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1005 lines (858 loc) · 28.4 KB
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//-----------------------------------------------------------------------------
// The symbolic algebra system used to write our constraint equations;
// routines to build expressions in software or from a user-provided string,
// and to compute the partial derivatives that we'll use when write our
// Jacobian matrix.
//
// Copyright 2008-2013 Jonathan Westhues.
//-----------------------------------------------------------------------------
#include "solvespace.h"
namespace SolveSpace {
static inline Expr *AllocExpr() {
return (Expr *)Platform::AllocTemporary(sizeof(Expr));
}
ExprVector ExprVector::From(Expr *x, Expr *y, Expr *z) {
ExprVector r = { x, y, z};
return r;
}
ExprVector ExprVector::From(Vector vn) {
ExprVector ve;
ve.x = Expr::From(vn.x);
ve.y = Expr::From(vn.y);
ve.z = Expr::From(vn.z);
return ve;
}
ExprVector ExprVector::From(hParam x, hParam y, hParam z) {
ExprVector ve;
ve.x = Expr::From(x);
ve.y = Expr::From(y);
ve.z = Expr::From(z);
return ve;
}
ExprVector ExprVector::From(double x, double y, double z) {
ExprVector ve;
ve.x = Expr::From(x);
ve.y = Expr::From(y);
ve.z = Expr::From(z);
return ve;
}
ExprVector ExprVector::Minus(ExprVector b) const {
ExprVector r;
r.x = x->Minus(b.x);
r.y = y->Minus(b.y);
r.z = z->Minus(b.z);
return r;
}
ExprVector ExprVector::Plus(ExprVector b) const {
ExprVector r;
r.x = x->Plus(b.x);
r.y = y->Plus(b.y);
r.z = z->Plus(b.z);
return r;
}
Expr *ExprVector::Dot(ExprVector b) const {
Expr *r;
r = x->Times(b.x);
r = r->Plus(y->Times(b.y));
r = r->Plus(z->Times(b.z));
return r;
}
ExprVector ExprVector::Cross(ExprVector b) const {
ExprVector r;
r.x = (y->Times(b.z))->Minus(z->Times(b.y));
r.y = (z->Times(b.x))->Minus(x->Times(b.z));
r.z = (x->Times(b.y))->Minus(y->Times(b.x));
return r;
}
ExprVector ExprVector::ScaledBy(Expr *s) const {
ExprVector r;
r.x = x->Times(s);
r.y = y->Times(s);
r.z = z->Times(s);
return r;
}
ExprVector ExprVector::WithMagnitude(Expr *s) const {
Expr *m = Magnitude();
return ScaledBy(s->Div(m));
}
Expr *ExprVector::Magnitude() const {
Expr *r;
r = x->Square();
r = r->Plus(y->Square());
r = r->Plus(z->Square());
return r->Sqrt();
}
Vector ExprVector::Eval() const {
Vector r;
r.x = x->Eval();
r.y = y->Eval();
r.z = z->Eval();
return r;
}
ExprQuaternion ExprQuaternion::From(hParam w, hParam vx, hParam vy, hParam vz) {
ExprQuaternion q;
q.w = Expr::From(w);
q.vx = Expr::From(vx);
q.vy = Expr::From(vy);
q.vz = Expr::From(vz);
return q;
}
ExprQuaternion ExprQuaternion::From(Expr *w, Expr *vx, Expr *vy, Expr *vz)
{
ExprQuaternion q;
q.w = w;
q.vx = vx;
q.vy = vy;
q.vz = vz;
return q;
}
ExprQuaternion ExprQuaternion::From(Quaternion qn) {
ExprQuaternion qe;
qe.w = Expr::From(qn.w);
qe.vx = Expr::From(qn.vx);
qe.vy = Expr::From(qn.vy);
qe.vz = Expr::From(qn.vz);
return qe;
}
ExprVector ExprQuaternion::RotationU() const {
ExprVector u;
Expr *two = Expr::From(2);
u.x = w->Square();
u.x = (u.x)->Plus(vx->Square());
u.x = (u.x)->Minus(vy->Square());
u.x = (u.x)->Minus(vz->Square());
u.y = two->Times(w->Times(vz));
u.y = (u.y)->Plus(two->Times(vx->Times(vy)));
u.z = two->Times(vx->Times(vz));
