#ifndef NTL_RR__H #define NTL_RR__H #include #include #include NTL_OPEN_NNS class RR { public: ZZ x; long e; RR() { e = 0; } inline RR(INIT_VAL_TYPE, const ZZ& a); inline RR(INIT_VAL_TYPE, int a); inline RR(INIT_VAL_TYPE, long a); inline RR(INIT_VAL_TYPE, unsigned int a); inline RR(INIT_VAL_TYPE, unsigned long a); inline RR(INIT_VAL_TYPE, float a); inline RR(INIT_VAL_TYPE, double a); inline RR(INIT_VAL_TYPE, const xdouble& a); inline RR(INIT_VAL_TYPE, const quad_float& a); inline RR(INIT_VAL_TYPE, const char *a); // read from string inline RR(INIT_VAL_TYPE, const RR& a); inline RR& operator=(double a); RR(RR& z, INIT_TRANS_TYPE) : x(z.x, INIT_TRANS), e(z.e) { } ~RR() { } const ZZ& mantissa() const { return x; } long exponent() const { return e; } static long prec; static void SetPrecision(long p); static long precision() { return prec; } static long oprec; static void SetOutputPrecision(long p); static long OutputPrecision() { return oprec; } #ifdef NTL_TRANSITION private: RR& operator=(const RR&); RR(const RR&); #endif }; long IsZero(const RR& a); long IsOne(const RR& a); long sign(const RR& a); void clear(RR& z); void set(RR& z); void swap(RR& a, RR& b); void add(RR& z, const RR& a, const RR& b); void add(RR& z, const RR& a, double b); inline void add(RR& z, double a, const RR& b) { add(z, b, a); } void sub(RR& z, const RR& a, const RR& b); void sub(RR& z, const RR& a, double b); void sub(RR& z, double a, const RR& b); void negate(RR& z, const RR& a); void abs(RR& z, const RR& a); inline RR abs(const RR& a) { RR z; abs(z, a); NTL_OPT_RETURN(RR, z); } inline RR fabs(const RR& a) { RR z; abs(z, a); NTL_OPT_RETURN(RR, z); } void mul(RR& z, const RR& a, const RR& b); void mul(RR& z, const RR& a, double b); inline void mul(RR& z, double a, const RR& b) { mul(z, b, a); } void sqr(RR& z, const RR& a); inline RR sqr(const RR& a) { RR z; sqr(z, a); NTL_OPT_RETURN(RR, z); } void div(RR& z, const RR& a, const RR& b); void div(RR& z, const RR& a, double b); void div(RR& z, double a, const RR& b); void inv(RR& z, const RR& a); inline RR inv(const RR& a) { RR z; inv(z, a); NTL_OPT_RETURN(RR, z); } // operator notation: inline RR operator+(const RR& a, const RR& b) { RR x; add(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator+(const RR& a, double b) { RR x; add(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator+(double a, const RR& b) { RR x; add(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR& operator+=(RR& x, const RR& b) { add(x, x, b); return x; } inline RR& operator+=(RR& x, double b) { add(x, x, b); return x; } inline RR operator-(const RR& a, const RR& b) { RR x; sub(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator-(const RR& a, double b) { RR x; sub(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator-(double a, const RR& b) { RR x; sub(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR& operator-=(RR& x, const RR& b) { sub(x, x, b); return x; } inline RR& operator-=(RR& x, double b) { sub(x, x, b); return x; } inline RR operator*(const RR& a, const RR& b) { RR x; mul(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator*(const RR& a, double b) { RR x; mul(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator*(double a, const RR& b) { RR x; mul(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR& operator*=(RR& x, const RR& b) { mul(x, x, b); return x; } inline RR& operator*=(RR& x, double b) { mul(x, x, b); return x; } inline RR operator/(const RR& a, const RR& b) { RR x; div(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator/(const RR& a, double b) { RR x; div(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR operator/(double a, const RR& b) { RR