Annotation of sys/arch/sparc/fpu/fpu_mul.c, Revision 1.1
1.1 ! nbrk 1: /* $OpenBSD: fpu_mul.c,v 1.3 2003/06/02 23:27:54 millert Exp $ */
! 2: /* $NetBSD: fpu_mul.c,v 1.2 1994/11/20 20:52:44 deraadt 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: * All advertising materials mentioning features or use of this software
! 13: * must display the following acknowledgement:
! 14: * This product includes software developed by the University of
! 15: * California, Lawrence Berkeley Laboratory.
! 16: *
! 17: * Redistribution and use in source and binary forms, with or without
! 18: * modification, are permitted provided that the following conditions
! 19: * are met:
! 20: * 1. Redistributions of source code must retain the above copyright
! 21: * notice, this list of conditions and the following disclaimer.
! 22: * 2. Redistributions in binary form must reproduce the above copyright
! 23: * notice, this list of conditions and the following disclaimer in the
! 24: * documentation and/or other materials provided with the distribution.
! 25: * 3. Neither the name of the University nor the names of its contributors
! 26: * may be used to endorse or promote products derived from this software
! 27: * without specific prior written permission.
! 28: *
! 29: * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
! 30: * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
! 31: * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
! 32: * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
! 33: * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
! 34: * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
! 35: * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
! 36: * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
! 37: * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
! 38: * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
! 39: * SUCH DAMAGE.
! 40: *
! 41: * @(#)fpu_mul.c 8.1 (Berkeley) 6/11/93
! 42: */
! 43:
! 44: /*
! 45: * Perform an FPU multiply (return x * y).
! 46: */
! 47:
! 48: #include <sys/types.h>
! 49:
! 50: #include <machine/reg.h>
! 51:
! 52: #include <sparc/fpu/fpu_arith.h>
! 53: #include <sparc/fpu/fpu_emu.h>
! 54:
! 55: /*
! 56: * The multiplication algorithm for normal numbers is as follows:
! 57: *
! 58: * The fraction of the product is built in the usual stepwise fashion.
! 59: * Each step consists of shifting the accumulator right one bit
! 60: * (maintaining any guard bits) and, if the next bit in y is set,
! 61: * adding the multiplicand (x) to the accumulator. Then, in any case,
! 62: * we advance one bit leftward in y. Algorithmically:
! 63: *
! 64: * A = 0;
! 65: * for (bit = 0; bit < FP_NMANT; bit++) {
! 66: * sticky |= A & 1, A >>= 1;
! 67: * if (Y & (1 << bit))
! 68: * A += X;
! 69: * }
! 70: *
! 71: * (X and Y here represent the mantissas of x and y respectively.)
! 72: * The resultant accumulator (A) is the product's mantissa. It may
! 73: * be as large as 11.11111... in binary and hence may need to be
! 74: * shifted right, but at most one bit.
! 75: *
! 76: * Since we do not have efficient multiword arithmetic, we code the
! 77: * accumulator as four separate words, just like any other mantissa.
! 78: * We use local `register' variables in the hope that this is faster
! 79: * than memory. We keep x->fp_mant in locals for the same reason.
! 80: *
! 81: * In the algorithm above, the bits in y are inspected one at a time.
! 82: * We will pick them up 32 at a time and then deal with those 32, one
! 83: * at a time. Note, however, that we know several things about y:
! 84: *
! 85: * - the guard and round bits at the bottom are sure to be zero;
! 86: *
! 87: * - often many low bits are zero (y is often from a single or double
! 88: * precision source);
! 89: *
! 90: * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word.
! 91: *
! 92: * We can also test for 32-zero-bits swiftly. In this case, the center
! 93: * part of the loop---setting sticky, shifting A, and not adding---will
! 94: * run 32 times without adding X to A. We can do a 32-bit shift faster
! 95: * by simply moving words. Since zeros are common, we optimize this case.
! 96: * Furthermore, since A is initially zero, we can omit the shift as well
! 97: * until we reach a nonzero word.
! 98: */
! 99: struct fpn *
! 100: fpu_mul(fe)
! 101: register struct fpemu *fe;
! 102: {
! 103: register struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2;
! 104: register u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m;
! 105: register int sticky;
! 106: FPU_DECL_CARRY
! 107:
! 108: /*
! 109: * Put the `heavier' operand on the right (see fpu_emu.h).
