}
}
| FP_PINF_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { expr = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- +INFINITY)); }
+ { expr = MK_CONST(FloatingPoint::makeInf(FloatingPointSize(AntlrInput::tokenToUnsigned($eb),
+ AntlrInput::tokenToUnsigned($sb)),
+ false)); }
| FP_NINF_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { expr = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- -INFINITY)); }
+ { expr = MK_CONST(FloatingPoint::makeInf(FloatingPointSize(AntlrInput::tokenToUnsigned($eb),
+ AntlrInput::tokenToUnsigned($sb)),
+ true)); }
| FP_NAN_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { expr = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- NAN)); }
+ { expr = MK_CONST(FloatingPoint::makeNaN(FloatingPointSize(AntlrInput::tokenToUnsigned($eb),
+ AntlrInput::tokenToUnsigned($sb)))); }
+
+ | FP_PZERO_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
+ { expr = MK_CONST(FloatingPoint::makeZero(FloatingPointSize(AntlrInput::tokenToUnsigned($eb),
+ AntlrInput::tokenToUnsigned($sb)),
+ false)); }
+ | FP_NZERO_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
+ { expr = MK_CONST(FloatingPoint::makeZero(FloatingPointSize(AntlrInput::tokenToUnsigned($eb),
+ AntlrInput::tokenToUnsigned($sb)),
+ true)); }
// NOTE: Theory parametric constants go here
)
"bv2nat and int2bv are not part of SMT-LIB, and aren't available "
"in SMT-LIB strict compliance mode");
} }
- | FP_PINF_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { op = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- +INFINITY)); }
- | FP_NINF_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { op = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- -INFINITY)); }
- | FP_NAN_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { op = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- NAN)); }
- | FP_PZERO_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { op = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- +0.0)); }
- | FP_NZERO_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
- { op = MK_CONST(FloatingPoint(AntlrInput::tokenToUnsigned($eb),
- AntlrInput::tokenToUnsigned($sb),
- -0.0)); }
| FP_TO_FP_TOK eb=INTEGER_LITERAL sb=INTEGER_LITERAL
{ op = MK_CONST(FloatingPointToFPGeneric(
AntlrInput::tokenToUnsigned($eb),
break;
}
case kind::CONST_FLOATINGPOINT:
- out << n.getConst<FloatingPoint>().getLiteral();
+ out << n.getConst<FloatingPoint>();
break;
case kind::CONST_ROUNDINGMODE:
switch (n.getConst<RoundingMode>()) {
Unimplemented("Floating-point literals not yet implemented.");
}
+ FloatingPoint::FloatingPoint (unsigned e, unsigned s, const BitVector &bv) :
+ fpl(e,s,0.0),
+ t(e,s) {}
+
+
+ static FloatingPointLiteral constructorHelperBitVector (const FloatingPointSize &ct, const RoundingMode &rm, const BitVector &bv, bool signedBV) {
+ if (signedBV) {
+ return FloatingPointLiteral(2,2,0.0);
+ } else {
+ return FloatingPointLiteral(2,2,0.0);
+ }
+ Unreachable("Constructor helper broken");
+ }
+
+ FloatingPoint::FloatingPoint (const FloatingPointSize &ct, const RoundingMode &rm, const BitVector &bv, bool signedBV) :
+ fpl(constructorHelperBitVector(ct, rm, bv, signedBV)),
+ t(ct) {}
+
+
+ static FloatingPointLiteral constructorHelperRational (const FloatingPointSize &ct, const RoundingMode &rm, const Rational &ri) {
+ Rational r(ri);
+ Rational two(2,1);
+
+ if (r.isZero()) {
+ return FloatingPointLiteral(2,2,0.0);
+ } else {
+ //int negative = (r.sgn() < 0) ? 1 : 0;
+ r = r.abs();
+
+ // Compute the exponent
+ Integer exp(0U);
+ Integer inc(1U);
+ Rational working(1,1);
+
+ if (r == working) {
+
+ } else if ( r < working ) {
+ while (r < working) {
+ exp -= inc;
+ working /= two;
+ }
+ } else {
+ while (r >= working) {
+ exp += inc;
+ working *= two;
+ }
+ exp -= inc;
+ working /= two;
+ }
+
+ Assert(working <= r);
+ Assert(r < working * two);
+
+ // Work out the number of bits required to represent the exponent for a normal number
+ unsigned expBits = 2; // No point starting with an invalid amount
+
+ Integer doubleInt(2);
+ if (exp.strictlyPositive()) {
+ Integer representable(4); // 1 more than exactly representable with expBits
+ while (representable <= exp) {// hence <=
+ representable *= doubleInt;
+ ++expBits;
+ }
+ } else if (exp.strictlyNegative()) {
+ Integer representable(-4); // Exactly representable with expBits + sign
+ // but -2^n and -(2^n - 1) are both subnormal
+ while ((representable + doubleInt) > exp) {
+ representable *= doubleInt;
+ ++expBits;
+ }
+ }
+ ++expBits; // To allow for sign
+
+ BitVector exactExp(expBits, exp);
+
+
+
+ // Compute the significand.
