191174Stmm/* 291174Stmm * Copyright (c) 1992, 1993 391174Stmm * The Regents of the University of California. All rights reserved. 491174Stmm * 591174Stmm * This software was developed by the Computer Systems Engineering group 691174Stmm * at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and 791174Stmm * contributed to Berkeley. 891174Stmm * 991174Stmm * All advertising materials mentioning features or use of this software 1091174Stmm * must display the following acknowledgement: 1191174Stmm * This product includes software developed by the University of 1291174Stmm * California, Lawrence Berkeley Laboratory. 1391174Stmm * 1491174Stmm * Redistribution and use in source and binary forms, with or without 1591174Stmm * modification, are permitted provided that the following conditions 1691174Stmm * are met: 1791174Stmm * 1. Redistributions of source code must retain the above copyright 1891174Stmm * notice, this list of conditions and the following disclaimer. 1991174Stmm * 2. Redistributions in binary form must reproduce the above copyright 2091174Stmm * notice, this list of conditions and the following disclaimer in the 2191174Stmm * documentation and/or other materials provided with the distribution. 2291174Stmm * 4. Neither the name of the University nor the names of its contributors 2391174Stmm * may be used to endorse or promote products derived from this software 2491174Stmm * without specific prior written permission. 2591174Stmm * 2691174Stmm * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 2791174Stmm * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 2891174Stmm * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 2991174Stmm * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 3091174Stmm * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 3191174Stmm * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 3291174Stmm * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 3391174Stmm * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 3491174Stmm * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 3591174Stmm * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 3691174Stmm * SUCH DAMAGE. 3791174Stmm * 3891174Stmm * @(#)fpu_div.c 8.1 (Berkeley) 6/11/93 3992986Sobrien * $NetBSD: fpu_div.c,v 1.2 1994/11/20 20:52:38 deraadt Exp $ 4091174Stmm */ 4191174Stmm 4292986Sobrien#include <sys/cdefs.h> 4392986Sobrien__FBSDID("$FreeBSD$"); 4492986Sobrien 4591174Stmm/* 4691174Stmm * Perform an FPU divide (return x / y). 4791174Stmm */ 4891174Stmm 4991174Stmm#include <sys/types.h> 5091174Stmm 5191174Stmm#include <machine/frame.h> 5291174Stmm#include <machine/fp.h> 5391174Stmm#include <machine/fsr.h> 5491174Stmm 5591174Stmm#include "fpu_arith.h" 5691174Stmm#include "fpu_emu.h" 5791174Stmm#include "fpu_extern.h" 5891174Stmm 5991174Stmm/* 6091174Stmm * Division of normal numbers is done as follows: 6191174Stmm * 6291174Stmm * x and y are floating point numbers, i.e., in the form 1.bbbb * 2^e. 6391174Stmm * If X and Y are the mantissas (1.bbbb's), the quotient is then: 6491174Stmm * 6591174Stmm * q = (X / Y) * 2^((x exponent) - (y exponent)) 6691174Stmm * 6791174Stmm * Since X and Y are both in [1.0,2.0), the quotient's mantissa (X / Y) 6891174Stmm * will be in [0.5,2.0). Moreover, it will be less than 1.0 if and only 6991174Stmm * if X < Y. In that case, it will have to be shifted left one bit to 7091174Stmm * become a normal number, and the exponent decremented. Thus, the 7191174Stmm * desired exponent is: 7291174Stmm * 7391174Stmm * left_shift = x->fp_mant < y->fp_mant; 7491174Stmm * result_exp = x->fp_exp - y->fp_exp - left_shift; 7591174Stmm * 7691174Stmm * The quotient mantissa X/Y can then be computed one bit at a time 7791174Stmm * using the following algorithm: 7891174Stmm * 7991174Stmm * Q = 0; -- Initial quotient. 