! 110: * Then we will have one of the following cases, taken in the
! 111: * following order:
! 112: *
! 113: * - y = NaN. Implied: if only one is a signalling NaN, y is.
! 114: * The result is y.
! 115: * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN
! 116: * case was taken care of earlier).
! 117: * If x = 0, the result is NaN. Otherwise the result
! 118: * is y, with its sign reversed if x is negative.
! 119: * - x = 0. Implied: y is 0 or number.
! 120: * The result is 0 (with XORed sign as usual).
! 121: * - other. Implied: both x and y are numbers.
! 122: * The result is x * y (XOR sign, multiply bits, add exponents).
! 123: */
! 124: ORDER(x, y);
! 125: if (ISNAN(y)) {
! 126: y->fp_sign ^= x->fp_sign;
! 127: return (y);
! 128: }
! 129: if (ISINF(y)) {
! 130: if (ISZERO(x))
! 131: return (fpu_newnan(fe));
! 132: y->fp_sign ^= x->fp_sign;
! 133: return (y);
! 134: }
! 135: if (ISZERO(x)) {
! 136: x->fp_sign ^= y->fp_sign;
! 137: return (x);
! 138: }
! 139:
! 140: /*
! 141: * Setup. In the code below, the mask `m' will hold the current
! 142: * mantissa byte from y. The variable `bit' denotes the bit
! 143: * within m. We also define some macros to deal with everything.
! 144: */
! 145: x3 = x->fp_mant[3];
! 146: x2 = x->fp_mant[2];
! 147: x1 = x->fp_mant[1];
! 148: x0 = x->fp_mant[0];
! 149: sticky = a3 = a2 = a1 = a0 = 0;
! 150:
! 151: #define ADD /* A += X */ \
! 152: FPU_ADDS(a3, a3, x3); \
! 153: FPU_ADDCS(a2, a2, x2); \
! 154: FPU_ADDCS(a1, a1, x1); \
! 155: FPU_ADDC(a0, a0, x0)
! 156:
! 157: #define SHR1 /* A >>= 1, with sticky */ \
! 158: sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \
! 159: a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1
! 160:
! 161: #define SHR32 /* A >>= 32, with sticky */ \
! 162: sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0
! 163:
! 164: #define STEP /* each 1-bit step of the multiplication */ \
! 165: SHR1; if (bit & m) { ADD; }; bit <<= 1
! 166:
! 167: /*
! 168: * We are ready to begin. The multiply loop runs once for each
! 169: * of the four 32-bit words. Some words, however, are special.
! 170: * As noted above, the low order bits of Y are often zero. Even
! 171: * if not, the first loop can certainly skip the guard bits.
! 172: * The last word of y has its highest 1-bit in position FP_NMANT-1,
! 173: * so we stop the loop when we move past that bit.
! 174: */
! 175: if ((m = y->fp_mant[3]) == 0) {
! 176: /* SHR32; */ /* unneeded since A==0 */
! 177: } else {
! 178: bit = 1 << FP_NG;
! 179: do {
! 180: STEP;
! 181: } while (bit != 0);
! 182: }
! 183: if ((m = y->fp_mant[2]) == 0) {
! 184: SHR32;
! 185: } else {
! 186: bit = 1;
! 187: do {
! 188: STEP;
! 189: } while (bit != 0);
! 190: }
! 191: if ((m = y->fp_mant[1]) == 0) {
! 192: SHR32;
! 193: } else {
! 194: bit = 1;
! 195: do {
! 196: STEP;
! 197: } while (bit != 0);
! 198: }
! 199: m = y->fp_mant[0]; /* definitely != 0 */
! 200: bit = 1;
! 201: do {
! 202: STEP;
! 203: } while (bit <= m);
! 204:
! 205: /*
! 206: * Done with mantissa calculation. Get exponent and handle
! 207: * 11.111...1 case, then put result in place. We reuse x since
! 208: * it already has the right class (FP_NUM).
! 209: */
! 210: m = x->fp_exp + y->fp_exp;
! 211: if (a0 >= FP_2) {
! 212: SHR1;
! 213: m++;
! 214: }
! 215: x->fp_sign ^= y->fp_sign;
! 216: x->fp_exp = m;
! 217: x->fp_sticky = sticky;
! 218: x->fp_mant[3] = a3;
! 219: x->fp_mant[2] = a2;
! 220: x->fp_mant[1] = a1;
! 221: x->fp_mant[0] = a0;
! 222: return (x);
! 223: }
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