u.z = (u.z)->Minus(two->Times(w->Times(vy)));
return u;
}
ExprVector ExprQuaternion::RotationV() const {
ExprVector v;
Expr *two = Expr::From(2);
v.x = two->Times(vx->Times(vy));
v.x = (v.x)->Minus(two->Times(w->Times(vz)));
v.y = w->Square();
v.y = (v.y)->Minus(vx->Square());
v.y = (v.y)->Plus(vy->Square());
v.y = (v.y)->Minus(vz->Square());
v.z = two->Times(w->Times(vx));
v.z = (v.z)->Plus(two->Times(vy->Times(vz)));
return v;
}
ExprVector ExprQuaternion::RotationN() const {
ExprVector n;
Expr *two = Expr::From(2);
n.x = two->Times( w->Times(vy));
n.x = (n.x)->Plus (two->Times(vx->Times(vz)));
n.y = two->Times(vy->Times(vz));
n.y = (n.y)->Minus(two->Times( w->Times(vx)));
n.z = w->Square();
n.z = (n.z)->Minus(vx->Square());
n.z = (n.z)->Minus(vy->Square());
n.z = (n.z)->Plus (vz->Square());
return n;
}
ExprVector ExprQuaternion::Rotate(ExprVector p) const {
// Express the point in the new basis
return (RotationU().ScaledBy(p.x)).Plus(
RotationV().ScaledBy(p.y)).Plus(
RotationN().ScaledBy(p.z));
}
ExprQuaternion ExprQuaternion::Times(ExprQuaternion b) const {
Expr *sa = w, *sb = b.w;
ExprVector va = { vx, vy, vz };
ExprVector vb = { b.vx, b.vy, b.vz };
ExprQuaternion r;
r.w = (sa->Times(sb))->Minus(va.Dot(vb));
ExprVector vr = vb.ScaledBy(sa).Plus(
va.ScaledBy(sb).Plus(
va.Cross(vb)));
r.vx = vr.x;
r.vy = vr.y;
r.vz = vr.z;
return r;
}
Expr *ExprQuaternion::Magnitude() const {
return ((w ->Square())->Plus(
(vx->Square())->Plus(
(vy->Square())->Plus(
(vz->Square())))))->Sqrt();
}
Expr *Expr::From(hParam p) {
Expr *r = AllocExpr();
r->op = Op::PARAM;
r->parh = p;
return r;
}
Expr *Expr::From(double v) {
// Statically allocate common constants.
// Note: this is only valid because AllocExpr() uses AllocTemporary(),
// and Expr* is never explicitly freed.
if(v == 0.0) {
static Expr zero(0.0);
return &zero;
}
if(v == 1.0) {
static Expr one(1.0);
return &one;
}
if(v == -1.0) {
static Expr mone(-1.0);
return &mone;
}
if(v == 0.5) {
static Expr half(0.5);
return ½
}
if(v == -0.5) {
static Expr mhalf(-0.5);
return &mhalf;
}
Expr *r = AllocExpr();
r->op = Op::CONSTANT;
r->v = v;
return r;
}
Expr *Expr::AnyOp(Op newOp, Expr *b) {
Expr *r = AllocExpr();
r->op = newOp;
r->a = this;
r->b = b;
return r;
}
int Expr::Children() const {
switch(op) {
case Op::PARAM:
case Op::PARAM_PTR:
case Op::CONSTANT:
return 0;
case Op::PLUS:
case Op::MINUS:
case Op::TIMES:
case Op::DIV:
return 2;
case Op::NEGATE:
case Op::SQRT:
case Op::SQUARE:
case Op::SIN:
case Op::COS:
case Op::ASIN:
case Op::ACOS:
return 1;
}
ssassert(false, "Unexpected operation");
}
int Expr::Nodes() const {
switch(Children()) {
case 0: return 1;
case 1: return 1 + a->Nodes();
case 2: return 1 + a->Nodes() + b->Nodes();
default: ssassert(false, "Unexpected children count");
}
}
Expr *Expr::DeepCopy() const {
Expr *n = AllocExpr();
*n = *this;
int c = n->Children();
if(c > 0) n->a = a->DeepCopy();
if(c > 1) n->b = b->DeepCopy();
return n;
}
Expr *Expr::DeepCopyWithParamsAsPointers(ParamList *firstTry, ParamList *thenTry,
bool foldConstants) const {
Expr *n = AllocExpr();
if(op == Op::PARAM) {
// A param that is referenced by its hParam gets rewritten to go
// straight in to the parameter table with a pointer, or simply
// into a constant if it's already known.
