1 /* $OpenBSD: fpu_mul.c,v 1.2 2012/12/05 23:19:59 deraadt 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. All advertising materials mentioning features or use of this software 25 * must display the following acknowledgement: 26 * This product includes software developed by the University of 27 * California, Berkeley and its contributors. 28 * 4. Neither the name of the University nor the names of its contributors 29 * may be used to endorse or promote products derived from this software 30 * without specific prior written permission. 31 * 32 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 33 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 34 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 35 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 36 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 37 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 38 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 39 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 40 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 41 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 42 * SUCH DAMAGE. 43 * 44 * @(#)fpu_mul.c 8.1 (Berkeley) 6/11/93 45 * $NetBSD: fpu_mul.c,v 1.2 1994/11/20 20:52:44 deraadt Exp $ 46 */ 47 48 #if 0 49 __FBSDID("$FreeBSD: src/lib/libc/sparc64/fpu/fpu_mul.c,v 1.3 2002/03/22 21:52:58 obrien Exp $"); 50 #endif 51 52 /* 53 * Perform an FPU multiply (return x * y). 54 */ 55 56 #include <sys/types.h> 57 58 #include <machine/frame.h> 59 60 #include "fpu_arith.h" 61 #include "fpu_emu.h" 62 #include "fpu_extern.h" 63 64 /* 65 * The multiplication algorithm for normal numbers is as follows: 66 * 67 * The fraction of the product is built in the usual stepwise fashion. 68 * Each step consists of shifting the accumulator right one bit 69 * (maintaining any guard bits) and, if the next bit in y is set, 70 * adding the multiplicand (x) to the accumulator. Then, in any case, 71 * we advance one bit leftward in y. Algorithmically: 72 * 73 * A = 0; 74 * for (bit = 0; bit < FP_NMANT; bit++) { 75 * sticky |= A & 1, A >>= 1; 76 * if (Y & (1 << bit)) 77 * A += X; 78 * } 79 * 80 * (X and Y here represent the mantissas of x and y respectively.) 81 * The resultant accumulator (A) is the product's mantissa. It may 82 * be as large as 11.11111... in binary and hence may need to be 83 * shifted right, but at most one bit. 84 * 85 * Since we do not have efficient multiword arithmetic, we code the 86 * accumulator as four separate words, just like any other mantissa. 87 * We use local `register' variables in the hope that this is faster 88 * than memory. We keep x->fp_mant in locals for the same reason. 89 * 90 * In the algorithm above, the bits in y are inspected one at a time. 91 * We will pick them up 32 at a time and then deal with those 32, one 92 * at a time. Note, however, that we know several things about y: 93 * 94 * - the guard and round bits at the bottom are sure to be zero; 95 * 96 * - often many low bits are zero (y is often from a single or double 97 * precision source); 98 * 99 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word. 100 * 101 * We can also test for 32-zero-bits swiftly. In this case, the center 102 * part of the loop---setting sticky, shifting A, and not adding---will 103 * run 32 times without adding X to A. We can do a 32-bit shift faster 104 * by simply moving words. Since zeros are common, we optimize this case. 105 * Furthermore, since A is initially zero, we can omit the shift as well 106 * until we reach a nonzero word. 107 */ 108 struct fpn * 109 __fpu_mul(fe) 110 struct fpemu *fe; 111 { 112 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 113 u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m; 114 int sticky; 115 FPU_DECL_CARRY 116 117 /* 118 * Put the `heavier' operand on the right (see fpu_emu.h). 119 * Then we will have one of the following cases, taken in the 120 * following order: 121 * 122 * - y = NaN. Implied: if only one is a signalling NaN, y is. 123 * The result is y. 124 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN 125 * case was taken care of earlier). 126 * If x = 0, the result is NaN. Otherwise the result 127 * is y, with its sign reversed if x is negative. 128 * - x = 0. Implied: y is 0 or number. 129 * The result is 0 (with XORed sign as usual). 130 * - other. Implied: both x and y are numbers. 131 * The result is x * y (XOR sign, multiply bits, add exponents). 132 */ 133 ORDER(x, y); 134 if (ISNAN(y)) { 135 y->fp_sign ^= x->fp_sign; 136 return (y); 137 } 138 if (ISINF(y)) { 139 if (ISZERO(x)) 140 return (__fpu_newnan(fe)); 141 y->fp_sign ^= x->fp_sign; 142 return (y); 143 } 144 if (ISZERO(x)) { 145 x->fp_sign ^= y->fp_sign; 146 return (x); 147 } 148 149 /* 150 * Setup. In the code below, the mask `m' will hold the current 151 * mantissa byte from y. The variable `bit' denotes the bit 152 * within m. We also define some macros to deal with everything. 153 */ 154 x3 = x->fp_mant[3]; 155 x2 = x->fp_mant[2]; 156 x1 = x->fp_mant[1]; 157 x0 = x->fp_mant[0]; 158 sticky = a3 = a2 = a1 = a0 = 0; 159 160 #define ADD /* A += X */ \ 161 FPU_ADDS(a3, a3, x3); \ 162 FPU_ADDCS(a2, a2, x2); \ 163 FPU_ADDCS(a1, a1, x1); \ 164 FPU_ADDC(a0, a0, x0) 165 166 #define SHR1 /* A >>= 1, with sticky */ \ 167 sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \ 168 a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1 169 170 #define SHR32 /* A >>= 32, with sticky */ \ 171 sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0 172 173 #define STEP /* each 1-bit step of the multiplication */ \ 174 SHR1; if (bit & m) { ADD; }; bit <<= 1 175 176 /* 177 * We are ready to begin. The multiply loop runs once for each 178 * of the four 32-bit words. Some words, however, are special. 179 * As noted above, the low order bits of Y are often zero. Even 180 * if not, the first loop can certainly skip the guard bits. 181 * The last word of y has its highest 1-bit in position FP_NMANT-1, 182 * so we stop the loop when we move past that bit. 183 */ 184 if ((m = y->fp_mant[3]) == 0) { 185 /* SHR32; */ /* unneeded since A==0 */ 186 } else { 187 bit = 1 << FP_NG; 188 do { 189 STEP; 190 } while (bit != 0); 191 } 192 if ((m = y->fp_mant[2]) == 0) { 193 SHR32; 194 } else { 195 bit = 1; 196 do { 197 STEP; 198 } while (bit != 0); 199 } 200 if ((m = y->fp_mant[1]) == 0) { 201 SHR32; 202 } else { 203 bit = 1; 204 do { 205 STEP; 206 } while (bit != 0); 207 } 208 m = y->fp_mant[0]; /* definitely != 0 */ 209 bit = 1; 210 do { 211 STEP; 212 } while (bit <= m); 213 214 /* 215 * Done with mantissa calculation. Get exponent and handle 216 * 11.111...1 case, then put result in place. We reuse x since 217 * it already has the right class (FP_NUM). 218 */ 219 m = x->fp_exp + y->fp_exp; 220 if (a0 >= FP_2) { 221 SHR1; 222 m++; 223 } 224 x->fp_sign ^= y->fp_sign; 225 x->fp_exp = m; 226 x->fp_sticky = sticky; 227 x->fp_mant[3] = a3; 228 x->fp_mant[2] = a2; 229 x->fp_mant[1] = a1; 230 x->fp_mant[0] = a0; 231 return (x); 232 } 233