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

1.1     ! root        1: /*     $NetBSD: fpu_exp.c,v 1.9 2016/12/05 15:31:01 isaki Exp $        */
        !             2: 
        !             3: /*
        !             4:  * Copyright (c) 1995  Ken Nakata
        !             5:  *     All rights reserved.
        !             6:  *
        !             7:  * Redistribution and use in source and binary forms, with or without
        !             8:  * modification, are permitted provided that the following conditions
        !             9:  * are met:
        !            10:  * 1. Redistributions of source code must retain the above copyright
        !            11:  *    notice, this list of conditions and the following disclaimer.
        !            12:  * 2. Redistributions in binary form must reproduce the above copyright
        !            13:  *    notice, this list of conditions and the following disclaimer in the
        !            14:  *    documentation and/or other materials provided with the distribution.
        !            15:  * 3. Neither the name of the author nor the names of its contributors
        !            16:  *    may be used to endorse or promote products derived from this software
        !            17:  *    without specific prior written permission.
        !            18:  *
        !            19:  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
        !            20:  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
        !            21:  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
        !            22:  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
        !            23:  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
        !            24:  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
        !            25:  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
        !            26:  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
        !            27:  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
        !            28:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
        !            29:  * SUCH DAMAGE.
        !            30:  *
        !            31:  *     @(#)fpu_exp.c   10/24/95
        !            32:  */
        !            33: 
        !            34: #include "fpu_emulate.h"
        !            35: 
        !            36: /* The number of items to terminate the Taylor expansion */
        !            37: #define MAX_ITEMS      (2000)
        !            38: 
        !            39: /*
        !            40:  * fpu_exp.c: defines fpu_etox(), fpu_etoxm1(), fpu_tentox(), and fpu_twotox();
        !            41:  */
        !            42: 
        !            43: /*
        !            44:  *                  x^2   x^3   x^4
        !            45:  * exp(x) = 1 + x + --- + --- + --- + ...
        !            46:  *                   2!    3!    4!
        !            47:  */
        !            48: static struct fpn *
        !            49: fpu_etox_taylor(struct fpemu *fe)
        !            50: {
        !            51:        struct fpn res;
        !            52:        struct fpn x;
        !            53:        struct fpn s0;
        !            54:        struct fpn *s1;
        !            55:        struct fpn *r;
        !            56:        uint32_t k;
        !            57: 
        !            58:        CPYFPN(&x, &fe->fe_f2);
        !            59:        CPYFPN(&s0, &fe->fe_f2);
        !            60: 
        !            61:        /* res := 1 + x */
        !            62:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !            63:        r = fpu_add(fe);
        !            64:        CPYFPN(&res, r);
        !            65: 
        !            66:        k = 2;
        !            67:        for (; k < MAX_ITEMS; k++) {
        !            68:                /* s1 = s0 * x / k */
        !            69:                CPYFPN(&fe->fe_f1, &s0);
        !            70:                CPYFPN(&fe->fe_f2, &x);
        !            71:                r = fpu_mul(fe);
        !            72: 
        !            73:                CPYFPN(&fe->fe_f1, r);
        !            74:                fpu_explode(fe, &fe->fe_f2, FTYPE_LNG, &k);
        !            75:                s1 = fpu_div(fe);
        !            76: 
        !            77:                /* break if s1 is enough small */
        !            78:                if (ISZERO(s1))
        !            79:                        break;
        !            80:                if (res.fp_exp - s1->fp_exp >= EXT_FRACBITS)
        !            81:                        break;
        !            82: 
        !            83:                /* s0 := s1 for next loop */
        !            84:                CPYFPN(&s0, s1);
        !            85: 
        !            86:                /* res += s1 */
        !            87:                CPYFPN(&fe->fe_f2, s1);
        !            88:                CPYFPN(&fe->fe_f1, &res);
        !            89:                r = fpu_add(fe);
        !            90:                CPYFPN(&res, r);
        !            91:        }
        !            92: 
        !            93:        CPYFPN(&fe->fe_f2, &res);
        !            94:        return &fe->fe_f2;
        !            95: }
        !            96: 
        !            97: /*
        !            98:  * exp(x) = 2^k * exp(r) with k = round(x / ln2) and r = x - k * ln2
        !            99:  *
        !           100:  * Algorithm partially taken from libm, where exp(r) is approximated by a
        !           101:  * rational function of r. We use the Taylor expansion instead.
