dp_maddf.c

/*
 * IEEE754 floating point arithmetic
 * double precision: MADDF.f (Fused Multiply Add)
 * MADDF.fmt: FPR[fd] = FPR[fd] + (FPR[fs] x FPR[ft])
 *
 * MIPS floating point support
 * Copyright (C) 2015 Imagination Technologies, Ltd.
 * Author: Markos Chandras <markos.chandras@imgtec.com>
 *
 *  This program is free software; you can distribute it and/or modify it
 *  under the terms of the GNU General Public License as published by the
 *  Free Software Foundation; version 2 of the License.
 */

#include "ieee754dp.h"


static union ieee754dp _dp_maddf(union ieee754dp z, union ieee754dp x,
				 union ieee754dp y, enum maddf_flags flags)
{
	int re;
	int rs;
	u64 rm;
	unsigned lxm;
	unsigned hxm;
	unsigned lym;
	unsigned hym;
	u64 lrm;
	u64 hrm;
	u64 t;
	u64 at;
	int s;

	COMPXDP;
	COMPYDP;
	COMPZDP;

	EXPLODEXDP;
	EXPLODEYDP;
	EXPLODEZDP;

	FLUSHXDP;
	FLUSHYDP;
	FLUSHZDP;

	ieee754_clearcx();

	/*
	 * Handle the cases when at least one of x, y or z is a NaN.
	 * Order of precedence is sNaN, qNaN and z, x, y.
	 */
	if (zc == IEEE754_CLASS_SNAN)
		return ieee754dp_nanxcpt(z);
	if (xc == IEEE754_CLASS_SNAN)
		return ieee754dp_nanxcpt(x);
	if (yc == IEEE754_CLASS_SNAN)
		return ieee754dp_nanxcpt(y);
	if (zc == IEEE754_CLASS_QNAN)
		return z;
	if (xc == IEEE754_CLASS_QNAN)
		return x;
	if (yc == IEEE754_CLASS_QNAN)
		return y;

	if (zc == IEEE754_CLASS_DNORM)
		DPDNORMZ;
	/* ZERO z cases are handled separately below */

	switch (CLPAIR(xc, yc)) {

	/*
	 * Infinity handling
	 */
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
		ieee754_setcx(IEEE754_INVALID_OPERATION);
		return ieee754dp_indef();

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
		if ((zc == IEEE754_CLASS_INF) &&
		    ((!(flags & MADDF_NEGATE_PRODUCT) && (zs != (xs ^ ys))) ||
		     ((flags & MADDF_NEGATE_PRODUCT) && (zs == (xs ^ ys))))) {
			/*
			 * Cases of addition of infinities with opposite signs
			 * or subtraction of infinities with same signs.
			 */
			ieee754_setcx(IEEE754_INVALID_OPERATION);
			return ieee754dp_indef();
		}
		/*
		 * z is here either not an infinity, or an infinity having the
		 * same sign as product (x*y) (in case of MADDF.D instruction)
		 * or product -(x*y) (in MSUBF.D case). The result must be an
		 * infinity, and its sign is determined only by the value of
		 * (flags & MADDF_NEGATE_PRODUCT) and the signs of x and y.
		 */
		if (flags & MADDF_NEGATE_PRODUCT)
			return ieee754dp_inf(1 ^ (xs ^ ys));
		else
			return ieee754dp_inf(xs ^ ys);

	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
	case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
		if (zc == IEEE754_CLASS_INF)
			return ieee754dp_inf(zs);
		if (zc == IEEE754_CLASS_ZERO) {
			/* Handle cases +0 + (-0) and similar ones. */
			if ((!(flags & MADDF_NEGATE_PRODUCT)
					&& (zs == (xs ^ ys))) ||
			    ((flags & MADDF_NEGATE_PRODUCT)
					&& (zs != (xs ^ ys))))
				/*
				 * Cases of addition of zeros of equal signs
				 * or subtraction of zeroes of opposite signs.
				 * The sign of the resulting zero is in any
				 * such case determined only by the sign of z.
				 */
				return z;

			return ieee754dp_zero(ieee754_csr.rm == FPU_CSR_RD);
		}
		/* x*y is here 0, and z is not 0, so just return z */
		return z;

