// Specialize ZZ, quad_float and RR for numeric_limits.
using std::numeric_limits;
using NTL::quad_float;
template <> class numeric_limits<quad_float>
 {
 public:
		static const bool is_specialized = true;
		static const int radix = 2;
		static const int digits = 106; // radix digits (bits) in significand.
		static const int digits10 = 31; // decimal digits guaranteed.
		static const int max_digits = 33; // maximum significant decimal digits.
		static const bool is_signed = true;
		static const bool is_integer = false;
		static const bool is_exact = false;
		static quad_float min() throw() { return numeric_limits<double>::min();};
		static quad_float max() throw() { return
		quad_float(numeric_limits<double>::max(), numeric_limits<double>::max());};
		static quad_float epsilon() throw() { return
		2.4651903288156618919116517665087069677288E-32;}; // 2^(1-106) == 2^105
		static quad_float round_error() throw() { return 0.5;};
		static quad_float infinity() throw() { return
		quad_float(numeric_limits<double>::infinity(),
		numeric_limits<double>::infinity());};
		static quad_float quiet_NaN() throw() { return
		quad_float(numeric_limits<double>::quiet_NaN(),
		numeric_limits<double>::quiet_NaN());};
		static quad_float signaling_NaN() throw() { return
		quad_float(numeric_limits<double>::quiet_NaN(),
		numeric_limits<double>::quiet_NaN());};
		static quad_float denorm_min() throw() { return quad_float(0,
		numeric_limits<double>::denorm_min());};
		static const int min_exponent = numeric_limits<double>::min_exponent;
		static const int min_exponent10 = numeric_limits<double>::min_exponent10;
		static const int max_exponent = numeric_limits<double>::max_exponent;
		static const int max_exponent10 = numeric_limits<double>::max_exponent10;
		static const bool has_infinity = true;
		static const bool has_quiet_NaN = true;
		static const bool has_signaling_NaN = true;
		static const float_denorm_style has_denorm = denorm_absent; // enum from
		<limits>
		static const bool has_denorm_loss = false;
		static const bool is_ies559 = false;
		static const bool is_bounded = true;
		static const bool is_modulo = true;
		static const bool traps = true;
		static const bool tinyness_before = true;
		static const float_round_style round_style = round_to_nearest; // enum from
		<limits>
 }; // class numeric_limits<quad_float>

// Need to fix precision of RR class before specialization.
// long RR::prec = 150; is in RR.cpp,
// so need a macro in RR.h to be used in RR.cpp instead of 150
#define RR_PRECISION 150

using NTL::RR;
template <> class numeric_limits<RR>
 {
 public:
		static const bool is_specialized = true;
		static const int radix = 10;
		static const int digits = RR_PRECISION; // Radix digits (decimal) in
		significand.  ???
		static const int digits10 =RR_PRECISION -1; // Decimal digits guaranteed.
		static const int max_digits = RR_PRECISION; // Maximum significant decimal
		digits.
		static const bool is_signed = true;
		static const bool is_integer = false;
		static const bool is_exact = false;
		static RR min() throw() { return 0.;};
		static RR max() throw() { return NTL_OVFBND;};
		static RR epsilon() throw() { return pow(2., precision());};
		static RR round_error() throw() { return 0.5;};
		static RR infinity() throw() { return RR(numeric_limits<double>::infinity())};
		static RR quiet_NaN() throw() { return RR(numeric_limits<double>::quiet_NaN())};
		static RR signaling_NaN() throw() { return
		RR(numeric_limits<double>::quiet_NaN());};
		static RR denorm_min() throw() { return
		RR(numeric_limits<double>::denorm_min());};
		static const int min_exponent = numeric_limits<double>::min_exponent;
		static const int min_exponent10 = numeric_limits<double>::min_exponent10;
		static const int max_exponent = numeric_limits<double>::max_exponent;
		static const int max_exponent10 = numeric_limits<double>::max_exponent10;
		static const bool has_infinity = true;
		static const bool has_quiet_NaN = true;
		static const bool has_signaling_NaN = true;
		static const float_denorm_style has_denorm = denorm_absent; // enum from
		<limits>
		static const bool has_denorm_loss = false;
		static const bool is_ies559 = false;
		static const bool is_bounded = true;
		static const bool is_modulo = true;
		static const bool traps = false;
		static const bool tinyness_before = false;
		static const float_round_style round_style = round_to_nearest; // enum from
		<limits>
 }; // class numeric_limits<RR>

using NTL::ZZ;
template <> class numeric_limits<ZZ>
{ // Defined-precision integer class.
 public:
		static const bool is_specialized = true;
		static const int radix = 2;
		static const int digits = NTL_ZZ_NBITS; // radix digits (bits).
		static const int digits10 = NTL_FRADIX; // decimal digits guaranteed.
		static const int max_digits = NTL_FRADIX; // maximum significant decimal digits.
		static const bool is_signed = true;
		static const bool is_integer = true;
		static const bool is_exact = true;
		static ZZ min() throw() { return -(NTL_ZZ_NBITS+1);};
		static ZZ max() throw() { return NTL_ZZ_NBITS);};
  	static const bool has_infinity = false;
		static const bool has_quiet_NaN = false;
		static const bool has_signaling_NaN = false;
		static const bool has_denorm_loss = false;
		static const bool is_ies559 = false;
		static const bool is_bounded = true;
		static const bool is_modulo = true;
		static const bool traps = false;
		static const bool tinyness_before = false;
 }; // class numeric_limits<ZZ>