+ unsigned sigBits = ct.significand() + 2; // guard and sticky bits
+ BitVector sig(sigBits, 0U);
+ BitVector one(sigBits, 1U);
+ Rational workingSig(0,1);
+ for (unsigned i = 0; i < sigBits - 1; ++i) {
+ Rational mid(workingSig + working);
+
+ if (mid <= r) {
+ sig = sig | one;
+ workingSig = mid;
+ }
+
+ sig = sig.leftShift(one);
+ working /= two;
+ }
+
+ // Compute the sticky bit
+ Rational remainder(r - workingSig);
+ Assert(Rational(0,1) <= remainder);
+
+ if (!remainder.isZero()) {
+ sig = sig | one;
+ }
+
+ // Build an exact float
+ FloatingPointSize exactFormat(expBits, sigBits);
+
+ // A small subtlety... if the format has expBits the unpacked format
+ // may have more to allow subnormals to be normalised.
+ // Thus...
+ Unreachable("no concrete implementation of FloatingPointLiteral");
+ }
+ Unreachable("Constructor helper broken");
+ }
+
+ FloatingPoint::FloatingPoint (const FloatingPointSize &ct, const RoundingMode &rm, const Rational &r) :
+ fpl(constructorHelperRational(ct, rm, r)),
+ t(ct) {}
+
+
+ FloatingPoint FloatingPoint::makeNaN (const FloatingPointSize &t) {
+ return FloatingPoint(2, 2, BitVector(4U,0U));
+ }
+
+ FloatingPoint FloatingPoint::makeInf (const FloatingPointSize &t, bool sign) {
+ return FloatingPoint(2, 2, BitVector(4U,0U));
+ }
+
+ FloatingPoint FloatingPoint::makeZero (const FloatingPointSize &t, bool sign) {
+ return FloatingPoint(2, 2, BitVector(4U,0U));
+ }
+
+
+ /* Operations implemented using symfpu */
+ FloatingPoint FloatingPoint::absolute (void) const {
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::negate (void) const {
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::plus (const RoundingMode &rm, const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::sub (const RoundingMode &rm, const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::mult (const RoundingMode &rm, const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::fma (const RoundingMode &rm, const FloatingPoint &arg1, const FloatingPoint &arg2) const {
+ Assert(this->t == arg1.t);
+ Assert(this->t == arg2.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::div (const RoundingMode &rm, const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::sqrt (const RoundingMode &rm) const {
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::rti (const RoundingMode &rm) const {
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::rem (const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::maxTotal (const FloatingPoint &arg, bool zeroCaseLeft) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint FloatingPoint::minTotal (const FloatingPoint &arg, bool zeroCaseLeft) const {
+ Assert(this->t == arg.t);
+ return *this;
+ }
+
+ FloatingPoint::PartialFloatingPoint FloatingPoint::max (const FloatingPoint &arg) const {
+ FloatingPoint tmp(maxTotal(arg, true));
+ return PartialFloatingPoint(tmp, tmp == maxTotal(arg, false));
+ }
+
