BigMath.hpp

/*
	Copyright (c) 2012-2014 Christopher A. Taylor.  All rights reserved.

	Redistribution and use in source and binary forms, with or without
	modification, are permitted provided that the following conditions are met:

	* Redistributions of source code must retain the above copyright notice,
	  this list of conditions and the following disclaimer.
	* 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.
	* Neither the name of LibCat nor the names of its contributors may be used
	  to endorse or promote products derived from this software without
	  specific prior written permission.

	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
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*/

#ifndef CAT_BIG_MATH_HPP
#define CAT_BIG_MATH_HPP

#include "Platform.hpp"

namespace cat {


/*
	128-bit Arithmetic

	This wraps the best ways on each compiler and architecture to emulate 128-bit
	arithmetic, assuming that a 64-bit type is provided by the compiler.
*/

#ifndef CAT_HAS_U128
	struct u128 {
		u64 i[2];
	};
#endif

// r = x
// The high part is set to zero
CAT_INLINE void u128_set(u128 &r, const u64 x);

// r = high : low
CAT_INLINE void u128_set(u128 &r, const u64 low, const u64 high);

// x + y
CAT_INLINE u128 u128_sum(const u64 x, const u64 y);
CAT_INLINE u128 u128_sum(const u128 x, const u64 y);
CAT_INLINE u128 u128_sum(const u128 x, const u128 y);

// x - y
CAT_INLINE u128 u128_diff(const u64 x, const u64 y);
CAT_INLINE u128 u128_diff(const u128 x, const u64 y);
CAT_INLINE u128 u128_diff(const u128 x, const u128 y);

// r += x
CAT_INLINE void u128_add(u128 &r, const u128 x);
CAT_INLINE void u128_add(u128 &r, const u64 x);

// r = -r
CAT_INLINE u128 u128_neg(const u128 x);

// r -= x
CAT_INLINE void u128_sub(u128 &r, const u128 x);
CAT_INLINE void u128_sub(u128 &r, const u64 x);

// ~x
CAT_INLINE u128 u128_not(const u128 x);

// r |= x
CAT_INLINE void u128_or(u128 &r, const u64 x);

// x & y
CAT_INLINE u128 u128_and(const u128 x, const u128 y);

// Set bit x: 0..127
CAT_INLINE void u128_set_bit(u128 &r, int x);

// Get 32 bits from offset: 0..127
CAT_INLINE u32 u128_get_bits(const u128 x, int offset);

// r = u128_high(r) + x
// Negative r values are not sign-extended
CAT_INLINE void u128_carry_add(u128 &r, const u64 x);

CAT_INLINE void u128_carry_add(u128 &r, const u64 x, const u64 y)
{
	u128_carry_add(r, x);
	u128_add(r, y);
}

// r = (r >> 64) + x
// Note that the difference here is that r is signed,
// so negative values are sign-extended
CAT_INLINE void u128_borrow_add(u128 &r, const u64 x);

CAT_INLINE void u128_borrow_add_sub(u128 &r, const u64 x, const u64 y)
{
	u128_borrow_add(r, x);
	u128_sub(r, y);
}

// r >>= shift
// Precondition: 0 < shift < 64
CAT_INLINE void u128_rshift(u128 &r, int shift);

// r <<= shift
// Precondition: 0 < shift < 64
CAT_INLINE void u128_lshift(u128 &r, int shift);

// (x << shift) + z
// Precondition: 0 < shift < 64
CAT_INLINE u128 u128_lshift_sum(const u64 x, int shift, const u64 z);

// x * y
CAT_INLINE u128 u128_prod(const u64 x, const u64 y);

// x * y + z
CAT_INLINE u128 u128_prod_sum(const u64 x, const u64 y, const u64 z);

// x * y assuming MSB(x) = MSB(y) = 0
CAT_INLINE u128 u128_prod_63(const u64 x, const u64 y);

// get high/low halves
CAT_INLINE u64 u128_high(const u128 x);
CAT_INLINE u64 u128_low(const u128 x);

// Clear MSB of parameter
CAT_INLINE void u128_clear_msb(u128 &r);


/*
 * There are three main platforms to support:
 *
 * + 64-bit GCC/Clang with 128-bit emulated types
 * + 64-bit ICC/MSVC without 128-bit emulated types
 * + 32-bit with 64-bit emulated types
 */

#if defined(CAT_HAS_U128)
# include "BigMath128.inh"
#else
# include "BigMath64.inh"
#endif


} // namespace cat

#endif // CAT_BIG_MATH_HPP