libcat/BigMath64.inh at master · catid/libcat · GitHub

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#if defined(CAT_WORD_64) // 64-bit versions:


#if defined(CAT_ASM_ATT) && defined(CAT_ISA_X86) // X86-64:

# define CAT_ADD128(r_hi, r_lo, x_hi, x_lo)	\
	CAT_ASM_BEGIN							\
		"addq %3, %1 \n\t"					\
		"adcq %2, %0"						\
		: "+r"(r_hi),"+r"(r_lo)				\
		: "r"(x_hi),"r"(x_lo) : "cc"		\
	CAT_ASM_END

# define CAT_SUB128(r_hi, r_lo, x_hi, x_lo)	\
	CAT_ASM_BEGIN							\
		"subq %3, %1 \n\t"					\
		"sbbq %2, %0"						\
		: "+r"(r_hi),"+r"(r_lo)				\
		: "r"(x_hi),"r"(x_lo) : "cc"		\
	CAT_ASM_END

# define CAT_SHL128(r_hi, r_lo, shift)	\
	CAT_ASM_BEGIN						\
		"shldq %2, %0, %1 \n\t"			\
		"shlq %0, %0"					\
		: "+r"(r_hi),"+r"(r_lo)			\
		: "s"(shift) : "cc"				\
	CAT_ASM_END

# define CAT_MUL128(r_hi, r_lo, x, y)	\
	CAT_ASM_BEGIN						\
		"mulq %3"						\
		: "=a"(r_lo), "=d"(r_hi)		\
		: "a"(x), "r"(y) : "cc"			\
	CAT_ASM_END


#elif defined(CAT_ASM_ATT) && defined(CAT_ISA_PPC) // PPC-64:

# define CAT_ADD128(r_hi, r_lo, x_hi, x_lo)	\
	CAT_ASM_BEGIN							\
		"addc %1, %1, %3 \n\t"				\
		"adde %0, %0, %2"					\
		: "+r"(r_hi),"+r"(r_lo)				\
		: "r"(x_hi),"r"(x_lo) : "cc"		\
	CAT_ASM_END

# define CAT_SUB128(r_hi, r_lo, x_hi, x_lo)	\
	CAT_ASM_BEGIN							\
		"subc %1, %1, %3 \n\t"				\
		"sube %0, %0, %2"					\
		: "+r"(r_hi),"+r"(r_lo)				\
		: "r"(x_hi),"r"(x_lo) : "cc"		\
	CAT_ASM_END

# define CAT_MUL128(r_hi, r_lo, x, y)		\
	{										\
		u64 __x = x, __y = y;				\
		r_lo = __x * __y;					\
		CAT_ASM_BEGIN						\
			"mulhdu %0, %1, %2"				\
			: "=r" (r_hi)					\
			: "r" (__x), "r" (__y) : "cc"	\
		CAT_ASM_END							\
	}


#elif defined(CAT_COMPILER_MSVC) // MSVC-64:

# define CAT_MUL128(r_hi, r_lo, x, y)	\
	r_lo = _umul128(x, y, &(r_hi));

# define CAT_SHL128(r_hi, r_lo, shift)			\
	r_hi = __shiftleft128(r_lo, r_hi, shift);	\
	r_lo <<= shift;

#endif

#endif // end if 64-bit version


#if defined(CAT_COMPILER_MSVC) // MSVC-32:
# define CAT_MUL64(A, B) __emulu((u32)(A), (u32)(B)) /* slightly faster in ICC */
#else
# define CAT_MUL64(A, B) ( (u64)( (u32)(A) ) * (u32)(B) )
#endif


//// Fallback versions based on u64 ////

#if !defined(CAT_ADD128)
# define CAT_ADD128(r_hi, r_lo, x_hi, x_lo)		\
	{											\
		u64 __x_lo = x_lo;						\
		r_lo += __x_lo;							\
		r_hi += x_hi;							\
		r_hi += (r_lo) < __x_lo;				\
	}
#endif

#if !defined(CAT_PADD128)
# define CAT_PADD128(r_hi, r_lo, x)	\
	{								\
		u64 __x = x;				\
		r_lo += __x;				\
		r_hi += (r_lo) < __x;		\
	}
#endif

#if !defined(CAT_SUB128)
# define CAT_SUB128(r_hi, r_lo, x_hi, x_lo)		\
	{											\
		const u64 __r_lo = r_lo;				\
		const u64 __x_lo = x_lo;				\
		r_lo -= __x_lo;							\
		r_hi -= __r_lo < __x_lo;				\
		r_hi -= x_hi;							\
	}
#endif

