J.JSSAC Vol. 7, No. 2, Mathematica Maple,., Open asir Open xxx asir. Open xxx Open asir, asir., Open xxx, Linux Open asir Open sm1 (kan/sm1). C
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1 J.JSSAC (1999) Vol. 7, No. 2, pp Open asir HPC (Received 1997/12/1) 1 Open asir Open xxx,., ( ),,,,,.,., (1) (2) (3) (4),. Open xxx,.,., 1.,.,., 0 10, dx,.,., ohara@math.kobe-u.ac.jp taka@math.kobe-u.ac.jp noro@para.flab.fujitsu.co.jp c 1999 Japan Society for Symbolic and Algebraic Computation
2 J.JSSAC Vol. 7, No. 2, Mathematica Maple,., Open asir Open xxx asir. Open xxx Open asir, asir., Open xxx, Linux Open asir Open sm1 (kan/sm1). C, Java, Lisp ( asir, sm1), Open asir., MathLink, Mathematica. Open asir. Open asir,.,,.,.,.,,,.,., TCP/IP, Open xxx TCP/IP,, MPI PVM,. Open xxx [1]. [1] TEX Open xxx,,.,, OpenMath Open asir, Open xxx ( ), C., (, Redhat Linux 4.2 FreeBSD ), [1]. Open sm1., Linux Open asir., openxxx@math.kobe-u.ac.jp.
3 Open asir Open asir, ( )., ( ). Open asir Common Math Object (CMO). CMO. 32bit 1234, (CMO INT32, 1234) CMO. CMO expression. CMO expression, CMO, ( ). CMO INT32., 6 "abcdef" (CMO STRING, 6, abcdef ) CMO. CMO INT32, CMO STRING 32bit, Open xxx #define CMO_NULL 1 #define CMO_INT32 2 #define CMO_DATUM 3 #define CMO_STRING 4 #define CMO_LIST 17 #define CMO_MONOMIAL32 19 #define CMO_ZZ 20 #define CMO_QQ 21 #define CMO_ZERO 22 #define CMO_DMS 23. TCP/IP, (CMO INT32, 1234) d2 16. ( ).,, (bignum),.. 32bit n CMObject Integer32, int32 CMO INT32 int32 n.,,. n s, CMObject, Cstring int32 CMO STRING int32 n byte s[0] byte s[1] byte s[n 1]. C, 0.
4 J.JSSAC Vol. 7, No. 2, m int32 CMO LIST int32 m CMObject ob[0] CMObject ob[m 1].,, [1]. CMO. 3 Open asir,,.,,.,.,..,.,, UNIX. Open xxx,,.,,,.,. Section 5.,.,,.. #define PORT_CONTROL 1200 #define PORT_STREAM 1300 int fdcontrol, fdstream; int mysocketopen(const char* hostname, int portnum) struct sockaddr_in serv; struct hostent *host; int s; bzero(&serv, sizeof(serv));
5 serv.sin_family = AF_INET; serv.sin_port = htons(portnum); host = gethostbyname(hostname); bcopy(host->h_addr, (char *)&serv.sin_addr, host->h_length); s = socket(af_inet, SOCK_STREAM, 0); connect(s, (struct sockaddr *)&serv, sizeof(serv)); return s; void ox_start(char* servername) fdcontrol = mysocketopen(servername, PORT_CONTROL); fdstream = mysocketopen(servername, PORT_STREAM); int main() ox_start("localhost");,,, Open xxx 32bit (CMO INT32 ).,. 2. [1].,, Open xxx., C,,. 32bit. int send_int32(int fd, int integer32) integer32 = htonl(integer32); return write(fd, &integer32, sizeof(int));
6 J.JSSAC Vol. 7, No. 2, Open asir. Open xxx,.,. Open asir (32bit ),. Open xxx,. (OX COMMAND, serial number, SMObject) (OX DATA, serial number, CMObject) (OX SYNC BALL, serial number).. #define OX_COMMAND 513 #define OX_DATA 514 #define OX_SYNC_BALL bit...., SMObject,, CMObject, CMO. 32bit. [1]. #define SM_popCMO 262 #define SM_popString 263 #define SM_mathcap 264 #define SM_pops 265 #define SM_setName 266 #define SM_evalName 267 #define SM_executeStringByLocalParser 268 #define SM_executeFunction 269 #define SM_control_kill 1024 #define SM_control_reset_connection 1030 Open xxx., CPU. (1), (Open asir asir),.
