結果
| 問題 | No.313 π |
| ユーザー |
 ciel
|
| 提出日時 | 2015-12-06 02:00:54 |
| 言語 | Ruby (3.3.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 16,478 bytes |
| コンパイル時間 | 288 ms |
| コンパイル使用メモリ | 7,424 KB |
| 実行使用メモリ | 31,520 KB |
| 最終ジャッジ日時 | 2024-09-14 15:02:15 |
| 合計ジャッジ時間 | 13,317 ms |
|
ジャッジサーバーID （参考情報） |
judge6 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | RE | - |
| testcase_01 | RE | - |
| testcase_02 | RE | - |
| testcase_03 | RE | - |
| testcase_04 | RE | - |
| testcase_05 | RE | - |
| testcase_06 | RE | - |
| testcase_07 | RE | - |
| testcase_08 | RE | - |
| testcase_09 | RE | - |
| testcase_10 | RE | - |
| testcase_11 | RE | - |
| testcase_12 | RE | - |
| testcase_13 | RE | - |
| testcase_14 | RE | - |
| testcase_15 | RE | - |
| testcase_16 | RE | - |
| testcase_17 | RE | - |
| testcase_18 | RE | - |
| testcase_19 | RE | - |
| testcase_20 | RE | - |
| testcase_21 | RE | - |
| testcase_22 | RE | - |
| testcase_23 | RE | - |
| testcase_24 | RE | - |
| testcase_25 | RE | - |
| testcase_26 | RE | - |
| testcase_27 | RE | - |
| testcase_28 | RE | - |
| testcase_29 | RE | - |
| testcase_30 | RE | - |
| testcase_31 | RE | - |
| testcase_32 | RE | - |
| testcase_33 | RE | - |
コンパイルメッセージ
Syntax OK
ソースコード
#/usr/bin/ruby
IO.popen('gcc -xc -O2 -oZ - -lgmp',?w){|io|io.puts DATA.read}
t=gets.chomp
s=IO.popen('./Z 199999 1','r'){|io|'3.'+io.read[3...-2]}
File.unlink(?Z)
(0...s.size).each{|i|
if s[i]!=t[i]
puts [t[i],s[i]]*' '
exit
end
}
__END__
/* Pi computation using Chudnovsky's algortithm.
* Copyright 2002, 2005 Hanhong Xue (macroxue at yahoo dot com)
* Slightly modified 2005 by Torbjorn Granlund to allow more than 2G
digits to be computed.
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* 1. Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
* EVENT SHALL THE AUTHORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
* OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include "gmp.h"
#define A 13591409
#define B 545140134
#define C 640320
#define D 12
#define BITS_PER_DIGIT 3.32192809488736234787
#define DIGITS_PER_ITER 14.1816474627254776555
#define DOUBLE_PREC 53
#ifdef __GNUC__
#define inline __inline__
#endif
char *prog_name;
#if CHECK_MEMUSAGE
#undef CHECK_MEMUSAGE
#define CHECK_MEMUSAGE \
do { \
char buf[100]; \
snprintf (buf, 100, \
"ps aguxw | grep '[%c]%s'", prog_name[0], prog_name+1); \
system (buf); \
} while (0)
#else
#undef CHECK_MEMUSAGE
#define CHECK_MEMUSAGE
#endif
/* Return user CPU time measured in milliseconds. */
#if !defined (__sun) \
&& (defined (USG) || defined (__SVR4) || defined (_UNICOS) \
|| defined (__hpux))
int
cputime ()
{
return (int) ((double) clock () * 1000 / CLOCKS_PER_SEC);
}
#else
#include <sys/types.h>
#include <sys/time.h>
#include <sys/resource.h>
int
cputime ()
{
struct rusage rus;
getrusage (0, &rus);
return rus.ru_utime.tv_sec * 1000 + rus.ru_utime.tv_usec / 1000;
}
#endif
/*///////////////////////////////////////////////////////////////////////////*/
mpf_t t1, t2;
/* r = sqrt(x) */
void
my_sqrt_ui(mpf_t r, unsigned long x)
{
unsigned long prec, bits, prec0;
prec0 = mpf_get_prec(r);
if (prec0<=DOUBLE_PREC) {
mpf_set_d(r, sqrt(x));
return;
}
bits = 0;
for (prec=prec0; prec>DOUBLE_PREC;)
{
int bit = prec&1;
