fpu_mul.c

/*	$NetBSD: fpu_mul.c,v 1.4 2005/12/11 12:18:42 christos Exp $ */

/*
 * SPDX-License-Identifier: BSD-3-Clause
 *
 * Copyright (c) 1992, 1993
 *	The Regents of the University of California.  All rights reserved.
 *
 * This software was developed by the Computer Systems Engineering group
 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
 * contributed to Berkeley.
 *
 * All advertising materials mentioning features or use of this software
 * must display the following acknowledgement:
 *	This product includes software developed by the University of
 *	California, Lawrence Berkeley Laboratory.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. 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.
 * 3. Neither the name of the University 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 REGENTS 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 REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

/*
 * Perform an FPU multiply (return x * y).
 */

#include <sys/types.h>
#include <sys/systm.h>

#include <machine/fpu.h>

#include <powerpc/fpu/fpu_arith.h>
#include <powerpc/fpu/fpu_emu.h>

/*
 * The multiplication algorithm for normal numbers is as follows:
 *
 * The fraction of the product is built in the usual stepwise fashion.
 * Each step consists of shifting the accumulator right one bit
 * (maintaining any guard bits) and, if the next bit in y is set,
 * adding the multiplicand (x) to the accumulator.  Then, in any case,
 * we advance one bit leftward in y.  Algorithmically:
 *
 *	A = 0;
 *	for (bit = 0; bit < FP_NMANT; bit++) {
 *		sticky |= A & 1, A >>= 1;
 *		if (Y & (1 << bit))
 *			A += X;
 *	}
 *
 * (X and Y here represent the mantissas of x and y respectively.)
 * The resultant accumulator (A) is the product's mantissa.  It may
 * be as large as 11.11111... in binary and hence may need to be
 * shifted right, but at most one bit.
 *
 * Since we do not have efficient multiword arithmetic, we code the
 * accumulator as four separate words, just like any other mantissa.
 * We use local variables in the hope that this is faster than memory.
 * We keep x->fp_mant in locals for the same reason.
 *
 * In the algorithm above, the bits in y are inspected one at a time.
 * We will pick them up 32 at a time and then deal with those 32, one
 * at a time.  Note, however, that we know several things about y:
 *
 *    - the guard and round bits at the bottom are sure to be zero;
 *
 *    - often many low bits are zero (y is often from a single or double
 *	precision source);
 *
 *    - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
 *
 * We can also test for 32-zero-bits swiftly.  In this case, the center
 * part of the loop---setting sticky, shifting A, and not adding---will
 * run 32 times without adding X to A.  We can do a 32-bit shift faster
 * by simply moving words.  Since zeros are common, we optimize this case.
 * Furthermore, since A is initially zero, we can omit the shift as well
 * until we reach a nonzero word.
 */
struct fpn *
fpu_mul(struct fpemu *fe)
{
	struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
	u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
	int sticky;
	FPU_DECL_CARRY;

	/*
	 * Put the `heavier' operand on the right (see fpu_emu.h).
	 * Then we will have one of the following cases, taken in the
	 * following order:
	 *
	 *  - y = NaN.  Implied: if only one is a signalling NaN, y is.
	 *	The result is y.
	 *  - y = Inf.  Implied: x != NaN (is 0, number, or Inf: the NaN
	 *    case was taken care of earlier).
	 *	If x = 0, the result is NaN.  Otherwise the result
	 *	is y, with its sign reversed if x is negative.
	 *  - x = 0.  Implied: y is 0 or number.
	 *	The result is 0 (with XORed sign as usual).
	 *  - other.  Implied: both x and y are numbers.
	 *	The result is x * y (XOR sign, multiply bits, add exponents).
	 */
	DPRINTF(FPE_REG, ("fpu_mul:\n"));
	DUMPFPN(FPE_REG, x);
	DUMPFPN(FPE_REG, y);
	DPRINTF(FPE_REG, ("=>\n"));

	ORDER(x, y);
	if (ISNAN(y)) {
		y->fp_sign ^= x->fp_sign;
		fe->fe_cx |= FPSCR_VXSNAN;
		DUMPFPN(FPE_REG, y);
		return (y);
	}
	if (ISINF(y)) {
		if (ISZERO(x)) {
			fe->fe_cx |= FPSCR_VXIMZ;
			return (fpu_newnan(fe));
		}
		y->fp_sign ^= x->fp_sign;
			DUMPFPN(FPE_REG, y);
		return (y);
	}
	if (ISZERO(x)) {
		x->fp_sign ^= y->fp_sign;
		DUMPFPN(FPE_REG, x);
		return (x);
	}

	/*
	 * Setup.  In the code below, the mask `m' will hold the current
	 * mantissa byte from y.  The variable `bit' denotes the bit
	 * within m.  We also define some macros to deal with everything.
	 */
	x3 = x->fp_mant[3];
	x2 = x->fp_mant[2];
	x1 = x->fp_mant[1];
	x0 = x->fp_mant[0];
	sticky = a3 = a2 = a1 = a0 = 0;

#define	ADD	/* A += X */ \
	FPU_ADDS(a3, a3, x3); \
	FPU_ADDCS(a2, a2, x2); \
	FPU_ADDCS(a1, a1, x1); \
	FPU_ADDC(a0, a0, x0)

#define	SHR1	/* A >>= 1, with sticky */ \
	sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \
	a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1

#define	SHR32	/* A >>= 32, with sticky */ \
	sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0

#define	STEP	/* each 1-bit step of the multiplication */ \
	SHR1; if (bit & m) { ADD; }; bit <<= 1

	/*
	 * We are ready to begin.  The multiply loop runs once for each
	 * of the four 32-bit words.  Some words, however, are special.
	 * As noted above, the low order bits of Y are often zero.  Even
	 * if not, the first loop can certainly skip the guard bits.
	 * The last word of y has its highest 1-bit in position FP_NMANT-1,
	 * so we stop the loop when we move past that bit.
	 */
	if ((m = y->fp_mant[3]) == 0) {
		/* SHR32; */			/* unneeded since A==0 */
	} else {
		bit = 1 << FP_NG;
		do {
			STEP;
		} while (bit != 0);
	}
	if ((m = y->fp_mant[2]) == 0) {
		SHR32;
	} else {
		bit = 1;
		do {
			STEP;
		} while (bit != 0);
	}
	if ((m = y->fp_mant[1]) == 0) {
		SHR32;
	} else {
		bit = 1;
		do {
			STEP;
		} while (bit != 0);
	}
	m = y->fp_mant[0];		/* definitely != 0 */
	bit = 1;
	do {
		STEP;
	} while (bit <= m);

	/*
	 * Done with mantissa calculation.  Get exponent and handle
	 * 11.111...1 case, then put result in place.  We reuse x since
	 * it already has the right class (FP_NUM).
	 */
	m = x->fp_exp + y->fp_exp;
	if (a0 >= FP_2) {
		SHR1;
		m++;
	}
	x->fp_sign ^= y->fp_sign;
	x->fp_exp = m;
	x->fp_sticky = sticky;
	x->fp_mant[3] = a3;
	x->fp_mant[2] = a2;
	x->fp_mant[1] = a1;
	x->fp_mant[0] = a0;

	DUMPFPN(FPE_REG, x);
	return (x);
}