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EXPERIMENTAL
Network Working Group                                           C. DavisRequest for Comments: 1876                             Kapor EnterprisesUpdates:1034,1035                                             P. VixieCategory: Experimental                                 Vixie Enterprises                                                              T. Goodwin                                                            FORE Systems                                                            I. Dickinson                                                   University of Warwick                                                            January 1996A Means for Expressing Location Information in the Domain Name SystemStatus of this Memo   This memo defines an Experimental Protocol for the Internet   community.  This memo does not specify an Internet standard of any   kind.  Discussion and suggestions for improvement are requested.   Distribution of this memo is unlimited.1. Abstract   This memo defines a new DNS RR type for experimental purposes.  This   RFC describes a mechanism to allow the DNS to carry location   information about hosts, networks, and subnets.  Such information for   a small subset of hosts is currently contained in the flat-file UUCP   maps.  However, just as the DNS replaced the use of HOSTS.TXT to   carry host and network address information, it is possible to replace   the UUCP maps as carriers of location information.   This RFC defines the format of a new Resource Record (RR) for the   Domain Name System (DNS), and reserves a corresponding DNS type   mnemonic (LOC) and numerical code (29).   This RFC assumes that the reader is familiar with the DNS [RFC 1034,RFC 1035].  The data shown in our examples is for pedagogical use and   does not necessarily reflect the real Internet.Davis, et al                  Experimental                      [Page 1]

RFC 1876            Location Information in the DNS         January 19962. RDATA Format       MSB                                           LSB       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+      0|        VERSION        |         SIZE          |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+      2|       HORIZ PRE       |       VERT PRE        |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+      4|                   LATITUDE                    |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+      6|                   LATITUDE                    |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+      8|                   LONGITUDE                   |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+     10|                   LONGITUDE                   |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+     12|                   ALTITUDE                    |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+     14|                   ALTITUDE                    |       +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+   (octet)where:VERSION      Version number of the representation.  This must be zero.             Implementations are required to check this field and make             no assumptions about the format of unrecognized versions.SIZE         The diameter of a sphere enclosing the described entity, in             centimeters, expressed as a pair of four-bit unsigned             integers, each ranging from zero to nine, with the most             significant four bits representing the base and the second             number representing the power of ten by which to multiply             the base.  This allows sizes from 0e0 (<1cm) to 9e9             (90,000km) to be expressed.  This representation was chosen             such that the hexadecimal representation can be read by             eye; 0x15 = 1e5.  Four-bit values greater than 9 are             undefined, as are values with a base of zero and a non-zero             exponent.             Since 20000000m (represented by the value 0x29) is greater             than the equatorial diameter of the WGS 84 ellipsoid             (12756274m), it is therefore suitable for use as a             "worldwide" size.HORIZ PRE    The horizontal precision of the data, in centimeters,             expressed using the same representation as SIZE.  This is             the diameter of the horizontal "circle of error", ratherDavis, et al                  Experimental                      [Page 2]

RFC 1876            Location Information in the DNS         January 1996             than a "plus or minus" value.  (This was chosen to match             the interpretation of SIZE; to get a "plus or minus" value,             divide by 2.)VERT PRE     The vertical precision of the data, in centimeters,             expressed using the sane representation as for SIZE.  This             is the total potential vertical error, rather than a "plus             or minus" value.  (This was chosen to match the             interpretation of SIZE; to get a "plus or minus" value,             divide by 2.)  Note that if altitude above or below sea             level is used as an approximation for altitude relative to             the [WGS 84] ellipsoid, the precision value should be             adjusted.LATITUDE     The latitude of the center of the sphere described by the             SIZE field, expressed as a 32-bit integer, most significant             octet first (network standard byte order), in thousandths             of a second of arc.  2^31 represents the equator; numbers             above that are north latitude.LONGITUDE    The longitude of the center of the sphere described by the             SIZE field, expressed as a 32-bit integer, most significant             octet first (network standard byte order), in thousandths             of a second of arc, rounded away from the prime meridian.             2^31 represents the prime meridian; numbers above that are             east longitude.ALTITUDE     The altitude of the center of the sphere described by the             SIZE field, expressed as a 32-bit integer, most significant             octet first (network standard byte order), in centimeters,             from a base of 100,000m below the [WGS 84] reference             spheroid used by GPS (semimajor axis a=6378137.0,             reciprocal flattening rf=298.257223563).  Altitude above             (or below) sea level may be used as an approximation of             altitude relative to the the [WGS 84] spheroid, though due             to the Earth's surface not being a perfect spheroid, there             will be differences.  (For example, the geoid (which sea             level approximates) for the continental US ranges from 10             meters to 50 meters below the [WGS 84] spheroid.             Adjustments to ALTITUDE and/or VERT PRE will be necessary             in most cases.  The Defense Mapping Agency publishes geoid             height values relative to the [WGS 84] ellipsoid.Davis, et al                  Experimental                      [Page 3]