prec = (prec+bit)/2;
bits = bits*2+bit;
}
mpf_set_prec_raw(t1, DOUBLE_PREC);
mpf_set_d(t1, 1/sqrt(x));
while (prec<prec0)
{
prec *=2;
if (prec<prec0)
{
/* t1 = t1+t1*(1-x*t1*t1)/2; */
mpf_set_prec_raw(t2, prec);
mpf_mul(t2, t1, t1); /* half x half -> full */
mpf_mul_ui(t2, t2, x);
mpf_ui_sub(t2, 1, t2);
mpf_set_prec_raw(t2, prec/2);
mpf_div_2exp(t2, t2, 1);
mpf_mul(t2, t2, t1); /* half x half -> half */
mpf_set_prec_raw(t1, prec);
mpf_add(t1, t1, t2);
}
else
{
break;
}
prec -= (bits&1);
bits /=2;
}
/* t2=x*t1, t1 = t2+t1*(x-t2*t2)/2; */
mpf_set_prec_raw(t2, prec0/2);
mpf_mul_ui(t2, t1, x);
mpf_mul(r, t2, t2); /* half x half -> full */
mpf_ui_sub(r, x, r);
mpf_mul(t1, t1, r); /* half x half -> half */
mpf_div_2exp(t1, t1, 1);
mpf_add(r, t1, t2);
}
/* r = y/x WARNING: r cannot be the same as y. */
#if __GMP_MP_RELEASE >= 50001
#define my_div mpf_div
#else
void
my_div(mpf_t r, mpf_t y, mpf_t x)
{
unsigned long prec, bits, prec0;
prec0 = mpf_get_prec(r);
if (prec0<=DOUBLE_PREC) {
mpf_set_d(r, mpf_get_d(y)/mpf_get_d(x));
return;
}
bits = 0;
for (prec=prec0; prec>DOUBLE_PREC;) {
int bit = prec&1;
prec = (prec+bit)/2;
bits = bits*2+bit;
}
mpf_set_prec_raw(t1, DOUBLE_PREC);
mpf_ui_div(t1, 1, x);
while (prec<prec0) {
prec *=2;
if (prec<prec0) {
/* t1 = t1+t1*(1-x*t1); */
mpf_set_prec_raw(t2, prec);
mpf_mul(t2, x, t1); /* full x half -> full */
mpf_ui_sub(t2, 1, t2);
mpf_set_prec_raw(t2, prec/2);
mpf_mul(t2, t2, t1); /* half x half -> half */
mpf_set_prec_raw(t1, prec);
mpf_add(t1, t1, t2);
} else {
prec = prec0;
/* t2=y*t1, t1 = t2+t1*(y-x*t2); */
mpf_set_prec_raw(t2, prec/2);
mpf_mul(t2, t1, y); /* half x half -> half */
mpf_mul(r, x, t2); /* full x half -> full */
mpf_sub(r, y, r);
mpf_mul(t1, t1, r); /* half x half -> half */
mpf_add(r, t1, t2);
break;
}
prec -= (bits&1);
bits /=2;
}
}
#endif
/*///////////////////////////////////////////////////////////////////////////*/
#define min(x,y) ((x)<(y)?(x):(y))
#define max(x,y) ((x)>(y)?(x):(y))
typedef struct {
unsigned long max_facs;
unsigned long num_facs;
unsigned long *fac;
unsigned long *pow;
} fac_t[1];
typedef struct {
long int fac;
long int pow;
long int nxt;
} sieve_t;
sieve_t *sieve;
long int sieve_size;
fac_t ftmp, fmul;
#define INIT_FACS 32
void
fac_show(fac_t f)
{
long int i;
for (i=0; i<f[0].num_facs; i++)
if (f[0].pow[i]==1)
printf("%ld ", f[0].fac[i]);
else
printf("%ld^%ld ", f[0].fac[i], f[0].pow[i]);
printf("\n");
}
inline void
fac_reset(fac_t f)
{
f[0].num_facs = 0;
}
inline void
fac_init_size(fac_t f, long int s)
{
if (s<INIT_FACS)
s=INIT_FACS;
f[0].fac = malloc(s*sizeof(unsigned long)*2);
f[0].pow = f[0].fac + s;
f[0].max_facs = s;
fac_reset(f);
}
inline void
fac_init(fac_t f)
{
fac_init_size(f, INIT_FACS);
}
inline void
fac_clear(fac_t f)
{
free(f[0].fac);
}
inline void
fac_resize(fac_t f, long int s)
{
if (f[0].max_facs < s) {
fac_clear(f);
fac_init_size(f, s);
}
}
/* f = base^pow */
inline void
fac_set_bp(fac_t f, unsigned long base, long int pow)
{
long int i;
assert(base<sieve_size);
for (i=0, base/=2; base>0; i++, base = sieve[base].nxt) {
f[0].fac[i] = sieve[base].fac;
f[0].pow[i] = sieve[base].pow*pow;
}
f[0].num_facs = i;
assert(i<=f[0].max_facs);
}
/* r = f*g */
inline void
