1 /* $NetBSD: fpu_mul.c,v 1.4 2005/12/11 12:18:42 christos Exp $ */
2
3 /*
4 * SPDX-License-Identifier: BSD-3-Clause
5 *
6 * Copyright (c) 1992, 1993
7 * The Regents of the University of California. All rights reserved.
8 *
9 * This software was developed by the Computer Systems Engineering group
10 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
11 * contributed to Berkeley.
12 *
13 * All advertising materials mentioning features or use of this software
14 * must display the following acknowledgement:
15 * This product includes software developed by the University of
16 * California, Lawrence Berkeley Laboratory.
17 *
18 * Redistribution and use in source and binary forms, with or without
19 * modification, are permitted provided that the following conditions
20 * are met:
21 * 1. Redistributions of source code must retain the above copyright
22 * notice, this list of conditions and the following disclaimer.
23 * 2. Redistributions in binary form must reproduce the above copyright
24 * notice, this list of conditions and the following disclaimer in the
25 * documentation and/or other materials provided with the distribution.
26 * 3. Neither the name of the University nor the names of its contributors
27 * may be used to endorse or promote products derived from this software
28 * without specific prior written permission.
29 *
30 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
31 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
32 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
33 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
34 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
35 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
36 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
37 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
38 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
39 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
40 * SUCH DAMAGE.
41 */
42
43 /*
44 * Perform an FPU multiply (return x * y).
45 */
46
47 #include <sys/types.h>
48 #include <sys/systm.h>
49
50 #include <machine/fpu.h>
51
52 #include <powerpc/fpu/fpu_arith.h>
53 #include <powerpc/fpu/fpu_emu.h>
54
55 /*
56 * The multiplication algorithm for normal numbers is as follows:
57 *
58 * The fraction of the product is built in the usual stepwise fashion.
59 * Each step consists of shifting the accumulator right one bit
60 * (maintaining any guard bits) and, if the next bit in y is set,
61 * adding the multiplicand (x) to the accumulator. Then, in any case,
62 * we advance one bit leftward in y. Algorithmically:
63 *
64 * A = 0;
65 * for (bit = 0; bit < FP_NMANT; bit++) {
66 * sticky |= A & 1, A >>= 1;
67 * if (Y & (1 << bit))
68 * A += X;
69 * }
70 *
71 * (X and Y here represent the mantissas of x and y respectively.)
72 * The resultant accumulator (A) is the product's mantissa. It may
73 * be as large as 11.11111... in binary and hence may need to be
74 * shifted right, but at most one bit.
75 *
76 * Since we do not have efficient multiword arithmetic, we code the
77 * accumulator as four separate words, just like any other mantissa.
78 * We use local variables in the hope that this is faster than memory.
79 * We keep x->fp_mant in locals for the same reason.
80 *
81 * In the algorithm above, the bits in y are inspected one at a time.
82 * We will pick them up 32 at a time and then deal with those 32, one
83 * at a time. Note, however, that we know several things about y:
84 *
85 * - the guard and round bits at the bottom are sure to be zero;
86 *
87 * - often many low bits are zero (y is often from a single or double
88 * precision source);
89 *
90 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
91 *
92 * We can also test for 32-zero-bits swiftly. In this case, the center
93 * part of the loop---setting sticky, shifting A, and not adding---will
94 * run 32 times without adding X to A. We can do a 32-bit shift faster
95 * by simply moving words. Since zeros are common, we optimize this case.
96 * Furthermore, since A is initially zero, we can omit the shift as well
97 * until we reach a nonzero word.
98 */
99 struct fpn *
fpu_mul(struct fpemu * fe)100 fpu_mul(struct fpemu *fe)
101 {
102 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
103 u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
104 int sticky;
105 FPU_DECL_CARRY;
106
107 /*
108 * Put the `heavier' operand on the right (see fpu_emu.h).
109 * Then we will have one of the following cases, taken in the
110 * following order:
111 *
112 * - y = NaN. Implied: if only one is a signalling NaN, y is.
113 * The result is y.
114 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
115 * case was taken care of earlier).
116 * If x = 0, the result is NaN. Otherwise the result
117 * is y, with its sign reversed if x is negative.
