1/*
2 * Copyright (c) 1992, 1993
3 *	The Regents of the University of California.  All rights reserved.
4 *
5 * This software was developed by the Computer Systems Engineering group
6 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
7 * contributed to Berkeley.
8 *
9 * All advertising materials mentioning features or use of this software
10 * must display the following acknowledgement:
11 *	This product includes software developed by the University of
12 *	California, Lawrence Berkeley Laboratory.
13 *
14 * Redistribution and use in source and binary forms, with or without
15 * modification, are permitted provided that the following conditions
16 * are met:
17 * 1. Redistributions of source code must retain the above copyright
18 *    notice, this list of conditions and the following disclaimer.
19 * 2. Redistributions in binary form must reproduce the above copyright
20 *    notice, this list of conditions and the following disclaimer in the
21 *    documentation and/or other materials provided with the distribution.
22 * 3. Neither the name of the University nor the names of its contributors
23 *    may be used to endorse or promote products derived from this software
24 *    without specific prior written permission.
25 *
26 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
27 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
28 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
29 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
30 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
31 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
32 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
33 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
34 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
35 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
36 * SUCH DAMAGE.
37 *
38 *	@(#)fpu_mul.c	8.1 (Berkeley) 6/11/93
39 *	$NetBSD: fpu_mul.c,v 1.2 1994/11/20 20:52:44 deraadt Exp $
40 */
41
42#include <sys/cdefs.h>
43__FBSDID("$FreeBSD$");
44
45/*
46 * Perform an FPU multiply (return x * y).
47 */
48
49#include <sys/types.h>
50
51#include <machine/frame.h>
52#include <machine/fp.h>
53
54#include "fpu_arith.h"
55#include "fpu_emu.h"
56#include "fpu_extern.h"
57
58/*
59 * The multiplication algorithm for normal numbers is as follows:
60 *
61 * The fraction of the product is built in the usual stepwise fashion.
62 * Each step consists of shifting the accumulator right one bit
63 * (maintaining any guard bits) and, if the next bit in y is set,
64 * adding the multiplicand (x) to the accumulator.  Then, in any case,
65 * we advance one bit leftward in y.  Algorithmically:
66 *
67 *	A = 0;
68 *	for (bit = 0; bit < FP_NMANT; bit++) {
69 *		sticky |= A & 1, A >>= 1;
70 *		if (Y & (1 << bit))
71 *			A += X;
72 *	}
73 *
74 * (X and Y here represent the mantissas of x and y respectively.)
75 * The resultant accumulator (A) is the product's mantissa.  It may
76 * be as large as 11.11111... in binary and hence may need to be
77 * shifted right, but at most one bit.
78 *
79 * Since we do not have efficient multiword arithmetic, we code the
80 * accumulator as four separate words, just like any other mantissa.
81 * We use local `register' variables in the hope that this is faster
82 * than memory.  We keep x->fp_mant in locals for the same reason.
83 *
84 * In the algorithm above, the bits in y are inspected one at a time.
85 * We will pick them up 32 at a time and then deal with those 32, one
86 * at a time.  Note, however, that we know several things about y:
87 *
88 *    - the guard and round bits at the bottom are sure to be zero;
89 *
90 *    - often many low bits are zero (y is often from a single or double
91 *	precision source);
92 *
93 *    - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
94 *
95 * We can also test for 32-zero-bits swiftly.  In this case, the center
96 * part of the loop---setting sticky, shifting A, and not adding---will
97 * run 32 times without adding X to A.  We can do a 32-bit shift faster
98 * by simply moving words.  Since zeros are common, we optimize this case.
99 * Furthermore, since A is initially zero, we can omit the shift as well
100 * until we reach a nonzero word.
101 */
102struct fpn *
103__fpu_mul(fe)
104	struct fpemu *fe;
105{
106	struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
107	u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
108	int sticky;
109	FPU_DECL_CARRY
110
111	/*
112	 * Put the `heavier' operand on the right (see fpu_emu.h).