fac_mul2(fac_t r, fac_t f, fac_t g)
{
long int i, j, k;
for (i=j=k=0; i<f[0].num_facs && j<g[0].num_facs; k++) {
if (f[0].fac[i] == g[0].fac[j]) {
r[0].fac[k] = f[0].fac[i];
r[0].pow[k] = f[0].pow[i] + g[0].pow[j];
i++; j++;
} else if (f[0].fac[i] < g[0].fac[j]) {
r[0].fac[k] = f[0].fac[i];
r[0].pow[k] = f[0].pow[i];
i++;
} else {
r[0].fac[k] = g[0].fac[j];
r[0].pow[k] = g[0].pow[j];
j++;
}
}
for (; i<f[0].num_facs; i++, k++) {
r[0].fac[k] = f[0].fac[i];
r[0].pow[k] = f[0].pow[i];
}
for (; j<g[0].num_facs; j++, k++) {
r[0].fac[k] = g[0].fac[j];
r[0].pow[k] = g[0].pow[j];
}
r[0].num_facs = k;
assert(k<=r[0].max_facs);
}
/* f *= g */
inline void
fac_mul(fac_t f, fac_t g)
{
fac_t tmp;
fac_resize(fmul, f[0].num_facs + g[0].num_facs);
fac_mul2(fmul, f, g);
tmp[0] = f[0];
f[0] = fmul[0];
fmul[0] = tmp[0];
}
/* f *= base^pow */
inline void
fac_mul_bp(fac_t f, unsigned long base, unsigned long pow)
{
fac_set_bp(ftmp, base, pow);
fac_mul(f, ftmp);
}
/* remove factors of power 0 */
inline void
fac_compact(fac_t f)
{
long int i, j;
for (i=0, j=0; i<f[0].num_facs; i++) {
if (f[0].pow[i]>0) {
if (j<i) {
f[0].fac[j] = f[0].fac[i];
f[0].pow[j] = f[0].pow[i];
}
j++;
}
}
f[0].num_facs = j;
}
/* convert factorized form to number */
void
bs_mul(mpz_t r, long int a, long int b)
{
long int i, j;
if (b-a<=32) {
mpz_set_ui(r, 1);
for (i=a; i<b; i++)
for (j=0; j<fmul[0].pow[i]; j++)
mpz_mul_ui(r, r, fmul[0].fac[i]);
} else {
mpz_t r2;
mpz_init(r2);
bs_mul(r2, a, (a+b)/2);
bs_mul(r, (a+b)/2, b);
mpz_mul(r, r, r2);
mpz_clear(r2);
}
}
mpz_t gcd, mgcd;
#if HAVE_DIVEXACT_PREINV
void mpz_invert_mod_2exp (mpz_ptr, mpz_srcptr);
void mpz_divexact_pre (mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr);
#endif
/* f /= gcd(f,g), g /= gcd(f,g) */
void
fac_remove_gcd(mpz_t p, fac_t fp, mpz_t g, fac_t fg)
{
long int i, j, k, c;
fac_resize(fmul, min(fp->num_facs, fg->num_facs));
for (i=j=k=0; i<fp->num_facs && j<fg->num_facs; ) {
if (fp->fac[i] == fg->fac[j]) {
c = min(fp->pow[i], fg->pow[j]);
fp->pow[i] -= c;
fg->pow[j] -= c;
fmul->fac[k] = fp->fac[i];
fmul->pow[k] = c;
i++; j++; k++;
} else if (fp->fac[i] < fg->fac[j]) {
i++;
} else {
j++;
}
}
fmul->num_facs = k;
assert(k <= fmul->max_facs);
if (fmul->num_facs) {
bs_mul(gcd, 0, fmul->num_facs);
#if HAVE_DIVEXACT_PREINV
mpz_invert_mod_2exp (mgcd, gcd);
mpz_divexact_pre (p, p, gcd, mgcd);
mpz_divexact_pre (g, g, gcd, mgcd);
#else
#define SIZ(x) x->_mp_size
mpz_divexact(p, p, gcd);
mpz_divexact(g, g, gcd);
#endif
fac_compact(fp);
fac_compact(fg);
}
}
/*///////////////////////////////////////////////////////////////////////////*/
int out=0;
mpz_t *pstack, *qstack, *gstack;
fac_t *fpstack, *fgstack;
long int top = 0;
double progress=0, percent;
#define p1 (pstack[top])
#define q1 (qstack[top])
#define g1 (gstack[top])
#define fp1 (fpstack[top])
#define fg1 (fgstack[top])
#define p2 (pstack[top+1])
#define q2 (qstack[top+1])
#define g2 (gstack[top+1])
#define fp2 (fpstack[top+1])
#define fg2 (fgstack[top+1])
long gcd_time = 0;
/* binary splitting */
void
bs(unsigned long a, unsigned long b, unsigned gflag, long int level)
{
unsigned long i, mid;
int ccc;
if (b-a==1) {
/*
g(b-1,b) = (6b-5)(2b-1)(6b-1)
p(b-1,b) = b^3 * C^3 / 24
q(b-1,b) = (-1)^b*g(b-1,b)*(A+Bb).