8091174Stmm * R = X; -- Initial remainder, 8191174Stmm * if (left_shift) -- but fixed up in advance. 8291174Stmm * R *= 2; 8391174Stmm * for (bit = FP_NMANT; --bit >= 0; R *= 2) { 8491174Stmm * if (R >= Y) { 8591174Stmm * Q |= 1 << bit; 8691174Stmm * R -= Y; 8791174Stmm * } 8891174Stmm * } 8991174Stmm * 9091174Stmm * The subtraction R -= Y always removes the uppermost bit from R (and 9191174Stmm * can sometimes remove additional lower-order 1 bits); this proof is 9291174Stmm * left to the reader. 9391174Stmm * 9491174Stmm * This loop correctly calculates the guard and round bits since they are 9591174Stmm * included in the expanded internal representation. The sticky bit 9691174Stmm * is to be set if and only if any other bits beyond guard and round 9791174Stmm * would be set. From the above it is obvious that this is true if and 9891174Stmm * only if the remainder R is nonzero when the loop terminates. 9991174Stmm * 10091174Stmm * Examining the loop above, we can see that the quotient Q is built 10191174Stmm * one bit at a time ``from the top down''. This means that we can 10291174Stmm * dispense with the multi-word arithmetic and just build it one word 10391174Stmm * at a time, writing each result word when it is done. 10491174Stmm * 10591174Stmm * Furthermore, since X and Y are both in [1.0,2.0), we know that, 10691174Stmm * initially, R >= Y. (Recall that, if X < Y, R is set to X * 2 and 10791174Stmm * is therefore at in [2.0,4.0).) Thus Q is sure to have bit FP_NMANT-1 10891174Stmm * set, and R can be set initially to either X - Y (when X >= Y) or 10991174Stmm * 2X - Y (when X < Y). In addition, comparing R and Y is difficult, 11091174Stmm * so we will simply calculate R - Y and see if that underflows. 11191174Stmm * This leads to the following revised version of the algorithm: 11291174Stmm * 11391174Stmm * R = X; 11491174Stmm * bit = FP_1; 11591174Stmm * D = R - Y; 11691174Stmm * if (D >= 0) { 11791174Stmm * result_exp = x->fp_exp - y->fp_exp; 11891174Stmm * R = D; 11991174Stmm * q = bit; 12091174Stmm * bit >>= 1; 12191174Stmm * } else { 12291174Stmm * result_exp = x->fp_exp - y->fp_exp - 1; 12391174Stmm * q = 0; 12491174Stmm * } 12591174Stmm * R <<= 1; 12691174Stmm * do { 12791174Stmm * D = R - Y; 12891174Stmm * if (D >= 0) { 12991174Stmm * q |= bit; 13091174Stmm * R = D; 13191174Stmm * } 13291174Stmm * R <<= 1; 13391174Stmm * } while ((bit >>= 1) != 0); 13491174Stmm * Q[0] = q; 13591174Stmm * for (i = 1; i < 4; i++) { 13691174Stmm * q = 0, bit = 1 << 31; 13791174Stmm * do { 13891174Stmm * D = R - Y; 13991174Stmm * if (D >= 0) { 14091174Stmm * q |= bit; 14191174Stmm * R = D; 14291174Stmm * } 14391174Stmm * R <<= 1; 14491174Stmm * } while ((bit >>= 1) != 0); 14591174Stmm * Q[i] = q; 14691174Stmm * } 14791174Stmm * 14891174Stmm * This can be refined just a bit further by moving the `R <<= 1' 14991174Stmm * calculations to the front of the do-loops and eliding the first one. 15091174Stmm * The process can be terminated immediately whenever R becomes 0, but 15191174Stmm * this is relatively rare, and we do not bother. 15291174Stmm */ 15391174Stmm 15491174Stmmstruct fpn * 15591174Stmm__fpu_div(fe) 15692889Sobrien struct fpemu *fe; 15791174Stmm{ 15892889Sobrien struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2; 15992889Sobrien u_int q, bit; 16092889Sobrien u_int r0, r1, r2, r3, d0, d1, d2, d3, y0, y1, y2, y3; 16191174Stmm FPU_DECL_CARRY 16291174Stmm 16391174Stmm /* 16491174Stmm * Since divide is not commutative, we cannot just use ORDER. 