1 /* $NetBSD: fpu_add.c,v 1.9 2013/03/26 11:30:20 isaki 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_add.c 8.1 (Berkeley) 6/11/93
41 */
42
43 /*
44 * Perform an FPU add (return x + y).
45 *
46 * To subtract, negate y and call add.
47 */
48
49 #include <sys/cdefs.h>
50 __KERNEL_RCSID(0, "$NetBSD: fpu_add.c,v 1.9 2013/03/26 11:30:20 isaki Exp $");
51
52 #include <sys/types.h>
53 #include <sys/systm.h>
54
55 #include <machine/reg.h>
56
57 #include "fpu_arith.h"
58 #include "fpu_emulate.h"
59
60 struct fpn *
fpu_add(struct fpemu * fe)61 fpu_add(struct fpemu *fe)
62 {
63 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2, *r;
64 uint32_t r0, r1, r2;
65 int rd;
66
67 /*
68 * Put the `heavier' operand on the right (see fpu_emu.h).
69 * Then we will have one of the following cases, taken in the
70 * following order:
71 *
72 * - y = NaN. Implied: if only one is a signalling NaN, y is.
73 * The result is y.
74 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
75 * case was taken care of earlier).
76 * If x = -y, the result is NaN. Otherwise the result
77 * is y (an Inf of whichever sign).
78 * - y is 0. Implied: x = 0.
79 * If x and y differ in sign (one positive, one negative),
80 * the result is +0 except when rounding to -Inf. If same:
81 * +0 + +0 = +0; -0 + -0 = -0.
82 * - x is 0. Implied: y != 0.
83 * Result is y.
84 * - other. Implied: both x and y are numbers.
85 * Do addition a la Hennessey & Patterson.
86 */
87 ORDER(x, y);
88 if (ISNAN(y))
89 return (y);
90 if (ISINF(y)) {
91 if (ISINF(x) && x->fp_sign != y->fp_sign)
92 return (fpu_newnan(fe));
93 return (y);
94 }
95 rd = (fe->fe_fpcr & FPCR_ROUND);
96 if (ISZERO(y)) {
97 if (rd != FPCR_MINF) /* only -0 + -0 gives -0 */
98 y->fp_sign &= x->fp_sign;
99 else /* any -0 operand gives -0 */
100 y->fp_sign |= x->fp_sign;
101 return (y);
102 }
103 if (ISZERO(x))
104 return (y);
105 /*
106 * We really have two numbers to add, although their signs may
107 * differ. Make the exponents match, by shifting the smaller
108 * number right (e.g., 1.011 => 0.1011) and increasing its
109 * exponent (2^3 => 2^4). Note that we do not alter the exponents
110 * of x and y here.
111 */
112 r = &fe->fe_f3;
113 r->fp_class = FPC_NUM;
114 if (x->fp_exp == y->fp_exp) {
115 r->fp_exp = x->fp_exp;
116 r->fp_sticky = 0;
117 } else {
118 if (x->fp_exp < y->fp_exp) {
119 /*
120 * Try to avoid subtract case iii (see below).
121 * This also guarantees that x->fp_sticky = 0.
122 */
123 SWAP(x, y);
124 }
125 /* now x->fp_exp > y->fp_exp */
126 r->fp_exp = x->fp_exp;
127 r->fp_sticky = fpu_shr(y, x->fp_exp - y->fp_exp);
128 }
129 r->fp_sign = x->fp_sign;
130 if (x->fp_sign == y->fp_sign) {
131 FPU_DECL_CARRY
132
133 /*
134 * The signs match, so we simply add the numbers. The result
135 * may be `supernormal' (as big as 1.111...1 + 1.111...1, or
136 * 11.111...0). If so, a single bit shift-right will fix it
137 * (but remember to adjust the exponent).
138 */
139 /* r->fp_mant = x->fp_mant + y->fp_mant */
140 FPU_ADDS(r->fp_mant[2], x->fp_mant[2], y->fp_mant[2]);
141 FPU_ADDCS(r->fp_mant[1], x->fp_mant[1], y->fp_mant[1]);
142 FPU_ADDC(r0, x->fp_mant[0], y->fp_mant[0]);
143 if ((r->fp_mant[0] = r0) >= FP_2) {
144 (void) fpu_shr(r, 1);
145 r->fp_exp++;
146 }
147 } else {
148 FPU_DECL_CARRY
149
150 /*
151 * The signs differ, so things are rather more difficult.
152 * H&P would have us negate the negative operand and add;
153 * this is the same as subtracting the negative operand.
154 * This is quite a headache. Instead, we will subtract
155 * y from x, regardless of whether y itself is the negative
156 * operand. When this is done one of three conditions will
157 * hold, depending on the magnitudes of x and y:
158 * case i) |x| > |y|. The result is just x - y,
159 * with x's sign, but it may need to be normalized.
160 * case ii) |x| = |y|. The result is 0 (maybe -0)
161 * so must be fixed up.
162 * case iii) |x| < |y|. We goofed; the result should
163 * be (y - x), with the same sign as y.
164 * We could compare |x| and |y| here and avoid case iii,
165 * but that would take just as much work as the subtract.
166 * We can tell case iii has occurred by an overflow.
167 *
168 * N.B.: since x->fp_exp >= y->fp_exp, x->fp_sticky = 0.
169 */
170 /* r->fp_mant = x->fp_mant - y->fp_mant */
171 FPU_SET_CARRY(y->fp_sticky);
172 FPU_SUBCS(r2, x->fp_mant[2], y->fp_mant[2]);
173 FPU_SUBCS(r1, x->fp_mant[1], y->fp_mant[1]);
174 FPU_SUBC(r0, x->fp_mant[0], y->fp_mant[0]);
175 if (r0 < FP_2) {
176 /* cases i and ii */
177 if ((r0 | r1 | r2) == 0) {
178 /* case ii */
179 r->fp_class = FPC_ZERO;
180 r->fp_sign = (rd == FPCR_MINF);
181 return (r);
182 }
183 } else {
184 /*
185 * Oops, case iii. This can only occur when the
186 * exponents were equal, in which case neither
187 * x nor y have sticky bits set. Flip the sign
188 * (to y's sign) and negate the result to get y - x.
189 */
190 #ifdef DIAGNOSTIC
191 if (x->fp_exp != y->fp_exp || r->fp_sticky)
192 panic("fpu_add");
193 #endif
194 r->fp_sign = y->fp_sign;
195 FPU_SUBS(r2, 0, r2);
196 FPU_SUBCS(r1, 0, r1);
197 FPU_SUBC(r0, 0, r0);
198 }
199 r->fp_mant[2] = r2;
200 r->fp_mant[1] = r1;
201 r->fp_mant[0] = r0;
202 if (r0 < FP_1)
203 fpu_norm(r);
204 }
205 return (r);
206 }
207