1/* $NetBSD: divrem.m4,v 1.3 2002/10/29 04:40:56 chs 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 * from: Header: divrem.m4,v 1.4 92/06/25 13:23:57 torek Exp 40 */ 41 42#include <machine/asm.h> 43#include <machine/trap.h> 44 45/* 46 * Division and remainder, from Appendix E of the Sparc Version 8 47 * Architecture Manual, with fixes from Gordon Irlam. 48 */ 49 50#if defined(LIBC_SCCS) 51 RCSID("$NetBSD: divrem.m4,v 1.3 2002/10/29 04:40:56 chs Exp $") 52#endif 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, `%g5') 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 135FUNC(NAME) 136ifelse(S, `true', 137` ! compute sign of result; if neither is negative, no problem 138 orcc divisor, dividend, %g0 ! either negative? 139 bge 2f ! no, go do the divide 140 ifelse(OP, `div', 141 `xor divisor, dividend, SIGN', 142 `mov dividend, SIGN') ! compute sign in any case 143 tst divisor 144 bge 1f 145 tst dividend 146 ! divisor is definitely negative; dividend might also be negative 147 bge 2f ! if dividend not negative... 148 neg divisor ! in any case, make divisor nonneg 1491: ! dividend is negative, divisor is nonnegative 150 neg dividend ! make dividend nonnegative 1512: 152') 153 ! Ready to divide. Compute size of quotient; scale comparand. 154 orcc divisor, %g0, V 155 bnz 1f 156 mov dividend, R 157 158 ! Divide by zero trap. If it returns, return 0 (about as 159 ! wrong as possible, but that is what SunOS does...). 160 t ST_DIV0 161 retl 162 clr %o0 163 1641: 165 cmp R, V ! if divisor exceeds dividend, done 166 blu Lgot_result ! (and algorithm fails otherwise) 167 clr Q 168 sethi %hi(1 << (WORDSIZE - TOPBITS - 1)), T 169 cmp R, T 170 blu Lnot_really_big 171 clr ITER 172 173 ! `Here the dividend is >= 2^(31-N) or so. We must be careful here, 174 ! as our usual N-at-a-shot divide step will cause overflow and havoc. 175 ! The number of bits in the result here is N*ITER+SC, where SC <= N. 176 ! Compute ITER in an unorthodox manner: know we need to shift V into 177 ! the top decade: so do not even bother to compare to R.' 178 1: 179 cmp V, T 180 bgeu 3f 181 mov 1, SC 182 sll V, N, V 183 b 1b 184 inc ITER 185 186 ! Now compute SC. 187 2: addcc V, V, V 188 bcc Lnot_too_big 189 inc SC 190 191 ! We get here if the divisor overflowed while shifting. 192 ! This means that R has the high-order bit set. 193 ! Restore V and subtract from R. 194 sll T, TOPBITS, T ! high order bit 195 srl V, 1, V ! rest of V 196 add V, T, V 197 b Ldo_single_div 198 dec SC 199 200 Lnot_too_big: 201 3: cmp V, R 202 blu 2b 203 nop 204 be Ldo_single_div 205 nop 206 /* NB: these are commented out in the V8-Sparc manual as well */ 207 /* (I do not understand this) */ 208 ! V > R: went too far: back up 1 step 209 ! srl V, 1, V 210 ! dec SC 211 ! do single-bit divide steps 212 ! 213 ! We have to be careful here. We know that R >= V, so we can do the 214 ! first divide step without thinking. BUT, the others are conditional, 215 ! and are only done if R >= 0. Because both R and V may have the high- 216 ! order bit set in the first step, just falling into the regular 217 ! division loop will mess up the first time around. 218 ! So we unroll slightly... 219 Ldo_single_div: 220 deccc SC 221 bl Lend_regular_divide 222 nop 223 sub R, V, R 224 mov 1, Q 225 b Lend_single_divloop 226 nop 227 Lsingle_divloop: 228 sll Q, 1, Q 229 bl 1f 230 srl V, 1, V 231 ! R >= 0 232 sub R, V, R 233 b 2f 234 inc Q 235 1: ! R < 0 236 add R, V, R 237 dec Q 238 2: 239 Lend_single_divloop: 240 deccc SC 241 bge Lsingle_divloop 242 tst R 243 b,a Lend_regular_divide 244 245Lnot_really_big: 2461: 247 sll V, N, V 248 cmp V, R 249 bleu 1b 250 inccc ITER 251 be Lgot_result 252 dec ITER 253 254 tst R ! set up for initial iteration 255Ldivloop: 256 sll Q, N, Q 257 DEVELOP_QUOTIENT_BITS(1, 0) 258Lend_regular_divide: 259 deccc ITER 260 bge Ldivloop 261 tst R 262 bl,a Lgot_result 263 ! non-restoring fixup here (one instruction only!) 264ifelse(OP, `div', 265` dec Q 266', ` add R, divisor, R 267') 268 269Lgot_result: 270ifelse(S, `true', 271` ! check to see if answer should be < 0 272 tst SIGN 273 bl,a 1f 274 ifelse(OP, `div', `neg Q', `neg R') 2751:') 276 retl 277 ifelse(OP, `div', `mov Q, %o0', `mov R, %o0') 278