Param *p = firstTry->FindByIdNoOops(parh);
if(!p) p = thenTry->FindById(parh);
if(p->known) {
n->op = Op::CONSTANT;
n->v = p->val;
} else {
n->op = Op::PARAM_PTR;
n->parp = p;
}
return n;
}
*n = *this;
int c = n->Children();
if(c > 0) {
n->a = a->DeepCopyWithParamsAsPointers(firstTry, thenTry, foldConstants);
bool hasConstants = n->a->op == Op::CONSTANT;
if(c > 1) {
n->b = b->DeepCopyWithParamsAsPointers(firstTry, thenTry, foldConstants);
hasConstants |= n->b->op == Op::CONSTANT;
}
if(hasConstants && foldConstants) {
n = n->FoldConstants(false, 0);
}
}
return n;
}
double Expr::Eval() const {
switch(op) {
case Op::PARAM: return SK.GetParam(parh)->val;
case Op::PARAM_PTR: return parp->val;
case Op::CONSTANT: return v;
case Op::PLUS: return a->Eval() + b->Eval();
case Op::MINUS: return a->Eval() - b->Eval();
case Op::TIMES: return a->Eval() * b->Eval();
case Op::DIV: return a->Eval() / b->Eval();
case Op::NEGATE: return -(a->Eval());
case Op::SQRT: return sqrt(a->Eval());
case Op::SQUARE: { double r = a->Eval(); return r*r; }
case Op::SIN: return sin(a->Eval());
case Op::COS: return cos(a->Eval());
case Op::ACOS: return acos(a->Eval());
case Op::ASIN: return asin(a->Eval());
}
ssassert(false, "Unexpected operation");
}
Expr *Expr::PartialWrt(hParam p) const {
Expr *da, *db;
switch(op) {
case Op::PARAM_PTR: return From(p == parp->h ? 1 : 0);
case Op::PARAM: return From(p == parh ? 1 : 0);
case Op::CONSTANT: return From(0.0);
case Op::PLUS: return (a->PartialWrt(p))->Plus(b->PartialWrt(p));
case Op::MINUS: return (a->PartialWrt(p))->Minus(b->PartialWrt(p));
case Op::TIMES:
da = a->PartialWrt(p);
db = b->PartialWrt(p);
return (a->Times(db))->Plus(b->Times(da));
case Op::DIV:
da = a->PartialWrt(p);
db = b->PartialWrt(p);
return ((da->Times(b))->Minus(a->Times(db)))->Div(b->Square());
case Op::SQRT:
return (From(0.5)->Div(a->Sqrt()))->Times(a->PartialWrt(p));
case Op::SQUARE:
return (From(2.0)->Times(a))->Times(a->PartialWrt(p));
case Op::NEGATE: return (a->PartialWrt(p))->Negate();
case Op::SIN: return (a->Cos())->Times(a->PartialWrt(p));
case Op::COS: return ((a->Sin())->Times(a->PartialWrt(p)))->Negate();
case Op::ASIN:
return (From(1)->Div((From(1)->Minus(a->Square()))->Sqrt()))
->Times(a->PartialWrt(p));
case Op::ACOS:
return (From(-1)->Div((From(1)->Minus(a->Square()))->Sqrt()))
->Times(a->PartialWrt(p));
}
ssassert(false, "Unexpected operation");
}
void Expr::ParamsUsedList(ParamSet *list) const {
if(op == Op::PARAM || op == Op::PARAM_PTR) {
// leaf: just add ourselves if we aren't already there
hParam param = (op == Op::PARAM) ? parh : parp->h;
list->insert(param);
return;
}
int c = Children();
if(c >= 1) {
a->ParamsUsedList(list);
if(c >= 2) b->ParamsUsedList(list);
}
}
bool Expr::DependsOn(hParam p) const {
if(op == Op::PARAM) return (parh == p);
if(op == Op::PARAM_PTR) return (parp->h == p);
int c = Children();
if(c == 1) return a->DependsOn(p);
if(c == 2) return a->DependsOn(p) || b->DependsOn(p);
return false;
}
bool Expr::Tol(double a, double b) {
return fabs(a - b) < 0.001;
}
bool Expr::IsZeroConst() const {
return op == Op::CONSTANT && EXACT(v == 0.0);
}
