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authorgingold <gingold@cvs.openbsd.org>1997-10-14 07:25:35 +0000
committergingold <gingold@cvs.openbsd.org>1997-10-14 07:25:35 +0000
commitf6491d400ca651a8a1493d72c6a74c622aa231b1 (patch)
tree39f29255154f230f637c12e9214f12a9e64bd9d4 /sys/arch/kbus/fpu/fpu_div.c
parent7a9e3739a66bd0fadfdc611c72e879fcc6f9ef01 (diff)
Gingold's port for kbus Series5 machine. Not fully finished and not very stable
Diffstat (limited to 'sys/arch/kbus/fpu/fpu_div.c')
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+/* $NetBSD: fpu_div.c,v 1.2 1994/11/20 20:52:38 deraadt Exp $ */
+
+/*
+ * Copyright (c) 1992, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * This software was developed by the Computer Systems Engineering group
+ * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
+ * contributed to Berkeley.
+ *
+ * All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Lawrence Berkeley Laboratory.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * This product includes software developed by the University of
+ * California, Berkeley and its contributors.
+ * 4. Neither the name of the University nor the names of its contributors
+ * may be used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * @(#)fpu_div.c 8.1 (Berkeley) 6/11/93
+ */
+
+/*
+ * Perform an FPU divide (return x / y).
+ */
+
+#include <sys/types.h>
+
+#include <machine/reg.h>
+
+#include <fpu/fpu_arith.h>
+#include <fpu/fpu_emu.h>
+
+/*
+ * Division of normal numbers is done as follows:
+ *
+ * x and y are floating point numbers, i.e., in the form 1.bbbb * 2^e.
+ * If X and Y are the mantissas (1.bbbb's), the quotient is then:
+ *
+ * q = (X / Y) * 2^((x exponent) - (y exponent))
+ *
+ * Since X and Y are both in [1.0,2.0), the quotient's mantissa (X / Y)
+ * will be in [0.5,2.0). Moreover, it will be less than 1.0 if and only
+ * if X < Y. In that case, it will have to be shifted left one bit to
+ * become a normal number, and the exponent decremented. Thus, the
+ * desired exponent is:
+ *
+ * left_shift = x->fp_mant < y->fp_mant;
+ * result_exp = x->fp_exp - y->fp_exp - left_shift;
+ *
+ * The quotient mantissa X/Y can then be computed one bit at a time
+ * using the following algorithm:
+ *
+ * Q = 0; -- Initial quotient.
+ * R = X; -- Initial remainder,
+ * if (left_shift) -- but fixed up in advance.
+ * R *= 2;
+ * for (bit = FP_NMANT; --bit >= 0; R *= 2) {
+ * if (R >= Y) {
+ * Q |= 1 << bit;
+ * R -= Y;
+ * }
+ * }
+ *
+ * The subtraction R -= Y always removes the uppermost bit from R (and
+ * can sometimes remove additional lower-order 1 bits); this proof is
+ * left to the reader.
+ *
+ * This loop correctly calculates the guard and round bits since they are
+ * included in the expanded internal representation. The sticky bit
+ * is to be set if and only if any other bits beyond guard and round
+ * would be set. From the above it is obvious that this is true if and
+ * only if the remainder R is nonzero when the loop terminates.
+ *
+ * Examining the loop above, we can see that the quotient Q is built
+ * one bit at a time ``from the top down''. This means that we can
+ * dispense with the multi-word arithmetic and just build it one word
+ * at a time, writing each result word when it is done.
+ *
+ * Furthermore, since X and Y are both in [1.0,2.0), we know that,
+ * initially, R >= Y. (Recall that, if X < Y, R is set to X * 2 and
+ * is therefore at in [2.0,4.0).) Thus Q is sure to have bit FP_NMANT-1
+ * set, and R can be set initially to either X - Y (when X >= Y) or
+ * 2X - Y (when X < Y). In addition, comparing R and Y is difficult,
+ * so we will simply calculate R - Y and see if that underflows.