*/
mpz_set_ui(p1, b);
mpz_mul_ui(p1, p1, b);
mpz_mul_ui(p1, p1, b);
mpz_mul_ui(p1, p1, (C/24)*(C/24));
mpz_mul_ui(p1, p1, C*24);
mpz_set_ui(g1, 2*b-1);
mpz_mul_ui(g1, g1, 6*b-1);
mpz_mul_ui(g1, g1, 6*b-5);
mpz_set_ui(q1, b);
mpz_mul_ui(q1, q1, B);
mpz_add_ui(q1, q1, A);
mpz_mul (q1, q1, g1);
if (b%2)
mpz_neg(q1, q1);
i=b;
while ((i&1)==0) i>>=1;
fac_set_bp(fp1, i, 3); /* b^3 */
fac_mul_bp(fp1, 3*5*23*29, 3);
fp1[0].pow[0]--;
fac_set_bp(fg1, 2*b-1, 1); /* 2b-1 */
fac_mul_bp(fg1, 6*b-1, 1); /* 6b-1 */
fac_mul_bp(fg1, 6*b-5, 1); /* 6b-5 */
if (b>(int)(progress)) {
//printf("."); fflush(stdout);
progress += percent*2;
}
} else {
/*
p(a,b) = p(a,m) * p(m,b)
g(a,b) = g(a,m) * g(m,b)
q(a,b) = q(a,m) * p(m,b) + q(m,b) * g(a,m)
*/
mid = a+(b-a)*0.5224; /* tuning parameter */
bs(a, mid, 1, level+1);
top++;
bs(mid, b, gflag, level+1);
top--;
//if (level == 0)
// puts ("");
ccc = level == 0;
if (ccc) CHECK_MEMUSAGE;
if (level>=4) { /* tuning parameter */
#if 0
long t = cputime();
#endif
fac_remove_gcd(p2, fp2, g1, fg1);
#if 0
gcd_time += cputime()-t;
#endif
}
if (ccc) CHECK_MEMUSAGE;
mpz_mul(p1, p1, p2);
if (ccc) CHECK_MEMUSAGE;
mpz_mul(q1, q1, p2);
if (ccc) CHECK_MEMUSAGE;
mpz_mul(q2, q2, g1);
if (ccc) CHECK_MEMUSAGE;
mpz_add(q1, q1, q2);
if (ccc) CHECK_MEMUSAGE;
fac_mul(fp1, fp2);
if (gflag) {
mpz_mul(g1, g1, g2);
fac_mul(fg1, fg2);
}
}
if (out&2) {
printf("p(%ld,%ld)=",a,b); fac_show(fp1);
if (gflag)
printf("g(%ld,%ld)=",a,b); fac_show(fg1);
}
}
void
build_sieve(long int n, sieve_t *s)
{
long int m, i, j, k;
sieve_size = n;
m = (long int)sqrt(n);
memset(s, 0, sizeof(sieve_t)*n/2);
s[1/2].fac = 1;
s[1/2].pow = 1;
for (i=3; i<=n; i+=2) {
if (s[i/2].fac == 0) {
s[i/2].fac = i;
s[i/2].pow = 1;
if (i<=m) {
for (j=i*i, k=i/2; j<=n; j+=i+i, k++) {
if (s[j/2].fac==0) {
s[j/2].fac = i;
if (s[k].fac == i) {
s[j/2].pow = s[k].pow + 1;
s[j/2].nxt = s[k].nxt;
} else {
s[j/2].pow = 1;
s[j/2].nxt = k;
}
}
}
}
}
}
}
int
main(int argc, char *argv[])
{
mpf_t pi, qi;
long int d=100, i, depth=1, terms;
unsigned long psize, qsize;
long begin, mid0, mid1, mid2, mid3, mid4, end;
prog_name = argv[0];
if (argc>1)
d = strtoul(argv[1], 0, 0);
if (argc>2)
out = atoi(argv[2]);
terms = d/DIGITS_PER_ITER;
while ((1L<<depth)<terms)
depth++;
depth++;
percent = terms/100.0;
//printf("#terms=%ld, depth=%ld\n", terms, depth);
begin = cputime();
//printf("sieve "); fflush(stdout);
sieve_size = max(3*5*23*29+1, terms*6);
sieve = (sieve_t *)malloc(sizeof(sieve_t)*sieve_size/2);
build_sieve(sieve_size, sieve);
mid0 = cputime();
//printf("time = %6.3f\n", (double)(mid0-begin)/1000);