113	 * Then we will have one of the following cases, taken in the
114	 * following order:
115	 *
116	 *  - y = NaN.  Implied: if only one is a signalling NaN, y is.
117	 *	The result is y.
118	 *  - y = Inf.  Implied: x != NaN (is 0, number, or Inf: the NaN
119	 *    case was taken care of earlier).
120	 *	If x = 0, the result is NaN.  Otherwise the result
121	 *	is y, with its sign reversed if x is negative.
122	 *  - x = 0.  Implied: y is 0 or number.
123	 *	The result is 0 (with XORed sign as usual).
124	 *  - other.  Implied: both x and y are numbers.
125	 *	The result is x * y (XOR sign, multiply bits, add exponents).
126	 */
127	ORDER(x, y);
128	if (ISNAN(y))
129		return (y);
130	if (ISINF(y)) {
131		if (ISZERO(x))
132			return (__fpu_newnan(fe));
133		y->fp_sign ^= x->fp_sign;
134		return (y);
135	}
136	if (ISZERO(x)) {
137		x->fp_sign ^= y->fp_sign;
138		return (x);
139	}
140
141	/*
142	 * Setup.  In the code below, the mask `m' will hold the current
143	 * mantissa byte from y.  The variable `bit' denotes the bit
144	 * within m.  We also define some macros to deal with everything.
145	 */
146	x3 = x->fp_mant[3];
147	x2 = x->fp_mant[2];
148	x1 = x->fp_mant[1];
149	x0 = x->fp_mant[0];
150	sticky = a3 = a2 = a1 = a0 = 0;
151
152#define	ADD	/* A += X */ \
153	FPU_ADDS(a3, a3, x3); \
154	FPU_ADDCS(a2, a2, x2); \
155	FPU_ADDCS(a1, a1, x1); \
156	FPU_ADDC(a0, a0, x0)
157
158#define	SHR1	/* A >>= 1, with sticky */ \
159	sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \
160	a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1
161
162#define	SHR32	/* A >>= 32, with sticky */ \
163	sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0
164
165#define	STEP	/* each 1-bit step of the multiplication */ \
166	SHR1; if (bit & m) { ADD; }; bit <<= 1
167
168	/*
169	 * We are ready to begin.  The multiply loop runs once for each
170	 * of the four 32-bit words.  Some words, however, are special.
171	 * As noted above, the low order bits of Y are often zero.  Even
172	 * if not, the first loop can certainly skip the guard bits.
173	 * The last word of y has its highest 1-bit in position FP_NMANT-1,
174	 * so we stop the loop when we move past that bit.
175	 */
176	if ((m = y->fp_mant[3]) == 0) {
177		/* SHR32; */			/* unneeded since A==0 */
178	} else {
179		bit = 1 << FP_NG;
180		do {
181			STEP;
182		} while (bit != 0);
183	}
184	if ((m = y->fp_mant[2]) == 0) {
185		SHR32;
186	} else {
187		bit = 1;
188		do {
189			STEP;
190		} while (bit != 0);
191	}
192	if ((m = y->fp_mant[1]) == 0) {
193		SHR32;
194	} else {
195		bit = 1;
196		do {
197			STEP;
198		} while (bit != 0);
199	}
200	m = y->fp_mant[0];		/* definitely != 0 */
201	bit = 1;
202	do {
203		STEP;
204	} while (bit <= m);
205
206	/*
207	 * Done with mantissa calculation.  Get exponent and handle
208	 * 11.111...1 case, then put result in place.  We reuse x since
209	 * it already has the right class (FP_NUM).
210	 */
211	m = x->fp_exp + y->fp_exp;
212	if (a0 >= FP_2) {
213		SHR1;
214		m++;
215	}
216	x->fp_sign ^= y->fp_sign;
217	x->fp_exp = m;
218	x->fp_sticky = sticky;
219	x->fp_mant[3] = a3;
220	x->fp_mant[2] = a2;
221	x->fp_mant[1] = a1;
222	x->fp_mant[0] = a0;
223	return (x);
224}
225