+ FloatingPoint::PartialFloatingPoint FloatingPoint::min (const FloatingPoint &arg) const {
+ FloatingPoint tmp(minTotal(arg, true));
+ return PartialFloatingPoint(tmp, tmp == minTotal(arg, false));
+ }
+
+ bool FloatingPoint::operator ==(const FloatingPoint& fp) const {
+ return ( (t == fp.t) );
+ }
+
+ bool FloatingPoint::operator <= (const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return false;
+ }
+
+ bool FloatingPoint::operator < (const FloatingPoint &arg) const {
+ Assert(this->t == arg.t);
+ return false;
+ }
+
+ bool FloatingPoint::isNormal (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isSubnormal (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isZero (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isInfinite (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isNaN (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isNegative (void) const {
+ return false;
+ }
+
+ bool FloatingPoint::isPositive (void) const {
+ return false;
+ }
+
+ FloatingPoint FloatingPoint::convert (const FloatingPointSize &target, const RoundingMode &rm) const {
+ return *this;
+ }
+
+ BitVector FloatingPoint::convertToBVTotal (BitVectorSize width, const RoundingMode &rm, bool signedBV, BitVector undefinedCase) const {
+ if (signedBV)
+ return undefinedCase;
+ else
+ return undefinedCase;
+ }
+
+ Rational FloatingPoint::convertToRationalTotal (Rational undefinedCase) const {
+ PartialRational p(convertToRational());
+
+ return p.second ? p.first : undefinedCase;
+ }
+
+ FloatingPoint::PartialBitVector FloatingPoint::convertToBV (BitVectorSize width, const RoundingMode &rm, bool signedBV) const {
+ BitVector tmp(convertToBVTotal (width, rm, signedBV, BitVector(width, 0U)));
+ BitVector confirm(convertToBVTotal (width, rm, signedBV, BitVector(width, 1U)));
+
+ return PartialBitVector(tmp, tmp == confirm);
+ }
+
+ FloatingPoint::PartialRational FloatingPoint::convertToRational (void) const {
+ if (this->isNaN() || this->isInfinite()) {
+ return PartialRational(Rational(0U, 1U), false);
+ }
+ if (this->isZero()) {
+ return PartialRational(Rational(0U, 1U), true);
+
+ } else {
+
+ Integer sign(0);
+ Integer exp(0);
+ Integer significand(0);
+ Integer signedSignificand(sign * significand);
+
+ // Only have pow(uint32_t) so we should check this.
+ Assert(this->t.significand() <= 32);
+
+ if (!(exp.strictlyNegative())) {
+ Integer r(signedSignificand.multiplyByPow2(exp.toUnsignedInt()));
+ return PartialRational(Rational(r), true);
+ } else {
+ Integer one(1U);
+ Integer q(one.multiplyByPow2((-exp).toUnsignedInt()));
+ Rational r(signedSignificand, q);
+ return PartialRational(r, true);
+ }
+ }
+
+ Unreachable("Convert float literal to real broken.");
+ }
+
+ BitVector FloatingPoint::pack (void) const {
+ BitVector bv(4u,0u);
+ return bv;
+ }
+
+
+
}/* CVC4 namespace */
#include <fenv.h>
#include "util/bitvector.h"
+#include "util/rational.h"
namespace CVC4 {
// Inline these!