Expr *Expr::FoldConstants(bool allocCopy, size_t depth) {
Expr *n;
if(!allocCopy) {
n = this;
} else {
n = AllocExpr();
*n = *this;
}
switch(op) {
case Op::PARAM_PTR:
case Op::PARAM:
case Op::CONSTANT:
break;
case Op::MINUS:
case Op::TIMES:
case Op::DIV:
case Op::PLUS:
if(depth > 0) {
n->a = a->FoldConstants(allocCopy, depth - 1);
n->b = b->FoldConstants(allocCopy, depth - 1);
}
// If both ops are known, then we can evaluate immediately
if(n->a->op == Op::CONSTANT && n->b->op == Op::CONSTANT) {
double nv = n->Eval();
n->op = Op::CONSTANT;
n->v = nv;
break;
}
// x + 0 = 0 + x = x
if(op == Op::PLUS && n->b->op == Op::CONSTANT && Tol(n->b->v, 0)) {
*n = *(n->a); break;
}
if(op == Op::PLUS && n->a->op == Op::CONSTANT && Tol(n->a->v, 0)) {
*n = *(n->b); break;
}
// 1*x = x*1 = x
if(op == Op::TIMES && n->b->op == Op::CONSTANT && Tol(n->b->v, 1)) {
*n = *(n->a); break;
}
if(op == Op::TIMES && n->a->op == Op::CONSTANT && Tol(n->a->v, 1)) {
*n = *(n->b); break;
}
// 0*x = x*0 = 0
if(op == Op::TIMES && n->b->op == Op::CONSTANT && Tol(n->b->v, 0)) {
n->op = Op::CONSTANT; n->v = 0; break;
}
if(op == Op::TIMES && n->a->op == Op::CONSTANT && Tol(n->a->v, 0)) {
n->op = Op::CONSTANT; n->v = 0; break;
}
break;
case Op::SQRT:
case Op::SQUARE:
case Op::NEGATE:
case Op::SIN:
case Op::COS:
case Op::ASIN:
case Op::ACOS:
if(depth > 0) {
n->a = a->FoldConstants(allocCopy, depth - 1);
}
if(n->a->op == Op::CONSTANT) {
double nv = n->Eval();
n->op = Op::CONSTANT;
n->v = nv;
}
break;
}
return n;
}
void Expr::Substitute(const SubstitutionMap &subMap) {
ssassert(op != Op::PARAM_PTR, "Expected an expression that refer to params via handles");
if(op == Op::PARAM) {
auto it = subMap.find(parh);
if(it != subMap.end()) {
parh = it->second->h;
}
} else {
int c = Children();
if(c >= 1) {
a->Substitute(subMap);
if(c >= 2) b->Substitute(subMap);
}
}
}
//-----------------------------------------------------------------------------
// If the expression references only one parameter that appears in pl, then
// return that parameter. If no param is referenced, then return NO_PARAMS.
// If multiple params are referenced, then return MULTIPLE_PARAMS.
//-----------------------------------------------------------------------------
const hParam Expr::NO_PARAMS = { 0 };
const hParam Expr::MULTIPLE_PARAMS = { std::numeric_limits<decltype(hParam::v)>::max() };
hParam Expr::ReferencedParams(ParamList *pl) const {
if(op == Op::PARAM) {
if(pl->FindByIdNoOops(parh)) {
return parh;
} else {
return NO_PARAMS;
}
}
ssassert(op != Op::PARAM_PTR, "Expected an expression that refer to params via handles");
int c = Children();
if(c == 0) {
return NO_PARAMS;
} else if(c == 1) {
return a->ReferencedParams(pl);
} else if(c == 2) {
hParam pa, pb;
pa = a->ReferencedParams(pl);
pb = b->ReferencedParams(pl);
if(pa == NO_PARAMS) {
return pb;
} else if(pb == NO_PARAMS) {
return pa;
} else if(pa == pb) {
return pa; // either, doesn't matter
} else {
return MULTIPLE_PARAMS;
}
} else ssassert(false, "Unexpected children count");
}
//-----------------------------------------------------------------------------
// Routines to pretty-print an expression. Mostly for debugging.
