1200576Sroberto/* $NetBSD: fpu_mul.c,v 1.4 2005/12/11 12:18:42 christos Exp $ */ 2181834Sroberto 3181834Sroberto/* 4200576Sroberto * SPDX-License-Identifier: BSD-3-Clause 5181834Sroberto * 6181834Sroberto * Copyright (c) 1992, 1993 7181834Sroberto * The Regents of the University of California. All rights reserved. 8181834Sroberto * 9181834Sroberto * This software was developed by the Computer Systems Engineering group 10181834Sroberto * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 11181834Sroberto * contributed to Berkeley. 12181834Sroberto * 13181834Sroberto * All advertising materials mentioning features or use of this software 14181834Sroberto * must display the following acknowledgement: 15181834Sroberto * This product includes software developed by the University of 16181834Sroberto * California, Lawrence Berkeley Laboratory. 17181834Sroberto * 18181834Sroberto * Redistribution and use in source and binary forms, with or without 19181834Sroberto * modification, are permitted provided that the following conditions 20181834Sroberto * are met: 21181834Sroberto * 1. Redistributions of source code must retain the above copyright 22181834Sroberto * notice, this list of conditions and the following disclaimer. 23181834Sroberto * 2. Redistributions in binary form must reproduce the above copyright 24181834Sroberto * notice, this list of conditions and the following disclaimer in the 25181834Sroberto * documentation and/or other materials provided with the distribution. 26181834Sroberto * 3. Neither the name of the University nor the names of its contributors 27181834Sroberto * may be used to endorse or promote products derived from this software 28181834Sroberto * without specific prior written permission. 29181834Sroberto * 30181834Sroberto * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 31181834Sroberto * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 32181834Sroberto * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 33181834Sroberto * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 34181834Sroberto * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 35181834Sroberto * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 36181834Sroberto * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 37181834Sroberto * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 38181834Sroberto * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 39181834Sroberto * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 40181834Sroberto * SUCH DAMAGE. 41181834Sroberto */ 42181834Sroberto 43181834Sroberto/* 44181834Sroberto * Perform an FPU multiply (return x * y). 45181834Sroberto */ 46181834Sroberto 47181834Sroberto#include <sys/types.h> 48181834Sroberto#include <sys/systm.h> 49181834Sroberto 50181834Sroberto#include <machine/fpu.h> 51181834Sroberto 52181834Sroberto#include <powerpc/fpu/fpu_arith.h> 53181834Sroberto#include <powerpc/fpu/fpu_emu.h> 54181834Sroberto 55181834Sroberto/* 56181834Sroberto * The multiplication algorithm for normal numbers is as follows: 57181834Sroberto * 58181834Sroberto * The fraction of the product is built in the usual stepwise fashion. 59181834Sroberto * Each step consists of shifting the accumulator right one bit 60181834Sroberto * (maintaining any guard bits) and, if the next bit in y is set, 61181834Sroberto * adding the multiplicand (x) to the accumulator. Then, in any case, 62181834Sroberto * we advance one bit leftward in y. Algorithmically: 63181834Sroberto * 64181834Sroberto * A = 0; 65181834Sroberto * for (bit = 0; bit < FP_NMANT; bit++) { 66181834Sroberto * sticky |= A & 1, A >>= 1; 67181834Sroberto * if (Y & (1 << bit)) 68181834Sroberto * A += X; 69181834Sroberto * } 70181834Sroberto * 71181834Sroberto * (X and Y here represent the mantissas of x and y respectively.) 