// validat2.cpp - originally written and placed in the public domain by Wei Dai and Jeffrey Walton
//                Routines in this source file are only tested in Debug builds.
//                Source files split in July 2018 to expedite compiles.

#include "pch.h"

#define CRYPTOPP_ENABLE_NAMESPACE_WEAK 1

#include "cryptlib.h"
#include "cpu.h"
#include "validate.h"

#include "algebra.h"
#include "integer.h"
#include "nbtheory.h"

#include <iostream>
#include <iomanip>
#include <sstream>

// Aggressive stack checking with VS2005 SP1 and above.
#if (_MSC_FULL_VER >= 140050727)
# pragma strict_gs_check (on)
#endif

#if CRYPTOPP_MSC_VERSION
# pragma warning(disable: 4505 4355)
#endif

NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Test)

#if defined(CRYPTOPP_EXTENDED_VALIDATION)
bool TestIntegerBitops()
{
    std::cout << "\nTesting Integer bit operations...\n\n";

    struct Bitops_TestTuple
    {
        // m,n are operands; a,o,x are and,or,xor results
        const char *m, *n, *a, *o, *x;
    };
    static const Bitops_TestTuple tests[] = {
        {
            "0xc2cea8a4", "0xb36e5794", "0x824e0084", "0xf3eeffb4", "0x71a0ff30"
        },
        {
            "0x436eb828", "0x1b375cb4", "0x3261820", "0x5b7ffcbc", "0x5859e49c"
        },
        {
            "0x1e5c0b28", "0x4fded465", "0xe5c0020", "0x5fdedf6d", "0x5182df4d"
        },
        {
            "0xeb71fde7", "0xf7bb47cf", "0xe33145c7", "0xfffbffef", "0x1ccaba28"
        },
        {
            "0xa6b0f01f", "0x8a8ca98", "0xa0c018", "0xaeb8fa9f", "0xae183a87"
        },
        {
            "0xa70bd8b7", "0x5c758cf5", "0x40188b5", "0xff7fdcf7", "0xfb7e5442"
        },
        {
            "0xf91af382", "0x718a9995", "0x710a9180", "0xf99afb97", "0x88906a17"
        },
        {
            "0xbd2a76ad", "0xddd8dfeb", "0x9d0856a9", "0xfdfaffef", "0x60f2a946"
        },
        {
            "0xd4b559cc", "0x91a53295", "0x90a51084", "0xd5b57bdd", "0x45106b59"
        },
        {
            "0x89434e9e", "0xa42fdaf9", "0x80034a98", "0xad6fdeff", "0x2d6c9467"
        },
        {
            "0xb947ac04", "0xd4201e52", "0x90000c00", "0xfd67be56", "0x6d67b256"
        },
        {
            "0xa83945c1", "0x3a9c5dba", "0x28184580", "0xbabd5dfb", "0x92a5187b"
        },
        {
            "0xbca38ffa", "0x881ba9fd", "0x880389f8", "0xbcbbafff", "0x34b82607"
        },
        {
            "0xfcd0b92", "0xeaad8534", "0xa8d0110", "0xefed8fb6", "0xe5608ea6"
        },
        {
            "0x50d160d0", "0x64646f75", "0x40406050", "0x74f56ff5", "0x34b50fa5"
        },
        {
            "0x165ccff8", "0x67d49127", "0x6548120", "0x77dcdfff", "0x71885edf"
        },
        {
            "0x8c4f4bbb7adaacb5", "0x2566b7a909b24aa9", "0x44603a9089208a1", "0xad6fffbb7bfaeebd", "0xa929fc127368e61c"
        },
        {
            "0x6f9ef50aafb31e8d", "0x7a93b2ccd1bbbff2", "0x6a92b00881b31e80", "0x7f9ff7ceffbbbfff", "0x150d47c67e08a17f"
        },
        {
            "0x4c99e967f8de5294", "0x1f4699e0c14e6974", "0xc008960c04e4014", "0x5fdff9e7f9de7bf4", "0x53df708739903be0"