#if !defined(CAT_PSUB128)
# define CAT_PSUB128(r_hi, r_lo, x)	\
	{								\
		u64 __r = r_lo;				\
		u64 __x = x;				\
		r_lo -= __x;				\
		r_hi -= __r < __x;			\
	}
#endif

#if !defined(CAT_SHL128)
# define CAT_SHL128(r_hi, r_lo, shift)							\
	{															\
		if (shift >= 64) {										\
			r_hi = r_lo << (shift - 64);						\
			r_lo = 0;											\
		} else {												\
			r_hi = (r_hi << shift) | (r_lo >> (64 - shift));	\
			r_lo <<= shift;										\
		}														\
	}
#endif


//// 128-bit API

CAT_INLINE void u128_set(u128 &r, const u64 x)
{
	r.i[0] = x;
	r.i[1] = 0;
}

CAT_INLINE void u128_set(u128 &r, const u64 low, const u64 high)
{
	r.i[0] = low;
	r.i[1] = high;
}

CAT_INLINE u128 u128_sum(const u64 x, const u64 y)
{
	u128 r;

	r.i[1] = 0;
	r.i[0] = x;

	CAT_PADD128(r.i[1], r.i[0], y);

	return r;
}

CAT_INLINE u128 u128_sum(const u128 x, const u64 y)
{
	u128 r;

	r.i[1] = x.i[1];
	r.i[0] = x.i[0];

	CAT_PADD128(r.i[1], r.i[0], y);

	return r;
}

CAT_INLINE u128 u128_sum(const u128 x, const u128 y)
{
	u128 r;

	r.i[1] = x.i[1];
	r.i[0] = x.i[0];

	CAT_ADD128(r.i[1], r.i[0], y.i[1], y.i[0]);

	return r;
}

CAT_INLINE void u128_add(u128 &r, const u128 x)
{
	CAT_ADD128(r.i[1], r.i[0], x.i[1], x.i[0]);
}

CAT_INLINE void u128_add(u128 &r, const u64 x)
{
	CAT_PADD128(r.i[1], r.i[0], x);
}

CAT_INLINE void u128_sub(u128 &r, const u128 x)
{
	CAT_SUB128(r.i[1], r.i[0], x.i[1], x.i[0]);
}

CAT_INLINE void u128_sub(u128 &r, const u64 x)
{
	CAT_PSUB128(r.i[1], r.i[0], x);
}

CAT_INLINE void u128_or(u128 &r, const u64 x)
{
	r.i[0] |= x;
}

CAT_INLINE u128 u128_and(const u128 x, const u128 y)
{
	u128 r;

	r.i[0] = x.i[0] & y.i[0];
	r.i[1] = x.i[1] & y.i[1];

	return r;
}

CAT_INLINE u128 u128_not(const u128 x)
{
	u128 r;

	r.i[0] = ~x.i[0];
	r.i[1] = ~x.i[1];

	return r;
}

CAT_INLINE void u128_set_bit(u128 &r, int x)
{
	r.i[x >> 6] |= (u64)1 << (x & 63);
}

CAT_INLINE u32 u128_get_bits(const u128 x, int offset)
{
	if (offset >= 64) {
		return (u32)(x.i[1] >> (offset - 64));
	} else if (offset > 32) {
		return (u32)((x.i[1] << (64 - offset)) | (x.i[0] >> offset));
	} else {
		return (u32)(x.i[0] >> offset);
	}
}

CAT_INLINE u128 u128_diff(const u64 x, const u64 y)
{
	u128 r;

	r.i[1] = 0;
	r.i[0] = x;

	CAT_PSUB128(r.i[1], r.i[0], y);

	return r;
}

CAT_INLINE u128 u128_diff(const u128 x, const u64 y)
{
	u128 r;

	r.i[1] = x.i[1];
	r.i[0] = x.i[0];

	CAT_PSUB128(r.i[1], r.i[0], y);

	return r;
}

CAT_INLINE u128 u128_diff(const u128 x, const u128 y)
{
	u128 r;

	r.i[1] = x.i[1];
	r.i[0] = x.i[0];

