Пример #1
0
union ieee754dp ieee754dp_abs(union ieee754dp x)
{
	unsigned int oldrm;
	union ieee754dp y;

	oldrm = ieee754_csr.rm;
	ieee754_csr.rm = FPU_CSR_RD;
	if (DPSIGN(x))
		y = ieee754dp_sub(ieee754dp_zero(0), x);
	else
		y = ieee754dp_add(ieee754dp_zero(0), x);
	ieee754_csr.rm = oldrm;
	return y;
}
Пример #2
0
/* modf function is always exact for a finite number
*/
ieee754dp ieee754dp_modf(ieee754dp x, ieee754dp *ip)
{
	COMPXDP;

	CLEARCX;

	EXPLODEXDP;

	switch (xc) {
	case IEEE754_CLASS_SNAN:
	case IEEE754_CLASS_QNAN:
	case IEEE754_CLASS_INF:
	case IEEE754_CLASS_ZERO:
		*ip = x;
		return x;
	case IEEE754_CLASS_DNORM:
		/* far to small */
		*ip = ieee754dp_zero(xs);
		return x;
	case IEEE754_CLASS_NORM:
		break;
	}
	if (xe < 0) {
		*ip = ieee754dp_zero(xs);
		return x;
	}
	if (xe >= DP_MBITS) {
		*ip = x;
		return ieee754dp_zero(xs);
	}
	/* generate ipart mantissa by clearing bottom bits
	 */
	*ip = builddp(xs, xe + DP_EBIAS,
		      ((xm >> (DP_MBITS - xe)) << (DP_MBITS - xe)) &
		      ~DP_HIDDEN_BIT);

	/* generate fpart mantissa by clearing top bits
	 * and normalizing (must be able to normalize)
	 */
	xm = (xm << (64 - (DP_MBITS - xe))) >> (64 - (DP_MBITS - xe));
	if (xm == 0)
		return ieee754dp_zero(xs);

	while ((xm >> DP_MBITS) == 0) {
		xm <<= 1;
		xe--;
	}
	return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
}
Пример #3
0
ieee754dp ieee754dp_ceil(ieee754dp x)
{
	ieee754dp i;

	if (ieee754dp_gt(ieee754dp_modf(x, &i), ieee754dp_zero(0)))
		return ieee754dp_add(i, ieee754dp_one(0));
	else
		return i;
}
Пример #4
0
ieee754dp ieee754dp_floor(ieee754dp x)
{
	ieee754dp i;

	if (ieee754dp_lt(ieee754dp_modf(x, &i), ieee754dp_zero(0)))
		return ieee754dp_sub(i, ieee754dp_one(0));
	else
		return i;
}
Пример #5
0
union ieee754dp ieee754dp_neg(union ieee754dp x)
{
	unsigned int oldrm;
	union ieee754dp y;

	oldrm = ieee754_csr.rm;
	ieee754_csr.rm = FPU_CSR_RD;
	y = ieee754dp_sub(ieee754dp_zero(0), x);
	ieee754_csr.rm = oldrm;
	return y;
}
Пример #6
0
union ieee754dp ieee754dp_fsp(union ieee754sp x)
{
	COMPXSP;

	EXPLODEXSP;

	ieee754_clearcx();

	FLUSHXSP;

	switch (xc) {
	case IEEE754_CLASS_SNAN:
		return ieee754dp_nanxcpt(ieee754dp_nan_fsp(xs, xm));

	case IEEE754_CLASS_QNAN:
		return ieee754dp_nan_fsp(xs, xm);

	case IEEE754_CLASS_INF:
		return ieee754dp_inf(xs);

	case IEEE754_CLASS_ZERO:
		return ieee754dp_zero(xs);

	case IEEE754_CLASS_DNORM:
		/* normalize */
		while ((xm >> SP_FBITS) == 0) {
			xm <<= 1;
			xe--;
		}
		break;

	case IEEE754_CLASS_NORM:
		break;
	}

	/*
	 * Can't possibly overflow,underflow, or need rounding
	 */

	/* drop the hidden bit */
	xm &= ~SP_HIDDEN_BIT;

	return builddp(xs, xe + DP_EBIAS,
		       (u64) xm << (DP_FBITS - SP_FBITS));
}
Пример #7
0
ieee754dp ieee754dp_fsp(ieee754sp x)
{
	COMPXSP;

	EXPLODEXSP;

	CLEARCX;

