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Annotation of nono/fpe/fpu_add.c, revision 1.1

1.1     ! root        1: /*     $NetBSD: fpu_add.c,v 1.9 2013/03/26 11:30:20 isaki 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. Neither the name of the University nor the names of its contributors
        !            25:  *    may be used to endorse or promote products derived from this software
        !            26:  *    without specific prior written permission.
        !            27:  *
        !            28:  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
        !            29:  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
        !            30:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
        !            31:  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
        !            32:  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
        !            33:  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
        !            34:  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
        !            35:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
        !            36:  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
        !            37:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
        !            38:  * SUCH DAMAGE.
        !            39:  *
        !            40:  *     @(#)fpu_add.c   8.1 (Berkeley) 6/11/93
        !            41:  */
        !            42: 
        !            43: /*
        !            44:  * Perform an FPU add (return x + y).
        !            45:  *
        !            46:  * To subtract, negate y and call add.
        !            47:  */
        !            48: 
        !            49: #include "fpu_arith.h"
        !            50: #include "fpu_emulate.h"
        !            51: 
        !            52: struct fpn *
        !            53: fpu_add(struct fpemu *fe)
        !            54: {
        !            55:        struct fpn *x = &fe->fe_f1, *y = &fe->fe_f2, *r;
        !            56:        uint32_t r0, r1, r2;
        !            57:        int rd;
        !            58: 
        !            59:        /*
        !            60:         * Put the `heavier' operand on the right (see fpu_emu.h).
        !            61:         * Then we will have one of the following cases, taken in the
        !            62:         * following order:
        !            63:         *
        !            64:         *  - y = NaN.  Implied: if only one is a signalling NaN, y is.
        !            65:         *      The result is y.
        !            66:         *  - y = Inf.  Implied: x != NaN (is 0, number, or Inf: the NaN
        !            67:         *    case was taken care of earlier).
        !            68:         *      If x = -y, the result is NaN.  Otherwise the result
        !            69:         *      is y (an Inf of whichever sign).
        !            70:         *  - y is 0.  Implied: x = 0.
        !            71:         *      If x and y differ in sign (one positive, one negative),
        !            72:         *      the result is +0 except when rounding to -Inf.  If same:
        !            73:         *      +0 + +0 = +0; -0 + -0 = -0.
        !            74:         *  - x is 0.  Implied: y != 0.
        !            75:         *      Result is y.
        !            76:         *  - other.  Implied: both x and y are numbers.
        !            77:         *      Do addition a la Hennessey & Patterson.
        !            78:         */
        !            79:        ORDER(x, y);
        !            80:        if (ISNAN(y))
        !            81:                return (y);
        !            82:        if (ISINF(y)) {
        !            83:                if (ISINF(x) && x->fp_sign != y->fp_sign)
        !            84:                        return (fpu_newnan(fe));
        !            85:                return (y);
        !            86:        }
        !            87:        rd = (fe->fe_fpcr & FPCR_ROUND);
        !            88:        if (ISZERO(y)) {
        !            89:                if (rd != FPCR_MINF)    /* only -0 + -0 gives -0 */
        !            90:                        y->fp_sign &= x->fp_sign;
        !            91:                else                    /* any -0 operand gives -0 */
        !            92:                        y->fp_sign |= x->fp_sign;
        !            93:                return (y);
        !            94:        }
        !            95:        if (ISZERO(x))
        !            96:                return (y);
        !            97:        /*
        !            98:         * We really have two numbers to add, although their signs may
        !            99:         * differ.  Make the exponents match, by shifting the smaller
        !           100:         * number right (e.g., 1.011 => 0.1011) and increasing its
        !           101:         * exponent (2^3 => 2^4).  Note that we do not alter the exponents
        !           102:         * of x and y here.
        !           103:         */
        !           104:        r = &fe->fe_f3;
        !           105:        r->fp_class = FPC_NUM;
        !           106:        if (x->fp_exp == y->fp_exp) {
        !           107:                r->fp_exp = x->fp_exp;
        !           108:                r->fp_sticky = 0;
        !           109:        } else {
        !           110:                if (x->fp_exp < y->fp_exp) {
        !           111:                        /*
        !           112:                         * Try to avoid subtract case iii (see below).
        !           113:                         * This also guarantees that x->fp_sticky = 0.
        !           114:                         */
        !           115:                        SWAP(x, y);
        !           116:                }
        !           117:                /* now x->fp_exp > y->fp_exp */
        !           118:                r->fp_exp = x->fp_exp;
        !           119:                r->fp_sticky = fpu_shr(y, x->fp_exp - y->fp_exp);
        !           120:        }
        !           121:        r->fp_sign = x->fp_sign;
        !           122:        if (x->fp_sign == y->fp_sign) {
        !           123:                FPU_DECL_CARRY
        !           124: 
        !           125:                /*
        !           126:                 * The signs match, so we simply add the numbers.  The result
        !           127:                 * may be `supernormal' (as big as 1.111...1 + 1.111...1, or
        !           128:                 * 11.111...0).  If so, a single bit shift-right will fix it
        !           129:                 * (but remember to adjust the exponent).
