1 /* $OpenBSD: fpu_div.c,v 1.2 2012/12/05 23:19:59 deraadt 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 #if 0 49 __FBSDID("$FreeBSD: src/lib/libc/sparc64/fpu/fpu_div.c,v 1.3 2002/03/22 21:52:58 obrien Exp $"); 50 #endif 51 52 /* 53 * Perform an FPU divide (return x / y). 54 */ 55 56 #include <sys/types.h> 57 58 #include <machine/frame.h> 59 #include <machine/fsr.h> 60 61 #include "fpu_arith.h" 62 #include "fpu_emu.h" 63 #include "fpu_extern.h" 64 65 /* 66 * Division of normal numbers is done as follows: 67 * 68 * x and y are floating point numbers, i.e., in the form 1.bbbb * 2^e. 69 * If X and Y are the mantissas (1.bbbb's), the quotient is then: 70 * 71 * q = (X / Y) * 2^((x exponent) - (y exponent)) 72 * 73 * Since X and Y are both in [1.0,2.0), the quotient's mantissa (X / Y) 74 * will be in [0.5,2.0). Moreover, it will be less than 1.0 if and only 75 * if X < Y. In that case, it will have to be shifted left one bit to 76 * become a normal number, and the exponent decremented. Thus, the 77 * desired exponent is: 78 * 79 * left_shift = x->fp_mant < y->fp_mant; 80 * result_exp = x->fp_exp - y->fp_exp - left_shift; 81 * 82 * The quotient mantissa X/Y can then be computed one bit at a time 83 * using the following algorithm: 84 * 85 * Q = 0; -- Initial quotient. 86 * R = X; -- Initial remainder, 87 * if (left_shift) -- but fixed up in advance. 88 * R *= 2; 89 * for (bit = FP_NMANT; --bit >= 0; R *= 2) { 90 * if (R >= Y) { 91 * Q |= 1 << bit; 92 * R -= Y; 93 * } 94 * } 95 * 96 * The subtraction R -= Y always removes the uppermost bit from R (and 97 * can sometimes remove additional lower-order 1 bits); this proof is 98 * left to the reader. 99 * 100 * This loop correctly calculates the guard and round bits since they are 101 * included in the expanded internal representation. The sticky bit 102 * is to be set if and only if any other bits beyond guard and round 103 * would be set. From the above it is obvious that this is true if and 104 * only if the remainder R is nonzero when the loop terminates. 105 * 106 * Examining the loop above, we can see that the quotient Q is built 107 * one bit at a time ``from the top down''. This means that we can 108 * dispense with the multi-word arithmetic and just build it one word 109 * at a time, writing each result word when it is done. 110 * 111 * Furthermore, since X and Y are both in [1.0,2.0), we know that, 112 * initially, R >= Y. (Recall that, if X < Y, R is set to X * 2 and 113 * is therefore at in [2.0,4.0).) Thus Q is sure to have bit FP_NMANT-1 114 * set, and R can be set initially to either X - Y (when X >= Y) or 115 * 2X - Y (when X < Y). In addition, comparing R and Y is difficult, 116 * so we will simply calculate R - Y and see if that underflows. 117 * This leads to the following revised version of the algorithm: 118 * 119 * R = X; 120 * bit = FP_1; 121 * D = R - Y; 122 * if (D >= 0) { 123 * result_exp = x->fp_exp - y->fp_exp; 124 * R = D; 125 * q = bit; 126 * bit >>= 1; 127 * } else { 128 * result_exp = x->fp_exp - y->fp_exp - 1; 129 * q = 0; 130 * } 131 * R <<= 1; 132 * do { 133 * D = R - Y; 134 * if (D >= 0) { 135 * q |= bit; 136 * R = D; 137 * } 138 * R <<= 1; 139 * } while ((bit >>= 1) != 0); 140 * Q[0] = q; 141 * for (i = 1; i < 4; i++) { 142 * q = 0, bit = 1 << 31; 143 * do { 144 * D = R - Y; 145 * if (D >= 0) { 146 * q |= bit; 147 * R = D; 148 * } 149 * R <<= 1; 150 * } while ((bit >>= 1) != 0); 151 * Q[i] = q; 152 * } 153 * 154 * This can be refined just a bit further by moving the `R <<= 1' 155 * calculations to the front of the do-loops and eliding the first one. 156 * The process can be terminated immediately whenever R becomes 0, but 157 * this is relatively rare, and we do not bother. 