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Diffstat (limited to 'sys/lib/libkern/muldi3.c')
| -rw-r--r-- | sys/lib/libkern/muldi3.c | 252 |
1 files changed, 252 insertions, 0 deletions
diff --git a/sys/lib/libkern/muldi3.c b/sys/lib/libkern/muldi3.c new file mode 100644 index 00000000000..1df8b0f7b9e --- /dev/null +++ b/sys/lib/libkern/muldi3.c @@ -0,0 +1,252 @@ +/* $NetBSD: muldi3.c,v 1.5 1995/10/07 09:26:33 mycroft 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. 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) +#if 0 +static char sccsid[] = "@(#)muldi3.c 8.1 (Berkeley) 6/4/93"; +#else +static char rcsid[] = "$NetBSD: muldi3.c,v 1.5 1995/10/07 09:26:33 mycroft 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_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); +} |