x; div(x, a, b); NTL_OPT_RETURN(RR, x); } inline RR& operator/=(RR& x, const RR& b) { div(x, x, b); return x; } inline RR& operator/=(RR& x, double b) { div(x, x, b); return x; } inline RR operator-(const RR& a) { RR x; negate(x, a); NTL_OPT_RETURN(RR, x); } inline RR& operator++(RR& x) { add(x, x, 1); return x; } inline void operator++(RR& x, int) { add(x, x, 1); } inline RR& operator--(RR& x) { sub(x, x, 1); return x; } inline void operator--(RR& x, int) { sub(x, x, 1); } long compare(const RR& a, const RR& b); long compare(const RR& a, double b); inline long compare(double a, const RR& b) { return -compare(b, a); } long operator==(const RR& a, const RR& b); inline long operator!=(const RR& a, const RR& b) { return !(a == b); } inline long operator<=(const RR& a, const RR& b) { return compare(a, b) <= 0; } inline long operator>=(const RR& a, const RR& b) { return compare(a, b) >= 0; } inline long operator <(const RR& a, const RR& b) { return compare(a, b) < 0; } inline long operator >(const RR& a, const RR& b) { return compare(a, b) > 0; } long operator==(const RR& a, double b); inline long operator!=(const RR& a, double b) { return !(a == b); } inline long operator<=(const RR& a, double b) { return compare(a, b) <= 0; } inline long operator>=(const RR& a, double b) { return compare(a, b) >= 0; } inline long operator <(const RR& a, double b) { return compare(a, b) < 0; } inline long operator >(const RR& a, double b) { return compare(a, b) > 0; } inline long operator==(double a, const RR& b) { return (b == a); } inline long operator!=(double a, const RR& b) { return !(a == b); } inline long operator<=(double a, const RR& b) { return compare(a, b) <= 0; } inline long operator>=(double a, const RR& b) { return compare(a, b) >= 0; } inline long operator <(double a, const RR& b) { return compare(a, b) < 0; } inline long operator >(double a, const RR& b) { return compare(a, b) > 0; } void ceil(RR& z, const RR& a); inline RR ceil(const RR& a) { RR z; ceil(z, a); NTL_OPT_RETURN(RR, z); } void floor(RR& z, const RR& a); inline RR floor(const RR& a) { RR z; floor(z, a); NTL_OPT_RETURN(RR, z); } void trunc(RR& z, const RR& a); inline RR trunc(const RR& a) { RR z; trunc(z, a); NTL_OPT_RETURN(RR, z); } void round(RR& z, const RR& a); inline RR round(const RR& a) { RR z; round(z, a); NTL_OPT_RETURN(RR, z); } void RoundToPrecision(RR& z, const RR& a, long p); inline RR RoundToPrecision(const RR& a, long p) { RR z; RoundToPrecision(z, a, p); NTL_OPT_RETURN(RR, z); } // routines with a precision parameter void ConvPrec(RR& z, const RR& a, long p); inline RR ConvPrec(const RR& a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void AddPrec(RR& z, const RR& a, const RR& b, long p); inline RR AddPrec(const RR& a, const RR& b, long p) { RR z; AddPrec(z, a, b, p); NTL_OPT_RETURN(RR, z); } void SubPrec(RR& z, const RR& a, const RR& b, long p); inline RR SubPrec(const RR& a, const RR& b, long p) { RR z; SubPrec(z, a, b, p); NTL_OPT_RETURN(RR, z); } void NegatePrec(RR& z, const RR& a, long p); inline RR NegatePrec(const RR& a, long p) { RR z; NegatePrec(z, a, p); NTL_OPT_RETURN(RR, z); } void AbsPrec(RR& z, const RR& a, long p); inline RR AbsPrec(const RR& a, long p) { RR z; AbsPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void MulPrec(RR& z, const RR& a, const RR& b, long p); inline RR MulPrec(const RR& a, const RR& b, long p) { RR z; MulPrec(z, a, b, p); NTL_OPT_RETURN(RR, z); } void SqrPrec(RR& z, const RR& a, long p); inline RR SqrPrec(const RR& a, long p) { RR z; SqrPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void DivPrec(RR& z, const RR& a, const RR& b, long p); inline RR DivPrec(const RR& a, const RR& b, long