1 /* 2 * Copyright (c) 1992 The Regents of the University of California. 3 * 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 * %sccs.include.redist.c% 15 * 16 * @(#)fpu_mul.c 7.4 (Berkeley) 04/20/93 17 * 18 * from: $Header: fpu_mul.c,v 1.3 92/11/26 01:39:50 torek Exp $ 19 */ 20 21 /* 22 * Perform an FPU multiply (return x * y). 23 */ 24 25 #include <sys/types.h> 26 27 #include <machine/reg.h> 28 29 #include <sparc/fpu/fpu_arith.h> 30 #include <sparc/fpu/fpu_emu.h> 31 32 /* 33 * The multiplication algorithm for normal numbers is as follows: 34 * 35 * The fraction of the product is built in the usual stepwise fashion. 36 * Each step consists of shifting the accumulator right one bit 37 * (maintaining any guard bits) and, if the next bit in y is set, 38 * adding the multiplicand (x) to the accumulator. Then, in any case, 39 * we advance one bit leftward in y. Algorithmically: 40 * 41 * A = 0; 42 * for (bit = 0; bit < FP_NMANT; bit++) { 43 * sticky |= A & 1, A >>= 1; 44 * if (Y & (1 << bit)) 45 * A += X; 46 * } 47 * 48 * (X and Y here represent the mantissas of x and y respectively.) 49 * The resultant accumulator (A) is the product's mantissa. It may 50 * be as large as 11.11111... in binary and hence may need to be 51 * shifted right, but at most one bit. 52 * 53 * Since we do not have efficient multiword arithmetic, we code the 54 * accumulator as four separate words, just like any other mantissa. 55 * We use local `register' variables in the hope that this is faster 56 * than memory. We keep x->fp_mant in locals for the same reason. 57 * 58 * In the algorithm above, the bits in y are inspected one at a time. 59 * We will pick them up 32 at a time and then deal with those 32, one 60 * at a time. Note, however, that we know several things about y: 61 * 62 * - the guard and round bits at the bottom are sure to be zero; 63 * 64 * - often many low bits are zero (y is often from a single or double 65 * precision source); 66 * 67 * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word. 68 * 69 * We can also test for 32-zero-bits swiftly. In this case, the center 70 * part of the loop---setting sticky, shifting A, and not adding---will 71 * run 32 times without adding X to A. We can do a 32-bit shift faster 72 * by simply moving words. Since zeros are common, we optimize this case. 73 * Furthermore, since A is initially zero, we can omit the shift as well 74 * until we reach a nonzero word. 75 */ 76 struct fpn * 77 fpu_mul(fe) 78 register struct fpemu *fe; 79 { 80 register struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 81 register u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m; 82 register int sticky; 83 FPU_DECL_CARRY 84 85 /* 86 * Put the `heavier' operand on the right (see fpu_emu.h). 87 * Then we will have one of the following cases, taken in the 88 * following order: 89 * 90 * - y = NaN. Implied: if only one is a signalling NaN, y is. 91 * The result is y. 92 * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN 93 * case was taken care of earlier). 94 * If x = 0, the result is NaN. Otherwise the result 95 * is y, with its sign reversed if x is negative. 96 * - x = 0. Implied: y is 0 or number. 97 * The result is 0 (with XORed sign as usual). 98 * - other. Implied: both x and y are numbers. 99 * The result is x * y (XOR sign, multiply bits, add exponents). 100 */ 101 ORDER(x, y); 102 if (ISNAN(y)) { 103 y->fp_sign ^= x->fp_sign; 104 return (y); 105 } 106 if (ISINF(y)) { 107 if (ISZERO(x)) 108 return (fpu_newnan(fe)); 109 y->fp_sign ^= x->fp_sign; 110 return (y); 111 } 112 if (ISZERO(x)) { 113 x->fp_sign ^= y->fp_sign; 114 return (x); 115 } 116 117 /* 118 * Setup. In the code below, the mask `m' will hold the current 119 * mantissa byte from y. The variable `bit' denotes the bit 120 * within m. We also define some macros to deal with everything. 121 */ 122 x3 = x->fp_mant[3]; 123 x2 = x->fp_mant[2]; 124 x1 = x->fp_mant[1]; 125 x0 = x->fp_mant[0]; 126 sticky = a3 = a2 = a1 = a0 = 0; 127 128 #define ADD /* A += X */ \ 129 FPU_ADDS(a3, a3, x3); \ 130 FPU_ADDCS(a2, a2, x2); \ 131 FPU_ADDCS(a1, a1, x1); \ 132 FPU_ADDC(a0, a0, x0) 133 134 #define SHR1 /* A >>= 1, with sticky */ \ 135 sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \ 136 a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1 137 138 #define SHR32 /* A >>= 32, with sticky */ \ 139 sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0 140 141 #define STEP /* each 1-bit step of the multiplication */ \ 142 SHR1; if (bit & m) { ADD; }; bit <<= 1 143 144 /* 145 * We are ready to begin. The multiply loop runs once for each 146 * of the four 32-bit words. Some words, however, are special. 147 * As noted above, the low order bits of Y are often zero. Even 148 * if not, the first loop can certainly skip the guard bits. 149 * The last word of y has its highest 1-bit in position FP_NMANT-1, 150 * so we stop the loop when we move past that bit. 151 */ 152 if ((m = y->fp_mant[3]) == 0) { 153 /* SHR32; */ /* unneeded since A==0 */ 154 } else { 155 bit = 1 << FP_NG; 156 do { 157 STEP; 158 } while (bit != 0); 159 } 160 if ((m = y->fp_mant[2]) == 0) { 161 SHR32; 162 } else { 163 bit = 1; 164 do { 165 STEP; 166 } while (bit != 0); 167 } 168 if ((m = y->fp_mant[1]) == 0) { 169 SHR32; 170 } else { 171 bit = 1; 172 do { 173 STEP; 174 } while (bit != 0); 175 } 176 m = y->fp_mant[0]; /* definitely != 0 */ 177 bit = 1; 178 do { 179 STEP; 180 } while (bit <= m); 181 182 /* 183 * Done with mantissa calculation. Get exponent and handle 184 * 11.111...1 case, then put result in place. We reuse x since 185 * it already has the right class (FP_NUM). 186 */ 187 m = x->fp_exp + y->fp_exp; 188 if (a0 >= FP_2) { 189 SHR1; 190 m++; 191 } 192 x->fp_sign ^= y->fp_sign; 193 x->fp_exp = m; 194 x->fp_sticky = sticky; 195 x->fp_mant[3] = a3; 196 x->fp_mant[2] = a2; 197 x->fp_mant[1] = a1; 198 x->fp_mant[0] = a0; 199 return (x); 200 } 201