This patch imports the unmodified current version of NetBSD libc. The NetBSD includes are in /nbsd_include, while the libc code itself is split between lib/nbsd_libc and common/lib/libc.
248 lines
7 KiB
C
248 lines
7 KiB
C
/* $NetBSD: muldi3.c,v 1.2 2009/03/15 22:31:12 cegger 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 1.2 2009/03/15 22:31:12 cegger 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(quad_t a, quad_t 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);
|
|
}
|