p) { RR z; DivPrec(z, a, b, p); NTL_OPT_RETURN(RR, z); } void InvPrec(RR& z, const RR& a, long p); inline RR InvPrec(const RR& a, long p) { RR z; InvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void SqrRootPrec(RR& z, const RR& a, long p); inline RR SqrRootPrec(const RR& a, long p) { RR z; SqrRootPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void TruncPrec(RR& z, const RR& a, long p); inline RR TruncPrec(const RR& a, long p) { RR z; TruncPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void FloorPrec(RR& z, const RR& a, long p); inline RR FloorPrec(const RR& a, long p) { RR z; FloorPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void CeilPrec(RR& z, const RR& a, long p); inline RR CeilPrec(const RR& a, long p) { RR z; CeilPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void RoundPrec(RR& z, const RR& a, long p); inline RR RoundPrec(const RR& a, long p) { RR z; RoundPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, const ZZ& a, long p); inline RR ConvPrec(const ZZ& a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, long a, long p); inline RR ConvPrec(long a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } inline void ConvPrec(RR& z, int a, long p) { ConvPrec(z, long(a), p); } inline RR ConvPrec(int a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, unsigned long a, long p); inline RR ConvPrec(unsigned long a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } inline void ConvPrec(RR& z, unsigned int a, long p) { ConvPrec(z, (unsigned long)(a), p); } inline RR ConvPrec(unsigned int a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, double a, long p); inline RR ConvPrec(double a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, const xdouble& a, long p); inline RR ConvPrec(const xdouble& a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, const quad_float& a, long p); inline RR ConvPrec(const quad_float& a, long p) { RR z; ConvPrec(z, a, p); NTL_OPT_RETURN(RR, z); } void ConvPrec(RR& z, const char *s, long p); inline RR ConvPrec(const char *s, long p) { RR z; ConvPrec(z, s, p); NTL_OPT_RETURN(RR, z); } void InputPrec(RR& z, NTL_SNS istream& s, long p); inline RR InputPrec(NTL_SNS istream& s, long p) { RR z; InputPrec(z, s, p); NTL_OPT_RETURN(RR, z); } void MakeRRPrec(RR& z, const ZZ& a, long e, long p); inline RR MakeRRPrec(const ZZ& a, long e, long p) { RR z; MakeRRPrec(z, a, e, p); NTL_OPT_RETURN(RR, z); } void conv(RR& z, const ZZ& a); void conv(RR& z, long a); inline void conv(RR& z, int a) { conv(z, long(a)); } void conv(RR& z, unsigned long a); inline void conv(RR& z, unsigned int a) { conv(z, (unsigned long)(a)); } void conv(RR& z, const char *s); void conv(RR& z, double a); inline void conv(RR& z, float a) { conv(z, double(a)); } void conv(RR& z, const xdouble& a); void conv(RR& z, const quad_float& a); void conv(RR& z, const RR& a); inline RR::RR(INIT_VAL_TYPE, int a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, long a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, unsigned int a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, unsigned long a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, float a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, double a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, const RR& a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, const ZZ& a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, const xdouble& a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, const quad_float& a) { e = 0; conv(*this, a); } inline RR::RR(INIT_VAL_TYPE, const char *a) { e = 0; conv(*this, a); } inline RR to_RR(int a) { return RR(INIT_VAL, a); } inline RR to_RR(long a) { return