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tommath/demo/demo.c
Tom St Denis b1756f2f98 added libtommath-0.15
2010-07-15 17:25:18 +02:00

489 lines
23 KiB
C
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#include <time.h>
#ifdef U_MPI
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <limits.h>
#include "mpi.h"
#ifdef _MSC_VER
typedef __int64 ulong64;
#else
typedef unsigned long long ulong64;
#endif
#else
#include "tommath.h"
#endif
#ifdef TIMER
ulong64 _tt;
void reset(void) { _tt = clock(); }
ulong64 rdtsc(void) { return clock() - _tt; }
#endif
#ifndef DEBUG
int _ifuncs;
#else
extern int _ifuncs;
extern void dump_timings(void);
extern void reset_timings(void);
#endif
void ndraw(mp_int *a, char *name)
{
char buf[4096];
printf("%s: ", name);
mp_toradix(a, buf, 10);
printf("%s\n", buf);
}
static void draw(mp_int *a)
{
ndraw(a, "");
}
unsigned long lfsr = 0xAAAAAAAAUL;
int lbit(void)
{
if (lfsr & 0x80000000UL) {
lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
return 1;
} else {
lfsr <<= 1;
return 0;
}
}
#ifdef U_MPI
int mp_reduce_setup(mp_int *a, mp_int *b)
{
int res;
mp_set(a, 1);
if ((res = s_mp_lshd(a, b->used * 2)) != MP_OKAY) {
return res;
}
return mp_div(a, b, a, NULL);
}
int mp_rand(mp_int *a, int c)
{
long z = abs(rand()) & 65535;
mp_set(a, z?z:1);
while (c--) {
s_mp_lshd(a, 1);
mp_add_d(a, abs(rand()), a);
}
return MP_OKAY;
}
#endif
char cmd[4096], buf[4096];
int main(void)
{
mp_int a, b, c, d, e, f;
unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, inv_n,
div2_n, mul2_n;
unsigned rr;
int cnt, ix;
#ifdef TIMER
int n;
ulong64 tt;
FILE *log;
#endif
mp_init(&a);
mp_init(&b);
mp_init(&c);
mp_init(&d);
mp_init(&e);
mp_init(&f);
/* test the DR reduction */
#if 0
srand(time(NULL));
for (cnt = 2; cnt < 32; cnt++) {
printf("%d digit modulus\n", cnt);
mp_grow(&a, cnt);
mp_zero(&a);
for (ix = 1; ix < cnt; ix++) {
a.dp[ix] = MP_MASK;
}
a.used = cnt;
mp_prime_next_prime(&a, 3);
mp_rand(&b, cnt - 1);
mp_copy(&b, &c);
rr = 0;
do {
if (!(rr & 127)) { printf("%9lu\r", rr); fflush(stdout); }
mp_sqr(&b, &b); mp_add_d(&b, 1, &b);
mp_copy(&b, &c);
mp_mod(&b, &a, &b);
mp_dr_reduce(&c, &a, (1<<DIGIT_BIT)-a.dp[0]);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("Failed on trial %lu\n", rr); exit(-1);
}
} while (++rr < 1000000);
printf("Passed DR test for %d digits\n", cnt);
}
#endif
#ifdef TIMER
printf("CLOCKS_PER_SEC == %lu\n", CLOCKS_PER_SEC);
log = fopen("add.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
mp_rand(&a, cnt);
mp_rand(&b, cnt);
reset();
for (rr = 0; rr < 10000000; rr++) {
mp_add(&a, &b, &c);
}
tt = rdtsc();
printf("Adding\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
log = fopen("sub.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
mp_rand(&a, cnt);
mp_rand(&b, cnt);
reset();
for (rr = 0; rr < 10000000; rr++) {
mp_sub(&a, &b, &c);
}
tt = rdtsc();
printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
log = fopen("sqr.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
mp_rand(&a, cnt);
reset();
for (rr = 0; rr < 250000; rr++) {
mp_sqr(&a, &b);
}
tt = rdtsc();
printf("Squaring\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
log = fopen("mult.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
mp_rand(&a, cnt);
mp_rand(&b, cnt);
reset();
for (rr = 0; rr < 250000; rr++) {
mp_mul(&a, &b, &c);
}
tt = rdtsc();
printf("Multiplying\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
{
char *primes[] = {
/* DR moduli */
"14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
