multi_arith.h

内核linux2.4.20,可跟rtlinux3.2打补丁 组成实时linux系统,编译内核

	fp_mul64(dest->m32[0], dest->m32[1], src1->mant.m32[0], src2->mant.m32[0]);
	fp_mul64(dest->m32[2], dest->m32[3], src1->mant.m32[1], src2->mant.m32[1]);

	fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[0], src2->mant.m32[1]);
	fp_addx96(dest, temp);

	fp_mul64(temp.m32[0], temp.m32[1], src1->mant.m32[1], src2->mant.m32[0]);
	fp_addx96(dest, temp);
}

extern inline void fp_dividemant(union fp_mant128 *dest, struct fp_ext *src, struct fp_ext *div)
{
	union fp_mant128 tmp;
	union fp_mant64 tmp64;
	unsigned long *mantp = dest->m32;
	unsigned long fix, rem, first, dummy;
	int i;

	/* the algorithm below requires dest to be smaller than div,
	   but both have the high bit set */
	if (src->mant.m64 >= div->mant.m64) {
		fp_sub64(src->mant, div->mant);
		*mantp = 1;
	} else
		*mantp = 0;
	mantp++;

	/* basic idea behind this algorithm: we can't divide two 64bit numbers
	   (AB/CD) directly, but we can calculate AB/C0, but this means this
	   quotient is off by C0/CD, so we have to multiply the first result
	   to fix the result, after that we have nearly the correct result
	   and only a few corrections are needed. */

	/* C0/CD can be precalculated, but it's an 64bit division again, but
	   we can make it a bit easier, by dividing first through C so we get
	   10/1D and now only a single shift and the value fits into 32bit. */
	fix = 0x80000000;
	dummy = div->mant.m32[1] / div->mant.m32[0] + 1;
	dummy = (dummy >> 1) | fix;
	fp_div64(fix, dummy, fix, 0, dummy);
	fix--;

	for (i = 0; i < 3; i++, mantp++) {
		if (src->mant.m32[0] == div->mant.m32[0]) {
			fp_div64(first, rem, 0, src->mant.m32[1], div->mant.m32[0]);

			fp_mul64(*mantp, dummy, first, fix);
			*mantp += fix;
		} else {
			fp_div64(first, rem, src->mant.m32[0], src->mant.m32[1], div->mant.m32[0]);

			fp_mul64(*mantp, dummy, first, fix);
		}

		fp_mul64(tmp.m32[0], tmp.m32[1], div->mant.m32[0], first - *mantp);
		fp_add64(tmp.m32[0], tmp.m32[1], 0, rem);
		tmp.m32[2] = 0;

		fp_mul64(tmp64.m32[0], tmp64.m32[1], *mantp, div->mant.m32[1]);
		fp_sub96c(tmp, 0, tmp64.m32[0], tmp64.m32[1]);

		src->mant.m32[0] = tmp.m32[1];
		src->mant.m32[1] = tmp.m32[2];

		while (!fp_sub96c(tmp, 0, div->mant.m32[0], div->mant.m32[1])) {
			src->mant.m32[0] = tmp.m32[1];
			src->mant.m32[1] = tmp.m32[2];
			*mantp += 1;
		}
	}
}

#if 0
extern inline unsigned int fp_fls128(union fp_mant128 *src)
{
	unsigned long data;
	unsigned int res, off;

	if ((data = src->m32[0]))
		off = 0;
	else if ((data = src->m32[1]))
		off = 32;
	else if ((data = src->m32[2]))
		off = 64;
	else if ((data = src->m32[3]))
		off = 96;
	else
		return 128;

	asm ("bfffo %1{#0,#32},%0" : "=d" (res) : "dm" (data));
	return res + off;
}

extern inline void fp_shiftmant128(union fp_mant128 *src, int shift)
{
	unsigned long sticky;