	CAT_SUB128(r.i[1], r.i[0], y.i[1], y.i[0]);

	return r;
}

CAT_INLINE void u128_carry_add(u128 &r, const u64 x)
{
	const u64 old = r.i[1];

	r.i[0] = old + x;
	r.i[1] = r.i[0] < old;
}

CAT_INLINE void u128_borrow_add(u128 &r, const u64 x)
{
	const u64 old = r.i[1];

	r.i[0] = old + x;
	r.i[1] = (r.i[0] < old) - (old >> 63);
}

CAT_INLINE u128 u128_neg(const u128 x)
{
	u128 r;

	r.i[0] = 0;
	r.i[1] = 0;

	CAT_SUB128(r.i[1], r.i[0], x.i[1], x.i[0]);

	return r;
}

CAT_INLINE void u128_rshift(u128 &r, int shift)
{
	r.i[0] = (r.i[1] << (64 - shift)) | (r.i[0] >> shift);
	r.i[1] >>= shift;
}

CAT_INLINE void u128_lshift(u128 &r, int shift)
{
	CAT_SHL128(r.i[1], r.i[0], shift);
}

CAT_INLINE u64 u128_high(const u128 x)
{
	return x.i[1];
}

CAT_INLINE u64 u128_low(const u128 x)
{
	return x.i[0];
}

CAT_INLINE u128 u128_prod(const u64 x, const u64 y)
{
	u128 r;

#ifdef CAT_MUL128
	CAT_MUL128(r.i[1], r.i[0], x, y);
#else
	u64 prod, sum;

	prod = CAT_MUL64(x, y);

	u32 lo = (u32)prod;

	prod = CAT_MUL64(x >> 32, y) + (u32)(prod >> 32);
	sum = (u32)(prod >> 32);
	prod = CAT_MUL64(x, y >> 32) + (u32)prod;
	sum += (u32)(prod >> 32);

	r.i[0] = ((u64)( (u32)prod ) << 32) | lo;

	prod = CAT_MUL64(x >> 32, y >> 32) + (u32)sum;

	u32 hi = (u32)(sum >> 32) + (u32)(prod >> 32);

	r.i[1] = ((u64)( hi ) << 32) | (u32)prod;
#endif

	return r;
}

CAT_INLINE u128 u128_prod_sum(const u64 x, const u64 y, const u64 z)
{
	u128 r;

#ifdef CAT_MUL128
	CAT_MUL128(r.i[1], r.i[0], x, y);
	CAT_PADD128(r.i[1], r.i[0], z);
#else
	u64 prod, sum;

	prod = CAT_MUL64(x, y) + (u32)z;

	u32 lo = (u32)prod;

	prod = CAT_MUL64(x >> 32, y) + (u32)(prod >> 32) + (u32)(z >> 32);
	sum = (u32)(prod >> 32);
	prod = CAT_MUL64(x, y >> 32) + (u32)prod;
	sum += (u32)(prod >> 32);

	r.i[0] = ((u64)( (u32)prod ) << 32) | lo;

	prod = CAT_MUL64(x >> 32, y >> 32) + (u32)sum;

	u32 hi = (u32)(sum >> 32) + (u32)(prod >> 32);

	r.i[1] = ((u64)( hi ) << 32) | (u32)prod;
#endif

	return r;
}

CAT_INLINE u128 u128_prod_63_sum(const u64 x, const u64 y, const u64 z)
{
	u128 r;

#ifdef CAT_MUL128
	CAT_MUL128(r.i[1], r.i[0], x, y);
	CAT_PADD128(r.i[1], r.i[0], z);
#else
	u64 prod;

	prod = CAT_MUL64(x, y) + (u32)z;

	u32 lo = (u32)prod;

	prod = CAT_MUL64(x, y >> 32) + CAT_MUL64(x >> 32, y) + (u32)(prod >> 32) + (u32)(z >> 32);

	r.i[0] = ((u64)( (u32)prod ) << 32) | lo;

	r.i[1] = CAT_MUL64(x >> 32, y >> 32) + (u32)(prod >> 32);
#endif

	return r;
}

CAT_INLINE u128 u128_lshift_sum(const u64 x, int shift, const u64 z)
{
	u128 r;

	r.i[1] = x >> (64 - shift);

	const u64 old = x << shift;

	r.i[0] = old + z;
	r.i[1] += (r.i[0] < old);

	return r;
}

CAT_INLINE bool u128_is_neg(const u128 x)
{
	return (s64)x.i[1] < 0;
}

CAT_INLINE void u128_clear_msb(u128 &r)
{
	r.i[1] &= 0x7fffffffffffffffULL;
}