        },
        {
            "0xcc55f5d6d3ea45c", "0x6805b4ddb6390c2f", "0x805145d2438040c", "0x6cc5ffddff3fac7f", "0x64c0eb80db07a873"
        },
        {
            "0x90620d1a012459e7", "0x89d31098ce3fed42", "0x8042001800244942", "0x99f31d9acf3ffde7", "0x19b11d82cf1bb4a5"
        },
        {
            "0xb87d1674e90a935a", "0x75ea466cbb782ac4", "0x30680664a9080240", "0xfdff567cfb7abbde", "0xcd9750185272b99e"
        },
        {
            "0x1f135732240701f0", "0x6aa09a1614bf4dd4", "0xa001212040701d0", "0x7fb3df3634bf4df4", "0x75b3cd2430b84c24"
        },
        {
            "0xc9a88d8300099a31", "0xdc8e91df745169ee", "0xc888818300010820", "0xddae9ddf7459fbff", "0x15261c5c7458f3df"
        },
        {
            "0xc8c828d15228b562", "0x43f86cffa3d15d80", "0x40c828d102001500", "0xcbf86cfff3f9fde2", "0x8b30442ef1f9e8e2"
        },
        {
            "0x41fdc0bc2009563f", "0x59dd1c417e3c07bc", "0x41dd00002008063c", "0x59fddcfd7e3d57bf", "0x1820dcfd5e355183"
        },
        {
            "0x9e2f78600c3a84e7", "0xac69a0e1fe7887b0", "0x8c2920600c3884a0", "0xbe6ff8e1fe7a87f7", "0x3246d881f2420357"
        },
        {
            "0xd424d1d9a955f617", "0x9608f5bde1c4d893", "0x9400d199a144d013", "0xd62cf5fde9d5fe97", "0x422c246448912e84"
        },
        {
            "0x1aa8b60a0627719a", "0x5b26e6aca95f5f60", "0x1a20a60800075100", "0x5baef6aeaf7f7ffa", "0x418e50a6af782efa"
        },
        {
            "0xcf5db499233fac00", "0xf33e7a29c3c33da8", "0xc31c300903032c00", "0xff7ffeb9e3ffbda8", "0x3c63ceb0e0fc91a8"
        },
        {
            "0x6b47c03d576e878d", "0x2032d13574d67da4", "0x2002c03554460584", "0x6b77d13d77feffad", "0x4b75110823b8fa29"
        },
        {
            "0xd47eeb3aefebf074", "0x6d7ba17a42c66b89", "0x447aa13a42c26000", "0xfd7feb7aefeffbfd", "0xb9054a40ad2d9bfd"
        },
        {
            "0x33ad9c5d20b03f5c05535f20a2941c8f4ae0f1f19500759151060dce39e5dfed41ec4f",
            "0x277401dc000fde7eda4d60a5698935f7febd8fbe49e5d6f56ca2e7f6118380d3cd655da392df3ba6c1b13dc0119af34cfa1d18a65",
            "0x10a9841c002016480453410020041c8640c0312191006411110401082924cfa1418845",
            "0x277401dc000fde7eda4d60a5698935f7febfbfffcdf7dff7fde2f7f7f38ba9d3cdf5ffaf9fdf7ba7d9b53de0ddfbff5dfedd1ee6f",
            "0x277401dc000fde7eda4d60a5698935f7febeb5678c37ddf69962b2c3e389a9920591f3ac8dc66ba198a42da0cd796d1104c90662a"
        },
        {
            "0xb6ea335c13111216862e370d12fb9c761a6266617f62a1904b0d7944ab3cddc71f11752ad9424b0",
            "0xa6b380f048a9cbe45ff4ea824064c831eb03ff875e1e3e",
            "0xa62200104028090410d480020044c831e1035285140430",
            "0xb6ea335c13111216862e370d12fb9c761a6b7e6f7feabdbe4fff7fecaf3eddc71fb17ffafde3ebe",
            "0xb6ea335c13111216862e370d12fb9c7610095e6e7be83d2e0ef237ec8f3a914401a14ad2aca3a8e"
        },
        {
            "0x8fb9486ad1f89ca5b3f6da9f0d5ef9ec328b8cc3e5122afbd8a67bd1b2b4ab5c548b90cf9fe1933a0362922f1e84ef0",
