path: root/include/mcl/fp.hpp

#pragma once
/**
    @file
    @brief finite field class
    @author MITSUNARI Shigeo(@herumi)
    @license modified new BSD license
    http://opensource.org/licenses/BSD-3-Clause
*/
#include <iostream>
#include <sstream>
#include <vector>
#ifdef _MSC_VER
    #pragma warning(push)
    #pragma warning(disable : 4127)
    #pragma warning(disable : 4458)
    #ifndef NOMINMAX
        #define NOMINMAX
    #endif
    #ifndef MCL_NO_AUTOLINK
        #ifdef NDEBUG
            #pragma comment(lib, "mcl.lib")
        #else
            #pragma comment(lib, "mcld.lib")
        #endif
    #endif
#endif
#include <cybozu/hash.hpp>
#include <mcl/op.hpp>
#include <mcl/util.hpp>
#include <mcl/operator.hpp>

namespace mcl {

struct FpTag;
struct ZnTag;

enum IoMode {
    IoAuto = 0, // dec or hex according to ios_base::fmtflags
    IoPrefix = 1, // append '0b'(bin) or '0x'(hex)
    IoBin = 2, // binary number without prefix
    IoDec = 10, // decimal number without prefix
    IoHex = 16, // hexadecimal number without prefix
    IoBinPrefix = IoBin | IoPrefix,
    IoHexPrefix = IoHex | IoPrefix,
    IoArray = 32, // array of Unit(fixed size)
    IoArrayRaw = 64 // raw array of Unit without Montgomery conversion
};

namespace fp {

static inline const char* getIoSeparator(int ioMode)
{
    return (ioMode & (IoArray | IoArrayRaw)) ? "" : " ";
}

static inline int detectIoMode(int ioMode, const std::ios_base& ios)
{
    if (ioMode & ~IoPrefix) return ioMode;
    // IoAuto or IoPrefix
    const std::ios_base::fmtflags f = ios.flags();
    if (f & std::ios_base::oct) throw cybozu::Exception("mcl:fp:detectIoMode:oct is not supported");
    ioMode |= (f & std::ios_base::hex) ? IoHex : IoDec;
    if (f & std::ios_base::showbase) {
        ioMode |= IoPrefix;
    }
    return ioMode;
}

void arrayToStr(std::string& str, const Unit *x, size_t n, int base, bool withPrefix);

/*
    set x and y[] with abs(str)
    pBitSize is set if not null
    return true if str is negative
*/
bool strToMpzArray(size_t *pBitSize, Unit *y, size_t maxBitSize, mpz_class& x, const std::string& str, int base);

void copyAndMask(Unit *y, const void *x, size_t xByteSize, const Op& op, bool doMask);

uint64_t getUint64(bool *pb, const fp::Block& b);
int64_t getInt64(bool *pb, fp::Block& b, const fp::Op& op);

const char *ModeToStr(Mode mode);

Mode StrToMode(const std::string& s);

void dumpUnit(Unit x);
void UnitToHex(char *buf, size_t maxBufSize, Unit x);

bool isEnableJIT(); // 1st call is not threadsafe

// hash msg
std::string hash(size_t bitSize, const char *msg, size_t msgSize);

