1 /* $OpenBSD: muldi3.c,v 1.3 1998/06/27 00:32:26 mickey Exp $ */ 2 /* $NetBSD: muldi3.c,v 1.5 1995/10/07 09:26:33 mycroft Exp $ */ 3 4 /*- 5 * Copyright (c) 1992, 1993 6 * The Regents of the University of California. All rights reserved. 7 * 8 * This software was developed by the Computer Systems Engineering group 9 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 10 * contributed to Berkeley. 11 * 12 * Redistribution and use in source and binary forms, with or without 13 * modification, are permitted provided that the following conditions 14 * are met: 15 * 1. Redistributions of source code must retain the above copyright 16 * notice, this list of conditions and the following disclaimer. 17 * 2. Redistributions in binary form must reproduce the above copyright 18 * notice, this list of conditions and the following disclaimer in the 19 * documentation and/or other materials provided with the distribution. 20 * 3. All advertising materials mentioning features or use of this software 21 * must display the following acknowledgement: 22 * This product includes software developed by the University of 23 * California, Berkeley and its contributors. 24 * 4. Neither the name of the University nor the names of its contributors 25 * may be used to endorse or promote products derived from this software 26 * without specific prior written permission. 27 * 28 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 29 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 30 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 31 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 32 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 33 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 34 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 35 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 37 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 38 * SUCH DAMAGE. 39 */ 40 41 #if defined(LIBC_SCCS) && !defined(lint) 42 #if 0 43 static char sccsid[] = "@(#)muldi3.c 8.1 (Berkeley) 6/4/93"; 44 #else 45 static char rcsid[] = "$OpenBSD: muldi3.c,v 1.3 1998/06/27 00:32:26 mickey Exp $"; 46 #endif 47 #endif /* LIBC_SCCS and not lint */ 48 49 #include "quad.h" 50 51 /* 52 * Multiply two quads. 53 * 54 * Our algorithm is based on the following. Split incoming quad values 55 * u and v (where u,v >= 0) into 56 * 57 * u = 2^n u1 * u0 (n = number of bits in `u_long', usu. 32) 58 * 59 * and 60 * 61 * v = 2^n v1 * v0 62 * 63 * Then 64 * 65 * uv = 2^2n u1 v1 + 2^n u1 v0 + 2^n v1 u0 + u0 v0 66 * = 2^2n u1 v1 + 2^n (u1 v0 + v1 u0) + u0 v0 67 * 68 * Now add 2^n u1 v1 to the first term and subtract it from the middle, 69 * and add 2^n u0 v0 to the last term and subtract it from the middle. 70 * This gives: 71 * 72 * uv = (2^2n + 2^n) (u1 v1) + 73 * (2^n) (u1 v0 - u1 v1 + u0 v1 - u0 v0) + 74 * (2^n + 1) (u0 v0) 75 * 76 * Factoring the middle a bit gives us: 77 * 78 * uv = (2^2n + 2^n) (u1 v1) + [u1v1 = high] 79 * (2^n) (u1 - u0) (v0 - v1) + [(u1-u0)... = mid] 80 * (2^n + 1) (u0 v0) [u0v0 = low] 81 * 82 * The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done 83 * in just half the precision of the original. (Note that either or both 84 * of (u1 - u0) or (v0 - v1) may be negative.) 85 * 86 * This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278. 87 * 88 * Since C does not give us a `long * long = quad' operator, we split 89 * our input quads into two longs, then split the two longs into two 90 * shorts. We can then calculate `short * short = long' in native 91 * arithmetic. 92 * 93 * Our product should, strictly speaking, be a `long quad', with 128 94 * bits, but we are going to discard the upper 64. In other words, 95 * we are not interested in uv, but rather in (uv mod 2^2n). This 96 * makes some of the terms above vanish, and we get: 97 * 98 * (2^n)(high) + (2^n)(mid) + (2^n + 1)(low) 99 * 100 * or 101 * 102 * (2^n)(high + mid + low) + low 103 * 104 * Furthermore, `high' and `mid' can be computed mod 2^n, as any factor 105 * of 2^n in either one will also vanish. Only `low' need be computed 106 * mod 2^2n, and only because of the final term above. 