1/* $NetBSD: divrem.m4,v 1.2 1994/10/26 06:39:56 cgd 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 * Redistribution and use in source and binary forms, with or without 12 * modification, are permitted provided that the following conditions 13 * are met: 14 * 1. Redistributions of source code must retain the above copyright 15 * notice, this list of conditions and the following disclaimer. 16 * 2. Redistributions in binary form must reproduce the above copyright 17 * notice, this list of conditions and the following disclaimer in the 18 * documentation and/or other materials provided with the distribution. 19 * 3. All advertising materials mentioning features or use of this software 20 * must display the following acknowledgement: 21 * This product includes software developed by the University of 22 * California, Berkeley and its contributors. 23 * 4. Neither the name of the University nor the names of its contributors 24 * may be used to endorse or promote products derived from this software 25 * without specific prior written permission. 26 * 27 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 28 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 29 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 30 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 31 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 32 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 33 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 34 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 35 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 36 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 37 * SUCH DAMAGE. 38 * 39 * Header: divrem.m4,v 1.4 92/06/25 13:23:57 torek Exp 40 */ 41 42/* 43 * Division and remainder, from Appendix E of the Sparc Version 8 44 * Architecture Manual, with fixes from Gordon Irlam. 45 */ 46 47#if defined(LIBC_SCCS) && !defined(lint) 48#ifdef notdef 49 .asciz "@(#)divrem.m4 8.1 (Berkeley) 6/4/93" 50#endif 51 .asciz "$NetBSD: divrem.m4,v 1.2 1994/10/26 06:39:56 cgd Exp $" 52#endif /* LIBC_SCCS and not lint */ 53 54/* 55 * Input: dividend and divisor in %o0 and %o1 respectively. 56 * 57 * m4 parameters: 58 * NAME name of function to generate 59 * OP OP=div => %o0 / %o1; OP=rem => %o0 % %o1 60 * S S=true => signed; S=false => unsigned 61 * 62 * Algorithm parameters: 63 * N how many bits per iteration we try to get (4) 64 * WORDSIZE total number of bits (32) 65 * 66 * Derived constants: 67 * TWOSUPN 2^N, for label generation (m4 exponentiation currently broken) 68 * TOPBITS number of bits in the top `decade' of a number 69 * 70 * Important variables: 71 * Q the partial quotient under development (initially 0) 72 * R the remainder so far, initially the dividend 73 * ITER number of main division loop iterations required; 74 * equal to ceil(log2(quotient) / N). Note that this 75 * is the log base (2^N) of the quotient. 76 * V the current comparand, initially divisor*2^(ITER*N-1) 77 * 78 * Cost: 79 * Current estimate for non-large dividend is 80 * ceil(log2(quotient) / N) * (10 + 7N/2) + C 81 * A large dividend is one greater than 2^(31-TOPBITS) and takes a 82 * different path, as the upper bits of the quotient must be developed 83 * one bit at a time. 84 */ 85 86define(N, `4') 87define(TWOSUPN, `16') 88define(WORDSIZE, `32') 89define(TOPBITS, eval(WORDSIZE - N*((WORDSIZE-1)/N))) 90 91define(dividend, `%o0') 92define(divisor, `%o1') 93define(Q, `%o2') 94define(R, `%o3') 95define(ITER, `%o4') 96define(V, `%o5') 97 98/* m4 reminder: ifelse(a,b,c,d) => if a is b, then c, else d */ 99define(T, `%g1') 100define(SC, `%g7') 101ifelse(S, `true', `define(SIGN, `%g6')') 102 103/* 104 * This is the recursive definition for developing quotient digits. 105 * 106 * Parameters: 107 * $1 the current depth, 1 <= $1 <= N 108 * $2 the current accumulation of quotient bits 109 * N max depth 110 * 111 * We add a new bit to $2 and either recurse or insert the bits in 112 * the quotient. R, Q, and V are inputs and outputs as defined above; 113 * the condition codes are expected to reflect the input R, and are 114 * modified to reflect the output R. 115 */ 116define(DEVELOP_QUOTIENT_BITS, 117` ! depth $1, accumulated bits $2 118 bl L.