//-----------------------------------------------------------------------------
std::string Expr::Print() const {
char c;
switch(op) {
case Op::PARAM: return ssprintf("param(%08x)", parh.v);
case Op::PARAM_PTR: return ssprintf("param(p%08x)", parp->h.v);
case Op::CONSTANT: return ssprintf("%.3f", v);
case Op::PLUS: c = '+'; goto p;
case Op::MINUS: c = '-'; goto p;
case Op::TIMES: c = '*'; goto p;
case Op::DIV: c = '/'; goto p;
p:
return "(" + a->Print() + " " + c + " " + b->Print() + ")";
break;
case Op::NEGATE: return "(- " + a->Print() + ")";
case Op::SQRT: return "(sqrt " + a->Print() + ")";
case Op::SQUARE: return "(square " + a->Print() + ")";
case Op::SIN: return "(sin " + a->Print() + ")";
case Op::COS: return "(cos " + a->Print() + ")";
case Op::ASIN: return "(asin " + a->Print() + ")";
case Op::ACOS: return "(acos " + a->Print() + ")";
}
ssassert(false, "Unexpected operation");
}
//-----------------------------------------------------------------------------
// A parser; convert a string to an expression. Infix notation, with the
// usual shift/reduce approach. I had great hopes for user-entered eq
// constraints, but those don't seem very useful, so right now this is just
// to provide calculator type functionality wherever numbers are entered.
//-----------------------------------------------------------------------------
class ExprParser {
public:
enum class TokenType {
ERROR = 0,
PAREN_LEFT,
PAREN_RIGHT,
BINARY_OP,
UNARY_OP,
OPERAND,
END,
};
class Token {
public:
TokenType type;
Expr *expr;
static Token From(TokenType type = TokenType::ERROR, Expr *expr = NULL);
static Token From(TokenType type, Expr::Op op);
bool IsError() const { return type == TokenType::ERROR; }
};
std::string::const_iterator it, end;
std::vector<Token> stack;
// The named parameters that may be used, or NULL if there are none
const ParamNames *names;
int namesUsed;
char ReadChar();
char PeekChar();
std::string ReadWord();
void SkipSpace();
Token PopOperator(std::string *error);
Token PopOperand(std::string *error);
int Precedence(Token token);
Token LexNumber(std::string *error);
Token Lex(std::string *error);
bool Reduce(std::string *error);
bool Parse(std::string *error, size_t reduceUntil = 0);
static Expr *Parse(const std::string &input, std::string *error,
const ParamNames *names, int *namesUsed);
};
ExprParser::Token ExprParser::Token::From(TokenType type, Expr *expr) {
Token t;
t.type = type;
t.expr = expr;
return t;
}
ExprParser::Token ExprParser::Token::From(TokenType type, Expr::Op op) {
Token t;
t.type = type;
t.expr = AllocExpr();
t.expr->op = op;
return t;
}
char ExprParser::ReadChar() {
return *it++;
}
char ExprParser::PeekChar() {
if(it == end) {
return '\0';
} else {
return *it;
}
}
std::string ExprParser::ReadWord() {
std::string s;
while(char c = PeekChar()) {
if(!isalnum(c)) break;
s.push_back(ReadChar());
}
return s;
}
void ExprParser::SkipSpace() {
while(char c = PeekChar()) {
if(!isspace(c)) break;
ReadChar();
}
}
ExprParser::Token ExprParser::LexNumber(std::string *error) {
std::string s;
while(char c = PeekChar()) {
if(!((c >= '0' && c <= '9') || c == 'e' || c == 'E' || c == '.' || c == '_')) break;
if(c == '_') {
ReadChar();
continue;
}
s.push_back(ReadChar());
}
char *endptr;
double d = strtod(s.c_str(), &endptr);
Token t = Token::From();
if(endptr == s.c_str() + s.size()) {
t = Token::From(TokenType::OPERAND, Expr::Op::CONSTANT);
t.expr->v = d;
} else {