RFC 1876            Location Information in the DNS         January 19963. Master File Format   The LOC record is expressed in a master file in the following format:   <owner> <TTL> <class> LOC ( d1 [m1 [s1]] {"N"|"S"} d2 [m2 [s2]]                               {"E"|"W"} alt["m"] [siz["m"] [hp["m"]                               [vp["m"]]]] )   (The parentheses are used for multi-line data as specified in [RFC   1035]section 5.1.)   where:       d1:     [0 .. 90]            (degrees latitude)       d2:     [0 .. 180]           (degrees longitude)       m1, m2: [0 .. 59]            (minutes latitude/longitude)       s1, s2: [0 .. 59.999]        (seconds latitude/longitude)       alt:    [-100000.00 .. 42849672.95] BY .01 (altitude in meters)       siz, hp, vp: [0 .. 90000000.00] (size/precision in meters)   If omitted, minutes and seconds default to zero, size defaults to 1m,   horizontal precision defaults to 10000m, and vertical precision   defaults to 10m.  These defaults are chosen to represent typical   ZIP/postal code area sizes, since it is often easy to find   approximate geographical location by ZIP/postal code.4. Example Data;;;;;; note that these data would not all appear in one zone file;;;;; network LOC RR derived from ZIP data.  note use of precision defaultscambridge-net.kei.com.        LOC   42 21 54 N 71 06 18 W -24m 30m;; higher-precision host LOC RR.  note use of vertical precision defaultloiosh.kei.com.               LOC   42 21 43.952 N 71 5 6.344 W                                    -24m 1m 200mpipex.net.                    LOC   52 14 05 N 00 08 50 E 10mcurtin.edu.au.                LOC   32 7 19 S 116 2 25 E 10mrwy04L.logan-airport.boston.  LOC   42 21 28.764 N 71 00 51.617 W                                    -44m 2000mDavis, et al                  Experimental                      [Page 4]

RFC 1876            Location Information in the DNS         January 19965. Application use of the LOC RR5.1 Suggested Uses   Some uses for the LOC RR have already been suggested, including the   USENET backbone flow maps, a "visual traceroute" application showing   the geographical path of an IP packet, and network management   applications that could use LOC RRs to generate a map of hosts and   routers being managed.5.2 Search Algorithms   This section specifies how to use the DNS to translate domain names   and/or IP addresses into location information.   If an application wishes to have a "fallback" behavior, displaying a   less precise or larger area when a host does not have an associated   LOC RR, it MAY support use of the algorithm insection 5.2.3, as   noted in sections5.2.1 and5.2.2.  If fallback is desired, this   behaviour is the RECOMMENDED default, but in some cases it may need   to be modified based on the specific requirements of the application   involved.   This search algorithm is designed to allow network administrators to   specify the location of a network or subnet without requiring LOC RR   data for each individual host.  For example, a computer lab with 24   workstations, all of which are on the same subnet and in basically   the same location, would only need a LOC RR for the subnet.   (However, if the file server's location has been more precisely   measured, a separate LOC RR for it can be placed in the DNS.)5.2.1 Searching by Name   If the application is beginning with a name, rather than an IP   address (as the USENET backbone flow maps do), it MUST check for a   LOC RR associated with that name.  (CNAME records should be followed   as for any other RR type.)   If there is no LOC RR for that name, all A records (if any)   associated with the name MAY be checked for network (or subnet) LOC   RRs using the "Searching by Network or Subnet" algorithm (5.2.3).  If   multiple A records exist and have associated network or subnet LOC   RRs, the application may choose to use any, some, or all of the LOC   RRs found, possibly in combination.  It is suggested that multi-homed   hosts have LOC RRs for their name in the DNS to avoid any ambiguity   in these cases.Davis, et al                  Experimental                      [Page 5]