            "0x10615f963dffc13718ed1ecdb9cfbef33148befeb91b190dc7e7d28d8821ff248ab26a34e1b89885c643e447c72",
            "0x6051901ca58136188d0c4cb9cc32830040a412281b180443c192848800540080820a208138000082030404c70",
            "0x8fb9586bdffebdfff3f7daff1fdff9efbefbbdcbfffebbfbd9affff7f2bdab7dffaf9afffff5f3ba9be7d66ffec7ef2",
            "0x8fb9580b8e6ea15a72c1c272139340238c78bd8b5bec93e0c1abbc366039237dabaf1a7df5d572829be7546cfac3282"
        },
        {
            "0x10af96443b186faf790279bf3bbe0517d56ffc01e7fec8c88e765d48cc32333390224f4d762d1ba788c50801cba02524cb49",
            "0x95d44e7344fb1701bace3ae83affbb6290bf282f7565b9a82c386823f5f213a53eccb2cfe5deb4dd040067a64ada8c1b6828599b96cc70647e7d19dc7dfba393addabe689ffbe1a36642bc9844b81c6c4c2e178",
            "0x2c96442b084000000260ad288004028509b800c70640c080144548883032118022094d3608122408c1000181800400c148",
            "0x95d44e7344fb1701bace3ae83affbb6290bf282f7565b9a82c386823f5f213a53ecdbaffe5dfb5dffef7f7a7dbfbbffb797d5fffd6de7fecfefdfffdfdffe3b3bffbbe6cffffe3f3fe7abcd8c4bcbe6e5e6eb79",
            "0x95d44e7344fb1701bace3ae83affbb6290bf282f7565b9a82c386823f5f213a53ecdb836819d055bfef7f781d12937fb39550f6456d20f88f2f5feb9a97760b09ee3bc4c6b2c8372dc3a30c8c4a4a66e1e62a31"
        },
        {
            "0x5fc77dab8cd9c1da8c91eb7ba9c23ce85375b61bf3b9a8c4e4df7bc917aa8a14e747888c9756a2be2fd2e256e44194ce093a0185594de0dcf8340c45b6af7dbdc7682fbef6313f9f1cb234689d9f1ff603e1273faad89d0fe1ab57fbc7c32d29dce125fafc973754464b55ae5de58a8a5661c2065b95c2c94d7ec34",
            "0xd4a9158961d4c11258cd047eda13d6804c16c3a374b7f4115bd835bde0b5",
            "0x1080158800548100504504649012c480480081221420641158081495e034",
            "0x5fc77dab8cd9c1da8c91eb7ba9c23ce85375b61bf3b9a8c4e4df7bc917aa8a14e747888c9756a2be2fd2e256e44194ce093a0185594de0dcf8340c45b6af7dbdc7682fbef6313f9f1cb234689d9f1ff603e1273faad89d0fe1ab57fbc7cf6fb9dcf73dfefdb7bfd447eff5bf7de5cbee7e77cb7f5b95ffcb5ffecb5",
            "0x5fc77dab8cd9c1da8c91eb7ba9c23ce85375b61bf3b9a8c4e4df7bc917aa8a14e747888c9756a2be2fd2e256e44194ce093a0185594de0dcf8340c45b6af7dbdc7682fbef6313f9f1cb234689d9f1ff603e1273faad89d0fe1ab57fbc7ce67b8847738b6edb2bb8401a6f49335e14be66c5689791a807f4a16a0c81"
        },
        {
            "0x52cbea1f4d78445fb8f9267203f0f04bddf65b69b1acb0877143e77317f2d9679cb",
            "0x331e156a1e1daa0039926a08ec80c2d7c1500bc435a53ebfc32fa398a3304fcd79d90725528e320add050da666b9de42b8307b",
            "0x88421a41684412b839023200f0d00990725128a120a0805042666315e0090304b",
            "0x331e156a1e1daa0039926a08ec80c2d7c1552ffeb5f5ffbfc7ffaf9ae7307fcf7dfddf65f69f3acbdd771dbe77b9ff6fbe79fb",
            "0x331e156a1e1daa0039926a08ec80c2d7c155277a9451e93b86d42c0ac41070c27d64d840e41528c1d57219981188a16f2e49b0"
        },
        {
            "0xbde7e20f37c3ed822555d36050240dcfb5a9a3867d149cffe78e92b95573cbdde33a8c9495148e04cafa1325aae058b4a98c50f7019de1345de6dce12436bed4b86eca2d",
            "0xee480b4096f0c1ac565d623dd53b62dba81c507d3c8e15372396fa49de0ecf074fb0ed1785f00f8094022ff50fc436a7cbd18de8ff317c33ea9bdbd8814a7658fcd1fd10b2ed10eaf7e4c2b8f409df3c36f1f0c986a49805a9ed08bbcd603e2eec9e18",