	switch (shift) {
	case 0:
		return;
	case 1:
		asm volatile ("lsl.l #1,%0"
			: "=d" (src->m32[3]) : "0" (src->m32[3]));
		asm volatile ("roxl.l #1,%0"
			: "=d" (src->m32[2]) : "0" (src->m32[2]));
		asm volatile ("roxl.l #1,%0"
			: "=d" (src->m32[1]) : "0" (src->m32[1]));
		asm volatile ("roxl.l #1,%0"
			: "=d" (src->m32[0]) : "0" (src->m32[0]));
		return;
	case 2 ... 31:
		src->m32[0] = (src->m32[0] << shift) | (src->m32[1] >> (32 - shift));
		src->m32[1] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift));
		src->m32[2] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift));
		src->m32[3] = (src->m32[3] << shift);
		return;
	case 32 ... 63:
		shift -= 32;
		src->m32[0] = (src->m32[1] << shift) | (src->m32[2] >> (32 - shift));
		src->m32[1] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift));
		src->m32[2] = (src->m32[3] << shift);
		src->m32[3] = 0;
		return;
	case 64 ... 95:
		shift -= 64;
		src->m32[0] = (src->m32[2] << shift) | (src->m32[3] >> (32 - shift));
		src->m32[1] = (src->m32[3] << shift);
		src->m32[2] = src->m32[3] = 0;
		return;
	case 96 ... 127:
		shift -= 96;
		src->m32[0] = (src->m32[3] << shift);
		src->m32[1] = src->m32[2] = src->m32[3] = 0;
		return;
	case -31 ... -1:
		shift = -shift;
		sticky = 0;
		if (src->m32[3] << (32 - shift))
			sticky = 1;
		src->m32[3] = (src->m32[3] >> shift) | (src->m32[2] << (32 - shift)) | sticky;
		src->m32[2] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift));
		src->m32[1] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift));
		src->m32[0] = (src->m32[0] >> shift);
		return;
	case -63 ... -32:
		shift = -shift - 32;
		sticky = 0;
		if ((src->m32[2] << (32 - shift)) || src->m32[3])
			sticky = 1;
		src->m32[3] = (src->m32[2] >> shift) | (src->m32[1] << (32 - shift)) | sticky;
		src->m32[2] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift));
		src->m32[1] = (src->m32[0] >> shift);
		src->m32[0] = 0;
		return;
	case -95 ... -64:
		shift = -shift - 64;
		sticky = 0;
		if ((src->m32[1] << (32 - shift)) || src->m32[2] || src->m32[3])
			sticky = 1;
		src->m32[3] = (src->m32[1] >> shift) | (src->m32[0] << (32 - shift)) | sticky;
		src->m32[2] = (src->m32[0] >> shift);
		src->m32[1] = src->m32[0] = 0;
		return;
	case -127 ... -96:
		shift = -shift - 96;
		sticky = 0;
		if ((src->m32[0] << (32 - shift)) || src->m32[1] || src->m32[2] || src->m32[3])
			sticky = 1;
		src->m32[3] = (src->m32[0] >> shift) | sticky;
		src->m32[2] = src->m32[1] = src->m32[0] = 0;
		return;
	}

	if (shift < 0 && (src->m32[0] || src->m32[1] || src->m32[2] || src->m32[3]))
		src->m32[3] = 1;
	else
		src->m32[3] = 0;
	src->m32[2] = 0;
	src->m32[1] = 0;
	src->m32[0] = 0;
}
#endif

extern inline void fp_putmant128(struct fp_ext *dest, union fp_mant128 *src, int shift)
{
	unsigned long tmp;

	switch (shift) {
	case 0:
		dest->mant.m64 = src->m64[0];
		dest->lowmant = src->m32[2] >> 24;
		if (src->m32[3] || (src->m32[2] << 8))
			dest->lowmant |= 1;
		break;
	case 1:
		asm volatile ("lsl.l #1,%0"
			: "=d" (tmp) : "0" (src->m32[2]));
		asm volatile ("roxl.l #1,%0"
			: "=d" (dest->mant.m32[1]) : "0" (src->m32[1]));
		asm volatile ("roxl.l #1,%0"
			: "=d" (dest->mant.m32[0]) : "0" (src->m32[0]));
		dest->lowmant = tmp >> 24;
		if (src->m32[3] || (tmp << 8))
			dest->lowmant |= 1;
		break;
	case 31:
		asm volatile ("lsr.l #1,%1; roxr.l #1,%0"
			: "=d" (dest->mant.m32[0])
			: "d" (src->m32[0]), "0" (src->m32[1]));
		asm volatile ("roxr.l #1,%0"
			: "=d" (dest->mant.m32[1]) : "0" (src->m32[2]));
		asm volatile ("roxr.l #1,%0"
			: "=d" (tmp) : "0" (src->m32[3]));
		dest->lowmant = tmp >> 24;
		if (src->m32[3] << 7)
			dest->lowmant |= 1;
		break;
	case 32:
		dest->mant.m32[0] = src->m32[1];
		dest->mant.m32[1] = src->m32[2];
		dest->lowmant = src->m32[3] >> 24;
		if (src->m32[3] << 8)
			dest->lowmant |= 1;
		break;
	}
}

#if 0 /* old code... */
extern inline int fls(unsigned int a)
{
	int r;

	asm volatile ("bfffo %1{#0,#32},%0"
		      : "=d" (r) : "md" (a));
	return r;
}

/* fls = "find last set" (cf. ffs(3)) */
extern inline int fls128(const int128 a)
{
	if (a[MSW128])
		return fls(a[MSW128]);
	if (a[NMSW128])
		return fls(a[NMSW128]) + 32;
	/* XXX: it probably never gets beyond this point in actual
	   use, but that's indicative of a more general problem in the
	   algorithm (i.e. as per the actual 68881 implementation, we
	   really only need at most 67 bits of precision [plus
	   overflow]) so I'm not going to fix it. */
	if (a[NLSW128])
		return fls(a[NLSW128]) + 64;
	if (a[LSW128])
		return fls(a[LSW128]) + 96;
	else
		return -1;
}

extern inline int zerop128(const int128 a)
{
	return !(a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]);
}

extern inline int nonzerop128(const int128 a)
{
	return (a[LSW128] | a[NLSW128] | a[NMSW128] | a[MSW128]);
}