$1.eval(TWOSUPN+$2) 119 srl V,1,V 120 ! remainder is positive 121 subcc R,V,R 122 ifelse($1, N, 123 ` b 9f 124 add Q, ($2*2+1), Q 125 ', ` DEVELOP_QUOTIENT_BITS(incr($1), `eval(2*$2+1)')') 126L.$1.eval(TWOSUPN+$2): 127 ! remainder is negative 128 addcc R,V,R 129 ifelse($1, N, 130 ` b 9f 131 add Q, ($2*2-1), Q 132 ', ` DEVELOP_QUOTIENT_BITS(incr($1), `eval(2*$2-1)')') 133 ifelse($1, 1, `9:')') 134 135#include "DEFS.h" 136#include <machine/trap.h> 137 138FUNC(NAME) 139ifelse(S, `true', 140` ! compute sign of result; if neither is negative, no problem 141 orcc divisor, dividend, %g0 ! either negative? 142 bge 2f ! no, go do the divide 143 xor divisor, dividend, SIGN ! compute sign in any case 144 tst divisor 145 bge 1f 146 tst dividend 147 ! divisor is definitely negative; dividend might also be negative 148 bge 2f ! if dividend not negative... 149 neg divisor ! in any case, make divisor nonneg 1501: ! dividend is negative, divisor is nonnegative 151 neg dividend ! make dividend nonnegative 1522: 153') 154 ! Ready to divide. Compute size of quotient; scale comparand. 155 orcc divisor, %g0, V 156 bnz 1f 157 mov dividend, R 158 159 ! Divide by zero trap. If it returns, return 0 (about as 160 ! wrong as possible, but that is what SunOS does...). 161 t ST_DIV0 162 retl 163 clr %o0 164 1651: 166 cmp R, V ! if divisor exceeds dividend, done 167 blu Lgot_result ! (and algorithm fails otherwise) 168 clr Q 169 sethi %hi(1 << (WORDSIZE - TOPBITS - 1)), T 170 cmp R, T 171 blu Lnot_really_big 172 clr ITER 173 174 ! `Here the dividend is >= 2^(31-N) or so. We must be careful here, 175 ! as our usual N-at-a-shot divide step will cause overflow and havoc. 176 ! The number of bits in the result here is N*ITER+SC, where SC <= N. 177 ! Compute ITER in an unorthodox manner: know we need to shift V into 178 ! the top decade: so do not even bother to compare to R.' 179 1: 180 cmp V, T 181 bgeu 3f 182 mov 1, SC 183 sll V, N, V 184 b 1b 185 inc ITER 186 187 ! Now compute SC. 188 2: addcc V, V, V 189 bcc Lnot_too_big 190 inc SC 191 192 ! We get here if the divisor overflowed while shifting. 193 ! This means that R has the high-order bit set. 194 ! Restore V and subtract from R. 195 sll T, TOPBITS, T ! high order bit 196 srl V, 1, V ! rest of V 197 add V, T, V 198 b Ldo_single_div 199 dec SC 200 201 Lnot_too_big: 202 3: cmp V, R 203 blu 2b 204 nop 205 be Ldo_single_div 206 nop 207 /* NB: these are commented out in the V8-Sparc manual as well */ 208 /* (I do not understand this) */ 209 ! V > R: went too far: back up 1 step 210 ! srl V, 1, V 211 ! dec SC 212 ! do single-bit divide steps 213 ! 214 ! We have to be careful here. We know that R >= V, so we can do the 215 ! first divide step without thinking. BUT, the others are conditional, 216 ! and are only done if R >= 0. Because both R and V may have the high- 217 ! order bit set in the first step, just falling into the regular 218 ! division loop will mess up the first time around. 219 ! So we unroll slightly... 220 Ldo_single_div: 221 deccc SC 222 bl Lend_regular_divide 223 nop 224 sub R, V, R 225 mov 1, Q 226 b Lend_single_divloop 227 nop 228 Lsingle_divloop: 229 sll Q, 1, Q 230 bl 1f 231 srl V, 1, V 232 ! R >= 0 233 sub R, V, R 234 b 2f 235 inc Q 236 1: ! R < 0 237 add R, V, R 238 dec Q 239 2: 240 Lend_single_divloop: 241 deccc SC 242 bge Lsingle_divloop 243 tst R 244 b,a Lend_regular_divide 245 246Lnot_really_big: 2471: 248 sll V, N, V 249 cmp V, R 250 bleu 1b 251 inccc ITER 252 be Lgot_result 253 dec ITER 254 255 tst R ! set up for initial iteration 256Ldivloop: 257 sll Q, N, Q 258 DEVELOP_QUOTIENT_BITS(1, 0) 259Lend_regular_divide: 260 deccc ITER 261 bge Ldivloop 262 tst R 263 bl,a Lgot_result 264 ! non-restoring fixup here (one instruction only!) 265ifelse(OP, `div', 266` dec Q 267', ` add R, divisor, R 268') 269 270Lgot_result: 271ifelse(S, `true', 272` ! check to see if answer should be < 0 273 tst SIGN 274 bl,a 1f 275 ifelse(OP, `div', `neg Q', `neg R') 2761:') 277 retl 278 ifelse(OP, `div', `mov Q, %o0', `mov R, %o0') 279