RFC 1876            Location Information in the DNS         January 1996   Note that domain names that do not have associated A records must   have a LOC RR associated with their name in order for location   information to be accessible.5.2.2 Searching by Address   If the application is beginning with an IP address (as a "visual   traceroute" application might be) it MUST first map the address to a   name using the IN-ADDR.ARPA namespace (see [RFC 1034],section5.2.1), then check for a LOC RR associated with that name.   If there is no LOC RR for the name, the address MAY be checked for   network (or subnet) LOC RRs using the "Searching by Network or   Subnet" algorithm (5.2.3).5.2.3 Searching by Network or Subnet   Even if a host's name does not have any associated LOC RRs, the   network(s) or subnet(s) it is on may.  If the application wishes to   search for such less specific data, the following algorithm SHOULD be   followed to find a network or subnet LOC RR associated with the IP   address.  This algorithm is adapted slightly from that specified in   [RFC 1101], sections4.3 and4.4.   Since subnet LOC RRs are (if present) more specific than network LOC   RRs, it is best to use them if available.  In order to do so, we   build a stack of network and subnet names found while performing the   [RFC 1101] search, then work our way down the stack until a LOC RR is   found.   1. create a host-zero address using the network portion of the IP      address (one, two, or three bytes for class A, B, or C networks,      respectively).  For example, for the host 128.9.2.17, on the class      B network 128.9, this would result in the address "128.9.0.0".   2. Reverse the octets, suffix IN-ADDR.ARPA, and query for PTR and A      records.  Retrieve:               0.0.9.128.IN-ADDR.ARPA.  PTR    isi-net.isi.edu.                                        A      255.255.255.0      Push the name "isi-net.isi.edu" onto the stack of names to be      searched for LOC RRs later.Davis, et al                  Experimental                      [Page 6]

RFC 1876            Location Information in the DNS         January 1996   3. Since an A RR was found, repeat using mask from RR      (255.255.255.0), constructing a query for 0.2.9.128.IN-ADDR.ARPA.      Retrieve:               0.2.9.128.IN-ADDR.ARPA.  PTR    div2-subnet.isi.edu.                                        A      255.255.255.240      Push the name "div2-subnet.isi.edu" onto the stack of names to be      searched for LOC RRs later.   4. Since another A RR was found, repeat using mask 255.255.255.240      (x'FFFFFFF0'), constructing a query for 16.2.9.128.IN-ADDR.ARPA.      Retrieve:               16.2.9.128.IN-ADDR.ARPA. PTR    inc-subsubnet.isi.edu.      Push the name "inc-subsubnet.isi.edu" onto the stack of names to      be searched for LOC RRs later.   5. Since no A RR is present at 16.2.9.128.IN-ADDR.ARPA., there are no      more subnet levels to search.  We now pop the top name from the      stack and check for an associated LOC RR.  Repeat until a LOC RR      is found.      In this case, assume that inc-subsubnet.isi.edu does not have an      associated LOC RR, but that div2-subnet.isi.edu does.  We will      then use div2-subnet.isi.edu's LOC RR as an approximation of this      host's location.  (Note that even if isi-net.isi.edu has a LOC RR,      it will not be used if a subnet also has a LOC RR.)5.3 Applicability to non-IN Classes and non-IP Addresses   The LOC record is defined for all RR classes, and may be used with   non-IN classes such as HS and CH.  The semantics of such use are not   defined by this memo.   The search algorithm insection 5.2.3 may be adapted to other   addressing schemes by extending [RFC 1101]'s encoding of network   names to cover those schemes.  Such extensions are not defined by   this memo.Davis, et al                  Experimental                      [Page 7]