            "0x547a00d1781e0020014022050040406a58981846814107c238a929950014a544038809410108c00caf20000a8e00894280450f00184a01005a0cc0020042014286c8a08",
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            "0xee480b4096f0c1ac565d623dd53b62dba81c507d3c8e15372396fa49de0ecfbaa852e220461d8da5c1d14fa52bc9f91262720b95ebad83d46409628df281abbbc65d6985a66314200df7e71214516b95baa107c81b45ac584f31e99ffbdeea96825435"
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        {
            "0x17ed0a1aa80542396e82ab79f6d4dda731d10f9487467fcfa5c8b501fa86488fbe268605c01beb257c9e301a42833d22965ea2ff0eda5f18427481a300a8f9aa81e76d774ea1dbed40268eca094bef627d2c206f6885fc12f71557bfda836",
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            "0x17ed0a1aa80542396e82ab79f6d4dda731d10f9487467fcfa5c8b501fa86488fbe268605c01beb257c9e301a42833d22965ea2ff0eda5f18427481a300a8f9aac3c42d9fb19a9a9aaf837b4b18b5df08db2ef86d69e10626363f9a0c04028"
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        {
            "0x290796408a0b8baa742b9d466afc4958528f7976fdce50caa83ed63285f58d200e4c65842ea24c3d4a3850a1824b61d25af9d3b41b9e64407a5262a75d9efd08481cfbc339ae26b0755438894b9e2298a35ed9",
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        {
            "0x31d126e874580b754389fad8b64aaa61cabb4f8eb6904fe7e504341ed903f7daa3e74d4da3afca80b2415672a",
            "0x16fb17a0468c0afa6bad456efa4f9baf26860eda9d7c00c2520c8c9b6026fb50df59b8cb74f6d9be861052c5e831158e7ffd98746328ce11f91d9ea22f0803a8b059aea22d1715ca1abeae53a8bc6b8bfb9b6c9d24ae714767",
            "0x11100e0745803440288e0189048aa20c0800a8a04904a22c10014008902e51a83c6080da1a6c880024114722",
            "0x16fb17a0468c0afa6bad456efa4f9baf26860eda9d7c00c2520c8c9b6026fb50df59b8cb74f6d9be861052c5eb3d17eefffd98f77738dfbdfb7dbea63fabb7f8fb79aefe7f5757cbffbebf7faabe7fdffbbbfcbd2fae75676f",
            "0x16fb17a0468c0afa6bad456efa4f9baf26860eda9d7c00c2520c8c9b6026fb50df59b8cb74f6d9be861052c5eb2c07e0f8b818c3371051bc7279340433a3b7505b30aa5c5347568bf72e912e02821f5f21a190352f8a64204d"
        },
        {
            "0xbf1a14e469c234b72d56324d100e016bc38cdf7158e35f230c047585e7b107acc8e222e7f19552541e59316affd90e96ca657b6112f5e8c786dfcff342fc46252fcdab10c632578540dbf6235f164bc5711924c7c6ba9da85ab",
            "0x5dd3fb9a3de26cd89eb9517af6bb25678f149f906e8751a0c20d7646d21c17191237022a990e0156541e376986fd6a680c60228e5955df08bae5789c81751cdcafe5a2e72d45b09",
            "0x5d5158821d220c001481413006a800620204919042041000000876400214020112210220880600564412026806252a480800020251054008b22158140145101824c582a20d00109",
            "0xbf1a14e469c234b72d56324d100e016bc38cdff3fbfb7fe36cdcffbdf7fbf7bfede7aff7ff957ed75ff9f36fffdfde9edf7d7b7712fff9cf87dfdfff77fdc6fd6fedaf70e6be5fd5dfdbfee77f9ecbf57dddafe7e6ffbdedfab",
            "0xbf1a14e469c234b72d56324d100e016bc38c82a2a37962c160dceb3cb6cbf117ed85adf36e053cd34ff9f367899fdc8add7c695610df71c987899bed7595c0d845a5a770e4bc0ed09fd34cc6278acab06dc58b22645db0edea2"
        },
    };