107 */ 108 static quad_t __lmulq __P((u_long, u_long)); 109 110 quad_t 111 __muldi3(a, b) 112 quad_t a, b; 113 { 114 union uu u, v, low, prod; 115 register u_long high, mid, udiff, vdiff; 116 register int negall, negmid; 117 #define u1 u.ul[H] 118 #define u0 u.ul[L] 119 #define v1 v.ul[H] 120 #define v0 v.ul[L] 121 122 /* 123 * Get u and v such that u, v >= 0. When this is finished, 124 * u1, u0, v1, and v0 will be directly accessible through the 125 * longword fields. 126 */ 127 if (a >= 0) 128 u.q = a, negall = 0; 129 else 130 u.q = -a, negall = 1; 131 if (b >= 0) 132 v.q = b; 133 else 134 v.q = -b, negall ^= 1; 135 136 if (u1 == 0 && v1 == 0) { 137 /* 138 * An (I hope) important optimization occurs when u1 and v1 139 * are both 0. This should be common since most numbers 140 * are small. Here the product is just u0*v0. 141 */ 142 prod.q = __lmulq(u0, v0); 143 } else { 144 /* 145 * Compute the three intermediate products, remembering 146 * whether the middle term is negative. We can discard 147 * any upper bits in high and mid, so we can use native 148 * u_long * u_long => u_long arithmetic. 149 */ 150 low.q = __lmulq(u0, v0); 151 152 if (u1 >= u0) 153 negmid = 0, udiff = u1 - u0; 154 else 155 negmid = 1, udiff = u0 - u1; 156 if (v0 >= v1) 157 vdiff = v0 - v1; 158 else 159 vdiff = v1 - v0, negmid ^= 1; 160 mid = udiff * vdiff; 161 162 high = u1 * v1; 163 164 /* 165 * Assemble the final product. 166 */ 167 prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] + 168 low.ul[H]; 169 prod.ul[L] = low.ul[L]; 170 } 171 return (negall ? -prod.q : prod.q); 172 #undef u1 173 #undef u0 174 #undef v1 175 #undef v0 176 } 177 178 /* 179 * Multiply two 2N-bit longs to produce a 4N-bit quad, where N is half 180 * the number of bits in a long (whatever that is---the code below 181 * does not care as long as quad.h does its part of the bargain---but 182 * typically N==16). 183 * 184 * We use the same algorithm from Knuth, but this time the modulo refinement 185 * does not apply. On the other hand, since N is half the size of a long, 186 * we can get away with native multiplication---none of our input terms 187 * exceeds (ULONG_MAX >> 1). 188 * 189 * Note that, for u_long l, the quad-precision result 190 * 191 * l << N 192 * 193 * splits into high and low longs as HHALF(l) and LHUP(l) respectively. 194 */ 195 static quad_t 196 __lmulq(u, v) 197 u_long u; 198 u_long v; 199 { 200 u_long u1, u0, v1, v0, udiff, vdiff, high, mid, low; 201 u_long prodh, prodl, was; 202 union uu prod; 203 int neg; 204 205 u1 = HHALF(u); 206 u0 = LHALF(u); 207 v1 = HHALF(v); 208 v0 = LHALF(v); 209 210 low = u0 * v0; 211 212 /* This is the same small-number optimization as before. */ 213 if (u1 == 0 && v1 == 0) 214 return (low); 215 216 if (u1 >= u0) 217 udiff = u1 - u0, neg = 0; 218 else 219 udiff = u0 - u1, neg = 1; 220 if (v0 >= v1) 221 vdiff = v0 - v1; 222 else 223 vdiff = v1 - v0, neg ^= 1; 224 mid = udiff * vdiff; 225 226 high = u1 * v1; 227 228 /* prod = (high << 2N) + (high << N); */ 229 prodh = high + HHALF(high); 230 prodl = LHUP(high); 231 232 /* if (neg) prod -= mid << N; else prod += mid << N; */ 233 if (neg) { 234 was = prodl; 235 prodl -= LHUP(mid); 236 prodh -= HHALF(mid) + (prodl > was); 237 } else { 238 was = prodl; 239 prodl += LHUP(mid); 240 prodh += HHALF(mid) + (prodl < was); 241 } 242 243 /* prod += low << N */ 244 was = prodl; 245 prodl += LHUP(low); 246 prodh += HHALF(low) + (prodl < was); 247 /* ... + low; */ 248 if ((prodl += low) < low) 249 prodh++; 250 251 /* return 4N-bit product */ 252 prod.ul[H] = prodh; 253 prod.ul[L] = prodl; 254 return (prod.q); 255 } 256