7 SM executestringbylocalparser. (2), Open xxx., CMO,. (1)., Open asir diff((x+2*y)ˆ2,x);, (OX DATA, serial number, (CMO STRING, 18, diff((x+2*y)ˆ2,x); )) (OX COMMAND, serial number, SM executestringbylocalparser). diff((x+2*y)ˆ2,x);, diff((x+2*y)ˆ2,x); Open asir.. C. /* (OX_tag, serial number) */ int send_ox_tag(int fd, int tag) static int serial_number = 0; send_int32(fd, tag); return send_int32(fd, serial_number++); void send_ox_cmo_string(int fd, const char* str) int len; send_ox_tag(fd, OX_DATA); /* OX */ send_int32(fd, CMO_STRING); /* CMO_STRING */ len = strlen(str); send_int32(fd, len); write(fd, str, len); void send_ox_command(int fd, int sm_command) send_ox_tag(fd, OX_COMMAND); /* OX */ send_int32(fd, sm_command); int executestringbylocalparser(const char* str)
8 J.JSSAC Vol. 7, No. 2, send_ox_cmo_string(fdstream, str); send_ox_command(fdstream, SM_executeStringByLocalParser); int main() executestringbylocalparser("diff((x+2*y)^2,x);");, SM popstring., (OX COMMAND, serial number, SM popstring)., Open asir (OX DATA, serial number, (CMO STRING, 7, 2*x+4*y )),. typedef struct cmo_t int tag; union int integer; char *string; u; cmo_t; char *receive_cmo_string(int fd) int len = receive_int32(fd); char* str = malloc(len+1); bzero(str, len+1); read(fd, str, len); return str; cmo_t receive_cmo(int fd) cmo_t m;
9 m.tag = receive_int32(fd); switch(m.tag) case CMO_STRING: m.u.string = receive_cmo_string(fd); break; case CMO_INT32: m.u.integer = receive_int32(fd); break; default: return m; /* (OX_tag, serial number) */ int receive_ox_tag(int fd) int tag = receive_int32(fd); receive_serial_number(fd); return tag; char* popstring() cmo_t m; send_ox_command(fdstream, SM_popString); receive_ox_tag(fdstream); /* OX */ m = receive_cmo(fdstream); return m.u.str; int main() char *result; result = popstring(); puts(result);
10 J.JSSAC Vol. 7, No. 2, , Open xxx. asir. (OX ) synchronized object.,..,.,,,.,, (OX COMMAND, serial number, SM control reset connection).,.., (OX DATA, serial number, (CMO INT32, 0)),.,,,,.. (Open xxx ),.,, OX SYNC BALL. OX SYNC BALL, (OX SYNC BALL, serial number),. OX SYNC BALL OX SYNC BALL. OX SYNC BALL.