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
		DPDNORMX;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
		if (zc == IEEE754_CLASS_INF)
			return ieee754dp_inf(zs);
		DPDNORMY;
		break;

	case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
		if (zc == IEEE754_CLASS_INF)
			return ieee754dp_inf(zs);
		DPDNORMX;
		break;

	case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
		if (zc == IEEE754_CLASS_INF)
			return ieee754dp_inf(zs);
		/* fall through to real computations */
	}

	/* Finally get to do some computation */

	/*
	 * Do the multiplication bit first
	 *
	 * rm = xm * ym, re = xe + ye basically
	 *
	 * At this point xm and ym should have been normalized.
	 */
	assert(xm & DP_HIDDEN_BIT);
	assert(ym & DP_HIDDEN_BIT);

	re = xe + ye;
	rs = xs ^ ys;
	if (flags & MADDF_NEGATE_PRODUCT)
		rs ^= 1;

	/* shunt to top of word */
	xm <<= 64 - (DP_FBITS + 1);
	ym <<= 64 - (DP_FBITS + 1);

	/*
	 * Multiply 64 bits xm, ym to give high 64 bits rm with stickness.
	 */

	/* 32 * 32 => 64 */
#define DPXMULT(x, y)	((u64)(x) * (u64)y)

	lxm = xm;
	hxm = xm >> 32;
	lym = ym;
	hym = ym >> 32;

	lrm = DPXMULT(lxm, lym);
	hrm = DPXMULT(hxm, hym);

	t = DPXMULT(lxm, hym);

	at = lrm + (t << 32);
	hrm += at < lrm;
	lrm = at;

	hrm = hrm + (t >> 32);

	t = DPXMULT(hxm, lym);

	at = lrm + (t << 32);
	hrm += at < lrm;
	lrm = at;

	hrm = hrm + (t >> 32);

	rm = hrm | (lrm != 0);

	/*
	 * Sticky shift down to normal rounding precision.
	 */
	if ((s64) rm < 0) {
		rm = (rm >> (64 - (DP_FBITS + 1 + 3))) |
		     ((rm << (DP_FBITS + 1 + 3)) != 0);
		re++;
	} else {
		rm = (rm >> (64 - (DP_FBITS + 1 + 3 + 1))) |
		     ((rm << (DP_FBITS + 1 + 3 + 1)) != 0);
	}
	assert(rm & (DP_HIDDEN_BIT << 3));

	if (zc == IEEE754_CLASS_ZERO)
		return ieee754dp_format(rs, re, rm);

	/* And now the addition */
	assert(zm & DP_HIDDEN_BIT);

	/*
	 * Provide guard,round and stick bit space.
	 */
	zm <<= 3;

	if (ze > re) {
		/*
		 * Have to shift y fraction right to align.
		 */
		s = ze - re;
		rm = XDPSRS(rm, s);
		re += s;
	} else if (re > ze) {
		/*
		 * Have to shift x fraction right to align.
		 */
		s = re - ze;
		zm = XDPSRS(zm, s);
		ze += s;
	}
	assert(ze == re);
	assert(ze <= DP_EMAX);

	if (zs == rs) {
		/*
		 * Generate 28 bit result of adding two 27 bit numbers
		 * leaving result in xm, xs and xe.
		 */
		zm = zm + rm;

		if (zm >> (DP_FBITS + 1 + 3)) { /* carry out */
			zm = XDPSRS1(zm);
			ze++;
		}
	} else {
		if (zm >= rm) {
			zm = zm - rm;
		} else {
			zm = rm - zm;
			zs = rs;
		}
		if (zm == 0)
			return ieee754dp_zero(ieee754_csr.rm == FPU_CSR_RD);

		/*
		 * Normalize to rounding precision.
		 */
		while ((zm >> (DP_FBITS + 3)) == 0) {
			zm <<= 1;
			ze--;
		}
	}

	return ieee754dp_format(zs, ze, zm);
}

union ieee754dp ieee754dp_maddf(union ieee754dp z, union ieee754dp x,
				union ieee754dp y)
{
	return _dp_maddf(z, x, y, 0);
}

union ieee754dp ieee754dp_msubf(union ieee754dp z, union ieee754dp x,
				union ieee754dp y)
{
	return _dp_maddf(z, x, y, MADDF_NEGATE_PRODUCT);
}