1 /* 2 * Copyright (c) 1992, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * This software was developed by the Computer Systems Engineering group 6 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 7 * contributed to Berkeley. 8 * 9 * All advertising materials mentioning features or use of this software 10 * must display the following acknowledgement: 11 * This product includes software developed by the University of 12 * California, Lawrence Berkeley Laboratory. 13 * 14 * Redistribution and use in source and binary forms, with or without 15 * modification, are permitted provided that the following conditions 16 * are met: 17 * 1. Redistributions of source code must retain the above copyright 18 * notice, this list of conditions and the following disclaimer. 19 * 2. Redistributions in binary form must reproduce the above copyright 20 * notice, this list of conditions and the following disclaimer in the 21 * documentation and/or other materials provided with the distribution. 22 * 3. Neither the name of the University nor the names of its contributors 23 * may be used to endorse or promote products derived from this software 24 * without specific prior written permission. 25 * 26 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 27 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 28 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 29 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 30 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 31 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 32 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 33 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 34 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 35 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 36 * SUCH DAMAGE. 37 * 38 * @(#)fpu_mul.c 8.1 (Berkeley) 6/11/93 39 * $NetBSD: fpu_mul.c,v 1.2 1994/11/20 20:52:44 deraadt Exp $ 40 */ 41 42 #include <sys/cdefs.h> 43 44 /* 45 * Perform an FPU multiply (return x * y). 46 */ 47 48 #include <sys/types.h> 49 50 #include "fpu_arith.h" 51 #include "fpu_emu.h" 52 #include "fpu_extern.h" 53 54 /* 55 * The multiplication algorithm for normal numbers is as follows: 56 * 57 * The fraction of the product is built in the usual stepwise fashion. 58 * Each step consists of shifting the accumulator right one bit 59 * (maintaining any guard bits) and, if the next bit in y is set, 60 * adding the multiplicand (x) to the accumulator. Then, in any case, 61 * we advance one bit leftward in y. Algorithmically: 62 * 63 * A = 0; 64 * for (bit = 0; bit < FP_NMANT; bit++) { 65 * sticky |= A & 1, A >>= 1; 66 * if (Y & (1 << bit)) 67 * A += X; 68 * } 69 * 70 * (X and Y here represent the mantissas of x and y respectively.) 71 * The resultant accumulator (A) is the product's mantissa. It may 72 * be as large as 11.11111... in binary and hence may need to be 73 * shifted right, but at most one bit. 74 * 75 * Since we do not have efficient multiword arithmetic, we code the 76 * accumulator as four separate words, just like any other mantissa. 77 * We use local `register' variables in the hope that this is faster 78 * than memory. We keep x->fp_mant in locals for the same reason. 79 * 80 * In the algorithm above, the bits in y are inspected one at a time. 81 * We will pick them up 32 at a time and then deal with those 32, one 82 * at a time. Note, however, that we know several things about y: 83 * 84 * - the guard and round bits at the bottom are sure to be zero; 85 * 86 * - often many low bits are zero (y is often from a single or double 87 * precision source); 88 * 89 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word. 90 * 91 * We can also test for 32-zero-bits swiftly. In this case, the center 92 * part of the loop---setting sticky, shifting A, and not adding---will 93 * run 32 times without adding X to A. We can do a 32-bit shift faster 94 * by simply moving words. Since zeros are common, we optimize this case. 95 * Furthermore, since A is initially zero, we can omit the shift as well 96 * until we reach a nonzero word. 97 */ 98 struct fpn * 99 __fpu_mul(fe) 100 struct fpemu *fe; 101 { 102 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 103 u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m; 104 int sticky; 105 FPU_DECL_CARRY 106 107 /* 108 * Put the `heavier' operand on the right (see fpu_emu.h). 109 * Then we will have one of the following cases, taken in the 110 * following order: 111 * 112 * - y = NaN. Implied: if only one is a signalling NaN, y is. 113 * The result is y. 114 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN 115 * case was taken care of earlier). 116 * If x = 0, the result is NaN. Otherwise the result 117 * is y, with its sign reversed if x is negative. 118 * - x = 0. Implied: y is 0 or number. 119 * The result is 0 (with XORed sign as usual). 120 * - other. Implied: both x and y are numbers. 121 * The result is x * y (XOR sign, multiply bits, add exponents). 122 */ 123 ORDER(x, y); 124 if (ISNAN(y)) 125 return (y); 126 if (ISINF(y)) { 127 if (ISZERO(x)) 128 return (__fpu_newnan(fe)); 129 y->fp_sign ^= x->fp_sign; 130 return (y); 131 } 132 if (ISZERO(x)) { 133 x->fp_sign ^= y->fp_sign; 134 return (x); 135 } 136 137 /* 138 * Setup. In the code below, the mask `m' will hold the current 139 * mantissa byte from y. The variable `bit' denotes the bit 140 * within m. We also define some macros to deal with everything. 141 */ 142 x3 = x->fp_mant[3]; 143 x2 = x->fp_mant[2]; 144 x1 = x->fp_mant[1]; 145 x0 = x->fp_mant[0]; 146 sticky = a3 = a2 = a1 = a0 = 0; 147 148 #define ADD /* A += X */ \ 149 FPU_ADDS(a3, a3, x3); \ 150 FPU_ADDCS(a2, a2, x2); \ 151 FPU_ADDCS(a1, a1, x1); \ 152 FPU_ADDC(a0, a0, x0) 153 154 #define SHR1 /* A >>= 1, with sticky */ \ 155 sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \ 156 a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1 157 158 #define SHR32 /* A >>= 32, with sticky */ \ 159 sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0 160 161 #define STEP /* each 1-bit step of the multiplication */ \ 162 SHR1; if (bit & m) { ADD; }; bit <<= 1 163 164 /* 165 * We are ready to begin. The multiply loop runs once for each 166 * of the four 32-bit words. Some words, however, are special. 167 * As noted above, the low order bits of Y are often zero. Even 168 * if not, the first loop can certainly skip the guard bits. 169 * The last word of y has its highest 1-bit in position FP_NMANT-1, 170 * so we stop the loop when we move past that bit. 171 */ 172 if ((m = y->fp_mant[3]) == 0) { 173 /* SHR32; */ /* unneeded since A==0 */ 174 } else { 175 bit = 1 << FP_NG; 176 do { 177 STEP; 178 } while (bit != 0); 179 } 180 if ((m = y->fp_mant[2]) == 0) { 181 SHR32; 182 } else { 183 bit = 1; 184 do { 185 STEP; 186 } while (bit != 0); 187 } 188 if ((m = y->fp_mant[1]) == 0) { 189 SHR32; 190 } else { 191 bit = 1; 192 do { 193 STEP; 194 } while (bit != 0); 195 } 196 m = y->fp_mant[0]; /* definitely != 0 */ 197 bit = 1; 198 do { 199 STEP; 200 } while (bit <= m); 201 202 /* 203 * Done with mantissa calculation. Get exponent and handle 204 * 11.111...1 case, then put result in place. We reuse x since 205 * it already has the right class (FP_NUM). 206 */ 207 m = x->fp_exp + y->fp_exp; 208 if (a0 >= FP_2) { 209 SHR1; 210 m++; 211 } 212 x->fp_sign ^= y->fp_sign; 213 x->fp_exp = m; 214 x->fp_sticky = sticky; 215 x->fp_mant[3] = a3; 216 x->fp_mant[2] = a2; 217 x->fp_mant[1] = a1; 218 x->fp_mant[0] = a0; 219 return (x); 220 } 221