} // mcl::fp

template<class tag = FpTag, size_t maxBitSize = MCL_MAX_BIT_SIZE>
class FpT : public fp::Operator<FpT<tag, maxBitSize> > {
    typedef fp::Unit Unit;
    typedef fp::Operator<FpT<tag, maxBitSize> > Operator;
    static const size_t maxSize = (maxBitSize + fp::UnitBitSize - 1) / fp::UnitBitSize;
    template<class tag2, size_t maxBitSize2> friend class FpT;
    Unit v_[maxSize];
    static fp::Op op_;
    static FpT<tag, maxBitSize> inv2_;
    static IoMode ioMode_;
    template<class Fp> friend class FpDblT;
    template<class Fp> friend class Fp2T;
    template<class Fp> friend struct Fp6T;
public:
    typedef FpT<tag, maxBitSize> BaseFp;
    // return pointer to array v_[]
    const Unit *getUnit() const { return v_; }
    FpT* getFp0() { return this; }
    const FpT* getFp0() const { return this; }
    static inline size_t getUnitSize() { return op_.N; }
    static inline size_t getBitSize() { return op_.bitSize; }
    static inline size_t getByteSize() { return (op_.bitSize + 7) / 8; }
    static inline const fp::Op& getOp() { return op_; }
    void dump() const
    {
        const size_t N = op_.N;
        for (size_t i = 0; i < N; i++) {
            fp::dumpUnit(v_[N - 1 - i]);
        }
        printf("\n");
    }
    static inline void init(const mpz_class& m, fp::Mode mode = fp::FP_AUTO)
    {
        init(m.get_str(), mode);
    }
    static inline void init(const std::string& mstr, fp::Mode mode = fp::FP_AUTO)
    {
        assert(maxBitSize <= MCL_MAX_BIT_SIZE);
        op_.init(mstr, maxBitSize, mode);
        { // set oneRep
            FpT& one = *reinterpret_cast<FpT*>(op_.oneRep);
            one.clear();
            one.v_[0] = 1;
            one.toMont();
        }
        { // set half
            mpz_class half = (op_.mp + 1) / 2;
            gmp::getArray(op_.half, op_.N, half);
        }
        inv(inv2_, 2);
    }
    static inline void getModulo(std::string& pstr)
    {
        gmp::getStr(pstr, op_.mp);
    }
    static inline bool isFullBit() { return op_.isFullBit; }
    /*
        binary patter of p
        @note the value of p is zero
    */
    static inline const FpT& getP()
    {
        return *reinterpret_cast<const FpT*>(op_.p);
    }
    bool isOdd() const
    {
        fp::Block b;
        getBlock(b);
        return (b.p[0] & 1) == 1;
    }
    static inline bool squareRoot(FpT& y, const FpT& x)
    {
        mpz_class mx, my;
        x.getMpz(mx);
        bool b = op_.sq.get(my, mx);
        if (!b) return false;
        y.setMpz(my);
        return true;
    }
    FpT() {}
    FpT(const FpT& x)
    {
        op_.fp_copy(v_, x.v_);
    }
    FpT& operator=(const FpT& x)
    {
        op_.fp_copy(v_, x.v_);
        return *this;
    }
    void clear()
    {
        op_.fp_clear(v_);
    }
    FpT(int64_t x) { operator=(x); }
    explicit FpT(const std::string& str, int base = 0)
    {
        setStr(str, base);
    }
    FpT& operator=(int64_t x)
    {
        if (x == 1) {
            op_.fp_copy(v_, op_.oneRep);
        } else {
            clear();
            if (x) {
                int64_t y = x < 0 ? -x : x;
                if (sizeof(Unit) == 8) {
                    v_[0] = y;
                } else {
                    v_[0] = (uint32_t)y;
                    v_[1] = (uint32_t)(y >> 32);
                }
                if (x < 0) neg(*this, *this);
                toMont();
            }
        }
        return *this;
    }
    static inline bool isMont() { return op_.isMont; }
    /*
        convert normal value to Montgomery value
        do nothing is !isMont()
    */
    void toMont()
    {
        if (isMont()) op_.toMont(v_, v_);
    }
    /*
        convert Montgomery value to normal value
        do nothing is !isMont()
    */
    void fromMont()
    {
        if (isMont()) op_.fromMont(v_, v_);
    }
    void setStr(const std::string& str, int ioMode = 0)
    {
        if (ioMode & (IoArray | IoArrayRaw)) {
            const size_t n = getByteSize();
            if (str.size() != n) throw cybozu::Exception("FpT:setStr:bad size") << str.size() << n << ioMode;
            if (ioMode & IoArrayRaw) {
                memcpy(v_, str.c_str(), n);
                if (!isValid()) throw cybozu::Exception("FpT:setStr:bad value") << str;