/* Addition and subtraction */
/* Do these in "pure" assembly, because "extended" asm is unmanageable
   here */
extern inline void add128(const int128 a, int128 b)
{
	/* rotating carry flags */
	unsigned int carry[2];

	carry[0] = a[LSW128] > (0xffffffff - b[LSW128]);
	b[LSW128] += a[LSW128];

	carry[1] = a[NLSW128] > (0xffffffff - b[NLSW128] - carry[0]);
	b[NLSW128] = a[NLSW128] + b[NLSW128] + carry[0];

	carry[0] = a[NMSW128] > (0xffffffff - b[NMSW128] - carry[1]);
	b[NMSW128] = a[NMSW128] + b[NMSW128] + carry[1];

	b[MSW128] = a[MSW128] + b[MSW128] + carry[0];
}

/* Note: assembler semantics: "b -= a" */
extern inline void sub128(const int128 a, int128 b)
{
	/* rotating borrow flags */
	unsigned int borrow[2];

	borrow[0] = b[LSW128] < a[LSW128];
	b[LSW128] -= a[LSW128];

	borrow[1] = b[NLSW128] < a[NLSW128] + borrow[0];
	b[NLSW128] = b[NLSW128] - a[NLSW128] - borrow[0];

	borrow[0] = b[NMSW128] < a[NMSW128] + borrow[1];
	b[NMSW128] = b[NMSW128] - a[NMSW128] - borrow[1];

	b[MSW128] = b[MSW128] - a[MSW128] - borrow[0];
}

/* Poor man's 64-bit expanding multiply */
extern inline void mul64(unsigned long long a,
		  unsigned long long b,
		  int128 c)
{
	unsigned long long acc;
	int128 acc128;

	zero128(acc128);
	zero128(c);

	/* first the low words */
	if (LO_WORD(a) && LO_WORD(b)) {
		acc = (long long) LO_WORD(a) * LO_WORD(b);
		c[NLSW128] = HI_WORD(acc);
		c[LSW128] = LO_WORD(acc);
	}
	/* Next the high words */
	if (HI_WORD(a) && HI_WORD(b)) {
		acc = (long long) HI_WORD(a) * HI_WORD(b);
		c[MSW128] = HI_WORD(acc);
		c[NMSW128] = LO_WORD(acc);
	}
	/* The middle words */
	if (LO_WORD(a) && HI_WORD(b)) {
		acc = (long long) LO_WORD(a) * HI_WORD(b);
		acc128[NMSW128] = HI_WORD(acc);
		acc128[NLSW128] = LO_WORD(acc);
		add128(acc128, c);
	}
	/* The first and last words */
	if (HI_WORD(a) && LO_WORD(b)) {
		acc = (long long) HI_WORD(a) * LO_WORD(b);
		acc128[NMSW128] = HI_WORD(acc);
		acc128[NLSW128] = LO_WORD(acc);
		add128(acc128, c);
	}
}

/* Note: unsigned */
extern inline int cmp128(int128 a, int128 b)
{
	if (a[MSW128] < b[MSW128])
		return -1;
	if (a[MSW128] > b[MSW128])
		return 1;
	if (a[NMSW128] < b[NMSW128])
		return -1;
	if (a[NMSW128] > b[NMSW128])
		return 1;
	if (a[NLSW128] < b[NLSW128])
		return -1;
	if (a[NLSW128] > b[NLSW128])
		return 1;

	return (signed) a[LSW128] - b[LSW128];
}

inline void div128(int128 a, int128 b, int128 c)
{
	int128 mask;

	/* Algorithm:

	   Shift the divisor until it's at least as big as the
	   dividend, keeping track of the position to which we've
	   shifted it, i.e. the power of 2 which we've multiplied it
	   by.

	   Then, for this power of 2 (the mask), and every one smaller
	   than it, subtract the mask from the dividend and add it to
	   the quotient until the dividend is smaller than the raised
	   divisor.  At this point, divide the dividend and the mask
	   by 2 (i.e. shift one place to the right).  Lather, rinse,
	   and repeat, until there are no more powers of 2 left. */

	/* FIXME: needless to say, there's room for improvement here too. */

	/* Shift up */
	/* XXX: since it just has to be "at least as big", we can
	   probably eliminate this horribly wasteful loop.  I will
	   have to prove this first, though */
	set128(0, 0, 0, 1, mask);
	while (cmp128(b, a) < 0 && !btsthi128(b)) {
		lslone128(b);
		lslone128(mask);
	}

	/* Shift down */
	zero128(c);
	do {
		if (cmp128(a, b) >= 0) {
			sub128(b, a);
			add128(mask, c);
		}
		lsrone128(mask);
		lsrone128(b);
	} while (nonzerop128(mask));

	/* The remainder is in a... */
}
#endif

#endif	/* MULTI_ARITH_H */