    bool opa=true, opo=true, opx=true;

    //////////////////// AND ////////////////////

    for (size_t i=0; i<COUNTOF(tests); i++)
    {
        Integer m(tests[i].m), n(tests[i].n), a(tests[i].a);

        opa &= ((m & n) == a);
        opa &= ((-m & n) == a);
        opa &= ((m & -n) == a);
        opa &= ((-m & -n) == a);

        // And reversed
        opa &= ((n & m) == a);
        opa &= ((-n & m) == a);
        opa &= ((n & -m) == a);
        opa &= ((-n & -m) == a);

        Integer t(m); t &= n;
        opa &= (t == a);
        t = n; t &= m;
        opa &= (t == a);

        opa &= ((m & m) == m);
        opa &= ((n & n) == n);
    }

    if (opa)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Bitwise AND over 32-bits to 1024-bits\n";

    //////////////////// OR ////////////////////

    for (size_t i=0; i<COUNTOF(tests); i++)
    {
        Integer m(tests[i].m), n(tests[i].n), o(tests[i].o);

        opo &= ((m | n) == o);
        opo &= ((-m | n) == o);
        opo &= ((m | -n) == o);
        opo &= ((-m | -n) == o);

        // And reversed
        opo &= ((n | m) == o);
        opo &= ((-n | m) == o);
        opo &= ((n | -m) == o);
        opo &= ((-n | -m) == o);

        Integer t(m); t |= n;
        opo &= (t == o);
        t = n; t |= m;
        opo &= (t == o);

        opo &= ((m | m) == m);
        opo &= ((n | n) == n);
    }

    if (opo)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Bitwise OR over 32-bits to 1024-bits\n";

    //////////////////// XOR ////////////////////

    for (size_t i=0; i<COUNTOF(tests); i++)
    {
        Integer m(tests[i].m), n(tests[i].n), x(tests[i].x);

        opx &= ((m ^ n) == x);
        opx &= ((-m ^ n) == x);
        opx &= ((m ^ -n) == x);
        opx &= ((-m ^ -n) == x);

        // And reversed
        opx &= ((n ^ m) == x);
        opx &= ((-n ^ m) == x);
        opx &= ((n ^ -m) == x);
        opx &= ((-n ^ -m) == x);

        Integer t(m); t ^= n;
        opx &= (t == x);
        t = n; t ^= m;
        opx &= (t == x);

        opx &= ((m ^ m) == Integer::Zero());
        opx &= ((n ^ n) == Integer::Zero());
    }

    if (opx)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Bitwise XOR over 32-bits to 1024-bits\n";

    return opa && opo && opx;
}

bool TestIntegerOps()
{
    std::cout << "\nTesting Integer operations...\n\n";
    bool pass=true, result;
    RandomNumberGenerator& prng = GlobalRNG();

    // The tests below include 0^0 and 0^0%0. There are mixed opinions about what the result
    // should be. Some say it is undefined, others say it is 0, and yet others say it is 1.

    // Be careful with unfettered exponentiation using EuclideanDomainOf<Integer> and
    // Exponentiate(). It can easily consume all machine memory because it is an exponentiation
    // without a modular reduction.