            } else {
                setArray(&str[0], n);
            }
            return;
        }
        mpz_class x;
        bool isMinus = fp::strToMpzArray(0, v_, op_.N * fp::UnitBitSize, x, str, ioMode & ~IoPrefix);
        if (x >= op_.mp) throw cybozu::Exception("FpT:setStr:large str") << str << op_.mp;
        if (isMinus) {
            neg(*this, *this);
        }
        toMont();
    }
    /*
        throw exception if x >= p
    */
    template<class S>
    void setArray(const S *x, size_t n)
    {
        fp::copyAndMask(v_, x, sizeof(S) * n, op_, false);
        toMont();
    }
    /*
        mask inBuf with (1 << (bitLen - 1)) - 1
    */
    template<class S>
    void setArrayMask(const S *inBuf, size_t n)
    {
        fp::copyAndMask(v_, inBuf, sizeof(S) * n, op_, true);
        toMont();
    }
    template<class S>
    size_t getArray(S *outBuf, size_t n) const
    {
        const size_t SbyteSize = sizeof(S) * n;
        const size_t fpByteSize = sizeof(Unit) * op_.N;
        if (SbyteSize < fpByteSize) throw cybozu::Exception("FpT:getArray:bad n") << n << fpByteSize;
        assert(SbyteSize >= fpByteSize);
        fp::Block b;
        getBlock(b);
        memcpy(outBuf, b.p, fpByteSize);
        const size_t writeN = (fpByteSize + sizeof(S) - 1) / sizeof(S);
        memset((char *)outBuf + fpByteSize, 0, writeN * sizeof(S) - fpByteSize);
        return writeN;
    }
    void getBlock(fp::Block& b) const
    {
        b.n = op_.N;
        if (isMont()) {
            op_.fromMont(b.v_, v_);
            b.p = &b.v_[0];
        } else {
            b.p = &v_[0];
        }
    }
    template<class RG>
    void setRand(RG& rg)
    {
        fp::getRandVal(v_, rg, op_.p, op_.bitSize);
        toMont();
    }
    /*
        hash msg and mask with (1 << (bitLen - 1)) - 1
    */
    void setMsg(const char *msg, size_t msgSize)
    {
        std::string digest = mcl::fp::hash(op_.bitSize, msg, msgSize);
        setArrayMask(digest.c_str(), digest.size());
    }
    void setMsg(const std::string& msg)
    {
        setMsg(msg.data(), msg.size());
    }
    void getStr(std::string& str, int ioMode = 10) const
    {
        const size_t n = getByteSize();
        if (ioMode & IoArrayRaw) {
            str.resize(n);
            memcpy(&str[0], v_, str.size());
            return;
        }
        fp::Block b;
        getBlock(b);
        if (ioMode & IoArray) {
            str.resize(n);
            memcpy(&str[0], b.p, str.size());
            return;
        }
        fp::arrayToStr(str, b.p, b.n, ioMode & ~IoPrefix, (ioMode & IoPrefix) != 0);
    }
    std::string getStr(int ioMode = 10) const
    {
        std::string str;
        getStr(str, ioMode);
        return str;
    }
    void getMpz(mpz_class& x) const
    {
        fp::Block b;
        getBlock(b);
        gmp::setArray(x, b.p, b.n);
    }
    mpz_class getMpz() const
    {
        mpz_class x;
        getMpz(x);
        return x;
    }
    void setMpz(const mpz_class& x)
    {
        if (x < 0) throw cybozu::Exception("Fp:setMpz:negative is not supported") << x;
        setArray(gmp::getUnit(x), gmp::getUnitSize(x));
    }
    static inline void add(FpT& z, const FpT& x, const FpT& y) { op_.fp_add(z.v_, x.v_, y.v_, op_.p); }
    static inline void sub(FpT& z, const FpT& x, const FpT& y) { op_.fp_sub(z.v_, x.v_, y.v_, op_.p); }
    static inline void addPre(FpT& z, const FpT& x, const FpT& y) { op_.fp_addPre(z.v_, x.v_, y.v_); }
    static inline void subPre(FpT& z, const FpT& x, const FpT& y) { op_.fp_subPre(z.v_, x.v_, y.v_); }
    static inline void mul(FpT& z, const FpT& x, const FpT& y) { op_.fp_mul(z.v_, x.v_, y.v_, op_.p); }
    static inline void mulUnit(FpT& z, const FpT& x, const Unit y)
    {
        if (mulSmallUnit(z, x, y)) return;
        op_.fp_mulUnit(z.v_, x.v_, y, op_.p);
    }
    static inline void inv(FpT& y, const FpT& x) { op_.fp_invOp(y.v_, x.v_, op_); }
    static inline void neg(FpT& y, const FpT& x) { op_.fp_neg(y.v_, x.v_, op_.p); }
    static inline void sqr(FpT& y, const FpT& x) { op_.fp_sqr(y.v_, x.v_, op_.p); }
    static inline void divBy2(FpT& y, const FpT& x)
    {
#if 0
        mul(y, x, inv2_);
#else
        bool odd = (x.v_[0] & 1) != 0;
        op_.fp_shr1(y.v_, x.v_);
        if (odd) {
