+ * Test if the integer has an odd value
+ * @result true if the integer is odd, false otherwise
+ */
+ bool is_odd() const { return (get_bit(0) == 1); }
+
+ /**
+ * Test if the integer is not zero.
+ * @result true if the integer is non-zero, false otherwise
+ */
+ bool is_nonzero() const { return (!is_zero()); }
+
+ /**
+ * Test if the integer is zero.
+ * @result true if the integer is zero, false otherwise
+ */
+ bool is_zero() const
+ {
+ const u32bit sw = sig_words();
+
+ for(u32bit i = 0; i != sw; ++i)
+ if(reg[i])
+ return false;
+ return true;
+ }
+
+ /**
+ * Set bit at specified position
+ * @param n bit position to set
+ */
+ void set_bit(u32bit n);
+
+ /**
+ * Clear bit at specified position
+ * @param n bit position to clear
+ */
+ void clear_bit(u32bit n);
+
+ /**
+ * Clear all but the lowest n bits
+ * @param n amount of bits to keep
+ */
+ void mask_bits(u32bit n);
+
+ /**
+ * Return bit value at specified position
+ * @param n the bit offset to test
+ * @result true, if the bit at position n is set, false otherwise
+ */
+ bool get_bit(u32bit n) const;
+
+ /**
+ * Return (a maximum of) 32 bits of the complete value
+ * @param offset the offset to start extracting
+ * @param length amount of bits to extract (starting at offset)
+ * @result the integer extracted from the register starting at
+ * offset with specified length
+ */
+ u32bit get_substring(u32bit offset, u32bit length) const;
+
+ /**
+ * @param n the offset to get a byte from
+ * @result byte at offset n
+ */
+ byte byte_at(u32bit n) const;
+
+ /**
+ * Return the word at a specified position of the internal register
+ * @param n position in the register
+ * @return the value at position n
+ */
+ word word_at(u32bit n) const
+ { return ((n < size()) ? reg[n] : 0); }
+
+ /**
+ * Return the integer as an unsigned 32bit-integer-value. If the
+ * value is negative OR to big to be stored in 32bits, this
+ * function will throw an exception.
+ * @result a 32bit-integer
+ */
+ u32bit to_u32bit() const;
+
+ /**
+ * Tests if the sign of the integer is negative.
+ * @result true, if the integer has a negative sign,
+ */
+ bool is_negative() const { return (sign() == Negative); }
+
+ /**
+ * Tests if the sign of the integer is positive.
+ * @result true, if the integer has a positive sign,
+ */
+ bool is_positive() const { return (sign() == Positive); }
+
+ /**
+ * Return the sign of the integer
+ * @result the sign of the integer
+ */
+ Sign sign() const { return (signedness); }
+
+ /**
+ * Return the opposite sign of the represented integer value
+ * @result the opposite sign of the represented integer value
+ */
+ Sign reverse_sign() const;
+
+ /**
+ * Flip (mutate) the sign of the integer to its opposite value
+ */
+ void flip_sign();
+
+ /**
+ * Set sign of the integer
+ * @param sign new Sign to set
+ */
+ void set_sign(Sign sign);
+
+ /**
+ * @result absolute (positive) value of this
+ */
+ BigInt abs() const;
+
+ /**
+ * Give size of internal register
+ * @result size of internal register in words
+ */
+ u32bit size() const { return get_reg().size(); }
+
+ /**
+ * Give significant words of the represented integer value
+ * @result significant words of the represented integer value
+ */
+ u32bit sig_words() const
+ {
+ const word* x = reg.begin();
+ u32bit sig = reg.size();
+
+ while(sig && (x[sig-1] == 0))
+ sig--;
+ return sig;
+ }
+
+ /**
+ * Give byte-length of the integer
+ * @result byte-length of the represented integer value
+ */
+ u32bit bytes() const;
+
+ /**
+ * Get the bit-length of the integer.
+ * @result bit-length of the represented integer value
+ */
+ u32bit bits() const;
+
+ /**
+ * Return a pointer to the big integer word register.
+ * @result a pointer to the start of the internal register of
+ * the integer value
+ */
+ const word* data() const { return reg.begin(); }
+
+ /**
+ * return a reference to the internal register containing the value
+ * @result a reference to the word-array (SecureVector<word>)
+ * with the internal register value (containing the integer
+ * value)
+ */
+ SecureVector<word>& get_reg() { return reg; }
+
+ /**
+ * return a const reference to the internal register containing the value
+ * @result a const reference to the word-array (SecureVector<word>)
+ * with the internal register value (containing the integer value)
+ */
+ const SecureVector<word>& get_reg() const { return reg; }
+
+ /**
+ * Increase internal register buffer by n words
+ * @param n increase by n words
+ */
+ void grow_reg(u32bit n);
+
+ void grow_to(u32bit n);
+
+ /**
+ * Fill BigInt with a random number with size of bitsize
+ * @param rng the random number generator to use
+ * @param bitsize number of bits the created random value should have
+ */
+ void randomize(RandomNumberGenerator& rng, u32bit bitsize = 0);
+
+ /**
+ * Store BigInt-value in a given byte array
+ * @param buf destination byte array for the integer value
+ */
+ void binary_encode(byte buf[]) const;
+
+ /**
+ * Read integer value from a byte array with given size
+ * @param buf byte array buffer containing the integer
+ * @param length size of buf
+ */
+ void binary_decode(const byte buf[], u32bit length);
+
+ /**
+ * Read integer value from a byte array (MemoryRegion<byte>)
+ * @param buf the BigInt value to compare to this.