*error = "'" + s + "' is not a valid number";
}
return t;
}
ExprParser::Token ExprParser::Lex(std::string *error) {
SkipSpace();
Token t = Token::From();
char c = PeekChar();
if(isalpha(c)) {
std::string s = ReadWord();
if(s == "sqrt") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::SQRT);
} else if(s == "square") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::SQUARE);
} else if(s == "sin") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::SIN);
} else if(s == "cos") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::COS);
} else if(s == "asin") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::ASIN);
} else if(s == "acos") {
t = Token::From(TokenType::UNARY_OP, Expr::Op::ACOS);
} else if(s == "pi") {
t = Token::From(TokenType::OPERAND, Expr::Op::CONSTANT);
t.expr->v = PI;
} else if(names != NULL && names->count(s) > 0) {
t = Token::From(TokenType::OPERAND, Expr::Op::PARAM);
t.expr->parh = names->at(s);
namesUsed++;
} else {
*error = "'" + s + "' is not a valid variable, function or constant";
}
} else if(isdigit(c) || c == '.') {
return LexNumber(error);
} else if(ispunct(c)) {
ReadChar();
if(c == '+') {
t = Token::From(TokenType::BINARY_OP, Expr::Op::PLUS);
} else if(c == '-') {
t = Token::From(TokenType::BINARY_OP, Expr::Op::MINUS);
} else if(c == '*') {
t = Token::From(TokenType::BINARY_OP, Expr::Op::TIMES);
} else if(c == '/') {
t = Token::From(TokenType::BINARY_OP, Expr::Op::DIV);
} else if(c == '(') {
t = Token::From(TokenType::PAREN_LEFT);
} else if(c == ')') {
t = Token::From(TokenType::PAREN_RIGHT);
} else {
*error = "'" + std::string(1, c) + "' is not a valid operator";
}
} else if(c == '\0') {
t = Token::From(TokenType::END);
} else {
*error = "Unexpected character '" + std::string(1, c) + "'";
}
return t;
}
ExprParser::Token ExprParser::PopOperand(std::string *error) {
Token t = Token::From();
if(stack.empty() || stack.back().type != TokenType::OPERAND) {
*error = "Expected an operand";
} else {
t = stack.back();
stack.pop_back();
}
return t;
}
ExprParser::Token ExprParser::PopOperator(std::string *error) {
Token t = Token::From();
if(stack.empty() || (stack.back().type != TokenType::UNARY_OP &&
stack.back().type != TokenType::BINARY_OP)) {
*error = "Expected an operator";
} else {
t = stack.back();
stack.pop_back();
}
return t;
}
int ExprParser::Precedence(Token t) {
ssassert(t.type == TokenType::BINARY_OP ||
t.type == TokenType::UNARY_OP ||
t.type == TokenType::OPERAND,
"Unexpected token type");
if(t.type == TokenType::UNARY_OP) {
return 30;
} else if(t.expr->op == Expr::Op::TIMES ||
t.expr->op == Expr::Op::DIV) {
return 20;
} else if(t.expr->op == Expr::Op::PLUS ||
t.expr->op == Expr::Op::MINUS) {
return 10;
} else if(t.type == TokenType::OPERAND) {
return 0;
} else ssassert(false, "Unexpected operator");
}
bool ExprParser::Reduce(std::string *error) {
Token a = PopOperand(error);
if(a.IsError()) return false;
Token op = PopOperator(error);
if(op.IsError()) return false;
Token r = Token::From(TokenType::OPERAND);
switch(op.type) {
case TokenType::BINARY_OP: {
Token b = PopOperand(error);
if(b.IsError()) return false;
r.expr = b.expr->AnyOp(op.expr->op, a.expr);
break;
}
case TokenType::UNARY_OP: {
Expr *e = a.expr;
switch(op.expr->op) {
case Expr::Op::NEGATE: e = e->Negate(); break;
case Expr::Op::SQRT: e = e->Sqrt(); break;
case Expr::Op::SQUARE: e = e->Times(e); break;
case Expr::Op::SIN: e = e->Times(Expr::From(PI/180))->Sin(); break;