11 OX SYNC BALL,, (OX SYNC BALL, serial number),.,.,., OX SYNC BALL,, (, ),,., 1., ( ), OX SYNC BALL. 2., OX SYNC BALL.., OX SYNC BALL OX SYNC BALL,., OX SYNC BALL, OX SYNC BALL,,, OX SYNC BALL. OX SYNC BALL, OX SYNC BALL, OX SYNC BALL.,. void ox_reset() send_ox_command(fdcontrol, SM_control_reset_connection); receive_ox_tag(fdcontrol); /* OX */ receive_cmo(fdcontrol); /* */ while(receive_ox_tag(fdstream)!= OX_SYNC_BALL) receive_cmo(fdstream); /*. */ send_ox_tag(fdstream, OX_SYNC_BALL); int main()
12 J.JSSAC Vol. 7, No. 2, ox_reset(); 6, (OX COMMAND, serial number, SM control kill).,.,,. void ox_close() send_ox_command(fdcontrol, SM_control_kill); 7,, SM executestringbylocalparser. (2). (2) CMO STRING, CMO,. Open xxx. Open xxx,., asir igcd. [1]. Open asir, asir (2)., asir. Open xxx CMO SM executefunction..,,., CMO INT32,.,
13 CMO STRING,. SM executefunction,.,.. SM executefunction, asir print( Hello World. );.,. (OX DATA, serial number, (CMO STRING, 12, Hello World. )) (OX DATA, serial number, (CMO INT32, 1)) (OX DATA, serial number, (CMO STRING, 5, print )). (OX COMMAND, serial number, SM executefunction) print, Hello World.. (CMO NULL). 8 CMO ZZ Open xxx (bignum). Knuth [2]. Open xxx CMO ZZ GNU MP,. CMO ZZ [1]. int32 CMO ZZ int32 f byte b 1 byte b n f 32bit,. b 1,..., b n 1. n f. CMO f., 32bit 2. Open xxx CMO. sgn(f) (b 1 R n 1 + b 2 R n b n 1 R + b n ). R = 2 8., 14 CMO ZZ, (CMO ZZ, 1, e), e
14 J.JSSAC Vol. 7, No. 2, CMO ZZ (CMO ZZ, 4, 0, 0, 0, e), e. C,., SM executefunction, asir igcd., CMO ZZ, ( 2) igcd. (OX DATA, serial number, (CMO ZZ, 4, 0, 0, 0, e)) (OX DATA, serial number, (CMO ZZ, 4, 0, 0, 0, 16)) (OX DATA, serial number, (CMO INT32, 1)) (OX DATA, serial number, (CMO STRING, 4, igcd )) SM executefunction. (OX COMMAND, serial number, SM executefunction), SM popstring,. CMO, SM popcmo. C. typedef struct int size; unsigned char *mp_d; cmo_zz_t; cmo_zz_t cmo_zz_set_si(int integer) cmo_zz_t zz; zz.size = (integer < 0)? -sizeof(int): sizeof(int); integer = htonl(integer); zz.mp_d = malloc(sizeof(int)); bcopy(&integer, zz.mp_d, sizeof(int)); return zz;
15 void send_ox_cmo_zz(int fd, cmo_zz_t zz) int len = (zz.size < 0)? -zz.size: zz.size; send_ox_tag(fd, OX_DATA); /* OX */ send_int32(fd, CMO_ZZ); send_int32(fd, zz.size); write(fd, zz.mp_d, len); int main() send_ox_cmo_zz(fdstream, cmo_zz_set_si(14)); send_ox_cmo_zz(fdstream, cmo_zz_set_si(22)); send_ox_cmo_integer(fdstream, 2); /* number of arguments */ send_ox_cmo_string(fdstream, "igcd"); send_ox_command(fdstream, SM_executeFunction); fprintf(stderr, "igcd(%d, %d) == %s.\n", 14, 22, ox_popstring(fdstream)); 9. Open xxx, CMO ERROR2. CMO ERROR2,,. CMO ERROR2.. int32 CMO ERROR2 CMO LIST error error CMO LIST,. Integer32 CMObject, Integer32. error [1].
16 J.JSSAC Vol. 7, No. 2, ,., SM popcmo.,. CMO,. 10, Mathematical Sciences Research Institute (Berkeley), Parallel Symbolic Computation., URL (OpenMath) 2. (math web) 3. posso.lip6.fr/ jcf (Faugere F 4, parallel GB algorithm) 4. yelick (multipol) 5. (parallel mupad) 6. kaltofen (open math virtual machine) 7. norma.nkkhef.nl/ t68/summer (integral) 8. (Π it ) 9. (useful links to computer algebra projects including Frisco project) (useful links to computer algebra projects) (useful links to computer algebra projects) (KLIC, Fujise-Murao s project) 13. Parallel mathematica. [1],. Open xxx, xxx = asir,kan, 1998/06/16 [2] D. E. Knuth. /,, 1986.
10/ / /30 3. ( ) 11/ 6 4. UNIX + C socket 11/13 5. ( ) C 11/20 6. http, CGI Perl 11/27 7. ( ) Perl 12/ 4 8. Windows Winsock 12/11 9. JAV
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