+ */
+ void binary_decode(const MemoryRegion<byte>& buf);
+
+ u32bit encoded_size(Base = Binary) const;
+
+ /**
+ @param rng a random number generator
+ @result a random integer between min and max
+ */
+ static BigInt random_integer(RandomNumberGenerator& rng,
+ const BigInt& min, const BigInt& max);
+
+ /**
+ * Encode the integer value from a BigInt to a SecureVector of bytes
+ * @param n the BigInt to use as integer source
+ * @param base number-base of resulting byte array representation
+ * @result SecureVector of bytes containing the integer with given base
+ */
+ static SecureVector<byte> encode(const BigInt& n, Base base = Binary);
+
+ /**
+ * Encode the integer value from a BigInt to a byte array
+ * @param buf destination byte array for the encoded integer
+ * value with given base
+ * @param n the BigInt to use as integer source
+ * @param base number-base of resulting byte array representation
+ */
+ static void encode(byte buf[], const BigInt& n, Base base = Binary);
+
+ /**
+ * Create a BigInt from an integer in a byte array
+ * @param buf the BigInt value to compare to this.
+ * @param length size of buf
+ * @param base number-base of the integer in buf
+ * @result BigInt-representing the given integer read from the byte array
+ */
+ static BigInt decode(const byte buf[], u32bit length,
+ Base base = Binary);
+
+ static BigInt decode(const MemoryRegion<byte>&, Base = Binary);
+
+ /**
+ * Encode a BigInt to a byte array according to IEEE 1363
+ * @param n the BigInt to encode
+ * @param bytes the length of the resulting SecureVector<byte>
+ * @result a SecureVector<byte> containing the encoded BigInt
+ */
+ static SecureVector<byte> encode_1363(const BigInt& n, u32bit bytes);
+
+ /**
+ * Swap BigInt-value with given BigInt.
+ * @param bigint the BigInt to swap values with
+ */
+ void swap(BigInt& bigint);
+
+ /**
+ * Create empty BigInt
+ */
+ BigInt() { signedness = Positive; }
+
+ /**
+ * Create BigInt from 64bit-Integer value
+ * @param n 64bit-integer
+ */
+ BigInt(u64bit n);
+
+ /**
+ * Copy-Constructor: clone given BigInt
+ * @param bigint the BigInt to clone
+ */
+ BigInt(const BigInt& bigint);
+
+ /**
+ * Create BigInt from a string.
+ * If the string starts with 0x the rest of the string will be
+ * interpreted as hexadecimal digits.
+ * If the string starts with 0 and the second character is NOT
+ * an 'x' the string will be interpreted as octal digits.
+ * If the string starts with non-zero digit, it will be
+ * interpreted as a decimal number.
+ * @param str the string to parse for an integer value
+ */
+ BigInt(const std::string& str);
+
+ /**
+ * Create a BigInt from an integer in a byte array
+ * @param buf the BigInt value to compare to this.
+ * @param length size of buf
+ * @param base number-base of the integer in buf
+ */
+ BigInt(const byte buf[], u32bit length, Base base = Binary);
+
+ /**
+ * Create a random BigInt of the specified size
+ * @param rng random number generator
+ * @param bits size in bits
+ */
+ BigInt(RandomNumberGenerator& rng, u32bit bits);
+
+ /**
+ * Create BigInt from unsigned 32 bit integer value and an
+ * also specify the sign of the value
+ * @param n integer value
+ */
+ BigInt(Sign, u32bit n);
+
+ /**
+ * Create a number of the specified type and size
+ * @param type the type of number to create
+ * @param n the size
+ */
+ BigInt(NumberType type, u32bit n);
private:
SecureVector<word> reg;
@@ -492,14 +479,14 @@ class BOTAN_DLL BigInt
/*
* Arithmetic Operators
*/
-BigInt BOTAN_DLL operator+(const BigInt&, const BigInt&);
-BigInt BOTAN_DLL operator-(const BigInt&, const BigInt&);
-BigInt BOTAN_DLL operator*(const BigInt&, const BigInt&);
-BigInt BOTAN_DLL operator/(const BigInt&, const BigInt&);
-BigInt BOTAN_DLL operator%(const BigInt&, const BigInt&);
-word BOTAN_DLL operator%(const BigInt&, word);
-BigInt BOTAN_DLL operator<<(const BigInt&, u32bit);
-BigInt BOTAN_DLL operator>>(const BigInt&, u32bit);
+BigInt BOTAN_DLL operator+(const BigInt& x, const BigInt& y);
+BigInt BOTAN_DLL operator-(const BigInt& x, const BigInt& y);
+BigInt BOTAN_DLL operator*(const BigInt& x, const BigInt& y);
+BigInt BOTAN_DLL operator/(const BigInt& x, const BigInt& d);
+BigInt BOTAN_DLL operator%(const BigInt& x, const BigInt& m);
+word BOTAN_DLL operator%(const BigInt& x, word m);
+BigInt BOTAN_DLL operator<<(const BigInt& x, u32bit n);
+BigInt BOTAN_DLL operator>>(const BigInt&, x u32bit n);
/*
* Comparison Operators