Annotation of sys/arch/sparc/fpu/fpu_div.c, Revision 1.1.1.1
1.1 nbrk 1: /* $OpenBSD: fpu_div.c,v 1.3 2003/06/02 23:27:54 millert Exp $ */
2: /* $NetBSD: fpu_div.c,v 1.2 1994/11/20 20:52:38 deraadt Exp $ */
3:
4: /*
5: * Copyright (c) 1992, 1993
6: * The Regents of the University of California. All rights reserved.
7: *
8: * This software was developed by the Computer Systems Engineering group
9: * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
10: * contributed to Berkeley.
11: *
12: * All advertising materials mentioning features or use of this software
13: * must display the following acknowledgement:
14: * This product includes software developed by the University of
15: * California, Lawrence Berkeley Laboratory.
16: *
17: * Redistribution and use in source and binary forms, with or without
18: * modification, are permitted provided that the following conditions
19: * are met:
20: * 1. Redistributions of source code must retain the above copyright
21: * notice, this list of conditions and the following disclaimer.
22: * 2. Redistributions in binary form must reproduce the above copyright
23: * notice, this list of conditions and the following disclaimer in the
24: * documentation and/or other materials provided with the distribution.
25: * 3. Neither the name of the University nor the names of its contributors
26: * may be used to endorse or promote products derived from this software
27: * without specific prior written permission.
28: *
29: * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
30: * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
31: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
32: * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
33: * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
34: * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
35: * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
36: * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
37: * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
38: * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
39: * SUCH DAMAGE.
40: *
41: * @(#)fpu_div.c 8.1 (Berkeley) 6/11/93
42: */
43:
44: /*
45: * Perform an FPU divide (return x / y).
46: */
47:
48: #include <sys/types.h>
49:
50: #include <machine/reg.h>
51:
52: #include <sparc/fpu/fpu_arith.h>
53: #include <sparc/fpu/fpu_emu.h>
54:
55: /*
56: * Division of normal numbers is done as follows:
57: *
58: * x and y are floating point numbers, i.e., in the form 1.bbbb * 2^e.
59: * If X and Y are the mantissas (1.bbbb's), the quotient is then:
60: *
61: * q = (X / Y) * 2^((x exponent) - (y exponent))
62: *
63: * Since X and Y are both in [1.0,2.0), the quotient's mantissa (X / Y)
64: * will be in [0.5,2.0). Moreover, it will be less than 1.0 if and only
65: * if X < Y. In that case, it will have to be shifted left one bit to
66: * become a normal number, and the exponent decremented. Thus, the
67: * desired exponent is:
68: *
69: * left_shift = x->fp_mant < y->fp_mant;
70: * result_exp = x->fp_exp - y->fp_exp - left_shift;
71: *
72: * The quotient mantissa X/Y can then be computed one bit at a time
73: * using the following algorithm:
74: *
75: * Q = 0; -- Initial quotient.
76: * R = X; -- Initial remainder,
77: * if (left_shift) -- but fixed up in advance.
78: * R *= 2;
79: * for (bit = FP_NMANT; --bit >= 0; R *= 2) {
80: * if (R >= Y) {
81: * Q |= 1 << bit;
82: * R -= Y;
83: * }
84: * }
85: *
86: * The subtraction R -= Y always removes the uppermost bit from R (and
87: * can sometimes remove additional lower-order 1 bits); this proof is
88: * left to the reader.
89: *
90: * This loop correctly calculates the guard and round bits since they are
91: * included in the expanded internal representation. The sticky bit
92: * is to be set if and only if any other bits beyond guard and round
93: * would be set. From the above it is obvious that this is true if and
94: * only if the remainder R is nonzero when the loop terminates.
95: *
96: * Examining the loop above, we can see that the quotient Q is built
97: * one bit at a time ``from the top down''. This means that we can
98: * dispense with the multi-word arithmetic and just build it one word
99: * at a time, writing each result word when it is done.
100: *
101: * Furthermore, since X and Y are both in [1.0,2.0), we know that,
102: * initially, R >= Y. (Recall that, if X < Y, R is set to X * 2 and
103: * is therefore at in [2.0,4.0).) Thus Q is sure to have bit FP_NMANT-1
104: * set, and R can be set initially to either X - Y (when X >= Y) or
105: * 2X - Y (when X < Y). In addition, comparing R and Y is difficult,
106: * so we will simply calculate R - Y and see if that underflows.