"101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
"736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
"38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
"542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
"1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
"1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
/* generic unrestricted moduli */
"17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
"2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
"347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
"47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
"436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
"11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
"1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
NULL
};
log = fopen("expt.log", "w");
for (n = 0; primes[n]; n++) {
mp_read_radix(&a, primes[n], 10);
mp_zero(&b);
for (rr = 0; rr < mp_count_bits(&a); rr++) {
mp_mul_2(&b, &b);
b.dp[0] |= lbit();
b.used += 1;
}
mp_sub_d(&a, 1, &c);
mp_mod(&b, &c, &b);
mp_set(&c, 3);
reset();
for (rr = 0; rr < 50; rr++) {
mp_exptmod(&c, &b, &a, &d);
}
tt = rdtsc();
mp_sub_d(&a, 1, &e);
mp_sub(&e, &b, &b);
mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */
mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */
if (mp_cmp_d(&d, 1)) {
printf("Different (%d)!!!\n", mp_count_bits(&a));
draw(&d);
exit(0);
}
printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
}
fclose(log);
log = fopen("invmod.log", "w");
for (cnt = 4; cnt <= 128; cnt += 4) {
mp_rand(&a, cnt);
mp_rand(&b, cnt);
do {
mp_add_d(&b, 1, &b);
mp_gcd(&a, &b, &c);
} while (mp_cmp_d(&c, 1) != MP_EQ);
reset();
for (rr = 0; rr < 10000; rr++) {
mp_invmod(&b, &a, &c);
}
tt = rdtsc();
mp_mulmod(&b, &c, &a, &d);
if (mp_cmp_d(&d, 1) != MP_EQ) {
printf("Failed to invert\n");
return 0;
}
printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt, tt);
fprintf(log, "%d,%9llu\n", cnt, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
return 0;
#endif
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = 0;
for (;;) {
/* randomly clear and re-init one variable, this has the affect of triming the alloc space */
switch (abs(rand()) % 7) {
case 0: mp_clear(&a); mp_init(&a); break;
case 1: mp_clear(&b); mp_init(&b); break;
case 2: mp_clear(&c); mp_init(&c); break;
case 3: mp_clear(&d); mp_init(&d); break;
case 4: mp_clear(&e); mp_init(&e); break;
case 5: mp_clear(&f); mp_init(&f); break;
case 6: break; /* don't clear any */
}
printf("%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu/%7lu ", add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, expt_n, inv_n, div2_n, mul2_n);
fgets(cmd, 4095, stdin);
cmd[strlen(cmd)-1] = 0;
printf("%s ]\r",cmd); fflush(stdout);
if (!strcmp(cmd, "mul2d")) { ++mul2d_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
mp_mul_2d(&a, rr, &a);
a.sign = b.sign;
if (mp_cmp(&a, &b) != MP_EQ) {
printf("mul2d failed, rr == %d\n",rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "div2d")) { ++div2d_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); sscanf(buf, "%d", &rr);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
mp_div_2d(&a, rr, &a, &e);
a.sign = b.sign;
if (a.used == b.used && a.used == 0) { a.sign = b.sign = MP_ZPOS; }
if (mp_cmp(&a, &b) != MP_EQ) {
printf("div2d failed, rr == %d\n",rr);
draw(&a);
draw(&b);
return 0;
}
} else if (!strcmp(cmd, "add")) { ++add_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_copy(&a, &d);