RFC 1876            Location Information in the DNS         January 19966. References   [RFC 1034] Mockapetris, P., "Domain Names - Concepts and Facilities",              STD 13,RFC 1034, USC/Information Sciences Institute,              November 1987.   [RFC 1035] Mockapetris, P., "Domain Names - Implementation and              Specification", STD 13,RFC 1035, USC/Information Sciences              Institute, November 1987.   [RFC 1101] Mockapetris, P., "DNS Encoding of Network Names and Other              Types",RFC 1101, USC/Information Sciences Institute,              April 1989.   [WGS 84] United States Department of Defense; DoD WGS-1984 - Its            Definition and Relationships with Local Geodetic Systems;            Washington, D.C.; 1985; Report AD-A188 815 DMA; 6127; 7-R-            138-R; CV, KV;7. Security Considerations   High-precision LOC RR information could be used to plan a penetration   of physical security, leading to potential denial-of-machine attacks.   To avoid any appearance of suggesting this method to potential   attackers, we declined the opportunity to name this RR "ICBM".8. Authors' Addresses   The authors as a group can be reached as <loc@pipex.net>.   Christopher Davis   Kapor Enterprises, Inc.   238 Main Street, Suite 400   Cambridge, MA 02142   Phone: +1 617 576 4532   EMail: ckd@kei.com   Paul Vixie   Vixie Enterprises   Star Route Box 159A   Woodside, CA 94062   Phone: +1 415 747 0204   EMail: paul@vix.comDavis, et al                  Experimental                      [Page 8]

RFC 1876            Location Information in the DNS         January 1996   Tim Goodwin   Public IP Exchange Ltd (PIPEX)   216 The Science Park   Cambridge CB4 4WA   UK   Phone: +44 1223 250250   EMail: tim@pipex.net   Ian Dickinson   FORE Systems   2475 The Crescent   Solihull Parkway   Birmingham Business Park   B37 7YE   UK   Phone: +44 121 717 4444   EMail: idickins@fore.co.ukDavis, et al                  Experimental                      [Page 9]

RFC 1876            Location Information in the DNS         January 1996Appendix A: Sample Conversion Routines/* * routines to convert between on-the-wire RR format and zone file * format.  Does not contain conversion to/from decimal degrees; * divide or multiply by 60*60*1000 for that. */static unsigned int poweroften[10] = {1, 10, 100, 1000, 10000, 100000,                                 1000000,10000000,100000000,1000000000};/* takes an XeY precision/size value, returns a string representation.*/static const char *precsize_ntoa(prec)        u_int8_t prec;{        static char retbuf[sizeof("90000000.00")];        unsigned long val;        int mantissa, exponent;        mantissa = (int)((prec >> 4) & 0x0f) % 10;        exponent = (int)((prec >> 0) & 0x0f) % 10;        val = mantissa * poweroften[exponent];        (void) sprintf(retbuf,"%d.%.2d", val/100, val%100);        return (retbuf);}/* converts ascii size/precision X * 10**Y(cm) to 0xXY. moves pointer.*/static u_int8_tprecsize_aton(strptr)        char **strptr;{        unsigned int mval = 0, cmval = 0;        u_int8_t retval = 0;        register char *cp;        register int exponent;        register int mantissa;        cp = *strptr;        while (isdigit(*cp))                mval = mval * 10 + (*cp++ - '0');        if (*cp == '.') {               /* centimeters */                cp++;                if (isdigit(*cp)) {Davis, et al                  Experimental                     [Page 10]

RFC 1876            Location Information in the DNS         January 1996                        cmval = (*cp++ - '0') * 10;                        if (isdigit(*cp)) {                                cmval += (*cp++ - '0');                        }                }        }        cmval = (mval * 100) + cmval;        for (exponent = 0; exponent < 9; exponent++)                if (cmval < poweroften[exponent+1])                        break;        mantissa = cmval / poweroften[exponent];        if (mantissa > 9)                mantissa = 9;        retval = (mantissa << 4) | exponent;        *strptr = cp;        return (retval);}/* converts ascii lat/lon to unsigned encoded 32-bit number. *  moves pointer. */static u_int32_tlatlon2ul(latlonstrptr,which)        char **latlonstrptr;        int *which;{        register char *cp;        u_int32_t retval;        int deg = 0, min = 0, secs = 0, secsfrac = 0;        cp = *latlonstrptr;        while (isdigit(*cp))                deg = deg * 10 + (*cp++ - '0');        while (isspace(*cp))                cp++;        if (!(isdigit(*cp)))                goto fndhemi;        while (isdigit(*cp))                min = min * 10 + (*cp++ - '0');Davis, et al                  Experimental                     [Page 11]