16591174Stmm * Check either operand for NaN first; if there is at least one, 16691174Stmm * order the signalling one (if only one) onto the right, then 16791174Stmm * return it. Otherwise we have the following cases: 16891174Stmm * 16991174Stmm * Inf / Inf = NaN, plus NV exception 170205396Smarius * Inf / num = Inf [i.e., return x #] 171205396Smarius * Inf / 0 = Inf [i.e., return x #] 172205396Smarius * 0 / Inf = 0 [i.e., return x #] 173205396Smarius * 0 / num = 0 [i.e., return x #] 17491174Stmm * 0 / 0 = NaN, plus NV exception 175205396Smarius * num / Inf = 0 # 17691174Stmm * num / num = num (do the divide) 177205396Smarius * num / 0 = Inf #, plus DZ exception 178205396Smarius * 179205396Smarius * # Sign of result is XOR of operand signs. 18091174Stmm */ 18191174Stmm if (ISNAN(x) || ISNAN(y)) { 18291174Stmm ORDER(x, y); 18391174Stmm return (y); 18491174Stmm } 18591174Stmm if (ISINF(x) || ISZERO(x)) { 18691174Stmm if (x->fp_class == y->fp_class) 18791174Stmm return (__fpu_newnan(fe)); 188205396Smarius x->fp_sign ^= y->fp_sign; 18991174Stmm return (x); 19091174Stmm } 19191174Stmm 19291174Stmm x->fp_sign ^= y->fp_sign; 19391174Stmm if (ISINF(y)) { 19491174Stmm x->fp_class = FPC_ZERO; 19591174Stmm return (x); 19691174Stmm } 19791174Stmm if (ISZERO(y)) { 19891174Stmm fe->fe_cx = FSR_DZ; 19991174Stmm x->fp_class = FPC_INF; 20091174Stmm return (x); 20191174Stmm } 20291174Stmm 20391174Stmm /* 20491174Stmm * Macros for the divide. See comments at top for algorithm. 20591174Stmm * Note that we expand R, D, and Y here. 20691174Stmm */ 20791174Stmm 20891174Stmm#define SUBTRACT /* D = R - Y */ \ 20991174Stmm FPU_SUBS(d3, r3, y3); FPU_SUBCS(d2, r2, y2); \ 21091174Stmm FPU_SUBCS(d1, r1, y1); FPU_SUBC(d0, r0, y0) 21191174Stmm 21291174Stmm#define NONNEGATIVE /* D >= 0 */ \ 21391174Stmm ((int)d0 >= 0) 21491174Stmm 21591174Stmm#ifdef FPU_SHL1_BY_ADD 21691174Stmm#define SHL1 /* R <<= 1 */ \ 21791174Stmm FPU_ADDS(r3, r3, r3); FPU_ADDCS(r2, r2, r2); \ 21891174Stmm FPU_ADDCS(r1, r1, r1); FPU_ADDC(r0, r0, r0) 21991174Stmm#else 22091174Stmm#define SHL1 \ 22191174Stmm r0 = (r0 << 1) | (r1 >> 31), r1 = (r1 << 1) | (r2 >> 31), \ 22291174Stmm r2 = (r2 << 1) | (r3 >> 31), r3 <<= 1 22391174Stmm#endif 22491174Stmm 22591174Stmm#define LOOP /* do ... while (bit >>= 1) */ \ 22691174Stmm do { \ 22791174Stmm SHL1; \ 22891174Stmm SUBTRACT; \ 22991174Stmm if (NONNEGATIVE) { \ 23091174Stmm q |= bit; \ 23191174Stmm r0 = d0, r1 = d1, r2 = d2, r3 = d3; \ 23291174Stmm } \ 23391174Stmm } while ((bit >>= 1) != 0) 23491174Stmm 23591174Stmm#define WORD(r, i) /* calculate r->fp_mant[i] */ \ 23691174Stmm q = 0; \ 23791174Stmm bit = 1 << 31; \ 23891174Stmm LOOP; \ 23991174Stmm (x)->fp_mant[i] = q 24091174Stmm 24191174Stmm /* Setup. Note that we put our result in x. */ 24291174Stmm r0 = x->fp_mant[0]; 24391174Stmm r1 = x->fp_mant[1]; 24491174Stmm r2 = x->fp_mant[2]; 24591174Stmm r3 = x->fp_mant[3]; 24691174Stmm y0 = y->fp_mant[0]; 24791174Stmm y1 = y->fp_mant[1]; 24891174Stmm y2 = y->fp_mant[2]; 24991174Stmm y3 = y->fp_mant[3]; 25091174Stmm 25191174Stmm bit = FP_1; 25291174Stmm SUBTRACT; 25391174Stmm if (NONNEGATIVE) { 25491174Stmm x->fp_exp -= y->fp_exp; 25591174Stmm r0 = d0, r1 = d1, r2 = d2, r3 = d3; 25691174Stmm q = bit; 25791174Stmm bit >>= 1; 25891174Stmm } else { 25991174Stmm x->fp_exp -= y->fp_exp + 1; 26091174Stmm q = 0; 26191174Stmm } 26291174Stmm LOOP; 26391174Stmm x->fp_mant[0] = q; 26491174Stmm WORD(x, 1); 26591174Stmm WORD(x, 2); 26691174Stmm WORD(x, 3); 26791174Stmm x->fp_sticky = r0 | r1 | r2 | r3; 26891174Stmm 26991174Stmm return (x); 27091174Stmm} 271