RR(INIT_VAL, a); } inline RR to_RR(unsigned int a) { return RR(INIT_VAL, a); } inline RR to_RR(unsigned long a) { return RR(INIT_VAL, a); } inline RR to_RR(float a) { return RR(INIT_VAL, a); } inline RR to_RR(double a) { return RR(INIT_VAL, a); } inline RR to_RR(const ZZ& a) { return RR(INIT_VAL, a); } inline RR to_RR(const RR& a) { return RR(INIT_VAL, a); } inline RR to_RR(const xdouble& a) { return RR(INIT_VAL, a); } inline RR to_RR(const quad_float& a) { return RR(INIT_VAL, a); } inline RR to_RR(const char *a) { return RR(INIT_VAL, a); } inline RR& RR::operator=(double a) { conv(*this, a); return *this; } void conv(ZZ& z, const RR& a); void conv(long& z, const RR& a); void conv(double& z, const RR& a); void conv(xdouble& z, const RR& a); void conv(quad_float& z, const RR& a); inline void conv(int& z, const RR& a) { long t; conv(t, a); z = int(t); } inline void conv(float& z, const RR& a) { double t; conv(t, a); z = float(t); } inline int to_int(const RR& a) { int z; conv(z, a); return z; } inline long to_long(const RR& a) { long z; conv(z, a); return z; } inline float to_float(const RR& a) { float z; conv(z, a); return z; } inline double to_double(const RR& a) { double z; conv(z, a); return z; } inline xdouble to_xdouble(const RR& a) { xdouble z; conv(z, a); return z; } inline quad_float to_quad_float(const RR& a) { quad_float z; conv(z, a); return z; } inline ZZ to_ZZ(const RR& a) { ZZ z; conv(z, a); NTL_OPT_RETURN(ZZ, z); } void CeilToZZ(ZZ& z, const RR& a); inline ZZ CeilToZZ(const RR& a) { ZZ z; CeilToZZ(z, a); NTL_OPT_RETURN(ZZ, z); } void TruncToZZ(ZZ& z, const RR& a); inline ZZ TruncToZZ(const RR& a) { ZZ z; TruncToZZ(z, a); NTL_OPT_RETURN(ZZ, z); } void RoundToZZ(ZZ& z, const RR& a); inline ZZ RoundToZZ(const RR& a) { ZZ z; RoundToZZ(z, a); NTL_OPT_RETURN(ZZ, z); } inline void FloorToZZ(ZZ& z, const RR& a) { conv(z, a); } inline ZZ FloorToZZ(const RR& a) { ZZ z; conv(z, a); NTL_OPT_RETURN(ZZ, z); } void MakeRR(RR& z, const ZZ& a, long e); inline RR MakeRR(const ZZ& a, long e) { RR z; MakeRR(z, a, e); NTL_OPT_RETURN(RR, z); } void random(RR& z); inline RR random_RR() { RR z; random(z); NTL_OPT_RETURN(RR, z); } void power(RR& z, const RR& a, long e); inline RR power(const RR& a, long e) { RR z; power(z, a, e); NTL_OPT_RETURN(RR, z); } void power2(RR& z, long e); inline RR power2_RR(long e) { RR z; power2(z, e); NTL_OPT_RETURN(RR, z); } NTL_SNS ostream& operator<<(NTL_SNS ostream& s, const RR& a); NTL_SNS istream& operator>>(NTL_SNS istream& s, RR& x); void SqrRoot(RR& x, const RR& a); inline RR SqrRoot(const RR& a) { RR z; SqrRoot(z, a); NTL_OPT_RETURN(RR, z); } inline RR sqrt(const RR& a) { RR z; SqrRoot(z, a); NTL_OPT_RETURN(RR, z); } void exp(RR& res, const RR& x); inline RR exp(const RR& a) { RR z; exp(z, a); NTL_OPT_RETURN(RR, z); } void log(RR& res, const RR& x); inline RR log(const RR& a) { RR z; log(z, a); NTL_OPT_RETURN(RR, z); } void log10(RR& res, const RR& x); inline RR log10(const RR& a) { RR z; log10(z, a); NTL_OPT_RETURN(RR, z); } void expm1(RR& res, const RR& x); inline RR expm1(const RR& a) { RR z; expm1(z, a); NTL_OPT_RETURN(RR, z); } void log1p(RR& res, const RR& x); inline RR log1p(const RR& a) { RR z; log1p(z, a); NTL_OPT_RETURN(RR, z); } void pow(RR& res, const RR& x, const RR& y); inline RR pow(const RR& x, const RR& y) { RR z; pow(z, x, y); NTL_OPT_RETURN(RR, z); } void ComputePi(RR& res); inline RR ComputePi_RR() { RR z; ComputePi(z); NTL_OPT_RETURN(RR, z); } void sin(RR& res, const RR& x); inline RR sin(const RR& a) { RR z; sin(z, a); NTL_OPT_RETURN(RR, z); } void cos(RR& res, const RR& x); inline RR cos(const RR& a) { RR z; cos(z, a); NTL_OPT_RETURN(RR, z); } NTL_CLOSE_NNS #endif