	FLUSHXSP;

	switch (xc) {
	case IEEE754_CLASS_SNAN:
		SETCX(IEEE754_INVALID_OPERATION);
		return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp");
	case IEEE754_CLASS_QNAN:
		return ieee754dp_nanxcpt(builddp(xs,
						 DP_EMAX + 1 + DP_EBIAS,
						 ((u64) xm
						  << (DP_MBITS -
						      SP_MBITS))), "fsp",
					 x);
	case IEEE754_CLASS_INF:
		return ieee754dp_inf(xs);
	case IEEE754_CLASS_ZERO:
		return ieee754dp_zero(xs);
	case IEEE754_CLASS_DNORM:
		/* normalize */
		while ((xm >> SP_MBITS) == 0) {
			xm <<= 1;
			xe--;
		}
		break;
	case IEEE754_CLASS_NORM:
		break;
	}

	/* CAN'T possibly overflow,underflow, or need rounding
	 */

	/* drop the hidden bit */
	xm &= ~SP_HIDDEN_BIT;

	return builddp(xs, xe + DP_EBIAS,
		       (u64) xm << (DP_MBITS - SP_MBITS));
}
Пример #8
0
ieee754dp ieee754dp_fsp(ieee754sp x)
{
	COMPXSP;

	EXPLODEXSP;

	CLEARCX;

	FLUSHXSP;

	switch (xc) {
	case IEEE754_CLASS_SNAN:
		SETCX(IEEE754_INVALID_OPERATION);
		return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp");
	case IEEE754_CLASS_QNAN:
		return ieee754dp_nanxcpt(builddp(xs,
						 DP_EMAX + 1 + DP_EBIAS,
						 ((u64) xm
						  << (DP_MBITS -
						      SP_MBITS))), "fsp",
					 x);
	case IEEE754_CLASS_INF:
		return ieee754dp_inf(xs);
	case IEEE754_CLASS_ZERO:
		return ieee754dp_zero(xs);
	case IEEE754_CLASS_DNORM:
		
		while ((xm >> SP_MBITS) == 0) {
			xm <<= 1;
			xe--;
		}
		break;
	case IEEE754_CLASS_NORM:
		break;
	}


	
	xm &= ~SP_HIDDEN_BIT;

	return builddp(xs, xe + DP_EBIAS,
		       (u64) xm << (DP_MBITS - SP_MBITS));
}
Пример #9
0
ieee754dp ieee754dp_fint(int x)
{
	u64 xm;
	int xe;
	int xs;

	CLEARCX;

	if (x == 0)
		return ieee754dp_zero(0);
	if (x == 1 || x == -1)
		return ieee754dp_one(x < 0);
	if (x == 10 || x == -10)
		return ieee754dp_ten(x < 0);

	xs = (x < 0);
	if (xs) {
		if (x == (1 << 31))
			xm = ((unsigned) 1 << 31);	/* max neg can't be safely negated */
		else
			xm = -x;
	} else {
		xm = x;
	}

#if 1
	/* normalize - result can never be inexact or overflow */
	xe = DP_MBITS;
	while ((xm >> DP_MBITS) == 0) {
		xm <<= 1;
		xe--;
	}
	return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
#else
	/* normalize */
	xe = DP_MBITS + 3;
	while ((xm >> (DP_MBITS + 3)) == 0) {
		xm <<= 1;
		xe--;
	}
	DPNORMRET1(xs, xe, xm, "fint", x);
#endif
}
Пример #10
0
ieee754dp ieee754dp_fint(int x)
{
	u64 xm;
	int xe;
	int xs;

	CLEARCX;

	if (x == 0)
		return ieee754dp_zero(0);
	if (x == 1 || x == -1)
		return ieee754dp_one(x < 0);
	if (x == 10 || x == -10)
		return ieee754dp_ten(x < 0);

	xs = (x < 0);
	if (xs) {
		if (x == (1 << 31))
			xm = ((unsigned) 1 << 31);	
		else
			xm = -x;
	} else {
		xm = x;
	}

#if 1
	
	xe = DP_MBITS;
	while ((xm >> DP_MBITS) == 0) {
		xm <<= 1;
		xe--;
	}
	return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
#else
	
	xe = DP_MBITS + 3;
	while ((xm >> (DP_MBITS + 3)) == 0) {
		xm <<= 1;
		xe--;
	}
	DPNORMRET1(xs, xe, xm, "fint", x);
#endif
}
Пример #11
0
ieee754dp ieee754dp_div(ieee754dp x, ieee754dp y)
{
	COMPXDP;
	COMPYDP;

	EXPLODEXDP;
	EXPLODEYDP;

	CLEARCX;

	FLUSHXDP;
	FLUSHYDP;

	switch (CLPAIR(xc, yc)) {
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
		SETCX(IEEE754_INVALID_OPERATION);
		return ieee754dp_nanxcpt(ieee754dp_indef(), "div", x, y);

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
		return y;

	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
		return x;