    // ****************************** DivideByZero ******************************

    {
        try {
            Integer x = Integer(prng, 128) / Integer::Zero();
            result=false;
        } catch (const Exception&) {
            result=true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // The 0*0 % 0 test.
    {
        try {
            Integer x = 0;
            Integer y = 0;
            Integer z = ModularMultiplication(y, y, x);
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // Another 0*0 % 0 test.
    {
        try {
            Integer x = 0;
            Integer y = 0;
            Integer z = (y * y) % x;
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // The 0^0 % 0 test.
    {
        try {
            Integer x = 0;
            Integer y = 0;
            Integer z = ModularExponentiation(y, y, x);
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // Another 0^0 % 0 test.
    {
        try {
            Integer x = 0;
            Integer y = 0;
            Integer z = EuclideanDomainOf<Integer>().Exponentiate(y, y) % x;
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // Integer divide by 0
    {
        try {
            Integer r=1, q=1, a=1, d=0;
            Integer::Divide(r, q, a, d);
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    // Another Integer divide by 0
    {
        try {
            Integer q=1, a=1; word r=1, d=0;
            Integer::Divide(r, q, a, d);
            result = false;
        }
        catch(const Integer::DivideByZero&) {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Integer DivideByZero\n";
    }

    if (pass)
        std::cout << "passed:";
    else
        std::cout << "FAILED:";
    std::cout << "  Integer DivideByZero\n";

    // ************************ RandomNumberNotFound ************************

    try {
        // A run of 71 composites; see http://en.wikipedia.org/wiki/Prime_gap
        Integer x = Integer(GlobalRNG(), 31398, 31468, Integer::PRIME);
        result=false;
    } catch (const Exception&) {
        result=true;
    }

    pass = result && pass;
    if (result)
        std::cout << "passed:";
    else
        std::cout << "FAILED:";
    std::cout << "  Integer RandomNumberNotFound\n";

    // ************************ Carmichael pseudo-primes ************************

    result=true;
    if (IsPrime(Integer("561")))
        result = false;
    if (IsPrime(Integer("41041")))
        result = false;
    if (IsPrime(Integer("321197185")))
        result = false;
    if (IsPrime(Integer("5394826801")))
        result = false;
    if (IsPrime(Integer("232250619601")))
        result = false;
    if (IsPrime(Integer("974637772161")))
        result = false;

    pass = result && pass;
    if (result)
        std::cout << "passed:";
    else
        std::cout << "FAILED:";
    std::cout << "  Carmichael pseudo-primes\n";

    // ****************************** Integer Double ******************************

    try {
        Integer x = Integer::One().Doubled();
        result = (x == Integer::Two());
    } catch (const Exception&) {
        result=false;
    }

    pass = result && pass;
    if (!result)
        std::cout << "FAILED:  Integer Doubled\n";

    // ****************************** Integer Square ******************************

    try {
        Integer x = Integer::Two().Squared();
        result = (x == 4);
    } catch (const Exception&) {
        result=false;
    }

    pass = result && pass;
    if (!result)
        std::cout << "FAILED:  Integer Squared\n";

    try {
        Integer x = Integer::Two().Squared();
        result = (x == 4) && x.IsSquare();
    } catch (const Exception&) {
        result=false;
    }

    pass = result && pass;
    if (!result)
        std::cout << "FAILED:  Integer IsSquare\n";

    if (pass)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Squaring operations\n";

    // ****************************** Integer GCD ******************************

    {
        for (unsigned int i=0; i<128; ++i)
        {
            Integer x, y;
            switch(i%2)
            {
                case 0:
                {
                    AlgorithmParameters params =
                        MakeParameters("BitLength", 256)("RandomNumberType", Integer::PRIME);
                    x.GenerateRandom(prng, params);
                    y.GenerateRandom(prng, params);
                    break;
                }
                case 1:
                {
                    x = MaurerProvablePrime(prng, 256);
                    y = MihailescuProvablePrime(prng, 256);
                }
            }

            if (x != y)
            {
                result = (RelativelyPrime(x, y) == true);
                pass = result && pass;

                if (!result)
                    std::cout << "FAILED:  Integer GCD\n";
            }
        }

        if (pass)
           std::cout << "passed:";
        else
           std::cout << "FAILED:";
        std::cout << "  GCD operations\n";
    }