case Expr::Op::COS: e = e->Times(Expr::From(PI/180))->Cos(); break;
case Expr::Op::ASIN: e = e->ASin()->Times(Expr::From(180/PI)); break;
case Expr::Op::ACOS: e = e->ACos()->Times(Expr::From(180/PI)); break;
default: ssassert(false, "Unexpected unary operator");
}
r.expr = e;
break;
}
default: ssassert(false, "Unexpected operator");
}
stack.push_back(r);
return true;
}
bool ExprParser::Parse(std::string *error, size_t reduceUntil) {
while(true) {
Token t = Lex(error);
switch(t.type) {
case TokenType::ERROR:
return false;
case TokenType::END:
case TokenType::PAREN_RIGHT:
while(stack.size() > 1 + reduceUntil) {
if(!Reduce(error)) return false;
}
if(t.type == TokenType::PAREN_RIGHT) {
stack.push_back(t);
}
return true;
case TokenType::PAREN_LEFT: {
// sub-expression
if(!Parse(error, /*reduceUntil=*/stack.size())) return false;
if(stack.empty() || stack.back().type != TokenType::PAREN_RIGHT) {
*error = "Expected ')'";
return false;
}
stack.pop_back();
break;
}
case TokenType::BINARY_OP:
if((stack.size() > reduceUntil && stack.back().type != TokenType::OPERAND) ||
stack.size() == reduceUntil) {
if(t.expr->op == Expr::Op::MINUS) {
t.type = TokenType::UNARY_OP;
t.expr->op = Expr::Op::NEGATE;
stack.push_back(t);
break;
}
}
while(stack.size() > 1 + reduceUntil &&
Precedence(t) <= Precedence(stack[stack.size() - 2])) {
if(!Reduce(error)) return false;
}
stack.push_back(t);
break;
case TokenType::UNARY_OP:
case TokenType::OPERAND:
stack.push_back(t);
break;
}
}
return true;
}
Expr *ExprParser::Parse(const std::string &input, std::string *error,
const ParamNames *names, int *namesUsed) {
ExprParser parser;
parser.it = input.cbegin();
parser.end = input.cend();
parser.names = names;
parser.namesUsed = 0;
if(!parser.Parse(error)) return NULL;
Token r = parser.PopOperand(error);
if(r.IsError()) return NULL;
if(namesUsed != NULL) *namesUsed = parser.namesUsed;
return r.expr;
}
bool Expr::IsReservedName(const std::string &name) {
// The functions and constants that the parser knows by name.
return name == "sqrt" || name == "square" || name == "sin" || name == "cos" ||
name == "asin" || name == "acos" || name == "pi";
}
std::vector<std::string> Expr::FindUndefinedNames(const std::string &input,
const ParamNames *names) {
std::vector<std::string> result;
size_t i = 0;
while(i < input.size()) {
char c = input[i];
if(isdigit(c) || c == '.') {
// A number, which may have an exponent, like LexNumber() reads it
while(i < input.size() &&
(isdigit(input[i]) || input[i] == 'e' || input[i] == 'E' ||
input[i] == '.' || input[i] == '_')) {
i++;
}
} else if(isalpha(c)) {
// A name, like ReadWord() reads it
size_t start = i;
while(i < input.size() && isalnum(input[i])) i++;
std::string name = input.substr(start, i - start);
if(!IsReservedName(name) && names->count(name) == 0 &&
std::find(result.begin(), result.end(), name) == result.end()) {
result.push_back(name);
}
} else {
i++;
}
}
return result;
}
Expr *Expr::Parse(const std::string &input, std::string *error,
const ParamNames *names, int *namesUsed) {
return ExprParser::Parse(input, error, names, namesUsed);
}
Expr *Expr::From(const std::string &input, bool popUpError,
const ParamNames *names, int *namesUsed) {
std::string error;
Expr *e = ExprParser::Parse(input, &error, names, namesUsed);
if(!e) {
dbp("Parse/lex error: %s", error.c_str());
if(popUpError) {
Error("Not a valid number or expression: '%s'.\n%s.",
input.c_str(), error.c_str());
}