72181834Sroberto * The resultant accumulator (A) is the product's mantissa. It may 73181834Sroberto * be as large as 11.11111... in binary and hence may need to be 74181834Sroberto * shifted right, but at most one bit. 75181834Sroberto * 76181834Sroberto * Since we do not have efficient multiword arithmetic, we code the 77181834Sroberto * accumulator as four separate words, just like any other mantissa. 78181834Sroberto * We use local variables in the hope that this is faster than memory. 79181834Sroberto * We keep x->fp_mant in locals for the same reason. 80181834Sroberto * 81181834Sroberto * In the algorithm above, the bits in y are inspected one at a time. 82181834Sroberto * We will pick them up 32 at a time and then deal with those 32, one 83181834Sroberto * at a time. Note, however, that we know several things about y: 84181834Sroberto * 85181834Sroberto * - the guard and round bits at the bottom are sure to be zero; 86181834Sroberto * 87181834Sroberto * - often many low bits are zero (y is often from a single or double 88181834Sroberto * precision source); 89181834Sroberto * 90181834Sroberto * - bit FP_NMANT-1 is set, and FP_1*2 fits in a word. 91181834Sroberto * 92181834Sroberto * We can also test for 32-zero-bits swiftly. In this case, the center 93181834Sroberto * part of the loop---setting sticky, shifting A, and not adding---will 94181834Sroberto * run 32 times without adding X to A. We can do a 32-bit shift faster 95181834Sroberto * by simply moving words. Since zeros are common, we optimize this case. 96181834Sroberto * Furthermore, since A is initially zero, we can omit the shift as well 97181834Sroberto * until we reach a nonzero word. 98181834Sroberto */ 99181834Srobertostruct fpn * 100181834Srobertofpu_mul(struct fpemu *fe) 101181834Sroberto{ 102181834Sroberto struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 103181834Sroberto u_int a3, a2, a1, a0, x3, x2, x1, x0, bit, m; 104181834Sroberto int sticky; 105181834Sroberto FPU_DECL_CARRY; 106181834Sroberto 107181834Sroberto /* 108181834Sroberto * Put the `heavier' operand on the right (see fpu_emu.h). 109181834Sroberto * Then we will have one of the following cases, taken in the 110181834Sroberto * following order: 111181834Sroberto * 112181834Sroberto * - y = NaN. Implied: if only one is a signalling NaN, y is. 113181834Sroberto * The result is y. 114181834Sroberto * - y = Inf. Implied: x != NaN (is 0, number, or Inf: the NaN 115181834Sroberto * case was taken care of earlier). 116181834Sroberto * If x = 0, the result is NaN. Otherwise the result 117181834Sroberto * is y, with its sign reversed if x is negative. 118181834Sroberto * - x = 0. Implied: y is 0 or number. 119181834Sroberto * The result is 0 (with XORed sign as usual). 120181834Sroberto * - other. Implied: both x and y are numbers. 121181834Sroberto * The result is x * y (XOR sign, multiply bits, add exponents). 122181834Sroberto */ 123181834Sroberto DPRINTF(FPE_REG, ("fpu_mul:\n")); 124181834Sroberto DUMPFPN(FPE_REG, x); 125181834Sroberto DUMPFPN(FPE_REG, y); 126181834Sroberto DPRINTF(FPE_REG, ("=>\n")); 127181834Sroberto 128181834Sroberto ORDER(x, y); 129181834Sroberto if (ISNAN(y)) { 130181834Sroberto y->fp_sign ^= x->fp_sign; 131181834Sroberto fe->fe_cx |= FPSCR_VXSNAN; 132181834Sroberto DUMPFPN(FPE_REG, y); 133181834Sroberto return (y); 134181834Sroberto } 135181834Sroberto if (ISINF(y)) { 136181834Sroberto if (ISZERO(x)) { 137181834Sroberto fe->fe_cx |= FPSCR_VXIMZ; 138181834Sroberto return (fpu_newnan(fe)); 139181834Sroberto } 140181834Sroberto y->fp_sign ^= x->fp_sign; 141181834Sroberto DUMPFPN(FPE_REG, y); 142181834Sroberto return (y); 143181834Sroberto } 144181834Sroberto if (ISZERO(x)) { 145181834Sroberto x->fp_sign ^= y->fp_sign; 146181834Sroberto DUMPFPN(FPE_REG, x); 147181834Sroberto return (x); 148181834Sroberto } 149181834Sroberto 150181834Sroberto /* 151181834Sroberto * Setup. In the code below, the mask `m' will hold the current 152181834Sroberto * mantissa byte from y. The variable `bit' denotes the bit 153181834Sroberto * within m. We also define some macros to deal with everything. 