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以前投稿したミラーラビン法をC++で書いてみました。
#3894
多倍長計算にboostライブラリーを使用しました。
無限精度整数型(cpp_int型)を使用しています。
第2引数(NUM)は判定回数(精度)です。素数リストを1000個用意しましたので
2～1000までの数値を指定してください。
また、ビルドしたdllファイルは想定していたより大き過ぎたので
今回は掲示板への投稿は控えさせて頂きます。
しかしながら、C++開発環境を持たない方のため、VC++2015(x86)にてビルド(コンパイル)
したファイルをアップローダーにupしておきました。(miller rabin.zip)
ダウンロードパス:shibacchi
なお、上記URLには有効期限があり、現時点より１ヶ月間となります。
OPTION ARITHMETIC RATIONAL
LET S=10^500+1
LET E=S+10000
FOR I=S TO E STEP 2
LET A$=STR$(I)
IF ISPRIME(A$,100)<>0 THEN
PRINT A$
END IF
NEXT I
END
EXTERNAL FUNCTION ISPRIME(N$,NUM)
OPTION ARITHMETIC RATIONAL
ASSIGN "miller.dll","isprime"
END FUNCTION
EXTERNAL FUNCTION ISPRIME2(N$,NUM)
OPTION ARITHMETIC RATIONAL
ASSIGN "isprime.dll","isprime"
END FUNCTION
---------------------------------------------------------------------------------
miller.cpp
#include <boost/multiprecision/cpp_int.hpp>
using namespace boost::multiprecision;
using namespace std;
cpp_int powmod(cpp_int b,cpp_int p,cpp_int m)
{
cpp_int result=1;
while (p>0) {
if (p % 2==1) result=(result*b) % m;
b=(b*b) % m;
p=p/2;
}
return result;
}
cpp_int atocpp(char *str)
{
cpp_int result = 0;
while (*str>='0' && *str<='9'){
result=(result*10)+(*str++ - '0');
}
return result;
}
extern "C" __declspec(dllexport) int isprime(char *x,int num)
{
cpp_int d,r,n=0;
int i,j,isp,s=0;
int a[]={
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103
,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211
,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331
,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449
,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587
,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709
,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853
,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991
,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093
,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217
,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319
,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453
,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567
,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669
,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801
,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933
,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063
,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179
,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309
,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417
,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557
,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689
,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797
,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927
,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067
,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217
,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343
,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469
,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593
,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719
,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853
,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001
,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127
,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253
,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397
,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523
,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663
,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801
,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957
,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081
,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231
,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393
,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503
,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651
,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783
,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881
,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067
,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203
,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323
,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469
,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619
,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763
,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899
,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019
,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193
,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333
,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507
,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607
,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753
,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907
,7919 };
if (num>1000) num=1000;
if (num<2) num=2;
n=atocpp(x);
if (n<=1) return 0;
for (i=0;i<=num-1;i++)
if (a[i]==n) return 1;
else if (n % a[i]==0) return 0;
d=(n-1)/2;
while (d % 2==0) {
d=d/2;
s++;
}
for(i=0;i<=num-1;i++){
isp=0;
r=powmod(a[i],d,n);
if (r==1 || r==n-1) isp=1;
r=powmod(r,2,n);
for(j=0;j<=s-1;j++){
if (r==n-1) isp=1;
r=powmod(r,2,n);
}
if (isp==0) return 0;
}
return 1;
}
また、boostライブラリーには下記ソースのようにmiller-rabin法が定義されています。
こちらは素数リストではなく、乱数を使用しているようです。
第2引数(NUM)は判定回数を指定してください。
------------------------------------------------------------------------------------
isprime.cpp
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/miller_rabin.hpp>
using namespace boost::multiprecision;
using namespace std;
cpp_int atocpp(char *str)
{
cpp_int result = 0;
while (*str>='0' && *str<='9'){
result=(result*10)+(*str++ - '0');
}
return result;
}
extern "C" __declspec(dllexport) int isprime(char *x,int num)
{
cpp_int n;
n=atocpp(x);
if (n==2) return 1;
bool is_prime = miller_rabin_test(n, num);
return (is_prime ? 1:0);
}
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