RFC 1876            Location Information in the DNS         January 1996        while (isspace(*cp))                cp++;        if (!(isdigit(*cp)))                goto fndhemi;        while (isdigit(*cp))                secs = secs * 10 + (*cp++ - '0');        if (*cp == '.') {               /* decimal seconds */                cp++;                if (isdigit(*cp)) {                        secsfrac = (*cp++ - '0') * 100;                        if (isdigit(*cp)) {                                secsfrac += (*cp++ - '0') * 10;                                if (isdigit(*cp)) {                                        secsfrac += (*cp++ - '0');                                }                        }                }        }        while (!isspace(*cp))   /* if any trailing garbage */                cp++;        while (isspace(*cp))                cp++; fndhemi:        switch (*cp) {        case 'N': case 'n':        case 'E': case 'e':                retval = ((unsigned)1<<31)                        + (((((deg * 60) + min) * 60) + secs) * 1000)                        + secsfrac;                break;        case 'S': case 's':        case 'W': case 'w':                retval = ((unsigned)1<<31)                        - (((((deg * 60) + min) * 60) + secs) * 1000)                        - secsfrac;                break;        default:                retval = 0;     /* invalid value -- indicates error */                break;        }        switch (*cp) {Davis, et al                  Experimental                     [Page 12]

RFC 1876            Location Information in the DNS         January 1996        case 'N': case 'n':        case 'S': case 's':                *which = 1;     /* latitude */                break;        case 'E': case 'e':        case 'W': case 'w':                *which = 2;     /* longitude */                break;        default:                *which = 0;     /* error */                break;        }        cp++;                   /* skip the hemisphere */        while (!isspace(*cp))   /* if any trailing garbage */                cp++;        while (isspace(*cp))    /* move to next field */                cp++;        *latlonstrptr = cp;        return (retval);}/* converts a zone file representation in a string to an RDATA * on-the-wire representation. */u_int32_tloc_aton(ascii, binary)        const char *ascii;        u_char *binary;{        const char *cp, *maxcp;        u_char *bcp;        u_int32_t latit = 0, longit = 0, alt = 0;        u_int32_t lltemp1 = 0, lltemp2 = 0;        int altmeters = 0, altfrac = 0, altsign = 1;        u_int8_t hp = 0x16;    /* default = 1e6 cm = 10000.00m = 10km */        u_int8_t vp = 0x13;    /* default = 1e3 cm = 10.00m */        u_int8_t siz = 0x12;   /* default = 1e2 cm = 1.00m */        int which1 = 0, which2 = 0;        cp = ascii;        maxcp = cp + strlen(ascii);        lltemp1 = latlon2ul(&cp, &which1);Davis, et al                  Experimental                     [Page 13]

RFC 1876            Location Information in the DNS         January 1996        lltemp2 = latlon2ul(&cp, &which2);        switch (which1 + which2) {        case 3:                 /* 1 + 2, the only valid combination */                if ((which1 == 1) && (which2 == 2)) { /* normal case */                        latit = lltemp1;                        longit = lltemp2;                } else if ((which1 == 2) && (which2 == 1)) {/*reversed*/                        longit = lltemp1;                        latit = lltemp2;                } else {        /* some kind of brokenness */                        return 0;                }                break;        default:                /* we didn't get one of each */                return 0;        }        /* altitude */        if (*cp == '-') {                altsign = -1;                cp++;        }        if (*cp == '+')                cp++;        while (isdigit(*cp))                altmeters = altmeters * 10 + (*cp++ - '0');        if (*cp == '.') {               /* decimal meters */                cp++;                if (isdigit(*cp)) {                        altfrac = (*cp++ - '0') * 10;                        if (isdigit(*cp)) {                                altfrac += (*cp++ - '0');                        }                }        }        alt = (10000000 + (altsign * (altmeters * 100 + altfrac)));        while (!isspace(*cp) && (cp < maxcp))                                           /* if trailing garbage or m */                cp++;        while (isspace(*cp) && (cp < maxcp))                cp++;Davis, et al                  Experimental                     [Page 14]

