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

1.1     ! root        1: /*     $NetBSD: fpu_hyperb.c,v 1.17 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_hyperb.c        10/24/95
        !            32:  */
        !            33: 
        !            34: /*
        !            35:  * Copyright (c) 2011 Tetsuya Isaki. All rights reserved.
        !            36:  *
        !            37:  * Redistribution and use in source and binary forms, with or without
        !            38:  * modification, are permitted provided that the following conditions
        !            39:  * are met:
        !            40:  * 1. Redistributions of source code must retain the above copyright
        !            41:  *    notice, this list of conditions and the following disclaimer.
        !            42:  * 2. Redistributions in binary form must reproduce the above copyright
        !            43:  *    notice, this list of conditions and the following disclaimer in the
        !            44:  *    documentation and/or other materials provided with the distribution.
        !            45:  *
        !            46:  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
        !            47:  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
        !            48:  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
        !            49:  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
        !            50:  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
        !            51:  * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
        !            52:  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
        !            53:  * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
        !            54:  * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
        !            55:  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
        !            56:  * SUCH DAMAGE.
        !            57:  */
        !            58: 
        !            59: #include "fpu_emulate.h"
        !            60: 
        !            61: /*
        !            62:  * fpu_hyperb.c: defines the following functions
        !            63:  *
        !            64:  *     fpu_atanh(), fpu_cosh(), fpu_sinh(), and fpu_tanh()
        !            65:  */
        !            66: 
        !            67: /*
        !            68:  *             1       1 + x
        !            69:  * atanh(x) = ---*log(-------)
        !            70:  *             2       1 - x
        !            71:  */
        !            72: struct fpn *
        !            73: fpu_atanh(struct fpemu *fe)
        !            74: {
        !            75:        struct fpn x;
        !            76:        struct fpn t;
        !            77:        struct fpn *r;
        !            78: 
        !            79:        if (ISNAN(&fe->fe_f2))
        !            80:                return &fe->fe_f2;
        !            81:        if (ISINF(&fe->fe_f2))
        !            82:                return fpu_newnan(fe);
        !            83: 
        !            84:        /* if x is +0/-0, return +0/-0 */
        !            85:        if (ISZERO(&fe->fe_f2))
        !            86:                return &fe->fe_f2;
        !            87: 
        !            88:        /*
        !            89:         * -INF if x == -1
        !            90:         * +INF if x ==  1
        !            91:         */
        !            92:        r = &fe->fe_f2;
        !            93:        if (r->fp_exp == 0 && r->fp_mant[0] == FP_1 &&
        !            94:            r->fp_mant[1] == 0 && r->fp_mant[2] == 0) {
        !            95:                r->fp_class = FPC_INF;
        !            96:                return r;
        !            97:        }
        !            98: 
        !            99:        /* NAN if |x| > 1 */
        !           100:        if (fe->fe_f2.fp_exp >= 0)
        !           101:                return fpu_newnan(fe);
        !           102: 
        !           103:        CPYFPN(&x, &fe->fe_f2);
        !           104: 
        !           105:        /* t := 1 - x */
        !           106:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !           107:        fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
        !           108:        r = fpu_add(fe);
        !           109:        CPYFPN(&t, r);
        !           110: 
        !           111:        /* r := 1 + x */
        !           112:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !           113:        CPYFPN(&fe->fe_f2, &x);
        !           114:        r = fpu_add(fe);
        !           115: 
        !           116:        /* (1-x)/(1+x) */
        !           117:        CPYFPN(&fe->fe_f1, r);
        !           118:        CPYFPN(&fe->fe_f2, &t);
        !           119:        r = fpu_div(fe);
        !           120: 
        !           121:        /* log((1-x)/(1+x)) */
        !           122:        CPYFPN(&fe->fe_f2, r);
        !           123:        r = fpu_logn(fe);
        !           124: 
        !           125:        /* r /= 2 */
        !           126:        r->fp_exp--;
        !           127: 
        !           128:        return r;
        !           129: }
        !           130: 
        !           131: /*
        !           132:  *            exp(x) + exp(-x)
        !           133:  * cosh(x) = ------------------
        !           134:  *                   2
        !           135:  */
        !           136: struct fpn *
        !           137: fpu_cosh(struct fpemu *fe)
        !           138: {
        !           139:        struct fpn x, *fp;
        !           140: 