154181834Sroberto */ 155181834Sroberto x3 = x->fp_mant[3]; 156181834Sroberto x2 = x->fp_mant[2]; 157181834Sroberto x1 = x->fp_mant[1]; 158181834Sroberto x0 = x->fp_mant[0]; 159181834Sroberto sticky = a3 = a2 = a1 = a0 = 0; 160181834Sroberto 161181834Sroberto#define ADD /* A += X */ \ 162181834Sroberto FPU_ADDS(a3, a3, x3); \ 163181834Sroberto FPU_ADDCS(a2, a2, x2); \ 164181834Sroberto FPU_ADDCS(a1, a1, x1); \ 165181834Sroberto FPU_ADDC(a0, a0, x0) 166181834Sroberto 167181834Sroberto#define SHR1 /* A >>= 1, with sticky */ \ 168181834Sroberto sticky |= a3 & 1, a3 = (a3 >> 1) | (a2 << 31), \ 169181834Sroberto a2 = (a2 >> 1) | (a1 << 31), a1 = (a1 >> 1) | (a0 << 31), a0 >>= 1 170181834Sroberto 171181834Sroberto#define SHR32 /* A >>= 32, with sticky */ \ 172181834Sroberto sticky |= a3, a3 = a2, a2 = a1, a1 = a0, a0 = 0 173181834Sroberto 174181834Sroberto#define STEP /* each 1-bit step of the multiplication */ \ 175181834Sroberto SHR1; if (bit & m) { ADD; }; bit <<= 1 176181834Sroberto 177181834Sroberto /* 178181834Sroberto * We are ready to begin. The multiply loop runs once for each 179181834Sroberto * of the four 32-bit words. Some words, however, are special. 180181834Sroberto * As noted above, the low order bits of Y are often zero. Even 181181834Sroberto * if not, the first loop can certainly skip the guard bits. 182181834Sroberto * The last word of y has its highest 1-bit in position FP_NMANT-1, 183181834Sroberto * so we stop the loop when we move past that bit. 184181834Sroberto */ 185181834Sroberto if ((m = y->fp_mant[3]) == 0) { 186181834Sroberto /* SHR32; */ /* unneeded since A==0 */ 187181834Sroberto } else { 188181834Sroberto bit = 1 << FP_NG; 189181834Sroberto do { 190181834Sroberto STEP; 191181834Sroberto } while (bit != 0); 192181834Sroberto } 193181834Sroberto if ((m = y->fp_mant[2]) == 0) { 194181834Sroberto SHR32; 195181834Sroberto } else { 196181834Sroberto bit = 1; 197181834Sroberto do { 198181834Sroberto STEP; 199181834Sroberto } while (bit != 0); 200181834Sroberto } 201181834Sroberto if ((m = y->fp_mant[1]) == 0) { 202181834Sroberto SHR32; 203181834Sroberto } else { 204181834Sroberto bit = 1; 205181834Sroberto do { 206181834Sroberto STEP; 207181834Sroberto } while (bit != 0); 208181834Sroberto } 209181834Sroberto m = y->fp_mant[0]; /* definitely != 0 */ 210181834Sroberto bit = 1; 211181834Sroberto do { 212181834Sroberto STEP; 213181834Sroberto } while (bit <= m); 214181834Sroberto 215181834Sroberto /* 216181834Sroberto * Done with mantissa calculation. Get exponent and handle 217181834Sroberto * 11.111...1 case, then put result in place. We reuse x since 218181834Sroberto * it already has the right class (FP_NUM). 219181834Sroberto */ 220181834Sroberto m = x->fp_exp + y->fp_exp; 221181834Sroberto if (a0 >= FP_2) { 222181834Sroberto SHR1; 223181834Sroberto m++; 224181834Sroberto } 225181834Sroberto x->fp_sign ^= y->fp_sign; 226181834Sroberto x->fp_exp = m; 227181834Sroberto x->fp_sticky = sticky; 228181834Sroberto x->fp_mant[3] = a3; 229181834Sroberto x->fp_mant[2] = a2; 230181834Sroberto x->fp_mant[1] = a1; 231181834Sroberto x->fp_mant[0] = a0; 232181834Sroberto 233181834Sroberto DUMPFPN(FPE_REG, x); 234181834Sroberto return (x); 235181834Sroberto} 236181834Sroberto