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Annotation of 43BSDReno/lib/libm/ieee/cbrt.c, revision 1.1

1.1     ! root        1: /*
        !             2:  * Copyright (c) 1985 Regents of the University of California.
        !             3:  * All rights reserved.
        !             4:  *
        !             5:  * Redistribution and use in source and binary forms are permitted
        !             6:  * provided that: (1) source distributions retain this entire copyright
        !             7:  * notice and comment, and (2) distributions including binaries display
        !             8:  * the following acknowledgement:  ``This product includes software
        !             9:  * developed by the University of California, Berkeley and its contributors''
        !            10:  * in the documentation or other materials provided with the distribution
        !            11:  * and in all advertising materials mentioning features or use of this
        !            12:  * software. Neither the name of the University nor the names of its
        !            13:  * contributors may be used to endorse or promote products derived
        !            14:  * from this software without specific prior written permission.
        !            15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            18:  *
        !            19:  * All recipients should regard themselves as participants in an ongoing
        !            20:  * research project and hence should feel obligated to report their
        !            21:  * experiences (good or bad) with these elementary function codes, using
        !            22:  * the sendbug(8) program, to the authors.
        !            23:  */
        !            24: 
        !            25: #ifndef lint
        !            26: static char sccsid[] = "@(#)cbrt.c     5.7 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: #include <sys/stdc.h>
        !            30: 
        !            31: /* kahan's cube root (53 bits IEEE double precision)
        !            32:  * for IEEE machines only
        !            33:  * coded in C by K.C. Ng, 4/30/85
        !            34:  *
        !            35:  * Accuracy:
        !            36:  *     better than 0.667 ulps according to an error analysis. Maximum
        !            37:  * error observed was 0.666 ulps in an 1,000,000 random arguments test.
        !            38:  *
        !            39:  * Warning: this code is semi machine dependent; the ordering of words in
        !            40:  * a floating point number must be known in advance. I assume that the
        !            41:  * long interger at the address of a floating point number will be the
        !            42:  * leading 32 bits of that floating point number (i.e., sign, exponent,
        !            43:  * and the 20 most significant bits).
        !            44:  * On a National machine, it has different ordering; therefore, this code 
        !            45:  * must be compiled with flag -DNATIONAL. 
        !            46:  */
        !            47: #if !defined(vax)&&!defined(tahoe)
        !            48: 
        !            49: static const unsigned long
        !            50:                     B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
        !            51:                     B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
        !            52: static const double
        !            53:            C= 19./35.,
        !            54:            D= -864./1225.,
        !            55:            E= 99./70.,
        !            56:            F= 45./28.,
        !            57:            G= 5./14.;
        !            58: 
        !            59: double cbrt(x) 
        !            60: double x;
        !            61: {
        !            62:        double r,s,t=0.0,w;
        !            63:        unsigned long *px = (unsigned long *) &x,
        !            64:                      *pt = (unsigned long *) &t,
        !            65:                      mexp,sign;
        !            66: 
        !            67: #ifdef national /* ordering of words in a floating points number */
        !            68:        const int n0=1,n1=0;
        !            69: #else  /* national */
        !            70:        const int n0=0,n1=1;
        !            71: #endif /* national */
        !            72: 
        !            73:        mexp=px[n0]&0x7ff00000;
        !            74:        if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */
        !            75:        if(x==0.0) return(x);           /* cbrt(0) is itself */
        !            76: 
        !            77:        sign=px[n0]&0x80000000; /* sign= sign(x) */
        !            78:        px[n0] ^= sign;         /* x=|x| */
        !            79: 
        !            80: 
        !            81:     /* rough cbrt to 5 bits */
        !            82:        if(mexp==0)             /* subnormal number */
        !            83:          {pt[n0]=0x43500000;   /* set t= 2**54 */
        !            84:           t*=x; pt[n0]=pt[n0]/3+B2;
        !            85:          }
        !            86:        else
        !            87:          pt[n0]=px[n0]/3+B1;   
        !            88: 
        !            89: 
        !            90:     /* new cbrt to 23 bits, may be implemented in single precision */
        !            91:        r=t*t/x;
        !            92:        s=C+r*t;
        !            93:        t*=G+F/(s+E+D/s);       
        !            94: 
        !            95:     /* chopped to 20 bits and make it larger than cbrt(x) */ 
        !            96:        pt[n1]=0; pt[n0]+=0x00000001;
        !            97: 
        !            98: 
        !            99:     /* one step newton iteration to 53 bits with error less than 0.667 ulps */
        !           100:        s=t*t;          /* t*t is exact */
        !           101:        r=x/s;
        !           102:        w=t+t;
        !           103:        r=(r-t)/(w+r);  /* r-t is exact */
        !           104:        t=t+t*r;
        !           105: 
        !           106: 
        !           107:     /* retore the sign bit */
        !           108:        pt[n0] |= sign;
        !           109:        return(t);
        !           110: }
        !           111: #endif

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