mp_add(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("add %lu failure!\n", add_n);
draw(&a);draw(&b);draw(&c);draw(&d);
return 0;
}
/* test the sign/unsigned storage functions */
rr = mp_signed_bin_size(&c);
mp_to_signed_bin(&c, (unsigned char *)cmd);
memset(cmd+rr, rand()&255, sizeof(cmd)-rr);
mp_read_signed_bin(&d, (unsigned char *)cmd, rr);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mp_signed_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
rr = mp_unsigned_bin_size(&c);
mp_to_unsigned_bin(&c, (unsigned char *)cmd);
memset(cmd+rr, rand()&255, sizeof(cmd)-rr);
mp_read_unsigned_bin(&d, (unsigned char *)cmd, rr);
if (mp_cmp_mag(&c, &d) != MP_EQ) {
printf("mp_unsigned_bin failure!\n");
draw(&c);
draw(&d);
return 0;
}
} else if (!strcmp(cmd, "sub")) { ++sub_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_copy(&a, &d);
mp_sub(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("sub %lu failure!\n", sub_n);
draw(&a);draw(&b);draw(&c);draw(&d);
return 0;
}
} else if (!strcmp(cmd, "mul")) { ++mul_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_copy(&a, &d);
mp_mul(&d, &b, &d);
if (mp_cmp(&c, &d) != MP_EQ) {
printf("mul %lu failure!\n", mul_n);
draw(&a);draw(&b);draw(&c);draw(&d);
return 0;
}
} else if (!strcmp(cmd, "div")) { ++div_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&d, buf, 10);
mp_div(&a, &b, &e, &f);
if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
printf("div %lu failure!\n", div_n);
draw(&a);draw(&b);draw(&c);draw(&d); draw(&e); draw(&f);
return 0;
}
} else if (!strcmp(cmd, "sqr")) { ++sqr_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
mp_copy(&a, &c);
mp_sqr(&c, &c);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("sqr %lu failure!\n", sqr_n);
draw(&a);draw(&b);draw(&c);
return 0;
}
} else if (!strcmp(cmd, "gcd")) { ++gcd_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_copy(&a, &d);
mp_gcd(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("gcd %lu failure!\n", gcd_n);
draw(&a);draw(&b);draw(&c);draw(&d);
return 0;
}
} else if (!strcmp(cmd, "lcm")) { ++lcm_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_copy(&a, &d);
mp_lcm(&d, &b, &d);
d.sign = c.sign;
if (mp_cmp(&c, &d) != MP_EQ) {
printf("lcm %lu failure!\n", lcm_n);
draw(&a);draw(&b);draw(&c);draw(&d);
return 0;
}
} else if (!strcmp(cmd, "expt")) { ++expt_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&d, buf, 10);
mp_copy(&a, &e);
mp_exptmod(&e, &b, &c, &e);
if (mp_cmp(&d, &e) != MP_EQ) {
printf("expt %lu failure!\n", expt_n);
draw(&a);draw(&b);draw(&c);draw(&d); draw(&e);
return 0;
}
} else if (!strcmp(cmd, "invmod")) { ++inv_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&c, buf, 10);
mp_invmod(&a, &b, &d);
mp_mulmod(&d,&a,&b,&e);
if (mp_cmp_d(&e, 1) != MP_EQ) {
printf("inv [wrong value from MPI?!] failure\n");
draw(&a);draw(&b);draw(&c);draw(&d);
mp_gcd(&a, &b, &e);
draw(&e);
return 0;
}
} else if (!strcmp(cmd, "div2")) { ++div2_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
mp_div_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("div_2 %lu failure\n", div2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
} else if (!strcmp(cmd, "mul2")) { ++mul2_n;
fgets(buf, 4095, stdin); mp_read_radix(&a, buf, 10);
fgets(buf, 4095, stdin); mp_read_radix(&b, buf, 10);
mp_mul_2(&a, &c);
if (mp_cmp(&c, &b) != MP_EQ) {
printf("mul_2 %lu failure\n", mul2_n);
draw(&a);
draw(&b);
draw(&c);
return 0;
}
}
}
return 0;
}
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