+ * This leads to the following revised version of the algorithm:
+ *
+ * R = X;
+ * bit = FP_1;
+ * D = R - Y;
+ * if (D >= 0) {
+ * result_exp = x->fp_exp - y->fp_exp;
+ * R = D;
+ * q = bit;
+ * bit >>= 1;
+ * } else {
+ * result_exp = x->fp_exp - y->fp_exp - 1;
+ * q = 0;
+ * }
+ * R <<= 1;
+ * do {
+ * D = R - Y;
+ * if (D >= 0) {
+ * q |= bit;
+ * R = D;
+ * }
+ * R <<= 1;
+ * } while ((bit >>= 1) != 0);
+ * Q[0] = q;
+ * for (i = 1; i < 4; i++) {
+ * q = 0, bit = 1 << 31;
+ * do {
+ * D = R - Y;
+ * if (D >= 0) {
+ * q |= bit;
+ * R = D;
+ * }
+ * R <<= 1;
+ * } while ((bit >>= 1) != 0);
+ * Q[i] = q;
+ * }
+ *
+ * This can be refined just a bit further by moving the `R <<= 1'
+ * calculations to the front of the do-loops and eliding the first one.
+ * The process can be terminated immediately whenever R becomes 0, but
+ * this is relatively rare, and we do not bother.
+ */
+
+struct fpn *
+fpu_div(fe)
+ register struct fpemu *fe;
+{
+ register struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
+ register u_int q, bit;
+ register u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3;
+ FPU_DECL_CARRY
+
+ /*
+ * Since divide is not commutative, we cannot just use ORDER.
+ * Check either operand for NaN first; if there is at least one,
+ * order the signalling one (if only one) onto the right, then
+ * return it. Otherwise we have the following cases:
+ *
+ * Inf / Inf = NaN, plus NV exception
+ * Inf / num = Inf [i.e., return x]
+ * Inf / 0 = Inf [i.e., return x]
+ * 0 / Inf = 0 [i.e., return x]
+ * 0 / num = 0 [i.e., return x]
+ * 0 / 0 = NaN, plus NV exception
+ * num / Inf = 0
+ * num / num = num (do the divide)
+ * num / 0 = Inf, plus DZ exception
+ */
+ if (ISNAN(x) || ISNAN(y)) {
+ ORDER(x, y);
+ return (y);
+ }
+ if (ISINF(x) || ISZERO(x)) {
+ if (x->fp_class == y->fp_class)
+ return (fpu_newnan(fe));
+ return (x);
+ }
+
+ /* all results at this point use XOR of operand signs */
+ x->fp_sign ^= y->fp_sign;
+ if (ISINF(y)) {
+ x->fp_class = FPC_ZERO;
+ return (x);
+ }
+ if (ISZERO(y)) {
+ fe->fe_cx = FSR_DZ;
+ x->fp_class = FPC_INF;
+ return (x);
+ }
+
+ /*
+ * Macros for the divide. See comments at top for algorithm.
+ * Note that we expand R, D, and Y here.
+ */
+
+#define SUBTRACT /* D = R - Y */ \
+ FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \
+ FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0)
+
+#define NONNEGATIVE /* D >= 0 */ \
+ ((int)d0 >= 0)
+
+#ifdef FPU_SHL1_BY_ADD
+#define SHL1 /* R <<= 1 */ \
+ FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \
+ FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0)
+#else
+#define SHL1 \
+ r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \
+ r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1
+#endif
+
+#define LOOP /* do ... while (bit >>= 1) */ \
+ do { \
+ SHL1; \
+ SUBTRACT; \
+ if (NONNEGATIVE) { \
+ q |= bit; \
+ r0 = d0, r1 = d1, r2 = d2, r3 = d3; \
+ } \
+ } while ((bit >>= 1) != 0)
+
+#define WORD(r, i) /* calculate r->fp_mant[i] */ \
+ q = 0; \
+ bit = 1 << 31; \
+ LOOP; \
+ (x)->fp_mant[i] = q
+
+ /* Setup. Note that we put our result in x. */
+ r0 = x->fp_mant[0];
+ r1 = x->fp_mant[1];
+ r2 = x->fp_mant[2];
+ r3 = x->fp_mant[3];
+ y0 = y->fp_mant[0];
+ y1 = y->fp_mant[1];
+ y2 = y->fp_mant[2];
+ y3 = y->fp_mant[3];
+
+ bit = FP_1;
+ SUBTRACT;
+ if (NONNEGATIVE) {
+ x->fp_exp -= y->fp_exp;
+ r0 = d0, r1 = d1, r2 = d2, r3 = d3;
+ q = bit;
+ bit >>= 1;
+ } else {
+ x->fp_exp -= y->fp_exp + 1;
+ q = 0;
+ }
+ LOOP;
+ x->fp_mant[0] = q;
+ WORD(x, 1);
+ WORD(x, 2);
+ WORD(x, 3);
+ x->fp_sticky = r0 | r1 | r2 | r3;
+
+ return (x);
+}