            op_.fp_addPre(y.v_, y.v_, op_.half);
        }
#endif
    }
    static inline void divBy4(FpT& y, const FpT& x)
    {
        divBy2(y, x); // QQQ : optimize later
        divBy2(y, y);
    }
    bool isZero() const { return op_.fp_isZero(v_); }
    bool isOne() const { return fp::isEqualArray(v_, op_.oneRep, op_.N); }
    static const inline FpT& one() { return *reinterpret_cast<const FpT*>(op_.oneRep); }
    /*
        half = (p + 1) / 2
        return true if half <= x < p
        return false if 0 <= x < half
    */
    bool isNegative() const
    {
        fp::Block b;
        getBlock(b);
        return fp::isGreaterOrEqualArray(b.p, op_.half, op_.N);
    }
    bool isValid() const
    {
        return fp::isLessArray(v_, op_.p, op_.N);
    }
    uint64_t getUint64(bool *pb = 0) const
    {
        fp::Block b;
        getBlock(b);
        return fp::getUint64(pb, b);
    }
    int64_t getInt64(bool *pb = 0) const
    {
        fp::Block b;
        getBlock(b);
        return fp::getInt64(pb, b, op_);
    }
    bool operator==(const FpT& rhs) const { return fp::isEqualArray(v_, rhs.v_, op_.N); }
    bool operator!=(const FpT& rhs) const { return !operator==(rhs); }
    friend inline std::ostream& operator<<(std::ostream& os, const FpT& self)
    {
        return os << self.getStr(fp::detectIoMode(getIoMode(), os));
    }
    friend inline std::istream& operator>>(std::istream& is, FpT& self)
    {
        int ioMode = fp::detectIoMode(getIoMode(), is);
        std::string str;
        if (ioMode & (IoArray | IoArrayRaw)) {
            str.resize(getByteSize());
            is.read(&str[0], str.size());
        } else {
            is >> str;
        }
        self.setStr(str, ioMode);
        return is;
    }
    /*
        @note
        this compare functions is slow because of calling mul if isMont is true.
    */
    static inline int compare(const FpT& x, const FpT& y)
    {
        fp::Block xb, yb;
        x.getBlock(xb);
        y.getBlock(yb);
        return fp::compareArray(xb.p, yb.p, op_.N);
    }
    bool isLess(const FpT& rhs) const
    {
        fp::Block xb, yb;
        getBlock(xb);
        rhs.getBlock(yb);
        return fp::isLessArray(xb.p, yb.p, op_.N);
    }
    bool operator<(const FpT& rhs) const { return isLess(rhs); }
    bool operator>=(const FpT& rhs) const { return !operator<(rhs); }
    bool operator>(const FpT& rhs) const { return rhs < *this; }
    bool operator<=(const FpT& rhs) const { return !operator>(rhs); }
    /*
        @note
        return unexpected order if isMont is set.
    */
    static inline int compareRaw(const FpT& x, const FpT& y)
    {
        return fp::compareArray(x.v_, y.v_, op_.N);
    }
    bool isLessRaw(const FpT& rhs) const
    {
        return fp::isLessArray(v_, rhs.v_, op_.N);
    }
    void normalize() {} // dummy method
    /*
        set IoMode for operator<<(), or operator>>()
    */
    static inline void setIoMode(IoMode ioMode)
    {
        ioMode_ = ioMode;
    }
    static inline IoMode getIoMode() { return ioMode_; }
    static inline const char* getIoSeparator() { return fp::getIoSeparator(ioMode_); }
    // backward compatibility
    static inline void setModulo(const std::string& mstr, fp::Mode mode = fp::FP_AUTO)
    {
        init(mstr, mode);
    }
    static inline size_t getModBitLen() { return getBitSize(); }
};

template<class tag, size_t maxBitSize> fp::Op FpT<tag, maxBitSize>::op_;
template<class tag, size_t maxBitSize> FpT<tag, maxBitSize> FpT<tag, maxBitSize>::inv2_;
template<class tag, size_t maxBitSize> IoMode FpT<tag, maxBitSize>::ioMode_ = IoAuto;

} // mcl

#ifdef CYBOZU_USE_BOOST
namespace mcl {

template<class tag, size_t maxBitSize>
size_t hash_value(const mcl::FpT<tag, maxBitSize>& x, size_t v = 0)
{
    return static_cast<size_t>(cybozu::hash64(x.getUnit(), x.getUnitSize(), v));
}

}
#else
namespace std { CYBOZU_NAMESPACE_TR1_BEGIN

template<class tag, size_t maxBitSize>
struct hash<mcl::FpT<tag, maxBitSize> > {
    size_t operator()(const mcl::FpT<tag, maxBitSize>& x, uint64_t v = 0) const
    {
        return static_cast<size_t>(cybozu::hash64(x.getUnit(), x.getUnitSize(), v));
    }
};

CYBOZU_NAMESPACE_TR1_END } // std::tr1
#endif

#ifdef _WIN32
    #pragma warning(pop)
#endif