    // ******************** Integer Modulo and InverseMod ********************

    // http://github.com/weidai11/cryptopp/issues/602
    //   The bug report that uncovered the InverseMod problems
    {
        Integer a("0x2F0500010000018000000000001C1C000000000000000A000B0000000000000000000000000000FDFFFFFF00000000");
        Integer b("0x3D2F050001");

        result = (Integer("0x3529E4FEBC") == a.InverseMod(b));
        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  InverseMod operation\n";
    }

    // Integer Integer::InverseMod(const Integer &m)
    //   Large 'a' and 'm'
    for (unsigned int i=0; i<128; ++i)
    {
        Integer a(prng, 1024), m(prng, 1024);
        a++, m++;  // make non-0

        Integer x = a.InverseMod(m);
        Integer y = (a % m).InverseMod(m);
        Integer z = (a * y).Modulo(m);

        if (RelativelyPrime(a, m) == true)
            result = (x == y) && (z == 1) && (ModularMultiplication(a, x, m) == 1);
        else
            result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  InverseMod operation\n";
    }

    // Integer Integer::InverseMod(const Integer &m)
    //   Corner cases like 0, 2m-1 and 2m+1
    for (unsigned int i=0; i<128; ++i)
    {
        Integer a(prng, 1024), m(prng, 1024);
        a++, m++;  // make non-0

        // Corner cases
        int j = i % 12;
        switch (j)
        {
        case 0:
            a = -1; break;
        case 1:
            a = 0; break;
        case 2:
            a = 1; break;
        case 3:
            a = m-1; break;
        case 4:
            a = m; break;
        case 5:
            a = m+1; break;
        case 6:
            a = 2*m-1; break;
        case 7:
            a = 2*m; break;
        case 8:
            a = 2*m+1; break;
        case 9:
            a = (m<<256)-1; break;
        case 10:
            a = (m<<256); break;
        case 11:
            a = (m<<256)+1; break;
        default:
            ;
        }

        Integer x = a.InverseMod(m);
        Integer y = (a % m).InverseMod(m);
        Integer z = (a * y).Modulo(m);

        if (RelativelyPrime(a, m) == true)
            result = (x == y) && (z == 1) && (ModularMultiplication(a, x, m) == 1);
        else
            result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  InverseMod operation\n";
    }

    // Integer Integer::InverseMod(const Integer &m)
    //   Large 'a', small 'm'
    for (unsigned int i=0; i<128; ++i)
    {
        Integer a(prng, 4096), m(prng, 32);
        a++, m++; // make non-0

        Integer x = a.InverseMod(m);
        Integer y = (a % m).InverseMod(m);
        Integer z = (a * y).Modulo(m);

        if (RelativelyPrime(a, m) == true)
            result = (x == y) && (z == 1) && (ModularMultiplication(a, x, m) == 1);
        else
            result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  InverseMod operation\n";
    }

    // Integer Integer::InverseMod(word m)
    //   Small 'm' using word
    for (unsigned int i=0; i<128; ++i)
    {
        Integer a(prng, 4096); word m;
        prng.GenerateBlock((byte*)&m, sizeof(m));

        a++; // make non-0
        if (m == 0) m++;

        // Avoid the conversion from word to long
        Integer mi = Integer(Integer::POSITIVE, 0, m);
        Integer ri = a % Integer(Integer::POSITIVE, 0, m);

        Integer x = Integer(Integer::POSITIVE, 0, a.InverseMod(m));
        Integer y = Integer(Integer::POSITIVE, 0, ri.InverseMod(m));
        Integer z = Integer(Integer::POSITIVE, 0, (a * y).Modulo(m));

        if (GCD(a,mi) == 1)
            result = (x == y) && (z == 1);
        else
            result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  InverseMod operation\n";
    }

    if (pass)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  InverseMod operations\n";