107: * This leads to the following revised version of the algorithm:
108: *
109: * R = X;
110: * bit = FP_1;
111: * D = R - Y;
112: * if (D >= 0) {
113: * result_exp = x->fp_exp - y->fp_exp;
114: * R = D;
115: * q = bit;
116: * bit >>= 1;
117: * } else {
118: * result_exp = x->fp_exp - y->fp_exp - 1;
119: * q = 0;
120: * }
121: * R <<= 1;
122: * do {
123: * D = R - Y;
124: * if (D >= 0) {
125: * q |= bit;
126: * R = D;
127: * }
128: * R <<= 1;
129: * } while ((bit >>= 1) != 0);
130: * Q[0] = q;
131: * for (i = 1; i < 4; i++) {
132: * q = 0, bit = 1 << 31;
133: * do {
134: * D = R - Y;
135: * if (D >= 0) {
136: * q |= bit;
137: * R = D;
138: * }
139: * R <<= 1;
140: * } while ((bit >>= 1) != 0);
141: * Q[i] = q;
142: * }
143: *
144: * This can be refined just a bit further by moving the `R <<= 1'
145: * calculations to the front of the do-loops and eliding the first one.
146: * The process can be terminated immediately whenever R becomes 0, but
147: * this is relatively rare, and we do not bother.
148: */
149:
150: struct fpn *
151: fpu_div(fe)
152: register struct fpemu *fe;
153: {
154: register struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
155: register u_int q, bit;
156: register u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3;
157: FPU_DECL_CARRY
158:
159: /*
160: * Since divide is not commutative, we cannot just use ORDER.
161: * Check either operand for NaN first; if there is at least one,
162: * order the signalling one (if only one) onto the right, then
163: * return it. Otherwise we have the following cases:
164: *
165: * Inf / Inf = NaN, plus NV exception
166: * Inf / num = Inf [i.e., return x]
167: * Inf / 0 = Inf [i.e., return x]
168: * 0 / Inf = 0 [i.e., return x]
169: * 0 / num = 0 [i.e., return x]
170: * 0 / 0 = NaN, plus NV exception
171: * num / Inf = 0
172: * num / num = num (do the divide)
173: * num / 0 = Inf, plus DZ exception
174: */
175: if (ISNAN(x) || ISNAN(y)) {
176: ORDER(x, y);
177: return (y);
178: }
179: if (ISINF(x) || ISZERO(x)) {
180: if (x->fp_class == y->fp_class)
181: return (fpu_newnan(fe));
182: return (x);
183: }
184:
185: /* all results at this point use XOR of operand signs */
186: x->fp_sign ^= y->fp_sign;
187: if (ISINF(y)) {
188: x->fp_class = FPC_ZERO;
189: return (x);
190: }
191: if (ISZERO(y)) {
192: fe->fe_cx = FSR_DZ;
193: x->fp_class = FPC_INF;
194: return (x);
195: }
196:
197: /*
198: * Macros for the divide. See comments at top for algorithm.
199: * Note that we expand R, D, and Y here.
200: */
201:
202: #define SUBTRACT /* D = R - Y */ \
203: FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \
204: FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0)
205:
206: #define NONNEGATIVE /* D >= 0 */ \
207: ((int)d0 >= 0)
208:
209: #ifdef FPU_SHL1_BY_ADD
210: #define SHL1 /* R <<= 1 */ \
211: FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \
212: FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0)
213: #else
214: #define SHL1 \
215: r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \
216: r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1
217: #endif
218:
219: #define LOOP /* do ... while (bit >>= 1) */ \
220: do { \
221: SHL1; \
222: SUBTRACT; \
223: if (NONNEGATIVE) { \
224: q |= bit; \
225: r0 = d0, r1 = d1, r2 = d2, r3 = d3; \
226: } \
227: } while ((bit >>= 1) != 0)
228:
229: #define WORD(r, i) /* calculate r->fp_mant[i] */ \
230: q = 0; \
231: bit = 1 << 31; \
232: LOOP; \
233: (x)->fp_mant[i] = q
234:
235: /* Setup. Note that we put our result in x. */
236: r0 = x->fp_mant[0];
237: r1 = x->fp_mant[1];
238: r2 = x->fp_mant[2];
239: r3 = x->fp_mant[3];
240: y0 = y->fp_mant[0];
241: y1 = y->fp_mant[1];
242: y2 = y->fp_mant[2];
243: y3 = y->fp_mant[3];
244:
245: bit = FP_1;
246: SUBTRACT;
247: if (NONNEGATIVE) {
248: x->fp_exp -= y->fp_exp;
249: r0 = d0, r1 = d1, r2 = d2, r3 = d3;
250: q = bit;
251: bit >>= 1;
252: } else {
253: x->fp_exp -= y->fp_exp + 1;
254: q = 0;
255: }
256: LOOP;
257: x->fp_mant[0] = q;
258: WORD(x, 1);
259: WORD(x, 2);
260: WORD(x, 3);
261: x->fp_sticky = r0 | r1 | r2 | r3;
262:
263: return (x);
264: }
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