118 * - x = 0. Implied: y is 0 or number.
119 * The result is 0 (with XORed sign as usual).
120 * - other. Implied: both x and y are numbers.
121 * The result is x * y (XOR sign, multiply bits, add exponents).
122 */
123 DPRINTF(FPE_REG, ("fpu_mul:\n"));
124 DUMPFPN(FPE_REG, x);
125 DUMPFPN(FPE_REG, y);
126 DPRINTF(FPE_REG, ("=>\n"));
127
128 ORDER(x, y);
129 if (ISNAN(y)) {
130 y->fp_sign ^= x->fp_sign;
131 fe->fe_cx |= FPSCR_VXSNAN;
132 DUMPFPN(FPE_REG, y);
133 return (y);
134 }
135 if (ISINF(y)) {
136 if (ISZERO(x)) {
137 fe->fe_cx |= FPSCR_VXIMZ;
138 return (fpu_newnan(fe));
139 }
140 y->fp_sign ^= x->fp_sign;
141 DUMPFPN(FPE_REG, y);
142 return (y);
143 }
144 if (ISZERO(x)) {
145 x->fp_sign ^= y->fp_sign;
146 DUMPFPN(FPE_REG, x);
147 return (x);
148 }
149
150 /*
151 * Setup. In the code below, the mask `m' will hold the current
152 * mantissa byte from y. The variable `bit' denotes the bit
153 * within m. We also define some macros to deal with everything.
154 */
155 x3 = x->fp_mant[3];
156 x2 = x->fp_mant[2];
157 x1 = x->fp_mant[1];
158 x0 = x->fp_mant[0];
159 sticky = a3 = a2 = a1 = a0 = 0;
160
161 #define ADD /* A += X */ \
162 FPU_ADDS(a3, a3, x3); \
163 FPU_ADDCS(a2, a2, x2); \
164 FPU_ADDCS(a1, a1, x1); \
165 FPU_ADDC(a0, a0, x0)
166
167 #define SHR1 /* A >>= 1, with sticky */ \
168 sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \
169 a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1
170
171 #define SHR32 /* A >>= 32, with sticky */ \
172 sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0
173
174 #define STEP /* each 1-bit step of the multiplication */ \
175 SHR1; if (bit & m) { ADD; }; bit <<= 1
176
177 /*
178 * We are ready to begin. The multiply loop runs once for each
179 * of the four 32-bit words. Some words, however, are special.
180 * As noted above, the low order bits of Y are often zero. Even
181 * if not, the first loop can certainly skip the guard bits.
182 * The last word of y has its highest 1-bit in position FP_NMANT-1,
183 * so we stop the loop when we move past that bit.
184 */
185 if ((m = y->fp_mant[3]) == 0) {
186 /* SHR32; */ /* unneeded since A==0 */
187 } else {
188 bit = 1 << FP_NG;
189 do {
190 STEP;
191 } while (bit != 0);
192 }
193 if ((m = y->fp_mant[2]) == 0) {
194 SHR32;
195 } else {
196 bit = 1;
197 do {
198 STEP;
199 } while (bit != 0);
200 }
201 if ((m = y->fp_mant[1]) == 0) {
202 SHR32;
203 } else {
204 bit = 1;
205 do {
206 STEP;
207 } while (bit != 0);
208 }
209 m = y->fp_mant[0]; /* definitely != 0 */
210 bit = 1;
211 do {
212 STEP;
213 } while (bit <= m);
214
215 /*
216 * Done with mantissa calculation. Get exponent and handle
217 * 11.111...1 case, then put result in place. We reuse x since
218 * it already has the right class (FP_NUM).
219 */
220 m = x->fp_exp + y->fp_exp;
221 if (a0 >= FP_2) {
222 SHR1;
223 m++;
224 }
225 x->fp_sign ^= y->fp_sign;
226 x->fp_exp = m;
227 x->fp_sticky = sticky;
228 x->fp_mant[3] = a3;
229 x->fp_mant[2] = a2;
230 x->fp_mant[1] = a1;
231 x->fp_mant[0] = a0;
232
233 DUMPFPN(FPE_REG, x);
234 return (x);
235 }
236