enum class Op : uint32_t {

// A parameter, by the hParam handle

PARAM = 0,

// A parameter, by a pointer straight in to the param table (faster,

// if we know that the param table won't move around)

PARAM_PTR = 1,

// Operands

CONSTANT = 20,

VARIABLE = 21,

// Binary ops

PLUS = 100,

MINUS = 101,

TIMES = 102,

DIV = 103,

// Unary ops

NEGATE = 104,

SQRT = 105,

SQUARE = 106,

SIN = 107,

COS = 108,

ASIN = 109,

ACOS = 110,

};

Op op;

Expr *a;

union {

double v;

hParam parh;

Param *parp;

Expr *b;

};

Expr() { }

Expr(double val) : op(Op::CONSTANT) { v = val; }

static inline Expr *AllocExpr()

{ return (Expr *)AllocTemporary(sizeof(Expr)); }

static Expr *From(hParam p);

static Expr *From(double v);

Expr *AnyOp(Op op, Expr *b);

inline Expr *Plus (Expr *b_) { return AnyOp(Op::PLUS, b_); }

inline Expr *Minus(Expr *b_) { return AnyOp(Op::MINUS, b_); }

inline Expr *Times(Expr *b_) { return AnyOp(Op::TIMES, b_); }

inline Expr *Div (Expr *b_) { return AnyOp(Op::DIV, b_); }

inline Expr *Negate() { return AnyOp(Op::NEGATE, NULL); }

inline Expr *Sqrt () { return AnyOp(Op::SQRT, NULL); }

inline Expr *Square() { return AnyOp(Op::SQUARE, NULL); }

inline Expr *Sin () { return AnyOp(Op::SIN, NULL); }

inline Expr *Cos () { return AnyOp(Op::COS, NULL); }

inline Expr *ASin () { return AnyOp(Op::ASIN, NULL); }

inline Expr *ACos () { return AnyOp(Op::ACOS, NULL); }

Expr *PartialWrt(hParam p) const;

double Eval() const;

uint64_t ParamsUsed() const;

bool DependsOn(hParam p) const;

static bool Tol(double a, double b);

Expr *FoldConstants();

void Substitute(hParam oldh, hParam newh);

static const hParam NO_PARAMS, MULTIPLE_PARAMS;

hParam ReferencedParams(ParamList *pl) const;

void ParamsToPointers();

std::string Print() const;

// number of child nodes: 0 (e.g. constant), 1 (sqrt), or 2 (+)

int Children() const;

// total number of nodes in the tree

int Nodes() const;

// Make a simple copy

Expr *DeepCopy() const;

// Make a copy, with the parameters (usually referenced by hParam)

// resolved to pointers to the actual value. This speeds things up

// considerably.

Expr *DeepCopyWithParamsAsPointers(IdList<Param,hParam> *firstTry,

IdList<Param,hParam> *thenTry) const;

static Expr *Parse(const std::string &input, std::string *error);

static Expr *From(const std::string &input, bool popUpError);

Expr *x, *y, *z;

static ExprVector From(Expr *x, Expr *y, Expr *z);

static ExprVector From(Vector vn);

static ExprVector From(hParam x, hParam y, hParam z);

static ExprVector From(double x, double y, double z);

ExprVector Plus(ExprVector b) const;

ExprVector Minus(ExprVector b) const;

Expr *Dot(ExprVector b) const;

ExprVector Cross(ExprVector b) const;

ExprVector ScaledBy(Expr *s) const;

ExprVector WithMagnitude(Expr *s) const;

Expr *Magnitude() const;

Vector Eval() const;

Expr *w, *vx, *vy, *vz;

static ExprQuaternion From(Expr *w, Expr *vx, Expr *vy, Expr *vz);

static ExprQuaternion From(Quaternion qn);

static ExprQuaternion From(hParam w, hParam vx, hParam vy, hParam vz);

ExprVector RotationU() const;

ExprVector RotationV() const;

ExprVector RotationN() const;

ExprVector Rotate(ExprVector p) const;

ExprQuaternion Times(ExprQuaternion b) const;

Expr *Magnitude() const;