1 /* $NetBSD: fpu_mul.c,v 1.6 2009/03/14 15:36:09 dsl Exp $ */ 2 3 /* 4 * Copyright (c) 1992, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * This software was developed by the Computer Systems Engineering group 8 * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 9 * contributed to Berkeley. 10 * 11 * All advertising materials mentioning features or use of this software 12 * must display the following acknowledgement: 13 * This product includes software developed by the University of 14 * California, Lawrence Berkeley Laboratory. 15 * 16 * Redistribution and use in source and binary forms, with or without 17 * modification, are permitted provided that the following conditions 18 * are met: 19 * 1. Redistributions of source code must retain the above copyright 20 * notice, this list of conditions and the following disclaimer. 21 * 2. Redistributions in binary form must reproduce the above copyright 22 * notice, this list of conditions and the following disclaimer in the 23 * documentation and/or other materials provided with the distribution. 24 * 3. 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 * @(#)fpu_mul.c 8.1 (Berkeley) 6/11/93 41 */ 42 43 /* 44 * Perform an FPU multiply (return x * y). 45 */ 46 47 #include <sys/cdefs.h> 48 __KERNEL_RCSID(0, "$NetBSD: fpu_mul.c,v 1.6 2009/03/14 15:36:09 dsl Exp $"); 49 50 #include <sys/types.h> 51 52 #include <machine/reg.h> 53 54 #include "fpu_arith.h" 55 #include "fpu_emulate.h" 56 57 /* 58 * The multiplication algorithm for normal numbers is as follows: 59 * 60 * The fraction of the product is built in the usual stepwise fashion. 61 * Each step consists of shifting the accumulator right one bit 62 * (maintaining any guard bits) and, if the next bit in y is set, 63 * adding the multiplicand (x) to the accumulator. Then, in any case, 64 * we advance one bit leftward in y. Algorithmically: 65 * 66 * A = 0; 67 * for (bit = 0; bit < FP_NMANT; bit++) { 68 * sticky |= A & 1, A >>= 1; 69 * if (Y & (1 << bit)) 70 * A += X; 71 * } 72 * 73 * (X and Y here represent the mantissas of x and y respectively.) 74 * The resultant accumulator (A) is the product's mantissa. It may 75 * be as large as 11.11111... in binary and hence may need to be 76 * shifted right, but at most one bit. 77 * 78 * Since we do not have efficient multiword arithmetic, we code the 79 * accumulator as four separate words, just like any other mantissa. 80 * We use local `register' variables in the hope that this is faster 81 * than memory. We keep x->fp_mant in locals for the same reason. 82 * 83 * In the algorithm above, the bits in y are inspected one at a time. 84 * We will pick them up 32 at a time and then deal with those 32, one 85 * at a time. Note, however, that we know several things about y: 86 * 87 * - the guard and round bits at the bottom are sure to be zero; 88 * 89 * - often many low bits are zero (y is often from a single or double 90 * precision source); 91 * 92 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word. 93 * 94 * We can also test for 32-zero-bits swiftly. In this case, the center 95 * part of the loop---setting sticky, shifting A, and not adding---will 96 * run 32 times without adding X to A. We can do a 32-bit shift faster 97 * by simply moving words. Since zeros are common, we optimize this case. 98 * Furthermore, since A is initially zero, we can omit the shift as well 99 * until we reach a nonzero word. 100 */ 101 struct fpn * 102 fpu_mul(register struct fpemu *fe) 103 { 104 register struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 105 register u_int a2, a1, a0, x2, x1, x0, bit, m; 106 register int sticky; 107 FPU_DECL_CARRY 108 109 /* 110 * Put the `heavier' operand on the right (see fpu_emu.h). 111 * Then we will have one of the following cases, taken in the 112 * following order: 113 * 114 * - y = NaN. Implied: if only one is a signalling NaN, y is. 115 * The result is y. 116 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN 117 * case was taken care of earlier). 118 * If x = 0, the result is NaN. Otherwise the result 119 * is y, with its sign reversed if x is negative. 120 * - x = 0. Implied: y is 0 or number. 121 * The result is 0 (with XORed sign as usual). 122 * - other. Implied: both x and y are numbers. 123 * The result is x * y (XOR sign, multiply bits, add exponents). 124 */ 125 ORDER(x, y); 126 if (ISNAN(y)) { 127 y->fp_sign ^= x->fp_sign; 128 return (y); 129 } 130 if (ISINF(y)) { 131 if (ISZERO(x)) 132 return (fpu_newnan(fe)); 133 y->fp_sign ^= x->fp_sign; 134 return (y); 135 } 136 if (ISZERO(x)) { 137 x->fp_sign ^= y->fp_sign; 138 return (x); 139 } 140 141 /* 142 * Setup. In the code below, the mask `m' will hold the current 143 * mantissa byte from y. The variable `bit' denotes the bit 144 * within m. We also define some macros to deal with everything. 145 */ 146 x2 = x->fp_mant[2]; 147 x1 = x->fp_mant[1]; 148 x0 = x->fp_mant[0]; 149 sticky = a2 = a1 = a0 = 0; 150 151 #define ADD /* A += X */ \ 152 FPU_ADDS(a2, a2, x2); \ 153 FPU_ADDCS(a1, a1, x1); \ 154 FPU_ADDC(a0, a0, x0) 155 156 #define SHR1 /* A >>= 1, with sticky */ \ 157 sticky |= a2 & 1, \ 158 a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1 159 160 #define SHR32 /* A >>= 32, with sticky */ \ 161 sticky |= a2, a2 = a1, a1 = a0, a0 = 0 162 163 #define STEP /* each 1-bit step of the multiplication */ \ 164 SHR1; if (bit & m) { ADD; }; bit <<= 1 165 166 /* 167 * We are ready to begin. The multiply loop runs once for each 168 * of the four 32-bit words. Some words, however, are special. 169 * As noted above, the low order bits of Y are often zero. Even 170 * if not, the first loop can certainly skip the guard bits. 171 * The last word of y has its highest 1-bit in position FP_NMANT-1, 172 * so we stop the loop when we move past that bit. 173 */ 174 if ((m = y->fp_mant[2]) == 0) { 175 /* SHR32; */ /* unneeded since A==0 */ 176 } else { 177 bit = 1 << FP_NG; 178 do { 179 STEP; 180 } while (bit != 0); 181 } 182 if ((m = y->fp_mant[1]) == 0) { 183 SHR32; 184 } else { 185 bit = 1; 186 do { 187 STEP; 188 } while (bit != 0); 189 } 190 m = y->fp_mant[0]; /* definitely != 0 */ 191 bit = 1; 192 do { 193 STEP; 194 } while (bit <= m); 195 196 /* 197 * Done with mantissa calculation. Get exponent and handle 198 * 11.111...1 case, then put result in place. We reuse x since 199 * it already has the right class (FP_NUM). 200 */ 201 m = x->fp_exp + y->fp_exp; 202 if (a0 >= FP_2) { 203 SHR1; 204 m++; 205 } 206 x->fp_sign ^= y->fp_sign; 207 x->fp_exp = m; 208 x->fp_sticky = sticky; 209 x->fp_mant[2] = a2; 210 x->fp_mant[1] = a1; 211 x->fp_mant[0] = a0; 212 return (x); 213 } 214