1 /* $OpenBSD: fpu_div.c,v 1.1 2003/07/21 18:41:30 jason 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 * All advertising materials mentioning features or use of this software 12 * must display the following acknowledgement: 13 * This product includes software developed by the University of 14 * California, Lawrence Berkeley Laboratory. 15 * 16 * Redistribution and use in source and binary forms, with or without 17 * modification, are permitted provided that the following conditions 18 * are met: 19 * 1. Redistributions of source code must retain the above copyright 20 * notice, this list of conditions and the following disclaimer. 21 * 2. Redistributions in binary form must reproduce the above copyright 22 * notice, this list of conditions and the following disclaimer in the 23 * documentation and/or other materials provided with the distribution. 24 * 3. All advertising materials mentioning features or use of this software 25 * must display the following acknowledgement: 26 * This product includes software developed by the University of 27 * California, Berkeley and its contributors. 28 * 4. Neither the name of the University nor the names of its contributors 29 * may be used to endorse or promote products derived from this software 30 * without specific prior written permission. 31 * 32 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 33 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 34 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 35 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 36 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 37 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 38 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 39 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 40 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 41 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 42 * SUCH DAMAGE. 43 * 44 * @(#)fpu_div.c 8.1 (Berkeley) 6/11/93 45 * $NetBSD: fpu_div.c,v 1.2 1994/11/20 20:52:38 deraadt Exp $ 46 */ 47 48 #include <sys/cdefs.h> 49 #if 0 50 __FBSDID("$FreeBSD: src/lib/libc/sparc64/fpu/fpu_div.c,v 1.3 2002/03/22 21:52:58 obrien Exp $"); 51 #endif 52 53 /* 54 * Perform an FPU divide (return x / y). 55 */ 56 57 #include <sys/types.h> 58 59 #include <machine/frame.h> 60 #include <machine/fsr.h> 61 62 #include "fpu_arith.h" 63 #include "fpu_emu.h" 64 #include "fpu_extern.h" 65 66 /* 67 * Division of normal numbers is done as follows: 68 * 69 * x and y are floating point numbers, i.e., in the form 1.bbbb * 2^e. 70 * If X and Y are the mantissas (1.bbbb's), the quotient is then: 71 * 72 * q = (X / Y) * 2^((x exponent) - (y exponent)) 73 * 74 * Since X and Y are both in [1.0,2.0), the quotient's mantissa (X / Y) 75 * will be in [0.5,2.0). Moreover, it will be less than 1.0 if and only 76 * if X < Y. In that case, it will have to be shifted left one bit to 77 * become a normal number, and the exponent decremented. Thus, the 78 * desired exponent is: 79 * 80 * left_shift = x->fp_mant < y->fp_mant; 81 * result_exp = x->fp_exp - y->fp_exp - left_shift; 82 * 83 * The quotient mantissa X/Y can then be computed one bit at a time 84 * using the following algorithm: 85 * 86 * Q = 0; -- Initial quotient. 87 * R = X; -- Initial remainder, 88 * if (left_shift) -- but fixed up in advance. 89 * R *= 2; 90 * for (bit = FP_NMANT; --bit >= 0; R *= 2) { 91 * if (R >= Y) { 92 * Q |= 1 << bit; 93 * R -= Y; 94 * } 95 * } 96 * 97 * The subtraction R -= Y always removes the uppermost bit from R (and 98 * can sometimes remove additional lower-order 1 bits); this proof is 99 * left to the reader. 100 * 101 * This loop correctly calculates the guard and round bits since they are 102 * included in the expanded internal representation. The sticky bit 103 * is to be set if and only if any other bits beyond guard and round 104 * would be set. From the above it is obvious that this is true if and 105 * only if the remainder R is nonzero when the loop terminates. 