RFC 1876            Location Information in the DNS         January 1996        if (cp >= maxcp)                goto defaults;        siz = precsize_aton(&cp);        while (!isspace(*cp) && (cp < maxcp))/*if trailing garbage or m*/                cp++;        while (isspace(*cp) && (cp < maxcp))                cp++;        if (cp >= maxcp)                goto defaults;        hp = precsize_aton(&cp);        while (!isspace(*cp) && (cp < maxcp))/*if trailing garbage or m*/                cp++;        while (isspace(*cp) && (cp < maxcp))                cp++;        if (cp >= maxcp)                goto defaults;        vp = precsize_aton(&cp); defaults:        bcp = binary;        *bcp++ = (u_int8_t) 0;  /* version byte */        *bcp++ = siz;        *bcp++ = hp;        *bcp++ = vp;        PUTLONG(latit,bcp);        PUTLONG(longit,bcp);        PUTLONG(alt,bcp);        return (16);            /* size of RR in octets */}/* takes an on-the-wire LOC RR and prints it in zone file * (human readable) format. */char *loc_ntoa(binary,ascii)        const u_char *binary;        char *ascii;{Davis, et al                  Experimental                     [Page 15]

RFC 1876            Location Information in the DNS         January 1996        static char tmpbuf[255*3];        register char *cp;        register const u_char *rcp;        int latdeg, latmin, latsec, latsecfrac;        int longdeg, longmin, longsec, longsecfrac;        char northsouth, eastwest;        int altmeters, altfrac, altsign;        const int referencealt = 100000 * 100;        int32_t latval, longval, altval;        u_int32_t templ;        u_int8_t sizeval, hpval, vpval, versionval;        char *sizestr, *hpstr, *vpstr;        rcp = binary;        if (ascii)                cp = ascii;        else {                cp = tmpbuf;        }        versionval = *rcp++;        if (versionval) {                sprintf(cp,"; error: unknown LOC RR version");                return (cp);        }        sizeval = *rcp++;        hpval = *rcp++;        vpval = *rcp++;        GETLONG(templ,rcp);        latval = (templ - ((unsigned)1<<31));        GETLONG(templ,rcp);        longval = (templ - ((unsigned)1<<31));        GETLONG(templ,rcp);        if (templ < referencealt) { /* below WGS 84 spheroid */                altval = referencealt - templ;                altsign = -1;        } else {Davis, et al                  Experimental                     [Page 16]

RFC 1876            Location Information in the DNS         January 1996                altval = templ - referencealt;                altsign = 1;        }        if (latval < 0) {                northsouth = 'S';                latval = -latval;        }        else                northsouth = 'N';        latsecfrac = latval % 1000;        latval = latval / 1000;        latsec = latval % 60;        latval = latval / 60;        latmin = latval % 60;        latval = latval / 60;        latdeg = latval;        if (longval < 0) {                eastwest = 'W';                longval = -longval;        }        else                eastwest = 'E';        longsecfrac = longval % 1000;        longval = longval / 1000;        longsec = longval % 60;        longval = longval / 60;        longmin = longval % 60;        longval = longval / 60;        longdeg = longval;        altfrac = altval % 100;        altmeters = (altval / 100) * altsign;        sizestr = savestr(precsize_ntoa(sizeval));        hpstr = savestr(precsize_ntoa(hpval));        vpstr = savestr(precsize_ntoa(vpval));        sprintf(cp,                "%d %.2d %.2d.%.3d %c %d %.2d %.2d.%.3d %c %d.%.2dm                %sm %sm %sm",                latdeg, latmin, latsec, latsecfrac, northsouth,                longdeg, longmin, longsec, longsecfrac, eastwest,                altmeters, altfrac, sizestr, hpstr, vpstr);Davis, et al                  Experimental                     [Page 17]

RFC 1876            Location Information in the DNS         January 1996        free(sizestr);        free(hpstr);        free(vpstr);        return (cp);}Davis, et al                  Experimental                     [Page 18]

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