        !           130:                 */
        !           131:                /* r->fp_mant = x->fp_mant + y->fp_mant */
        !           132:                FPU_ADDS(r->fp_mant[2], x->fp_mant[2], y->fp_mant[2]);
        !           133:                FPU_ADDCS(r->fp_mant[1], x->fp_mant[1], y->fp_mant[1]);
        !           134:                FPU_ADDC(r0, x->fp_mant[0], y->fp_mant[0]);
        !           135:                if ((r->fp_mant[0] = r0) >= FP_2) {
        !           136:                        (void) fpu_shr(r, 1);
        !           137:                        r->fp_exp++;
        !           138:                }
        !           139:        } else {
        !           140:                FPU_DECL_CARRY
        !           141: 
        !           142:                /*
        !           143:                 * The signs differ, so things are rather more difficult.
        !           144:                 * H&P would have us negate the negative operand and add;
        !           145:                 * this is the same as subtracting the negative operand.
        !           146:                 * This is quite a headache.  Instead, we will subtract
        !           147:                 * y from x, regardless of whether y itself is the negative
        !           148:                 * operand.  When this is done one of three conditions will
        !           149:                 * hold, depending on the magnitudes of x and y:
        !           150:                 *   case i)   |x| > |y|.  The result is just x - y,
        !           151:                 *      with x's sign, but it may need to be normalized.
        !           152:                 *   case ii)  |x| = |y|.  The result is 0 (maybe -0)
        !           153:                 *      so must be fixed up.
        !           154:                 *   case iii) |x| < |y|.  We goofed; the result should
        !           155:                 *      be (y - x), with the same sign as y.
        !           156:                 * We could compare |x| and |y| here and avoid case iii,
        !           157:                 * but that would take just as much work as the subtract.
        !           158:                 * We can tell case iii has occurred by an overflow.
        !           159:                 *
        !           160:                 * N.B.: since x->fp_exp >= y->fp_exp, x->fp_sticky = 0.
        !           161:                 */
        !           162:                /* r->fp_mant = x->fp_mant - y->fp_mant */
        !           163:                FPU_SET_CARRY(y->fp_sticky);
        !           164:                FPU_SUBCS(r2, x->fp_mant[2], y->fp_mant[2]);
        !           165:                FPU_SUBCS(r1, x->fp_mant[1], y->fp_mant[1]);
        !           166:                FPU_SUBC(r0, x->fp_mant[0], y->fp_mant[0]);
        !           167:                if (r0 < FP_2) {
        !           168:                        /* cases i and ii */
        !           169:                        if ((r0 | r1 | r2) == 0) {
        !           170:                                /* case ii */
        !           171:                                r->fp_class = FPC_ZERO;
        !           172:                                r->fp_sign = (rd == FPCR_MINF);
        !           173:                                return (r);
        !           174:                        }
        !           175:                } else {
        !           176:                        /*
        !           177:                         * Oops, case iii.  This can only occur when the
        !           178:                         * exponents were equal, in which case neither
        !           179:                         * x nor y have sticky bits set.  Flip the sign
        !           180:                         * (to y's sign) and negate the result to get y - x.
        !           181:                         */
        !           182: #ifdef DIAGNOSTIC
        !           183:                        if (x->fp_exp != y->fp_exp || r->fp_sticky)
        !           184:                                panic("fpu_add");
        !           185: #endif
        !           186:                        r->fp_sign = y->fp_sign;
        !           187:                        FPU_SUBS(r2, 0, r2);
        !           188:                        FPU_SUBCS(r1, 0, r1);
        !           189:                        FPU_SUBC(r0, 0, r0);
        !           190:                }
        !           191:                r->fp_mant[2] = r2;
        !           192:                r->fp_mant[1] = r1;
        !           193:                r->fp_mant[0] = r0;
        !           194:                if (r0 < FP_1)
        !           195:                        fpu_norm(r);
        !           196:        }
        !           197:        return (r);
        !           198: }
        !           199: 
        !           200: #if defined(XM6i_FPE)
        !           201: struct fpn *
        !           202: fpu_sub(struct fpemu *fe)
        !           203: {
        !           204:        if (ISNAN(&fe->fe_f1))
        !           205:                return &fe->fe_f1;
        !           206:        if (ISNAN(&fe->fe_f2))
        !           207:                return &fe->fe_f2;
        !           208: 
        !           209:        fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
        !           210:        return fpu_add(fe);
        !           211: }
        !           212: #endif

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