106 * 107 * Examining the loop above, we can see that the quotient Q is built 108 * one bit at a time ``from the top down''. This means that we can 109 * dispense with the multi-word arithmetic and just build it one word 110 * at a time, writing each result word when it is done. 111 * 112 * Furthermore, since X and Y are both in [1.0,2.0), we know that, 113 * initially, R >= Y. (Recall that, if X < Y, R is set to X * 2 and 114 * is therefore at in [2.0,4.0).) Thus Q is sure to have bit FP_NMANT-1 115 * set, and R can be set initially to either X - Y (when X >= Y) or 116 * 2X - Y (when X < Y). In addition, comparing R and Y is difficult, 117 * so we will simply calculate R - Y and see if that underflows. 118 * This leads to the following revised version of the algorithm: 119 * 120 * R = X; 121 * bit = FP_1; 122 * D = R - Y; 123 * if (D >= 0) { 124 * result_exp = x->fp_exp - y->fp_exp; 125 * R = D; 126 * q = bit; 127 * bit >>= 1; 128 * } else { 129 * result_exp = x->fp_exp - y->fp_exp - 1; 130 * q = 0; 131 * } 132 * R <<= 1; 133 * do { 134 * D = R - Y; 135 * if (D >= 0) { 136 * q |= bit; 137 * R = D; 138 * } 139 * R <<= 1; 140 * } while ((bit >>= 1) != 0); 141 * Q[0] = q; 142 * for (i = 1; i < 4; i++) { 143 * q = 0, bit = 1 << 31; 144 * do { 145 * D = R - Y; 146 * if (D >= 0) { 147 * q |= bit; 148 * R = D; 149 * } 150 * R <<= 1; 151 * } while ((bit >>= 1) != 0); 152 * Q[i] = q; 153 * } 154 * 155 * This can be refined just a bit further by moving the `R <<= 1' 156 * calculations to the front of the do-loops and eliding the first one. 157 * The process can be terminated immediately whenever R becomes 0, but 158 * this is relatively rare, and we do not bother. 159 */ 160 161 struct fpn * 162 __fpu_div(fe) 163 struct fpemu *fe; 164 { 165 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 166 u_int q, bit; 167 u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3; 168 FPU_DECL_CARRY 169 170 /* 171 * Since divide is not commutative, we cannot just use ORDER. 172 * Check either operand for NaN first; if there is at least one, 173 * order the signalling one (if only one) onto the right, then 174 * return it. Otherwise we have the following cases: 175 * 176 * Inf / Inf = NaN, plus NV exception 177 * Inf / num = Inf [i.e., return x] 178 * Inf / 0 = Inf [i.e., return x] 179 * 0 / Inf = 0 [i.e., return x] 180 * 0 / num = 0 [i.e., return x] 181 * 0 / 0 = NaN, plus NV exception 182 * num / Inf = 0 183 * num / num = num (do the divide) 184 * num / 0 = Inf, plus DZ exception 185 */ 186 if (ISNAN(x) || ISNAN(y)) { 187 ORDER(x, y); 188 return (y); 189 } 190 if (ISINF(x) || ISZERO(x)) { 191 if (x->fp_class == y->fp_class) 192 return (__fpu_newnan(fe)); 193 return (x); 194 } 195 196 /* all results at this point use XOR of operand signs */ 197 x->fp_sign ^= y->fp_sign; 198 if (ISINF(y)) { 199 x->fp_class = FPC_ZERO; 200 return (x); 201 } 202 if (ISZERO(y)) { 203 fe->fe_cx = FSR_DZ; 204 x->fp_class = FPC_INF; 205 return (x); 206 } 207 208 /* 209 * Macros for the divide. See comments at top for algorithm. 210 * Note that we expand R, D, and Y here. 211 */ 212 213 #define SUBTRACT /* D = R - Y */ \ 214 FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \ 215 FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0) 216 217 #define NONNEGATIVE /* D >= 0 */ \ 218 ((int)d0 >= 0) 219 220 #ifdef FPU_SHL1_BY_ADD 221 #define SHL1 /* R <<= 1 */ \ 222 FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \ 223 FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0) 224 #else 225 #define SHL1 \ 226 r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \ 227 r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1 228 #endif 229 230 #define LOOP /* do ... while (bit >>= 1) */ \ 231 do { \ 232 SHL1; \ 233 SUBTRACT; \ 234 if (NONNEGATIVE) { \ 235 q |= bit; \ 236 r0 = d0, r1 = d1, r2 = d2, r3 = d3; \ 237 } \ 238 } while ((bit >>= 1) != 0) 239 240 #define WORD(r, i) /* calculate r->fp_mant[i] */ \ 241 q = 0; \ 242 bit = 1 << 31; \ 243 LOOP; \ 244 (x)->fp_mant[i] = q 245 246 /* Setup. Note that we put our result in x. */ 247 r0 = x->fp_mant[0]; 248 r1 = x->fp_mant[1]; 249 r2 = x->fp_mant[2]; 250 r3 = x->fp_mant[3]; 251 y0 = y->fp_mant[0]; 252 y1 = y->fp_mant[1]; 253 y2 = y->fp_mant[2]; 254 y3 = y->fp_mant[3]; 255 256 bit = FP_1; 257 SUBTRACT; 258 if (NONNEGATIVE) { 259 x->fp_exp -= y->fp_exp; 260 r0 = d0, r1 = d1, r2 = d2, r3 = d3; 261 q = bit; 262 bit >>= 1; 263 } else { 264 x->fp_exp -= y->fp_exp + 1; 265 q = 0; 266 } 267 LOOP; 268 x->fp_mant[0] = q; 269 WORD(x, 1); 270 WORD(x, 2); 271 WORD(x, 3); 272 x->fp_sticky = r0 | r1 | r2 | r3; 273 274 return (x); 275 } 276