/* allocate stacks */
pstack = malloc(sizeof(mpz_t)*depth);
qstack = malloc(sizeof(mpz_t)*depth);
gstack = malloc(sizeof(mpz_t)*depth);
fpstack = malloc(sizeof(fac_t)*depth);
fgstack = malloc(sizeof(fac_t)*depth);
for (i=0; i<depth; i++) {
mpz_init(pstack[i]);
mpz_init(qstack[i]);
mpz_init(gstack[i]);
fac_init(fpstack[i]);
fac_init(fgstack[i]);
}
mpz_init(gcd);
#if HAVE_DIVEXACT_PREINV
mpz_init(mgcd);
#endif
fac_init(ftmp);
fac_init(fmul);
/* begin binary splitting process */
if (terms<=0) {
mpz_set_ui(p2,1);
mpz_set_ui(q2,0);
mpz_set_ui(g2,1);
} else {
bs(0,terms,0,0);
}
mid1 = cputime();
//printf("\nbs time = %6.3f\n", (double)(mid1-mid0)/1000);
//printf(" gcd time = %6.3f\n", (double)(gcd_time)/1000);
/* printf("misc "); fflush(stdout); */
/* free some resources */
free(sieve);
#if HAVE_DIVEXACT_PREINV
mpz_clear(mgcd);
#endif
mpz_clear(gcd);
fac_clear(ftmp);
fac_clear(fmul);
for (i=1; i<depth; i++) {
mpz_clear(pstack[i]);
mpz_clear(qstack[i]);
mpz_clear(gstack[i]);
fac_clear(fpstack[i]);
fac_clear(fgstack[i]);
}
mpz_clear(gstack[0]);
fac_clear(fpstack[0]);
fac_clear(fgstack[0]);
free(gstack);
free(fpstack);
free(fgstack);
/* prepare to convert integers to floats */
mpf_set_default_prec((long int)(d*BITS_PER_DIGIT+16));
/*
p*(C/D)*sqrt(C)
pi = -----------------
(q+A*p)
*/
psize = mpz_sizeinbase(p1,10);
qsize = mpz_sizeinbase(q1,10);
mpz_addmul_ui(q1, p1, A);
mpz_mul_ui(p1, p1, C/D);
mpf_init(pi);
mpf_set_z(pi, p1);
mpz_clear(p1);
mpf_init(qi);
mpf_set_z(qi, q1);
mpz_clear(q1);
free(pstack);
free(qstack);
mid2 = cputime();
/* printf("time = %6.3f\n", (double)(mid2-mid1)/1000); */
/* initialize temp float variables for sqrt & div */
mpf_init(t1);
mpf_init(t2);
/* mpf_set_prec_raw(t1, mpf_get_prec(pi)); */
/* final step */
//printf("div "); fflush(stdout);
my_div(qi, pi, qi);
mid3 = cputime();
//printf("time = %6.3f\n", (double)(mid3-mid2)/1000);
//printf("sqrt "); fflush(stdout);
my_sqrt_ui(pi, C);
mid4 = cputime();
//printf("time = %6.3f\n", (double)(mid4-mid3)/1000);
//printf("mul "); fflush(stdout);
mpf_mul(qi, qi, pi);
end = cputime();
//printf("time = %6.3f\n", (double)(end-mid4)/1000);
//printf("total time = %6.3f\n", (double)(end-begin)/1000);
fflush(stdout);
//printf(" P size=%ld digits (%f)\n"
// " Q size=%ld digits (%f)\n",
// psize, (double)psize/d, qsize, (double)qsize/d);
/* output Pi and timing statistics */
if (out&1) {
//printf("pi(0,%ld)=\n", terms);
mpf_out_str(stdout, 10, d+2, qi);
//printf("\n");
}
/* free float resources */
mpf_clear(pi);
mpf_clear(qi);
mpf_clear(t1);
mpf_clear(t2);
exit (0);
}