public :
FloatingPointSize t;
- FloatingPoint (unsigned e, unsigned s, double d) : fpl(e,s,d), t(e,s) {}
- FloatingPoint (unsigned e, unsigned s, const std::string &bitString) : fpl(e,s,bitString), t(e,s) {}
+ FloatingPoint (unsigned e, unsigned s, const BitVector &bv);
+ FloatingPoint (const FloatingPointSize &oldt, const FloatingPointLiteral &oldfpl) : fpl(oldfpl), t(oldt) {}
FloatingPoint (const FloatingPoint &fp) : fpl(fp.fpl), t(fp.t) {}
+ FloatingPoint (const FloatingPointSize &ct, const RoundingMode &rm, const BitVector &bv, bool signedBV);
+ FloatingPoint (const FloatingPointSize &ct, const RoundingMode &rm, const Rational &r);
- bool operator ==(const FloatingPoint& fp) const {
- return ( (t == fp.t) && fpl == fp.fpl );
- }
+
+ static FloatingPoint makeNaN (const FloatingPointSize &t);
+ static FloatingPoint makeInf (const FloatingPointSize &t, bool sign);
+ static FloatingPoint makeZero (const FloatingPointSize &t, bool sign);
const FloatingPointLiteral & getLiteral (void) const {
return this->fpl;
}
+ // Gives the corresponding IEEE-754 transfer format
+ BitVector pack (void) const;
+
+
+ FloatingPoint absolute (void) const;
+ FloatingPoint negate (void) const;
+ FloatingPoint plus (const RoundingMode &rm, const FloatingPoint &arg) const;
+ FloatingPoint sub (const RoundingMode &rm, const FloatingPoint &arg) const;
+ FloatingPoint mult (const RoundingMode &rm, const FloatingPoint &arg) const;
+ FloatingPoint div (const RoundingMode &rm, const FloatingPoint &arg) const;
+ FloatingPoint fma (const RoundingMode &rm, const FloatingPoint &arg1, const FloatingPoint &arg2) const;
+ FloatingPoint sqrt (const RoundingMode &rm) const;
+ FloatingPoint rti (const RoundingMode &rm) const;
+ FloatingPoint rem (const FloatingPoint &arg) const;
+
+ // zeroCase is whether the left or right is returned in the case of min/max(-0,+0) or (+0,-0)
+ FloatingPoint maxTotal (const FloatingPoint &arg, bool zeroCaseLeft) const;
+ FloatingPoint minTotal (const FloatingPoint &arg, bool zeroCaseLeft) const;
+
+ // These detect when the answer is defined
+ typedef std::pair<FloatingPoint, bool> PartialFloatingPoint;
+
+ PartialFloatingPoint max (const FloatingPoint &arg) const;
+ PartialFloatingPoint min (const FloatingPoint &arg) const;
+
+
+ bool operator ==(const FloatingPoint& fp) const;
+ bool operator <= (const FloatingPoint &arg) const;
+ bool operator < (const FloatingPoint &arg) const;
+
+ bool isNormal (void) const;
+ bool isSubnormal (void) const;
+ bool isZero (void) const;
+ bool isInfinite (void) const;
+ bool isNaN (void) const;
+ bool isNegative (void) const;
+ bool isPositive (void) const;
+
+ FloatingPoint convert (const FloatingPointSize &target, const RoundingMode &rm) const;
+
+ // These require a value to return in the undefined case
+ BitVector convertToBVTotal (BitVectorSize width, const RoundingMode &rm,
+ bool signedBV, BitVector undefinedCase) const;
+ Rational convertToRationalTotal (Rational undefinedCase) const;
+
+ // These detect when the answer is defined
+ typedef std::pair<BitVector, bool> PartialBitVector;
+ typedef std::pair<Rational, bool> PartialRational;
+
+ PartialBitVector convertToBV (BitVectorSize width, const RoundingMode &rm,
+ bool signedBV) const;
+ PartialRational convertToRational (void) const;
+
}; /* class FloatingPoint */
struct CVC4_PUBLIC FloatingPointHashFunction {
- inline size_t operator() (const FloatingPoint& fp) const {
- FloatingPointSizeHashFunction h;
- return h(fp.t) ^ fp.getLiteral().hash();
+ size_t operator() (const FloatingPoint& fp) const {
+ FloatingPointSizeHashFunction fpshf;
+ BitVectorHashFunction bvhf;
+
+ return fpshf(fp.t) ^ bvhf(fp.pack());
}
}; /* struct FloatingPointHashFunction */
FloatingPointConvertSort (unsigned _e, unsigned _s)
: t(_e,_s) {}
+ FloatingPointConvertSort (const FloatingPointSize &fps)
+ : t(fps) {}
bool operator ==(const FloatingPointConvertSort& fpcs) const {
return t == fpcs.t;
*/
class CVC4_PUBLIC FloatingPointToFPIEEEBitVector : public FloatingPointConvertSort {
- public : FloatingPointToFPIEEEBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPIEEEBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPIEEEBitVector (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
+
class CVC4_PUBLIC FloatingPointToFPFloatingPoint : public FloatingPointConvertSort {
- public : FloatingPointToFPFloatingPoint (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPFloatingPoint (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPFloatingPoint (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
+
class CVC4_PUBLIC FloatingPointToFPReal : public FloatingPointConvertSort {
- public : FloatingPointToFPReal (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPReal (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPReal (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
+
class CVC4_PUBLIC FloatingPointToFPSignedBitVector : public FloatingPointConvertSort {
- public : FloatingPointToFPSignedBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPSignedBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPSignedBitVector (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
+
class CVC4_PUBLIC FloatingPointToFPUnsignedBitVector : public FloatingPointConvertSort {
- public : FloatingPointToFPUnsignedBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPUnsignedBitVector (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPUnsignedBitVector (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
+
class CVC4_PUBLIC FloatingPointToFPGeneric : public FloatingPointConvertSort {
- public : FloatingPointToFPGeneric (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ public :
+ FloatingPointToFPGeneric (unsigned _e, unsigned _s) : FloatingPointConvertSort(_e,_s) {}
+ FloatingPointToFPGeneric (const FloatingPointConvertSort &old) : FloatingPointConvertSort(old) {}
};
FloatingPointToBV (unsigned s)
: bvs(s) {}
+ FloatingPointToBV (const FloatingPointToBV &old) : bvs(old.bvs) {}
+ FloatingPointToBV (const BitVectorSize &old) : bvs(old) {}
operator unsigned () const { return bvs; }
};
class CVC4_PUBLIC FloatingPointToUBV : public FloatingPointToBV {
public : FloatingPointToUBV (unsigned _s) : FloatingPointToBV(_s) {}
+ FloatingPointToUBV (const FloatingPointToBV &old) : FloatingPointToBV(old) {}
};
class CVC4_PUBLIC FloatingPointToSBV : public FloatingPointToBV {
public : FloatingPointToSBV (unsigned _s) : FloatingPointToBV(_s) {}
+ FloatingPointToSBV (const FloatingPointToBV &old) : FloatingPointToBV(old) {}
+ };
+ class CVC4_PUBLIC FloatingPointToUBVTotal : public FloatingPointToBV {
+ public : FloatingPointToUBVTotal (unsigned _s) : FloatingPointToBV(_s) {}
+ FloatingPointToUBVTotal (const FloatingPointToBV &old) : FloatingPointToBV(old) {}
+ };
+ class CVC4_PUBLIC FloatingPointToSBVTotal : public FloatingPointToBV {
+ public : FloatingPointToSBVTotal (unsigned _s) : FloatingPointToBV(_s) {}
+ FloatingPointToSBVTotal (const FloatingPointToBV &old) : FloatingPointToBV(old) {}
};
}; /* struct FloatingPointToBVHashFunction */
-
+ // It is not possible to pack a number without a size to pack to,
+ // thus it is difficult to implement this in a sensible way. Use
+ // FloatingPoint instead...
+ /*
inline std::ostream& operator <<(std::ostream& os, const FloatingPointLiteral& fp) CVC4_PUBLIC;
inline std::ostream& operator <<(std::ostream& os, const FloatingPointLiteral& fp) {
- fp.unfinished();
- return os;
+ return os << "FloatingPointLiteral";
}
+ */
inline std::ostream& operator <<(std::ostream& os, const FloatingPoint& fp) CVC4_PUBLIC;
inline std::ostream& operator <<(std::ostream& os, const FloatingPoint& fp) {
- return os << fp.getLiteral();
+ BitVector bv(fp.pack());
+
+ unsigned largestSignificandBit = fp.t.significand() - 2; // -1 for -inclusive, -1 for hidden
+ unsigned largestExponentBit = (fp.t.exponent() - 1) + (largestSignificandBit + 1);
+
+ return os
+ << "(fp #b" << bv.extract(largestExponentBit + 1, largestExponentBit + 1)
+ << " #b" << bv.extract(largestExponentBit, largestSignificandBit + 1)
+ << " #b" << bv.extract(largestSignificandBit, 0)
+ << ")";
}
inline std::ostream& operator <<(std::ostream& os, const FloatingPointSize& fps) CVC4_PUBLIC;