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+/* $NetBSD: muldi3.c,v 1.10 2005/12/11 12:24:37 christos 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.
+ *
+ * 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. 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.
+ */
+
+/*#include <sys/cdefs.h>
+#if defined(LIBC_SCCS) && !defined(lint)
+#if 0
+static char sccsid[] = "@(#)muldi3.c 8.1 (Berkeley) 6/4/93";
+#else
+__RCSID("$NetBSD: muldi3.c,v 1.10 2005/12/11 12:24:37 christos Exp $");
+#endif
+#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_int', 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 `int * int = quad' operator, we split
+ * our input quads into two ints, then split the two ints into two
+ * shorts. We can then calculate `short * short = int' 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_int, u_int);
+
+quad_t
+__muldi3(a, b)
+ quad_t a, b;
+{
+ union uu u, v, low, prod;
+ u_int high, mid, udiff, vdiff;
+ 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
+ * int 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_int * u_int => u_int 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 ints to produce a 4N-bit quad, where N is half
+ * the number of bits in an int (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 an int,
+ * we can get away with native multiplication---none of our input terms
+ * exceeds (UINT_MAX >> 1).
+ *
+ * Note that, for u_int l, the quad-precision result
+ *
+ * l << N
+ *
+ * splits into high and low ints as HHALF(l) and LHUP(l) respectively.
+ */
+static quad_t
+__lmulq(u_int u, u_int v)
+{
+ u_int u1, u0, v1, v0, udiff, vdiff, high, mid, low;
+ u_int 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);
+}