        !           141:        if (ISNAN(&fe->fe_f2))
        !           142:                return &fe->fe_f2;
        !           143: 
        !           144:        if (ISINF(&fe->fe_f2)) {
        !           145:                fe->fe_f2.fp_sign = 0;
        !           146:                return &fe->fe_f2;
        !           147:        }
        !           148: 
        !           149:        fp = fpu_etox(fe);
        !           150:        CPYFPN(&x, fp);
        !           151: 
        !           152:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !           153:        CPYFPN(&fe->fe_f2, fp);
        !           154:        fp = fpu_div(fe);
        !           155: 
        !           156:        CPYFPN(&fe->fe_f1, fp);
        !           157:        CPYFPN(&fe->fe_f2, &x);
        !           158:        fp = fpu_add(fe);
        !           159: 
        !           160:        fp->fp_exp--;
        !           161: 
        !           162:        return fp;
        !           163: }
        !           164: 
        !           165: /*
        !           166:  *            exp(x) - exp(-x)
        !           167:  * sinh(x) = ------------------
        !           168:  *                   2
        !           169:  */
        !           170: struct fpn *
        !           171: fpu_sinh(struct fpemu *fe)
        !           172: {
        !           173:        struct fpn x, *fp;
        !           174: 
        !           175:        if (ISNAN(&fe->fe_f2))
        !           176:                return &fe->fe_f2;
        !           177:        if (ISINF(&fe->fe_f2))
        !           178:                return &fe->fe_f2;
        !           179: 
        !           180:        /* if x is +0/-0, return +0/-0 */
        !           181:        if (ISZERO(&fe->fe_f2))
        !           182:                return &fe->fe_f2;
        !           183: 
        !           184:        fp = fpu_etox(fe);
        !           185:        CPYFPN(&x, fp);
        !           186: 
        !           187:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !           188:        CPYFPN(&fe->fe_f2, fp);
        !           189:        fp = fpu_div(fe);
        !           190: 
        !           191:        fp->fp_sign = 1;
        !           192:        CPYFPN(&fe->fe_f1, fp);
        !           193:        CPYFPN(&fe->fe_f2, &x);
        !           194:        fp = fpu_add(fe);
        !           195: 
        !           196:        fp->fp_exp--;
        !           197: 
        !           198:        return fp;
        !           199: }
        !           200: 
        !           201: /*
        !           202:  *            sinh(x)
        !           203:  * tanh(x) = ---------
        !           204:  *            cosh(x)
        !           205:  */
        !           206: struct fpn *
        !           207: fpu_tanh(struct fpemu *fe)
        !           208: {
        !           209:        struct fpn x;
        !           210:        struct fpn s;
        !           211:        struct fpn *r;
        !           212:        struct fpn epx;
        !           213:        struct fpn emx;
        !           214: 
        !           215:        if (ISNAN(&fe->fe_f2))
        !           216:                return &fe->fe_f2;
        !           217: 
        !           218:        /* if x is +0/-0, return +0/-0 */
        !           219:        if (ISZERO(&fe->fe_f2))
        !           220:                return &fe->fe_f2;
        !           221: 
        !           222:        CPYFPN(&x, &fe->fe_f2);
        !           223: 
        !           224:        if (ISINF(&fe->fe_f2)) {
        !           225:                fpu_const(&fe->fe_f2, FPU_CONST_1);
        !           226:                fe->fe_f2.fp_sign = x.fp_sign;
        !           227:                return &fe->fe_f2;
        !           228:        }
        !           229:        if (fe->fe_f2.fp_exp >= 8) {
        !           230:                fpu_const(&fe->fe_f2, FPU_CONST_1);
        !           231:                fe->fe_f2.fp_sign = x.fp_sign;
        !           232:                fe->fe_fpsr |= FPSR_INEX2;      /* inexact */
        !           233:                return &fe->fe_f2;
        !           234:        }
        !           235: 
        !           236:        /* exp(x) */
        !           237:        CPYFPN(&fe->fe_f2, &x);
        !           238:        r = fpu_etox(fe);
        !           239:        CPYFPN(&epx, r);
        !           240: 
        !           241:        /* exp(-x) */
        !           242:        CPYFPN(&fe->fe_f2, &epx);
        !           243:        fpu_const(&fe->fe_f1, FPU_CONST_1);
        !           244:        r = fpu_div(fe);
        !           245:        CPYFPN(&emx, r);
        !           246: 
        !           247:        /* exp(x) - exp(-x) */
        !           248:        CPYFPN(&fe->fe_f1, &epx);
        !           249:        CPYFPN(&fe->fe_f2, &emx);
        !           250:        fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
        !           251:        r = fpu_add(fe);
        !           252:        CPYFPN(&s, r);
        !           253: 
        !           254:        /* exp(x) + exp(-x) */
        !           255:        CPYFPN(&fe->fe_f1, &epx);
        !           256:        CPYFPN(&fe->fe_f2, &emx);
        !           257:        r = fpu_add(fe);
        !           258: 
        !           259:        CPYFPN(&fe->fe_f2, r);
        !           260:        CPYFPN(&fe->fe_f1, &s);
        !           261:        r = fpu_div(fe);
        !           262: 
        !           263:        return r;
        !           264: }

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