    // ****************************** Integer Divide ******************************

    // Divide (Integer &r, Integer &q, const Integer &a, const Integer &d)
    for (unsigned int i=0; i<128; ++i)
    {
        Integer r, q, a(prng, 1024), d(prng, 1024);
        Integer::Divide(r, q, a, d);

        Integer xr = a % d;
        Integer xq = a / d;
        result = (r == xr) && (q == xq);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Divide operation\n";
    }

    // Divide (word &r, Integer &q, const Integer &a, word d)
    for (unsigned int i=0; i<128; ++i)
    {
        word r, d = prng.GenerateWord32();
        Integer q, a(prng, 1024);
        Integer::Divide(r, q, a, d);

        Integer xr = a % Integer(Integer::POSITIVE, 0, d);
        Integer xq = a / Integer(Integer::POSITIVE, 0, d);
        result = (Integer(Integer::POSITIVE, 0, r) == xr) && (q == xq);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Divide operation\n";
    }

    if (pass)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Divide operations\n";

    // ****************************** Integer Power2 ******************************

    {
        Integer x, y;

        x = Integer::Power2(0);
        result = (x == 1);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Power2 operation\n";

        x = Integer::Power2(1);
        result = (x == 2);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Power2 operation\n";
    }

    for (unsigned int i=0; i<128; i+=2)
    {
        Integer b = 2, m(prng, 2048);

        Integer x = EuclideanDomainOf<Integer>().Exponentiate(b, i) % m;
        Integer y = Integer::Power2(i) % m;
        result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Power2 operation\n";
    }

    if (pass)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Power2 operations\n";

    // ****************************** Integer Exponentiation ******************************

    {
        word32  m = prng.GenerateWord32();
        if (m == 0) m++;

        Integer z = Integer::Zero();
        Integer x = ModularExponentiation(z, z, m);
        Integer y = EuclideanDomainOf<Integer>().Exponentiate(z, z) % m;
        result = (x == y) && (x == 1);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // The 0^0 % 0 test.
    {
        try
        {
            Integer x = 0;
            Integer y = ModularExponentiation(x, x, x);
            result = false;
        }
        catch(const Integer::DivideByZero&)
        {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // Another 0^0 % 0 test.
    {
        try
        {
            Integer x = 0;
            Integer z = EuclideanDomainOf<Integer>().Exponentiate(0, 0) % x;
            result = false;
        }
        catch(const Integer::DivideByZero&)
        {
            result = true;
        }

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // Run the exponent 0 to 128 on base 0
    for (unsigned int i=0; i<128; i+=2)
    {
        Integer b = 0, m(prng, 2048);

        Integer x = ModularExponentiation(b, i, m);
        Integer y = EuclideanDomainOf<Integer>().Exponentiate(b, i) % m;
        result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // Run the exponent 1 to 128 on base 2
    for (unsigned int i=0; i<128; i+=2)
    {
        Integer b = 1, m(prng, 2048);

        Integer x = ModularExponentiation(b, i, m);
        Integer y = EuclideanDomainOf<Integer>().Exponentiate(b, i) % m;
        result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // Run the exponent 0 to 128 on base 2
    for (unsigned int i=0; i<128; i+=2)
    {
        Integer b = 2, m(prng, 2048);

        Integer x = ModularExponentiation(b, i, m);
        Integer y = EuclideanDomainOf<Integer>().Exponentiate(b, i) % m;
        result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    // Run the exponent 0 to 24 on random base
    for (unsigned int i=0; i<24; ++i)
    {
        Integer b(prng, 32), m(prng, 2048);

        Integer x = ModularExponentiation(b, i, m);
        Integer y = EuclideanDomainOf<Integer>().Exponentiate(b, i) % m;
        result = (x == y);

        pass = result && pass;
        if (!result)
            std::cout << "FAILED:  Exponentiation operation\n";
    }

    if (pass)
       std::cout << "passed:";
    else
       std::cout << "FAILED:";
    std::cout << "  Exponentiation operations\n";

    return pass;
}
#endif

NAMESPACE_END  // Test
NAMESPACE_END  // CryptoPP