        !           102:  */
        !           103: struct fpn *
        !           104: fpu_etox(struct fpemu *fe)
        !           105: {
        !           106:        struct fpn x, *fp;
        !           107:        int k;
        !           108: 
        !           109:        if (ISNAN(&fe->fe_f2))
        !           110:                return &fe->fe_f2;
        !           111:        if (ISINF(&fe->fe_f2)) {
        !           112:                if (fe->fe_f2.fp_sign)
        !           113:                        fpu_const(&fe->fe_f2, FPU_CONST_0);
        !           114:                return &fe->fe_f2;
        !           115:        }
        !           116:        if (ISZERO(&fe->fe_f2)) {
        !           117:                fpu_const(&fe->fe_f2, FPU_CONST_1);
        !           118:                return &fe->fe_f2;
        !           119:        }
        !           120: 
        !           121:        /*
        !           122:         * return inf if x >=  2^14
        !           123:         * return +0  if x <= -2^14
        !           124:         */
        !           125:        if (fe->fe_f2.fp_exp >= 14) {
        !           126:                if (fe->fe_f2.fp_sign) {
        !           127:                        fe->fe_f2.fp_class = FPC_ZERO;
        !           128:                        fe->fe_f2.fp_sign = 0;
        !           129:                } else {
        !           130:                        fe->fe_f2.fp_class = FPC_INF;
        !           131:                }
        !           132:                return &fe->fe_f2;
        !           133:        }
        !           134: 
        !           135:        CPYFPN(&x, &fe->fe_f2);
        !           136: 
        !           137:        /* k = round(x / ln2) */
        !           138:        CPYFPN(&fe->fe_f1, &fe->fe_f2);
        !           139:        fpu_const(&fe->fe_f2, FPU_CONST_LN_2);
        !           140:        fp = fpu_div(fe);
        !           141:        CPYFPN(&fe->fe_f2, fp);
        !           142:        fp = fpu_int(fe);
        !           143:        if (ISZERO(fp)) {
        !           144:                /* k = 0 */
        !           145:                CPYFPN(&fe->fe_f2, &x);
        !           146:                fp = fpu_etox_taylor(fe);
        !           147:                return fp;
        !           148:        }
        !           149:        /* extract k as integer format from fpn format */
        !           150:        k = fp->fp_mant[0] >> (FP_LG - fp->fp_exp);
        !           151:        if (fp->fp_sign)
        !           152:                k *= -1;
        !           153: 
        !           154:        /* exp(r) = exp(x - k * ln2) */
        !           155:        CPYFPN(&fe->fe_f1, fp);
        !           156:        fpu_const(&fe->fe_f2, FPU_CONST_LN_2);
        !           157:        fp = fpu_mul(fe);
        !           158:        fp->fp_sign = !fp->fp_sign;
        !           159:        CPYFPN(&fe->fe_f1, fp);
        !           160:        CPYFPN(&fe->fe_f2, &x);
        !           161:        fp = fpu_add(fe);
        !           162:        CPYFPN(&fe->fe_f2, fp);
        !           163:        fp = fpu_etox_taylor(fe);
        !           164: 
        !           165:        /* 2^k */
        !           166:        fp->fp_exp += k;
        !           167: 
        !           168:        return fp;
        !           169: }
        !           170: 
        !           171: /*
        !           172:  * exp(x) - 1
        !           173:  */
        !           174: struct fpn *
        !           175: fpu_etoxm1(struct fpemu *fe)
        !           176: {
        !           177:        struct fpn *fp;
        !           178: 
        !           179:        /* if x is +0/-0, return +0/-0 */
        !           180:        if (ISZERO(&fe->fe_f2))
        !           181:                return &fe->fe_f2;
        !           182: 
        !           183:        fp = fpu_etox(fe);
        !           184: 
        !           185:        CPYFPN(&fe->fe_f1, fp);
        !           186:        /* build a 1.0 */
        !           187:        fp = fpu_const(&fe->fe_f2, FPU_CONST_1);
        !           188:        fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
        !           189:        /* fp = f2 - 1.0 */
        !           190:        fp = fpu_add(fe);
        !           191: 
        !           192:        return fp;
        !           193: }
        !           194: 
        !           195: /*
        !           196:  * 10^x = exp(x * ln10)
        !           197:  */
        !           198: struct fpn *
        !           199: fpu_tentox(struct fpemu *fe)
        !           200: {
        !           201:        struct fpn *fp;
        !           202: 
        !           203:        /* build a ln10 */
        !           204:        fp = fpu_const(&fe->fe_f1, FPU_CONST_LN_10);
        !           205:        /* fp = ln10 * f2 */
        !           206:        fp = fpu_mul(fe);
        !           207: 
        !           208:        /* copy the result to the src opr */
        !           209:        CPYFPN(&fe->fe_f2, fp);
        !           210: 
        !           211:        return fpu_etox(fe);
        !           212: }
        !           213: 
        !           214: /*
        !           215:  * 2^x = exp(x * ln2)
        !           216:  */
        !           217: struct fpn *
        !           218: fpu_twotox(struct fpemu *fe)
        !           219: {
        !           220:        struct fpn *fp;
        !           221: 
        !           222:        /* build a ln2 */
        !           223:        fp = fpu_const(&fe->fe_f1, FPU_CONST_LN_2);
        !           224:        /* fp = ln2 * f2 */
        !           225:        fp = fpu_mul(fe);
        !           226: 
        !           227:        /* copy the result to the src opr */
        !           228:        CPYFPN(&fe->fe_f2, fp);
        !           229: 
        !           230:        return fpu_etox(fe);
        !           231: }

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