		/* Infinity handling
		 */

	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
		SETCX(IEEE754_INVALID_OPERATION);
		return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y);

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
		return ieee754dp_zero(xs ^ ys);

	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
		return ieee754dp_inf(xs ^ ys);

		/* Zero handling
		 */

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
		SETCX(IEEE754_INVALID_OPERATION);
		return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y);

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
		SETCX(IEEE754_ZERO_DIVIDE);
		return ieee754dp_xcpt(ieee754dp_inf(xs ^ ys), "div", x, y);

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
		return ieee754dp_zero(xs == ys ? 0 : 1);

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
		DPDNORMX;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
		DPDNORMY;
		break;

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
		DPDNORMX;
		break;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
		break;
	}
	assert(xm & DP_HIDDEN_BIT);
	assert(ym & DP_HIDDEN_BIT);

	/* provide rounding space */
	xm <<= 3;
	ym <<= 3;

	{
		/* now the dirty work */

		u64 rm = 0;
		int re = xe - ye;
		u64 bm;

		for (bm = DP_MBIT(DP_MBITS + 2); bm; bm >>= 1) {
			if (xm >= ym) {
				xm -= ym;
				rm |= bm;
				if (xm == 0)
					break;
			}
			xm <<= 1;
		}
		rm <<= 1;
		if (xm)
			rm |= 1;	/* have remainder, set sticky */

		assert(rm);

		/* normalise rm to rounding precision ?
		 */
		while ((rm >> (DP_MBITS + 3)) == 0) {
			rm <<= 1;
			re--;
		}

		DPNORMRET2(xs == ys ? 0 : 1, re, rm, "div", x, y);
	}
}
Пример #12
0
union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
{
	COMPXDP;
	COMPYDP;

	EXPLODEXDP;
	EXPLODEYDP;

	FLUSHXDP;
	FLUSHYDP;

	ieee754_clearcx();

	switch (CLPAIR(xc, yc)) {
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
		return ieee754dp_nanxcpt(y);

	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
		return ieee754dp_nanxcpt(x);

	/*
	 * Quiet NaN handling
	 */

	/*
	 *    The case of both inputs quiet NaNs
	 */
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
		return x;

	/*
	 *    The cases of exactly one input quiet NaN (numbers
	 *    are here preferred as returned values to NaNs)
	 */
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
		return x;

	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
		return y;

	/*
	 * Infinity and zero handling
	 */
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
		return xs ? y : x;

	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
		return ys ? x : y;

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
		return ieee754dp_zero(xs & ys);

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
		DPDNORMX;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
		DPDNORMY;
		break;

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
		DPDNORMX;
	}

	/* Finally get to do some computation */

	assert(xm & DP_HIDDEN_BIT);
	assert(ym & DP_HIDDEN_BIT);

	/* Compare signs */
	if (xs > ys)
		return y;
	else if (xs < ys)
		return x;

	/* Signs of inputs are equal, let's compare exponents */
	if (xs == 0) {
		/* Inputs are both positive */
		if (xe > ye)
			return x;
		else if (xe < ye)
			return y;
	} else {
		/* Inputs are both negative */
		if (xe > ye)
			return y;
		else if (xe < ye)
			return x;
	}

	/* Signs and exponents of inputs are equal, let's compare mantissas */
	if (xs == 0) {
		/* Inputs are both positive, with equal signs and exponents */
		if (xm <= ym)
			return y;
		return x;
	}
	/* Inputs are both negative, with equal signs and exponents */
	if (xm <= ym)
		return x;
	return y;
}
Пример #13
0
union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
{
	COMPXDP;
	COMPYDP;

	EXPLODEXDP;
	EXPLODEYDP;

	FLUSHXDP;
	FLUSHYDP;

	ieee754_clearcx();

	switch (CLPAIR(xc, yc)) {
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
		return ieee754dp_nanxcpt(y);

	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
		return ieee754dp_nanxcpt(x);

	/* numbers are preferred to NaNs */
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
		return x;

	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
		return y;

	/*
	 * Infinity and zero handling
	 */
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
		return xs ? y : x;

	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
		return ys ? x : y;

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
		if (xs == ys)
			return x;
		return ieee754dp_zero(1);

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
		DPDNORMX;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
		DPDNORMY;
		break;

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
		DPDNORMX;
	}

	/* Finally get to do some computation */

	assert(xm & DP_HIDDEN_BIT);
	assert(ym & DP_HIDDEN_BIT);

	/* Compare signs */
	if (xs > ys)
		return y;
	else if (xs < ys)
		return x;

	/* Compare exponent */
	if (xe > ye)
		return x;
	else if (xe < ye)
		return y;

	/* Compare mantissa */
	if (xm <= ym)
		return y;
	return x;
}