1 /* $NetBSD: fpu_mul.c,v 1.6 2022/08/28 22:09:26 rin Exp $ */
2
3 /*
4 * Copyright (c) 1992, 1993
5 * The Regents of the University of California. All rights reserved.
6 *
7 * This software was developed by the Computer Systems Engineering group
8 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
9 * contributed to Berkeley.
10 *
11 * All advertising materials mentioning features or use of this software
12 * must display the following acknowledgement:
13 * This product includes software developed by the University of
14 * California, Lawrence Berkeley Laboratory.
15 *
16 * Redistribution and use in source and binary forms, with or without
17 * modification, are permitted provided that the following conditions
18 * are met:
19 * 1. Redistributions of source code must retain the above copyright
20 * notice, this list of conditions and the following disclaimer.
21 * 2. Redistributions in binary form must reproduce the above copyright
22 * notice, this list of conditions and the following disclaimer in the
23 * documentation and/or other materials provided with the distribution.
24 * 3. Neither the name of the University nor the names of its contributors
25 * may be used to endorse or promote products derived from this software
26 * without specific prior written permission.
27 *
28 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
29 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
30 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
31 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
32 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
33 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
34 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
35 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
37 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
38 * SUCH DAMAGE.
39 *
40 * @(#)fpu_mul.c 8.1 (Berkeley) 6/11/93
41 */
42
43 /*
44 * Perform an FPU multiply (return x * y).
45 */
46
47 #include <sys/cdefs.h>
48 __KERNEL_RCSID(0, "$NetBSD: fpu_mul.c,v 1.6 2022/08/28 22:09:26 rin Exp $");
49
50 #include <sys/types.h>
51
52 #include <machine/reg.h>
53
54 #include <sparc/fpu/fpu_arith.h>
55 #include <sparc/fpu/fpu_emu.h>
56
57 /*
58 * The multiplication algorithm for normal numbers is as follows:
59 *
60 * The fraction of the product is built in the usual stepwise fashion.
61 * Each step consists of shifting the accumulator right one bit
62 * (maintaining any guard bits) and, if the next bit in y is set,
63 * adding the multiplicand (x) to the accumulator. Then, in any case,
64 * we advance one bit leftward in y. Algorithmically:
65 *
66 * A = 0;
67 * for (bit = 0; bit < FP_NMANT; bit++) {
68 * sticky |= A & 1, A >>= 1;
69 * if (Y & (1 << bit))
70 * A += X;
71 * }
72 *
73 * (X and Y here represent the mantissas of x and y respectively.)
74 * The resultant accumulator (A) is the product's mantissa. It may
75 * be as large as 11.11111... in binary and hence may need to be
76 * shifted right, but at most one bit.
77 *
78 * Since we do not have efficient multiword arithmetic, we code the
79 * accumulator as four separate words, just like any other mantissa.
80 * We use local variables in the hope that this is faster than memory.
81 * We keep x->fp_mant in locals for the same reason.
82 *
83 * In the algorithm above, the bits in y are inspected one at a time.
84 * We will pick them up 32 at a time and then deal with those 32, one
85 * at a time. Note, however, that we know several things about y:
86 *
87 * - the guard and round bits at the bottom are sure to be zero;
88 *
89 * - often many low bits are zero (y is often from a single or double
90 * precision source);
91 *
92 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
93 *
94 * We can also test for 32-zero-bits swiftly. In this case, the center
95 * part of the loop---setting sticky, shifting A, and not adding---will
96 * run 32 times without adding X to A. We can do a 32-bit shift faster
97 * by simply moving words. Since zeros are common, we optimize this case.
98 * Furthermore, since A is initially zero, we can omit the shift as well
99 * until we reach a nonzero word.
100 */
101 struct fpn *
fpu_mul(struct fpemu * fe)102 fpu_mul(struct fpemu *fe)
103 {
104 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
105 u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
106 int sticky;
107 FPU_DECL_CARRY
108
109 /*
110 * Put the `heavier' operand on the right (see fpu_emu.h).
111 * Then we will have one of the following cases, taken in the
112 * following order:
113 *
114 * - y = NaN. Implied: if only one is a signalling NaN, y is.
115 * The result is y.
116 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
117 * case was taken care of earlier).
118 * If x = 0, the result is NaN. Otherwise the result
119 * is y, with its sign reversed if x is negative.
120 * - x = 0. Implied: y is 0 or number.
121 * The result is 0 (with XORed sign as usual).
122 * - other. Implied: both x and y are numbers.
123 * The result is x * y (XOR sign, multiply bits, add exponents).
124 */
125 ORDER(x, y);
126 if (ISNAN(y)) {
127 y->fp_sign ^= x->fp_sign;
128 return (y);
129 }
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