158 */ 159 160 struct fpn * 161 __fpu_div(fe) 162 struct fpemu *fe; 163 { 164 struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 165 u_int q, bit; 166 u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3; 167 FPU_DECL_CARRY 168 169 /* 170 * Since divide is not commutative, we cannot just use ORDER. 171 * Check either operand for NaN first; if there is at least one, 172 * order the signalling one (if only one) onto the right, then 173 * return it. Otherwise we have the following cases: 174 * 175 * Inf / Inf = NaN, plus NV exception 176 * Inf / num = Inf [i.e., return x] 177 * Inf / 0 = Inf [i.e., return x] 178 * 0 / Inf = 0 [i.e., return x] 179 * 0 / num = 0 [i.e., return x] 180 * 0 / 0 = NaN, plus NV exception 181 * num / Inf = 0 182 * num / num = num (do the divide) 183 * num / 0 = Inf, plus DZ exception 184 */ 185 if (ISNAN(x) || ISNAN(y)) { 186 ORDER(x, y); 187 return (y); 188 } 189 if (ISINF(x) || ISZERO(x)) { 190 if (x->fp_class == y->fp_class) 191 return (__fpu_newnan(fe)); 192 return (x); 193 } 194 195 /* all results at this point use XOR of operand signs */ 196 x->fp_sign ^= y->fp_sign; 197 if (ISINF(y)) { 198 x->fp_class = FPC_ZERO; 199 return (x); 200 } 201 if (ISZERO(y)) { 202 fe->fe_cx = FSR_DZ; 203 x->fp_class = FPC_INF; 204 return (x); 205 } 206 207 /* 208 * Macros for the divide. See comments at top for algorithm. 209 * Note that we expand R, D, and Y here. 210 */ 211 212 #define SUBTRACT /* D = R - Y */ \ 213 FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \ 214 FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0) 215 216 #define NONNEGATIVE /* D >= 0 */ \ 217 ((int)d0 >= 0) 218 219 #ifdef FPU_SHL1_BY_ADD 220 #define SHL1 /* R <<= 1 */ \ 221 FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \ 222 FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0) 223 #else 224 #define SHL1 \ 225 r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \ 226 r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1 227 #endif 228 229 #define LOOP /* do ... while (bit >>= 1) */ \ 230 do { \ 231 SHL1; \ 232 SUBTRACT; \ 233 if (NONNEGATIVE) { \ 234 q |= bit; \ 235 r0 = d0, r1 = d1, r2 = d2, r3 = d3; \ 236 } \ 237 } while ((bit >>= 1) != 0) 238 239 #define WORD(r, i) /* calculate r->fp_mant[i] */ \ 240 q = 0; \ 241 bit = 1 << 31; \ 242 LOOP; \ 243 (x)->fp_mant[i] = q 244 245 /* Setup. Note that we put our result in x. */ 246 r0 = x->fp_mant[0]; 247 r1 = x->fp_mant[1]; 248 r2 = x->fp_mant[2]; 249 r3 = x->fp_mant[3]; 250 y0 = y->fp_mant[0]; 251 y1 = y->fp_mant[1]; 252 y2 = y->fp_mant[2]; 253 y3 = y->fp_mant[3]; 254 255 bit = FP_1; 256 SUBTRACT; 257 if (NONNEGATIVE) { 258 x->fp_exp -= y->fp_exp; 259 r0 = d0, r1 = d1, r2 = d2, r3 = d3; 260 q = bit; 261 bit >>= 1; 262 } else { 263 x->fp_exp -= y->fp_exp + 1; 264 q = 0; 265 } 266 LOOP; 267 x->fp_mant[0] = q; 268 WORD(x, 1); 269 WORD(x, 2); 270 WORD(x, 3); 271 x->fp_sticky = r0 | r1 | r2 | r3; 272 273 return (x); 274 } 275