BSD 4.4 Lite Kernel Sources

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+/*-
+ * 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.
+ *
+ * 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.
+ */
+
+#if defined(LIBC_SCCS) && !defined(lint)
+static char sccsid[] = "@(#)muldi3.c	8.1 (Berkeley) 6/4/93";
+#endif /* LIBC_SCCS and not lint */
+
+#include "quad.h"
+
+/*
+ * Multiply two quads.
+ *
+ * Our algorithm is based on the following.  Split incoming quad values
+ * u and v (where u,v >= 0) into
+ *
+ *	u = 2^n u1  *  u0	(n = number of bits in `u_long', usu. 32)
+ *
+ * and 
+ *
+ *	v = 2^n v1  *  v0
+ *
+ * Then
+ *
+ *	uv = 2^2n u1 v1  +  2^n u1 v0  +  2^n v1 u0  +  u0 v0
+ *	   = 2^2n u1 v1  +     2^n (u1 v0 + v1 u0)   +  u0 v0
+ *
+ * Now add 2^n u1 v1 to the first term and subtract it from the middle,
+ * and add 2^n u0 v0 to the last term and subtract it from the middle.
+ * This gives:
+ *
+ *	uv = (2^2n + 2^n) (u1 v1)  +
+ *	         (2^n)    (u1 v0 - u1 v1 + u0 v1 - u0 v0)  +
+ *	       (2^n + 1)  (u0 v0)
+ *
+ * Factoring the middle a bit gives us:
+ *
+ *	uv = (2^2n + 2^n) (u1 v1)  +			[u1v1 = high]
+ *		 (2^n)    (u1 - u0) (v0 - v1)  +	[(u1-u0)... = mid]
+ *	       (2^n + 1)  (u0 v0)			[u0v0 = low]
+ *
+ * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
+ * in just half the precision of the original.  (Note that either or both
+ * of (u1 - u0) or (v0 - v1) may be negative.)
+ *
+ * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
+ *
+ * Since C does not give us a `long * long = quad' operator, we split
+ * our input quads into two longs, then split the two longs into two
+ * shorts.  We can then calculate `short * short = long' in native
+ * arithmetic.
+ *
+ * Our product should, strictly speaking, be a `long quad', with 128
+ * bits, but we are going to discard the upper 64.  In other words,
+ * we are not interested in uv, but rather in (uv mod 2^2n).  This
+ * makes some of the terms above vanish, and we get:
+ *
+ *	(2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
+ *
+ * or
+ *
+ *	(2^n)(high + mid + low) + low
+ *
+ * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
+ * of 2^n in either one will also vanish.  Only `low' need be computed
+ * mod 2^2n, and only because of the final term above.
+ */
+static quad_t __lmulq(u_long, u_long);
+
+quad_t
+__muldi3(a, b)
+	quad_t a, b;
+{
+	union uu u, v, low, prod;
+	register u_long high, mid, udiff, vdiff;
+	register int negall, negmid;
+#define	u1	u.ul[H]
+#define	u0	u.ul[L]
+#define	v1	v.ul[H]
+#define	v0	v.ul[L]
+
+	/*
+	 * Get u and v such that u, v >= 0.  When this is finished,
+	 * u1, u0, v1, and v0 will be directly accessible through the
+	 * longword fields.
+	 */
+	if (a >= 0)
+		u.q = a, negall = 0;
+	else
+		u.q = -a, negall = 1;
+	if (b >= 0)
+		v.q = b;
+	else
+		v.q = -b, negall ^= 1;
+
+	if (u1 == 0 && v1 == 0) {
+		/*
+		 * An (I hope) important optimization occurs when u1 and v1
+		 * are both 0.  This should be common since most numbers
+		 * are small.  Here the product is just u0*v0.
+		 */
+		prod.q = __lmulq(u0, v0);
+	} else {
+		/*
+		 * Compute the three intermediate products, remembering
+		 * whether the middle term is negative.  We can discard
+		 * any upper bits in high and mid, so we can use native
+		 * u_long * u_long => u_long arithmetic.
+		 */
+		low.q = __lmulq(u0, v0);
+
+		if (u1 >= u0)
+			negmid = 0, udiff = u1 - u0;
+		else
+			negmid = 1, udiff = u0 - u1;
+		if (v0 >= v1)
+			vdiff = v0 - v1;
+		else
+			vdiff = v1 - v0, negmid ^= 1;
+		mid = udiff * vdiff;
+
+		high = u1 * v1;
+
+		/*
+		 * Assemble the final product.
+		 */
+		prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
+		    low.ul[H];
+		prod.ul[L] = low.ul[L];
+	}
+	return (negall ? -prod.q : prod.q);
+#undef u1
+#undef u0
+#undef v1
+#undef v0
+}
+
+/*
+ * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half
+ * the number of bits in a long (whatever that is---the code below
+ * does not care as long as quad.h does its part of the bargain---but
+ * typically N==16).
+ *
+ * We use the same algorithm from Knuth, but this time the modulo refinement
+ * does not apply.  On the other hand, since N is half the size of a long,
+ * we can get away with native multiplication---none of our input terms
+ * exceeds (ULONG_MAX >> 1).
+ *
+ * Note that, for u_long l, the quad-precision result
+ *
+ *	l << N
+ *
+ * splits into high and low longs as HHALF(l) and LHUP(l) respectively.
+ */
+static quad_t
+__lmulq(u_long u, u_long v)
+{
+	u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low;
+	u_long prodh, prodl, was;
+	union uu prod;
+	int neg;
+
+	u1 = HHALF(u);
+	u0 = LHALF(u);
+	v1 = HHALF(v);
+	v0 = LHALF(v);
+
+	low = u0 * v0;
+
+	/* This is the same small-number optimization as before. */
+	if (u1 == 0 && v1 == 0)
+		return (low);
+
+	if (u1 >= u0)
+		udiff = u1 - u0, neg = 0;
+	else
+		udiff = u0 - u1, neg = 1;
+	if (v0 >= v1)
+		vdiff = v0 - v1;
+	else
+		vdiff = v1 - v0, neg ^= 1;
+	mid = udiff * vdiff;
+
+	high = u1 * v1;
+
+	/* prod = (high << 2N) + (high << N); */
+	prodh = high + HHALF(high);
+	prodl = LHUP(high);
+
+	/* if (neg) prod -= mid << N; else prod += mid << N; */
+	if (neg) {
+		was = prodl;
+		prodl -= LHUP(mid);
+		prodh -= HHALF(mid) + (prodl > was);
+	} else {
+		was = prodl;
+		prodl += LHUP(mid);
+		prodh += HHALF(mid) + (prodl < was);
+	}
+
+	/* prod += low << N */
+	was = prodl;
+	prodl += LHUP(low);
+	prodh += HHALF(low) + (prodl < was);
+	/* ... + low; */
+	if ((prodl += low) < low)
+		prodh++;
+
+	/* return 4N-bit product */
+	prod.ul[H] = prodh;
+	prod.ul[L] = prodl;
+	return (prod.q);
+}